High Pressure Investigations on Some Geophysically relevant ...

HIGH PRESSURE INVESTIGATIONS ON SOME GEOPHYSICALLY

RELEVANT MATERIALS

By

AJAY KUMAR MISHRA

PHYS01200804013

High Pressure & Synchrotron Radiation Physics Division

Bhabha Atomic Research Centre

Mumbai - 400085

INDIA

A thesis submitted to the

Board of Studies in Physical Sciences

In partial fulfillment of requirements

For the Degree of

DOCTOR OF PHILOSOPHY

of

HOMI BHABHA NATIONAL INSTITUTE

May, 2013

Dedicated

to

My family

vi

ACKNOWLEDGEMENTS

At the outset I would like to thank all the people who have helped and motivated me

in any form during my doctoral thesis work.

My guide Prof. Surinder M. Sharma has played a crucial role in making my thesis

a reality. This thesis would not have been completed without his immense help. His

constant motivation encouraged me to complete my work enthusiastically. I would

also like to extend my thanks to the members of my doctoral committee; Prof. C.

S. Sunder, Prof. S. K. Gupta, Prof. S. L. Chaplot and Prof. S. C. Gupta for their

valuable suggestions and comments during long review sessions.

I am happy to have some wonderful colleagues like K.V. Shanavas, K. K. Pandey

and H K Poswal at my work place. I have learnt a lot through several insightful and

lively discussions with them. I am extremely grateful to Dr. Nandini Garg and Dr.

Chitra Murli, who have helped me in learning the basics of high pressure experiments.

In addition, I would also like to pay my sincere gratitude to both of them for critically

going through some of my chapters of the Thesis and for giving valuable suggestion

to improve upon.

I thank my all collaborators, teachers and persons who have helped me by sharing

their expertise and knowledge with me.

Last but not least, I would like to thank my parents and my elder brother for

supporting me throughout my life. I would like to express my very special thanks to

my wife Anita (Khusbu), for always being with me in all situations and for bearing

with me patiently during the writing of this thesis.

Contents

Contents

Contents ix

List of Figures xv

List of Tables xxv

Synopsis xxviii

1 Introduction 3

1.1 Introduction to high pressure physics . . . . . . . . . . . . . . . . . . 3

1.2 Pressure as a Thermodynamic Variable . . . . . . . . . . . . . . . . . 6

1.3 An overview of high Pressure Research in Materials . . . . . . . . . . 9

1.4 Crystallography under High Pressure . . . . . . . . . . . . . . . . . . 17

1.5 Phase Stability and High Pressure . . . . . . . . . . . . . . . . . . . . 22

1.6 High Pressure Generation and measurements . . . . . . . . . . . . . . 25

1.6.1 High pressure Cells . . . . . . . . . . . . . . . . . . . . . . . . 25

1.6.2 Diamond anvil cell . . . . . . . . . . . . . . . . . . . . . . . . 25

1.6.3 Background for high pressure experiments . . . . . . . . . . . 28

1.6.3.1 Alignment of the DAC . . . . . . . . . . . . . . . . . 28

1.6.3.2 Choice of the gasket material . . . . . . . . . . . . . 29

1.6.3.3 Pressure transmitting medium . . . . . . . . . . . . . 31

1.6.3.4 Pressure calibration . . . . . . . . . . . . . . . . . . 32

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1.6.4 Synchrotron sources and diffraction technique . . . . . . . . . 37

1.6.4.1 Wavelength selection . . . . . . . . . . . . . . . . . . 38

1.6.4.2 In-situ angle dispersive x-ray diffraction . . . . . . . 39

1.6.4.3 In-situ energy dispersive x-ray diffraction . . . . . . . 43

1.6.5 Raman Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . 44

1.7 Materials Studied . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

1.7.1 Zircon Structured Materials . . . . . . . . . . . . . . . . . . . 48

1.7.2 Pyrochlores . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

1.7.3 Perovskites . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

1.7.4 Phosphate material . . . . . . . . . . . . . . . . . . . . . . . . 50

1.8 Plan of thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

2 Phase Transformation in Zircon and scheelite Structured Materials 53

2.1 Zircon Structured Chromates . . . . . . . . . . . . . . . . . . . . . . 54

2.1.1 Structural Details . . . . . . . . . . . . . . . . . . . . . . . . . 54

2.1.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

2.1.3 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . 58

2.1.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . 59

2.1.4.1 The Raman spectroscopic studies . . . . . . . . . . . 59

2.1.4.2 X-ray diffraction studies at Elettra . . . . . . . . . . 62

2.1.4.3 X-ray diffraction studies at Spring8 . . . . . . . . . . 65

2.1.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

2.2 Scheelite Structured Fluoride . . . . . . . . . . . . . . . . . . . . . . 72


2.2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

2.2.3 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . 74


2.2.4.1 Structural Effects . . . . . . . . . . . . . . . . . . . . 75

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2.2.4.2 Spectroscopic effects . . . . . . . . . . . . . . . . . . 80

2.2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

3 Structural Transition in Frustrated Titanate Pyrochlores 87

3.1 Structural details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

3.3 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

3.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 93

3.4.1 Yb2Ti2O7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

3.4.1.1 X-ray diffraction measurements . . . . . . . . . . . . 93

3.4.1.2 Raman spectra at high pressures . . . . . . . . . . . 97

3.4.1.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . 100

3.4.2 Dy2Ti2O7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

3.4.2.1 Structural effects by XRD . . . . . . . . . . . . . . . 101

3.4.2.2 Raman Spectroscopic effect . . . . . . . . . . . . . . 104

3.4.2.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . 109

4 Structural Investigation of perovskites 111

4.1 Crystallography of the Perovskite structure . . . . . . . . . . . . . . . 113

4.2 Phase transitions in multiferroic BiFeO3 . . . . . . . . . . . . . . . . 115

4.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

4.2.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116


4.2.4 Bulk Modulus . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

4.2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

4.3 Structural evolution of Sr2MgWO6 . . . . . . . . . . . . . . . . . . . 124


4.3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

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Contents

4.3.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125


4.3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

4.4 Structural stability of BaLiF3 . . . . . . . . . . . . . . . . . . . . . . 132

4.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

4.4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133


4.4.3.1 X-ray diffraction . . . . . . . . . . . . . . . . . . . . 134

4.4.3.2 Bulk modulus by empirical methods . . . . . . . . . 136

4.4.3.3 Comparison with calculations . . . . . . . . . . . . . 140

4.4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

5 Pressure induced phase transformation in U2O(PO4)2 145

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

5.2 Structural Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

5.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

5.3.1 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

5.3.2 Experiemntal Details . . . . . . . . . . . . . . . . . . . . . . . 149

5.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 150

5.4.1 Raman Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . 150

5.4.1.1 Raman modes under ambient conditions . . . . . . . 150

5.4.1.2 High Pressure Raman studies . . . . . . . . . . . . . 152

5.4.2 X-ray diffraction studies . . . . . . . . . . . . . . . . . . . . . 158

5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

6 Development of EDXRD Beamline 163

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

6.2 Basic Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

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Contents

6.3 EDXRD Beamline at Indus-2 . . . . . . . . . . . . . . . . . . . . . . 167

6.3.1 Design and Description . . . . . . . . . . . . . . . . . . . . . . 167

6.3.2 Sample Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

6.4 A few studies at high pressures . . . . . . . . . . . . . . . . . . . . . 171

6.4.1 Natural uranium . . . . . . . . . . . . . . . . . . . . . . . . . 171

6.4.2 Sesquioxides . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

6.5 Adaptation for high temperature studies . . . . . . . . . . . . . . . . 174

A Structure Determination 177

A.1 Indexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

A.2 Rietveld Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

B List of Publications 185

References 189

xiii

Contents

xiv

List of Figures

List of Figures

1.1 Schematic of the Pressure Temperature- map of scientific interest . . 4

1.2 Variation of pressure with respect to radius of the earth . . . . . . . . 5

1.3 For high pressure x-ray diffraction experiments the choice of diffraction

geometry for stress analysis. σ1 and σ3 are the principal stress axes. ψ

is the angle between the diffracting plane normal and the load direction. 19

1.4 Configuration of opposed diamond anvil, a pre indented metallic gasket

with a hole is used as a sample chamber. . . . . . . . . . . . . . . . . 26

1.5 The side and top view of a brilliant cut diamond. . . . . . . . . . . . 27

1.6 (a) Hemispherical rocker and (b) cylindrical base plate. . . . . . . . . 28

1.7 schematic diagram of a lab based XRD set up for high pressure XRD

experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

1.8 RAG based high pressure XRD set up at laboratory. . . . . . . . . . 42

1.9 Depiction of stokes and antistokes Raman scattering. . . . . . . . . . 45

1.10 Micro Raman set up in confocal geometry for high pressure Raman

scattering measurement. . . . . . . . . . . . . . . . . . . . . . . . . . 46

1.11 Optical layout of dispersive Raman scattering set up. . . . . . . . . . 47

2.1 Crystal structure of Y CrO4/HoCrO4 in tetragonal zircon phase. . . . 54

2.2 Raman pattern of Y CrO4 at a few representative pressure. . . . . . . 60

2.3 Raman pattern of HoCrO4 at a few representative pressure. . . . . . 61

xv

List of Figures

2.4 Pressure induced variation of Raman shifts of (a) Y CrO4; triangle and

circle represent the prominent Raman mode corresponding to zircon

structure while the inverted triangle and square represent the Raman

modes for scheelite phase and (b) HoCrO4, square and circle represent

the main Raman mode corresponding to zircon and scheelite phase

respectively; here solid lines represent guide to an eye. . . . . . . . . . 62

2.5 Diffraction pattern of YCrO4 at a few representative pressures. . . . . 63

2.6 Diffraction pattern of HoCrO4 at a few representative pressures. . . . 64

2.7 The diffraction pattern of YCrO4 recorded at Spring8 at a few rep-

resentative pressures. The ambient pressure data has been indexed

with respect to the zircon structure. The diffraction peak marked as

(112) at high pressure refers to the scheelite phase. It is apparent that

background increases with pressure. . . . . . . . . . . . . . . . . . . . 66

2.8 The diffraction pattern of HoCrO4, recorded at Spring8 at a few rep-

resentative pressures. The ambient pressure data has been indexed

with respect to the zircon structure. The diffraction peaks of the high

pressure phase have been indicated by arrows. The diffraction peak

marked as (112) at high pressure refers to the scheelite phase. The

background of the lowest pressure phase has been subtracted from all

the subsequent pressure runs. . . . . . . . . . . . . . . . . . . . . . . 67

2.9 The increase in FWHM of some of the diffraction peaks of (a) YCrO4

at 4.6 GPa and (b) HoCrO4 at 6.5 GPa. The FWHM of the (200)

diffraction peak did not increase as the difference between the a and b

cell constants in the monoclinic phase is 0.01 %. . . . . . . . . . . . 68

xvi

List of Figures

2.10 Rietveld fits to the recorded diffraction pattern of YCrO4 at 4.6 GPa

(red) in the monoclinic structure. The blue line shows the subtracted

background and vertical bars give the expected positions of the diffrac-

tion peaks from the sample. The difference in the calculated and exper-

imental diffraction pattern is given at the bottom of the graph (green). 69

2.11 The (a) zircon and (b) monoclinic structure of YCrO4 as determined

from the diffraction data. The γ angle is 90.4◦. The chromium, Yt-

trium and oxygen atoms have been marked as Cr (grey), Y (blue) and

O (red) respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

2.12 Crystal structure of LiErF4 in tetragonal scheelite phase. . . . . . . . 72

2.13 X-ray diffraction patterns of lithium erbium fluoride stacked at a few

representative pressures. . . . . . . . . . . . . . . . . . . . . . . . . . 76

2.14 Pressure induced variation of c and a lattice parameters of LiErF4 and

BaMoO4 in scheelite phase. Symbols and lines represent observed data

and linear fit to these data respectively. The data for BaMoO4 has been

taken from Panchal et al. 2006 . . . . . . . . . . . . . . . . . . . . . . 77

2.15 Pressure dependence of c/a ratio in the scheelite structure of LiErF4,

LiYF4, BaMoO4 and CaWO4. The data for LiErF4 are from present

study and LiYF4, BaMoO4 and CaWO4 data are taken from references

(Grzechnik et al. 2002, Panchal et al. 2006 and Errandonea et al. 2005)

respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

2.16 The high pressure fergusonite structure of LiErF4 obtained from the

scheelite structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

2.17 Pressure versus volume of LiErF4. The circles and squares represent

the different experimental runs of the scheelite phase and the triangles

represent the fergusonite phase. The red line represents B-M fit for the

scheelite phase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

xvii

List of Figures

2.18 Raman spectra of lithium erbium fluoride stacked at ambient condi-

tions. The asterisk (*) presents the fluorescence for LiErF4. . . . . . . 82

2.19 Raman spectra of lithium erbium fluoride stacked at a few representa-

tive pressures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

2.20 Variation of Raman shifts of LiErF4 with pressure. Solid lines are guide

to eye. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

3.1 (a)Polyhedra of Yb/Dy and Ti and (b)Crystal structure of Yb2Ti2O7/

Dy2Ti2O7 in the cubic phase. . . . . . . . . . . . . . . . . . . . . . . 89

3.2 Geometrical frustration in (a) triangular and (b) tetrahedral spin lat-

tices. (c) represents the spin ice behavior; a pair of spin pointing inward

and another pair of spin pointing outward. . . . . . . . . . . . . . . . 90

3.3 X-ray diffraction profiles of Yb2Ti2O7 at a few representative pressures.

Arrows indicate the x-ray diffraction peaks due to monoclinic phase at

high pressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

3.4 The observed P-V variation fitted with 3rd order Birch- Murnaghan

(B-M) equation of state for Yb2Ti2O7 pyrochlore and high pressure

monoclinic phase. The red solid line is B-M fit of the experimentally

observed P-V data while the blue dashed line represents the pressure

induced volume variation obtained by the first principles calculations

(Mishra et al. 2012). Upper inset shows the variation of the x-position

parameter of the O48f atoms at various pressures. Lower inset shows

the crystal structure of the high pressure monoclinic phase. . . . . . . 95

3.5 Rietveld refinement of diffraction pattern of Yb2Ti2O7 at 40.4 GPa.

The diffraction pattern consists of contributions from pyrochlore phase,

high pressure monoclinic phase, tungsten gasket and Cu pressure marker. 96

3.6 Raman spectrum of Yb2Ti2O7 pyrochlore at ambient pressure. The

different raman modes have been labeled as pk1 to pk8. . . . . . . . . 98

xviii

List of Figures

3.7 The evolution of the Raman modes of Yb2Ti2O7 at a few representative

pressures (R stands for Release). . . . . . . . . . . . . . . . . . . . . . 99

3.8 Pressure induced variation of Raman mode frequencies of Yb2Ti2O7 . 100

3.9 Diffraction pattern of Dy2Ti2O7 pyrochlore stacked at a few represen-

tative pressures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

3.10 Full width at half maximum for different x-ray diffraction peaks of

Dy2Ti2O7 at various pressures. . . . . . . . . . . . . . . . . . . . . . . 103

3.11 Pressure induced variation of different dhkl values. . . . . . . . . . . . 104

3.12 Pressure induced variation of volume per unit cell. The black dot

symbols represent the observed data while the red solid line is obtained

from fitting the third order Birch-Murnaghan equation of state to the

observed variation of volume with pressure. . . . . . . . . . . . . . . . 105

3.13 Pressure induced variation of lattice parameter of pyrochlore phase. . 106

3.14 Raman spectrum of Dy2Ti2O7 pyrochlore at ambient pressure. The

different raman modes have been labeled as P1 to P11. . . . . . . . . 106

3.15 Raman spectra of Dy2Ti2O7 pyrochlore stacked at a few representative

pressures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

3.16 Variation of Raman shift of different modes with pressure. . . . . . . 108

4.1 Unit cell of cubic perovskite. Gray, green and red spheres represent

the A cations, B cations and oxygen anions respectively. B cation with

oxygen atoms forms an octahedra. . . . . . . . . . . . . . . . . . . . . 113

4.2 Distorted cubic perovskite structure of BiFeO3 in R3c space group.

The grey colored spheres are bismuth atoms, the yellow colored are

iron atoms while the one with red colors represent oxygen atoms. . . 114

xix

List of Figures

4.3 X-ray diffraction pattern of BiFeO3 at a few representative pressures.

X-ray diffraction peaks marked with the star are from impurity while

the peaks marked with solid and dotted arrows are from the new high

pressure phases with space group P2221 and Pnma respectively. The

inset shows the zoomed view of diffraction pattern at 4.1 GPa and

highlights the fact that the new XRD peaks of P2221 phase are distinct

from the impurity peaks. . . . . . . . . . . . . . . . . . . . . . . . . . 118

4.4 Rietveld refined monoclinic (C2/m) structure (from reference Haumont

et al. 2009). (b) Relaxed monoclinic structure after theoretical struc-

tural optimization (Mishra et al. 2013). The resulting bond lengths for

Bi-O and Fe-O changed from 2.22A to 2.44A and 1.86A to 1.89A re-

spectively (c) Rietveld refined orthorhombic (P2221) structure (present

study, without relaxation). (d) Relaxed orthorhombic (P2221) struc-

ture after theoretical structural optimization (Mishra et al. 2013) . . 120

4.5 Rietveld refined diffraction pattern of BiFeO3 at three different pres-

sures (ambient, 5.0 GPa and 15.0 GPa) representing Rhombohedral

(R3c), Orthorhombic (P2221) and (Pnma) symmetries respectively.

For Rietveld refinement three contributions viz. from BiFeO3, tungsten

(gasket) and copper (the pressure marker) were used at each pressure.

The red, green and blue solid lines represent the calculated intensity,

background and difference from observed data respectively while the

black dots represent the experimental data. . . . . . . . . . . . . . . . 122

4.6 (a) Crystal structure of BiFeO3 at ambient conditions. (b) The struc-

ture of the first high pressure phase (P2221). (c) Structure of the

second high pressure phase (Pnma). . . . . . . . . . . . . . . . . . . . 123

xx

List of Figures

4.7 Observed variation in the volume (per formula unit) of BiFeO3 as a

function of pressure. Symbols represent the experimentally observed

data while solid lines are obtained from fitting the P-V data with third

order Birch-Murnaghan equation of state. . . . . . . . . . . . . . . . . 123

4.8 Tetragonal crystal structure of Sr2MgWO6 at ambient conditions (Space

group I4/m). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

4.9 Diffraction pattern of Sr2MgWO6 at a few representative pressures.

Peaks marked as (hkl), W and Cu are from the sample, gasket and pres-

sure marker respectively. Asterisk (*) represents the impurity peak. . 127

4.10 Rietveld refinement of diffraction pattern at ambient conditions. The

diffraction pattern consists of contributions from Sr2MgWO6, tungsten

gasket and Cu pressure marker. . . . . . . . . . . . . . . . . . . . . . 128

4.11 Variation of normalized lattice parameters with pressure. Symbols rep-

resent the experimental data and the solid lines represent the computed

data taken from Mishra et al. 2010 . . . . . . . . . . . . . . . . . . . 129

4.12 The observed P-V variation fitted with Birch- Murnaghan (B.M.) equa-

tion of state (red) for Sr2MgWO6. Symbols represent the observe data.

Dash-dot line represents the results of our first principles calculations

taken from Mishra et al. 2010 for comparison. . . . . . . . . . . . . . 130

4.13 Variation of the frequencies of two prominent Raman active mode of

Sr2MgWO6 with pressure. . . . . . . . . . . . . . . . . . . . . . . . . 131

4.14 Diffraction patterns of BaLiF3 at a few representative pressures. The

gasket and copper pressure marker peaks have been marked as W and

Cu respectively. The diffraction patterns of the released runs have been

marked with r. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

4.15 The additional valence sum mismatch at both (Ba, Li) cation sites

(∆Vi (i = A, B) as a function of pressure. . . . . . . . . . . . . . . . 136

xxi

List of Figures

4.16 The observed P-V variation fitted with third order Birch-Murnaghan

equation of state for BaLiF3. The closed and open circles represent the

compression and decompression data respectively, while the red solid

line is the fitted curve with B-M equation of state. The dot-dashed

blue colour line shows the EOS obtained from ab-initio calculations of

Mishra et al. 2011 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

4.17 Pressure induced variation of normalized volume of KF12 and BaF12

polyhedra for several fluoro-perovskites. For KZnF3 and KMgF3 the

data are from reference Aguado et al. 2008 while for KCoF3 data was

taken from Aguado et al. 2009. BaLiF3 data is from the present high

pressure x-ray diffraction experiments. . . . . . . . . . . . . . . . . . 138

5.1 Edge Shared UO7 (pentagonal bipyramids) and PO4 (tetrahedra) as in

U2O(PO4)2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

5.2 The parent orthorhombic structure as viewed along [100]. . . . . . . 148

5.3 Correlation diagram of internal modes of U2O(PO4)2 based on PO4

smmetry group. The known frequencies of the isolated (PO4)3− tetra-

hedron are given in the parenthesis. . . . . . . . . . . . . . . . . . . . 150

5.4 Correlation diagram of internal vibrations of U2O(PO4)2 based on UO7

smmetry group. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

5.5 Raman spectrum of U2O(PO4)2 at ambient conditions in the spectral

region 180-800 cm−1; * indicates unidentified peaks. . . . . . . . . . 152

5.6 Raman spectrum of U2O(PO4)2 at ambient conditions in the spectral

region 800-1300 cm−1. . . . . . . . . . . . . . . . . . . . . . . . . . . 152

5.7 Raman spectra of U2O(PO4)2 under quasi hydrostatic conditions in

the spectral region 180-800 cm−1. . . . . . . . . . . . . . . . . . . . . 153

5.8 Raman spectra of U2O(PO4)2 under quasi hydrostatic conditions in

the spectral region 800-1300 cm−1. . . . . . . . . . . . . . . . . . . . 153

xxii

List of Figures

5.9 Variation of Raman mode frequencies with pressure under hydrostatic

conditions. (Error bars are larger beyond 6 GPa due to broad Raman

peaks). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

5.10 Raman spectra of U2O(PO4)2 under non-hydrostatic conditions in the

spectral region (a) 180-800 cm−1 and (b) 800-1300 cm−1. . . . . . . . 155

5.11 Variation of Raman mode frequencies with respect to pressure under

non- hydrostatic conditions. . . . . . . . . . . . . . . . . . . . . . . . 155

5.12 Raman spectra of U2O(PO4)2 on release of pressure (h) denotes from

hydrostatic and (nh) denotes from non-hydrostatic conditions. . . . . 158

5.13 X-ray diffraction patterns of U2O(PO4)2 at a few representative pressures.159

5.14 Pressure induced variation of dhkl. . . . . . . . . . . . . . . . . . . . 160

5.15 Le Bail fit to the diffraction pattern at 6 GPa; both the parent or-

thorhombic and high pressure triclinic phase have been fitted. . . . . 161

5.16 V/V0 versus pressure for the orthorhombic phase. The solid line is fit

to Birch-Murnaghan equation of state. . . . . . . . . . . . . . . . . . 161

6.1 Schematic layout of EDXRD beamline. . . . . . . . . . . . . . . . . 167

6.2 Mechanical layout of EDXRD beamline in top view. . . . . . . . . . 168

6.3 Photograph of EDXRD beam line installed at port no BL 11 at Indus-2

from (a) inside (b) outside. . . . . . . . . . . . . . . . . . . . . . . . . 168

6.4 Diffracting lozenge as defined by incident and diffracted beam. . . . . 170

6.5 Sample stage with DAC mounted on it. . . . . . . . . . . . . . . . . . 171

6.6 First diffraction pattern of (a) gold and (b)copper. . . . . . . . . . . . 172

6.7 (a) Stacked diffraction pattern of natural uranium at a few pressures;

(b) equation of state of natural uranium, symbol represents the ob-

served data and red line is B-M fit as per A. Lindbaum et al. . . . . 173

6.8 (a) EDXRD pattern of Yb2O3 at few representative pressures; (b) Pres-

sure induced variation of volume of phase A and phase C. . . . . . . . 174

xxiii

List of Figures

6.9 High temperature furnace installed at EDXRD beamline. . . . . . . . 175

xxiv

List of Tables

List of Tables

1.1 Orders of magnitude of natural and man made pressures . . . . . . . 7

1.2 Different units of pressure and their conversion factor . . . . . . . . . 8

1.3 Different pressure transmitting mediums with their range of application. 33

2.1 Bulk Modulus of different ABO4 compounds. . . . . . . . . . . . . . . 81

2.2 Tentative assignment of Raman modes of LiErF4. . . . . . . . . . . . 82

3.1 The refined atomic coordinates of the high pressure monoclinic phase

of Yb2Ti2O7 at 30.5 GPa (Space Group: P21/c , lattice parameters

being a=5.544 A, b=3.963 A, c=4.578 A and γ=104.663◦). . . . . . . 97

3.2 Mode Gruneisen parameter of Raman modes. . . . . . . . . . . . . . 101

3.3 Assignment of Raman modes of Dy2Ti2O7. The origin of modes with

(phonon) assignment has been discussed in text. . . . . . . . . . . . . 107

3.4 Raman mode frequencies (ν), their pressure dependence (dν/dP) and

corresponding Grneisen parameters (γ) in the cubic pyrochlore phase

of Dy2Ti2O7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

4.1 Atomic positions in the cubic perovskite . . . . . . . . . . . . . . . . 113

4.2 Fractional coordinates of orthorhombic phase (Pnma) at 11 GPa (2nd

high pressure phase) a=5.531 A, b=7.687 A, c=5.359 A with Z= 4 . . 119

xxv

List of Tables

4.3 Fractional coordinates of orthorhombic phase (P2221) at 4.1 GPa (First

high pressure phase) a=5.4858 A, b=5.5577 A and c=14.4582 A with

Z= 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

4.4 Bulk Modulii of various fluoro-perovskites determined from x-ray diffrac-

tion data as well as from the known elastic constants of these com-

pounds. Bulk moduli calculated using semi-empirical formulation of

Hazen et al and Errandonea et al are shown. Since both the octahedra

and dodecahedra have the same compressibilities the bulk modulii have

been calculated using the polyhedral cation formal charge and mean

cationanion distance (in A) of both the polyhedra (shown in column

7-10 of this table). It can be seen that the bulk moduli calculated

from our fit to the Scotts formulation 60 K0=(Y-Zλ)(V0)n where n =

0.1387, Y = 25.28 and Z = - 42.57 gives the closest agreement with

the experimental values. . . . . . . . . . . . . . . . . . . . . . . . . . 139

4.5 Ambient pressure elastic constants and moduli of ALiF3 (A= Ba, Sr,

Ca) determined from GGA ab-initio computations. For comparison

the experimentally determined elastic constants of BaLiF3 from Boum-

riche1994 have also been tabulated. . . . . . . . . . . . . . . . . . . . 141

4.6 Derived elastic constants characterizing mechanical stability (Mi eqs.

1-3) of BaLiF3 at different pressures, calculated from GGA ab-initio

computations reported in Mishra et al. 2011 . . . . . . . . . . . . . . 142

5.1 Tentative assignment of observed Raman modes of diuranium oxide

phosphate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

5.2 Raman active mode frequencies (ω), their pressure dependence (dω/dP)

and corresponding Gruneisen parameters (γ) of the Orthorhombic Cmca

phase of U2O(PO4)2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

xxvi

List of Tables

6.1 Salient designed parameters of Indus-2 synchrotron source. . . . . . . 164

A.1 Lattice parameters for the seven crystal systems . . . . . . . . . . . . 179

xxvii

SYNOPSIS

Structural knowledge of materials is important from technological as well as sci-

entific point of view. Structure governs the physical properties of materials and it

changes with varying thermodynamic conditions like pressure and temperature. Pres-

sure, an important thermodynamic parameter, favours the close packing of materials.

It produces more prominent effect in the materials in comparison to the tempera-

ture and is also a comparatively cleaner variable in the sense that generally it leaves

entropy unaffected. The study of materials under high pressures is of direct rele-

vance in mineralogy, geophysics and geochemistry. These studies help to understand

the nature of materials inside earth which in turn could be used in modelling the

internal structure of earth. Materials have different types of bonding like covalent,

ionic, metallic, Van der Waals or hydrogen bonding and weak polyhedral linkages.

High pressure investigations of these materials are of importance in order to under-

stand the changes in nature of bonding and structure as well as physical properties

and phenomena. Most of the geophysical materials have open framework structures

having corner shared polyhedra. On application of pressure, the polyhedra in these

materials may rotate and/or distort to favor the close packing of materials. The dis-

tortion in polyhedra may lead to changes in coordination numbers and the material

under study may show phase transitions including amorphization [1] etc. Thus high

pressure studies could help unravel the mechanism of phase transition, order-disorder

phenomenon, structural properties of quenched phases and structural evolution. In

this thesis I have investigated the high pressure behavior of some geophysically rele-

vant materials encompassing wide range of polyhedral materials like zircon/Scheelite

structured materials [2,3], pyrochlores [4, 5], perovskites [6-8] and phosphate materials

[9,10] using in-situ experimental techniques like angle dispersive x-ray diffraction and

Raman scattering. The X-ray diffraction technique using up to sub angstrom range

of wavelengths (λ) gives the information about long range ordering and the structure

xxviii

of materials at high pressures can be determined by utilizing this technique. The Ra-

man scattering typically probes length scales of the order of a few hundred angstrom

and gives information about the vibrational modes i.e. external (lattice modes) and

internal (molecular) modes. This is a very powerful technique in case of materials

having low atomic number (Z) elements for example organic materials [11-14] which

are difficult to study with powder x-ray diffraction. The proposed thesis is to be

submitted to the Homi Bhabha National Institute for Doctor of Philosophy (Ph. D.)

degree. The thesis comprises of six chapters. A brief description of the contents of

different chapters is given below.

Chapter 1 is an introductory chapter of the proposed thesis and it describes briefly

about the physics and high pressure behavior of geophysically important materials

and motivation of this work. A brief overview of the pressure as an important thermo-

dynamic variable, high pressure crystallography, structural phase transitions, phase

stability and a broad overview of high pressure research has been discussed. In ad-

dition to this the description of different types of instrumentation especially related

to high pressure measurements such as diamond anvil cell technique has been dis-

cussed in detail. In-situ structural and spectroscopic investigation techniques like x-

ray diffraction measurement and Raman scattering measurement has been presented

and the role of these techniques regarding investigation of high pressure behavior of

materials has also been elucidated.

Chapter 2 focuses on zircon /scheelite structured materials. Zircon is an important

mineral found in earth′s crust mainly in igneous rocks and sediments. In this chapter

I have discussed the effect of high pressure on chromates (YCrO4 and HoCrO4) and

fluorides (LiErF4). In case of chromate materials high pressure x-ray diffraction

studies and Raman scattering measurements have been carried out up to ∼ 40 GPa

and 20 GPa respectively. Our x-ray diffraction analyses indicate that some of the XRD

peaks like (321), (312) and (332) show a large increase in full width at half maximum

xxix

(FWHM) compared to that in (101), (200) and (202). The diffraction pattern at

intermediate pressure (before transformation to scheelite structure) could be indexed

to monoclinic phase with space group (SG) no. =15. The structure of this monoclinic

phase is similar to that of the zircon phase except for a slight rotation of the chromate

tetrahedra. With these studies I have shown that zircon to scheelite transformation

occurs through an intermediate monoclinic phase in chromates (YCrO4 and HoCrO4)

[2]. I have also studied the scheelite structured LiErF4 compound using in-situ x-ray

diffraction technique up to 28 GPa. It transforms to monoclinic ferguosonite phase

at ∼11 GPa and to another high pressure phase at ∼15 GPa [3].

Chapter 3 deals with our study of pyrochlore structured materials which are not

only geophysically relevant but also show a lot of novel phenomenon under pressure.

Pyrochlores occur in pegmatites associated with alkali rocks. These materials are

geometrically frustrated with many other competing interactions and hence pressure

may be a very useful tool to study these materials. In this chapter I have described

about the high pressure effect on titanate pyrochlores for example on Yb2Ti2O7 and

Dy2Ti2O7. In order to study the structural changes in ytterbium titanate pyrochlore,

I have performed in-situ high pressure x-ray diffraction and Raman scattering exper-

iments up to 40 GPa and 50 GPa respectively . The x-ray diffraction studies indicate

that this compound undergoes a structural phase transition at ∼29 GPa. The high

pressure phase has been determined to be of monoclinic symmetry. The detailed

Rietveld analysis has provided the evolution of its x-coordinate of 48f oxygen. The

bulk modulus of pyrochlore and high pressure monoclinic phase has been determined.

The Raman scattering measurements corroborate the x-ray diffraction results. I have

performed high pressure x-ray diffraction studies on dysprosium titanate, a spin ice

pyrochlore compound, up to 34 GPa [5] and Raman scattering studies up to ∼29

GPa. Its pressure volume (P-V) behavior shows that this compound undergoes a

subtle transition at ∼9 GPa. The bulk modulus and its derivative with respect to

xxx

pressure has been determined using third order Birch-Murghnan equation of state.

The Raman modes observed at 309 and 521 cm−1 stiffen with pressure while the

Raman modes at 552 and 703 cm−1 shows discontinuity at ∼9 GPa. The Gruneisen

parameter for Raman modes has been determined.

Chapter 4 discusses about the high pressure studies on perovskite structured mate-

rials which are important as many minerals in earth′s mantle belong to this structure

and knowledge of the high pressure behavior of these can help the understanding of

basic physics underlying geodynamical phenomena. Specifically the results of high

pressure behaviour of perovskite materials BiFeO3, BaLiF3 and double perovskite

Sr2MgWO6 are presented in this chapter. High pressure x-ray diffraction studies

have been carried out on BiFeO3 up to 27 GPa [6]. It undergoes two structural phase

transition at 4.1 GPa and 6.4 GPa. We have determined both the high pressure

phases to be orthorhombic in nature in contrast to earlier studies which claimed the

first high pressure phase to be monoclinic. The bulk modulus for all the phases has

been determined. In this study I have used Rietveld refinement in combination with

first principles calculations to determine the correct structure of first high pressure

phase. BaLiF3 is an inverse perovskite structured material which crystallizes into

cubic structure. High pressure x-ray diffraction studies have been carried out on this

material up to ∼ 50 GPa [7]. Careful analyses of the data established the stability

of the initial phase up to the highest pressure of the study. I have also determined

the bulk modulus of this material and have compared it with that obtained from

empirical as well as first principles methods. Sr2MgWO6 is a double perovskite ma-

terial. High pressure x-ray diffraction and Raman scattering measurement have been

carried out on this material up to ∼28 GPa and ∼40 GPa respectively to know its

high pressure behavior [8]. This compound is found to be structurally stable up to

the highest pressure of our studies. Bulk modulus of ambient phase is determined to

be 128 GPa which is in close agreement with the theoretical value of bulk modulus,

xxxi

132 GPa, obtained using first principles calculations.

In Chapter 5, I have discussed about an important class of geophysically impor-

tant phosphate materials. Inside earth′s mantle a lot of materials are found in their

phosphate complex. I have performed high pressure Raman measurements and x-

ray diffraction experiments on U2O(PO4)2 [9,10] up to 14 GPa and 6.5 GPa respec-

tively. We have observed several changes in the Raman spectra as well as in the x-ray

diffraction patterns. These changes suggest that this compound undergoes a phase

transition at ∼6 GPa to a mixture of disordered ambient phase and a new high pres-

sure phase. The new phase resembles the triclinic mixed-valence phase of uranium

orthophosphate. On release of pressure the initial phase is not retrieved. The nature

of phase transition is determined to be first order.

Chapter 6 describes the development of energy dispersive x-ray diffraction (EDXRD)

beam line at Indus-2 synchrotron source [15]. It focuses on the design and parameter

freezing of different components of this beam line. In addition to this, installation,

standardization and adaptation for high pressure studies with a few example of high

pressure studies carried out on this beam line has also been discussed. The state of

the art experimental station of this beam line is discussed in detail.

References

1. Surinder M. Sharma and S.K. Sikka Pressure induced amorphization of

materials Progress in Materials Science 40, 1, 1996.

2. A.K. Mishra, Nandini Garg, K. K. Pandey, K. V. Shanavas, A. K. Tyagi

and Surinder M. Sharma Zircon-monoclinic-scheelite transformation in

nanocrystalline chromates Phys. Rev. B 81, 104109, 2010.

3. Nandini Garg, A.K. Mishra, A.K. Tyagi, and Surinder M. Sharma High pres-

sure behaviour of lithium erbium flouride DAE SSPS (India) 53, 245,

2008.

xxxii

4. A. K. Mishra, H. K. Poswal, Surinder M Sharma, Surajit Saha, D. V. S. Muthu,

Surjeet Singh, R. Suryanarayanan, A. Revcolevschi, and A. K. Sood The study

of pressure induced Structural phase transition in spin-frustrated

Yb2Ti2O7 pyrochlore J. Appl. Phys. 111, 033509, 2012.

5. A. K. Mishra, H. K. Poswal, Surinder M. Sharma and A. Revcolevschi and A

K Sood Lattice instability in Dy2Ti2O7 at high pressures, to be commu-

nicated to J. Phys.:Condens Matter.

6. A. K. Mishra, Shanavas K. V., H. K. Poswal, B. P. Mandal, Nandini Garg and

Surinder M. Sharma Pressure induced phase transitions in multiferroic

BiFeO3 Solid state communications 154, 72, 2013.

7. A.K. Mishra, Nandini Garg, K.V. Shanavas, S.N. Achary, A. K. Tyagi and

Surinder M. Sharma High pressure structural stability of BaLiF3 J. Appl.

Phys. 110, 123505, 2011.

8. A.K. Mishra, H.K. Poswal,S.N. Acharya, A.K. Tyagi and S.M. Sharma Struc-

tural evolution of double perovskite Sr2MgWO6 under high pressure

Phys. Status Solidi B, 247(7), 1773, 2010.

9. A.K. Mishra, Chitra Murli, A. Singhal and Surinder M. Sharma Pressure

induced phase transformation in U2O(PO4)2, J. Solid Chem. 181(5),

1240-1248, 2008.

10. A.K. Mishra, K. K. Pandey, S. Karmakar, Surinder M. Sharma High Pressure

X-ray Diffraction Study of U2O(PO4)2 DAE SSPS (India) 51, 91, 2006.

11. A. K. Mishra, Chitra Murli and Surinder M Sharma High Pressure Raman

spectroscopic study of deuterated γ- glycine, J. Phys. Chem. B 112(49),

15867-15874, 2008.

xxxiii

12. A.K. Mishra, Chitra Murli, Nandini Garg, R. Chitra and Surinder M Sharma

Pressure induced structural transformations in Bis (glycinium) ox-

alate,J. Phys. Chem. B 114, 17084-17091, 2010.

13. Chitra Murli, A. K. Mishra, Susy Thomas and Surinder M. Sharma Ring open-

ing polymerization in carnosine under pressure, J. Phys. Chem. B 116,

4671-4676, 2012.

14. A.K. Mishra, Chitra Murli Ashok K. Verma, Yango Song, M. R. Suresh Ku-

mar,and Surinder M. Sharma Conformation and hydrogen bond assisted

polymerisation in glycine lithium sulphate, Communicated to J. Phys.

Chem B.

15. K.K. Pandey, H.K. Poswal, A.K. Mishra, Abhilash Dwivedi, R. Vasanthi, Nan-

dini Garg and Surinder M. Sharma Energy dispersive x-ray diffraction

beam line at Indus-2 Synchrotron source, Pramana 80, 607-619, 2013.

List of Tables

2

1

Introduction

1.1 Introduction to high pressure physics

Pressure plays a vital role in materials research from basic science as well as tech-

nological point of view. It can induce myriads of structural as well as electronic

changes and can also produce altogether new phenomenon and physical properties

related with materials [1]. For example it can change graphite, a layered and lubri-

cating material, into metastable diamond, known to be the hardest material on the

earth. Pressure can also lead to a rich variety of different phenomenon like polymor-

phism, stabilization of different phases, metallization of insulators; dramatic changes

in superconducting properties etc. which provides the researchers a vast playing field.

High pressure plays a significant role in todays technology also whether it is re-

lated with synthesis of various technologically advanced materials, abrasives, ceramics

and composite materials, processing of food stuffs at high pressure etc. Pressure is

important in all scientific domains. The relevant range of pressure for high pressure

biology, high pressure chemistry and high pressure physics is estimated to be 0.01

GPa- 1 GPa, 0.1 GPa-10 GPa and 1GPa- 10 Mbar respectively as shown in figure 1.1

3

1. Introduction

Figure 1.1: Schematic of the Pressure Temperature- map of scientific interest

High pressure studies are of immense relevance to the geophysical and planetary

phenomenon which is revealed by recent studies on post perovskite phase of MgSiO3

[2] providing insight into the nature of earths interior. Our planet, Earth, is sub-

divided into the following broad categories: crust, mantle and core. As we traverse

deeper and deeper inside the earth the pressure and the temperature goes on increas-

ing. At the centre of the earth the pressure and temperature are expected to be ∼3.6

Mbar and ∼6000 K respectively. Structural and related properties of materials under

such extreme conditions, quite different from those under ambient conditions, can

only be obtained from high pressure investigations.

These studies can also provide clues towards the origin and nature of the seis-

mically anomalous layers of mantle and core-mantle boundary[3] . The sharp jumps

observed in the seismic velocities at 400 km and 660 km depth in the mantle can be

understood with help of our high pressure investigations as at these depths the pres-

4

1.1. Introduction to high pressure physics

sure is expected to be in the range of 10-25 GPa as shown in figure 1.2. In general our

high pressure studies in the pressure range 1MPa to 40 GPa are vital to understand

and model the physical phenomenon up to earths mantle. The application of pressure

Figure 1.2: Variation of pressure with respect to radius of the earth

reduces the inter atomic distances consequently reducing the lattice parameters and

changing the fractional coordinates of the atoms in the unit cell for crystalline solids.

Thus compression tends to bring about closer packing of atoms, ions or molecules and

hence the increase in density is observed for compressed material. Although the close

packed structures are generally simpler and more symmetric structures, sometimes

the opposite is also quite true. In fact pressure can induce order as well as disor-

der. In general, compression leads to increase in the local coordination number- for

example a progressive increase from tetrahedral to octahedral coordination in case

of silicates [4] under high pressure. In fact the increase in coordination number is

intimately linked to the changes in the electronic states. The decrease in inter atomic

distances leads to the increased overlap of electronic wave functions of the system

in ground state, changing the localized electronic states around nuclei and ions into

5

1. Introduction

delocalized or itinerant ones. Thus the electronic states which were sharper in energy

in ground state become broad continuum or a band compressed state. This can lead

to dramatic consequences not only in the structural sense but also in terms of other

physical properties, such as evolution of insulating to metallic state.

A lot of progress has been made in the field of generation of static as well as

dynamic high pressures. As for as the dynamic high pressure is concerned it is gen-

erated primarily either by gas gun or by using high power lasers. In this thesis I

have worked only with static high pressure. Generation of static high pressure has

seen tremendous progress starting from Bridgman who used large hydraulic presses

to generate pressure ∼10 GPa to the modern era of pressure generation where palm

sized devices are available which can reach up to mega bar (4 to 5 Mbar) pressures.

In this chapter, significance of pressure as a thermodynamic variable is discussed

along with an overview of high pressure research in materials. In the subsequent

sections I have discussed the effect of high pressure from crystallography and phase

stability point of view. In the latter sections I have discussed in detail about the high

pressure devices i.e. basically diamond anvil cells (DAC) and experimental methods

to perform the in-situ measurements on materials under high pressure. Later on I

have noted the relevance of geophysical materials studied as part of my thesis.

1.2 Pressure as a Thermodynamic Variable

Pressure is defined as the force acting on a unit area and is termed as a scalar

quantity. Systematic studies as a function of pressure have led to considerable insight

into the properties of matter, especially its electronic properties. In fact pressure is

a unique thermodynamic variable spanning over 60 orders of magnitude in nature [5]

as shown in table 1.1. At one end the pressure in the interiors of neutron stars are

∼ 1032 bar and at the other end quite low pressures in the remotest vacua of outer

6

1.2. Pressure as a Thermodynamic Variable

Table 1.1: Orders of magnitude of natural and man made pressures

Pressure[bar] Places

10−32 Interstellar space10−16 Best laboratory vacuum10−8 Atmosphere 300 miles above Earths surface10−2 Water vapor at triple point100 Atmosphere at sea level103 Bottom of Marianas trench106 Center of Earth109 Center of Sun1032 Center of neutron star

space are ∼10−32 bar. In the very early days the Nobel Laureate P. W. Bridgman

recognized the importance of pressure as a thermodynamic parameter for studying

the materials and in fact he measured the electrical resistance of Germanium under

quasi-hydrostatic pressures and observed sharp decrease in the electronic mobility of

Ge which is now understood as a result of crossing of the X[111] band minima with

the Γ [100] band minima upon increasing the pressure [6]. Pressure is a rather cleaner

and stronger thermodynamic variable in comparison to temperature. A material can

be quite easily compressed to ∼50 % of its initial volume with the help of modern days

high pressure diamond anvil cells while temperature in the range of 0 K to its melting

point can induce volume change of ∼ a few percent only. The effect of temperature is

also complicated by entropic changes such as caused by increasing phonon population

while pressure effect is only manifested through change in volume. The generally used

units of pressure and their conversion in units of pascal are given in table 1.2. An

atomic unit of pressure is Pau=e2/2a40 =147.2 Mbar where ’e’ and a0 are electronic

charge and Bohrs radius respectively.

Pressure on a solid material i.e. forces acting on a unit area of the object from

different directions can have different values; therefore, in most real high-pressure

experiments scalar description of pressure is insufficient. In 1827 Cauchy introduced

7

1. Introduction

Table 1.2: Different units of pressure and their conversion factor

Pressure units Conversion factor (in pascal)

1 bar =1 atm 105

1 Torr = 1 mm Hg 133.3231Nm−2 = 10dyne/cm2 1

1lb/inch2(psi) 6.89× 103

1 inch Hg 33864

1ev/A3

0.110 kbar 1 GPa1 Mbar 100 GPa

the concept of stress tensor providing a generalized description of the forces acting

along different directions at a point in a body. The Cauchy stress is a second rank

Cartesian tensor of the form:

σ = σij =

∣∣∣∣∣∣∣∣∣∣∣∣

σ11 σ12 σ13

σ21 σ22 σ23

σ31 σ32 σ33

∣∣∣∣∣∣∣∣∣∣∣∣(1.1)

The application of such a stress gives rise to different strains along three crys-

tallographic directions except in cubic systems. Therefore strain in a solid is also a

second rank tensor denoted by ε. The general relationship between stress and strain

is given by the following tensor equation

εij = Sijklσkl (1.2)

Where S is the elastic compliance tensor. The diagonal elements of the stress

tensor are called normal stresses, whereas the off diagonal elements are shear stresses.

Because of the symmetry of the stress tensor (for a body in equilibrium (σij =σji).

Pressure is defined as the trace of stress matrix i.e.

8

1.3. An overview of high Pressure Research in Materials

P =1

3Tr(σ) =

1

3[σ11 + σ22 + σ33] (1.3)

Hydrostatic conditions can be defined in terms of the components of the stress

tensor. Ideal hydrostaticity requires all the normal stresses to be equal, and all the

shear stresses to be zero. In real experiments ideal hydrostaticity can be achieved

only with the use of fluid pressure media. Once pressure medium solidifies (either in

crystalline or amorphous state) the stress tensor can be at best described as quasi-

hydrostatic. For high pressure experiments carried out with solid pressure media

the components of the stress tensor are not only non-hydrostatic, but usually differ

from one point in space to another. e.g., in diamond anvil cell, assuming radial

symmetry, stress usually varies laterally, as a function of distance from the center of

the diamond anvil. However, in reality the heterogeneity in stresses could circumvent

the even radial symmetry.

1.3 An overview of high Pressure Research in Ma-

terials

Understanding the behaviour of condensed matter at high pressures has seen phe-

nomenal expansion with the advent of innovative and new pressure generating device

namely diamond anvil cells. For the first time P. W. Bridgman who received the Nobel

prize for the invention of high pressure generating device in 1946, [7] introduced the

opposed anvil devices and established the principles of high pressure technique. Us-

ing these devices Bridgman conducted several electrical resistance and compressibility

measurements up to 100 kbar. Later on Drickamer and his colleagues developed ultra-

high pressure supported tapered anvil devices and conducted several x-ray diffraction,

optical absorption, resistance and Mossbauer studies up to a few tens of GPa pressure

9

1. Introduction

enriching the high pressure behaviour of materials. Earlier, before the invention of

diamond anvil cell (DAC) researchers used to use large volume presses or tetrahedral

presses etc to generate high pressure. Opposed anvil design was used with anvils of

tungsten carbide to pressurise the samples or perform some studies on the quenched

samples. At the same time there have been tremendous improvements in the design of

piston cylinder device, multiple anvil devices and belt apparatus. These developments

provided very powerful tools for study of phase transition. Among above the tetra-

hedral press designed by Hall [8], the cubic [9] and the octahedral press [10] became

more useful for high pressure studies as well as material synthesis. Since diamond is

known to be hardest material it seemed logical to turn towards using diamond for

achieving higher pressures. Lawson and Tang [11] were the first to employ diamond

for containment of pressure and in 1950 a miniature piston cylinder cell with a 3 carat

single crystal diamond was developed for performing high pressure x-ray diffraction

studies. Later on, in 1958 Charlie Wier et al. [12] at National Bureau of Standards

and Jamieson, Lawson et al. [13] at the University of Chicago independently devel-

oped two different versions of the diamond anvil cell. Weir et al. were interested

in the infrared transmission measurements and adopted the 180◦ geometry in which

light beam is coincident with the stress axis while Jamieson et al. constructed a clamp

type DAC which was used in 90◦ configuration where x-ray beam is normal to the

stress axis. Since diamond is transparent over a wide range of electromagnetic wave

spectrum starting from visible and also for hard x-rays, invention of diamond anvil

cell has become an important milestone in the area of high pressure research. With

the advancement in diamond anvil cell technology the high pressure limit has been

enhanced by two orders of magnitude with the help of following major improvements.

1. Metallic gaskets with a hole inside it are used to create a sample chamber where

sample is loaded with a liquid medium to provide hydrostatic environment [14].

2. For measurement of pressure the usage of Ruby fluorescence technique provided

10


a simple and accurate method [15].

3. Alcohol mixtures (Methanol:ethanol::4:1) proved to be a very useful poor mans

liquid for hydrostatic environment up to 10 GPa [16] and for higher pressures

in the Mbar range helium and other rare gasses [17] are used as hydrostatic

medium.

4. The pressures in the Mbar range are achieved with bevelled diamond anvils [18].

It has been shown by finite element analysis method that bevelling parameter

of the anvil can be optimised to obtain the maximum and uniform pressure over

the entire culet region [19].

Concurrent with all the above developments there have been improvement in the

force generating mechanisms with the design of the mounts of anvils. Based on the

above force generating mechanism five types of DACs have evolved i.e. NBS Cell [20],

Merril-Besset Cell [21], Syassen-Holzaphel Cell [22], Mao-Bell Cell [23] and Membrane

Cell [24]. The detailed mechanism and working principle of DAC has been presented

in latter section of this chapter. The pressure increases from edge of the culet to

its centre and become maximum at the centre under loading. Primarily the shear

modulus of the diamond governs the maximum achievable pressure in a DAC. Earlier

it has been estimated based on the shear stress calculation of diamond crystal that

a DAC can reach up to the maximum pressure ∼400-540 GPa. [25, 26]. However

highest pressure achieved in a DAC depends on several other parameters, e.g., gasket

material thickness, its shear modulus, beveling parameters (beveling angle, diameter

of flat region). The maximum static pressure so far claimed to have been reached in a

DAC is 640 GPa using double stage diamond anvils and equation of state of rhenium

[27] has been extended up to 6.4 Mbar pressures. Interestingly ab initio molecular

dynamics simulations show that under hydrostatic compression, mechanical failure of

diamond occurs only at ∼30 Mbar of pressures, where diamond is expected to collapse

11

1. Introduction

into a denser and metallic form of carbon termed as SC4 [28]. Jayaraman[29] and

Eremets [30] have presented some of the initial diamond anvil cell techniques and

various experimental results.

Nowadays DACs are widely used to study the high pressure behaviour of materi-

als in the Mbar range in combination with several experimental techniques like Syn-

chrotron x-ray techniques (x-ray diffraction technique, x-ray absorption spectroscopy

(EXAFS and XANES) [31], x-ray emission spectroscopy, inelastic x-ray scattering,

x-ray magnetic circular dichroism etc.), optical spectroscopic techniques (Raman scat-

tering, Brillouin scattering, Photoluminescence, IR, optical absorption etc), electri-

cal resistivity measurements [32], Nuclear forward scattering[33] , Mossbauer spec-

troscopy [34] and thermoelectric power measurements [35] etc. As pressure squeezes

the material, it is expected that insulator may transform into metal under high pres-

sures. Monatomic hydrogen is like alkali metal and hence the molecular hydrogen

under pressure is expected to be metallic. That is why hydrogen metallization is one

of the most important sought after problem among many other relevant problems

in high pressure science. It is also important because it is speculated to be a room

temperature superconductor [36]. Recently Eremets et al.[37] claimed to observe the

conductive dense hydrogen in metallic state at 260-270 GPa. But later on WJ Nellis

et al. [38] found that there is no evidence of metallisation of hydrogen in the Eremetss

experiments. A lot of progress has also been made in the field of electrical resistivity

measurement by development of designer diamond anvil cells.

Nowadays in many studies, high pressure is applied in conjunction with other ther-

modynamic variables like temperature, magnetic field, electric field etc. The study

of behaviour of materials with high pressure and varying temperature is important

not only from its structural point of view but also from the physicochemical point

of view although the effect of temperature in changing in volume is relatively less

as compared to high pressure. Many materials are known to exhibit superconduct-

12


ing behaviour in a particular pressure temperature (P-T) range. For example iron

shows superconductivity in its non magnetic phase in the pressure range 15-20 GPa

and below 2K [39]. Pressure plays a role in changing the symmetry of the system

which in turn plays an important role in some of these types of studies. Pressure

induced enhancement of Tc has also been observed for some of cuprate systems and

iron chalocgenide systems. In fact highest Tc=164K has been observed for cuprate

system HgBa2CaCu3O8 at 30 GPa. For these type of studies miniature anvil devices

like clamp cells are used. In fact Eremets et al. have performed high pressure and

ultra low temperature studies up to 160 GPa and < 30mK [40].

High pressure in conjunction with high temperature is used mainly to determine

the phase behaviour (phase diagram) of geophysically relevant materials in a broader

range of pressure and temperature. In addition, HP-HT is also important for synthesis

of novel and technologically important materials under these extreme conditions.

High temperature in the DAC can be obtained by two methods; (1) external heating

with a resistance heater [41] which is located around the anvil and (2) local heating of

the sample with a laser beam, usually with a high power YAG laser which is capable

of delivering 50-100 W power. The laser heating technique was first introduced by

Ming and Bassett et al. [42] and they showed that sustained temperatures of 2000◦C

to 3000◦C could be obtained at pressures up to 26 GPa. In this case the temperature

was measured by optical pyrometry. The laser heating has the advantage that heating

effect is localised and hence the cell need not be specifically designed to be of heat

resistant material. But at the same time laser heating has a disadvantage of non

uniform heating and larger thermal gradients. In order to make it more uniform Mao

et al. introduced the double sided laser heating in DACs. On the other hand the

external heating produces a more uniform and reliable temperature, but weakens the

diamond support; the higher the temperature the lower the pressure limit. Arashi

and Ishigame [43] have claimed to reach ∼700◦C at pressures up to 7 GPa. Block

13

1. Introduction

et al. were able to achieve ∼700◦C and 3 GPa while Bassett et al. were able to

maintain 800◦C at pressures up to 30 GPa. In external heating the main problem is

that for more than 800◦C there is rapid graphitization of the diamonds and the loss

of strength of the diamond support. However Schiferl et al. [44] have developed a

HT-HP diamond anvil cell enclosed in a high vacuum chamber to prevent oxidation.

This cell can go up to 1200◦C and 11GPa. Boehler etal. [45] have devised a novel

method of heating, which is particularly suitable for metallic wires. They have also

employed a gasketed geometry, in which two T301 stainless-steel disks which are

electrically insulated by a disk of dense polycrystalline MgO of 0.05 mm thickness.

This serves the purpose of gaskets as well as electrical leads. Temperature is measured

by spectroradiometry using a diode array detector. Pressure calibration with the ruby

fluorescence method is not suitable for HT because with temperature the R1and R2

lines broaden. In this case generally internal standards such as gold is used for

pressure calibration. In laser heated DACs people have achieved temperatures ∼4000

K with pressures ∼200 GPa [46]. Temperatures ∼6000 K has also been reported at

lower pressures. These thermodynamic conditions are similar to that of environment

at the core of earth and inside the other giant planets of our solar system. Therefore

generating such conditions in Laboratories provide an ideal condition to understand

the phase and properties of the materials inside earth as well as inside other planets.

For example Iron and hydrogen are found inside Earth and Jupiter respectively. One

can also produce very high pressure and high temperature conditions by producing

shock with help of a gas-gun system. In this case the shock pressure is generated

by propelling a hard projectile usually with an air gun. The projectile then hits the

sample inside the target with great impact producing enormous pressure and heat.

The highest pressure and temperature achievable by this method can be as high as

600 GPa and 7500K [47]. But this HP-HT is sustained only for a few microseconds.

It is also possible to generate very high pressures ∼ 1 Gbar [48] by using pulsed

14


laser-generated shock waves in the solid materials. However the main advantage of

generating HP-HT conditions inside DAC over shock experiments is the stability of

pressure temperature conditions for a few hours. This makes it possible to investigate

the material by various techniques like x-ray diffraction, spectroscopic and visual

observations.

In order to understand the behaviour of physical properties, like transport prop-

erties (resistivity, magneto-conductance properties etc), dielectric properties, polar-

izability of materials under high pressure one has to conduct experiments under si-

multaneous application of pressure, temperature, magnetic field and electric field etc.

For magnetic measurement under high pressure one needs to use non magnetic cell,

for example made of Cu-Be alloy. Using superconducting quantum interference de-

vice (SQUID) magnetometers and Cu-Be high pressure cell it is possible to carry out

magnetotransport, magnetostriction and magnetisation measurements up to hydro-

static pressures of 5 GPa, temperatures down to sub Kelvin range and up to 20T of

magnetic field [49]. Susceptibility measurements have been performed up to very high

pressures ∼230 GPa using modified Mao-Bell kind of diamond anvil cell at very low

magnetic fields down to liquid helium temperature. Using ceramic type of diamond

anvil cells magneto optical measurements have also been carried out up to 7 GPa

down to liquid nitrogen temperature with pulsed magnetic field of 33T [50]. Several

other studies on magnetic behaviour of materials under high pressure and low tem-

perature have been performed like magneto-optical Kerr effect [51], Thermo-power

and magneto-resistance measurements [52], de hass-van Alphen effect [53], Mossbauer

effect [34], nuclear forward scattering [33], Nuclear magnetic resonance studies [54]

etc.

Neutron diffraction measurements have several advantages for the study of ma-

terials and complement the x-ray diffraction based studies specifically for materials

having low Z elements and for magnetic materials. The atomic scattering factor for

15

1. Introduction

x-ray is proportional to atomic number of elements and so higher the atomic num-

ber of the element higher the scattering. In contrast neutron scattering cross section

depends on its scattering length, a function of neutron and nucleus potential scat-

tering as well as resonance scattering due to absorption of neutrons by nucleus, with

different nuclei and it is not dependent on atomic number. It may be very random

across periodic table. It also varies drastically from one isotope to another isotope. In

addition to this, there may be magnetic scattering from the atoms. Hence the x-ray

diffraction pattern and neutron diffraction pattern may be quite different. Thus neu-

tron can be used to provide information about fractional coordinates of light elements,

their thermal motion and associated disorder if any. Since flux of neutron sources are

smaller than that of synchrotron sources and hence neutron diffraction studies under

high pressure are limited. With the recent improvements in the focussing of neutrons

using Ni-Ti super mirrors scientists have carried out high pressure neutron diffraction

studies up to 30 GPa using the new miniature Paris Edinburgh cell and up to 50 GPa

with small Kurchatov LLB cells [55]. The inelastic neutron scattering studies using

Paris Edinburgh Cell have been possible only up to 10 GPa.

To summarise, there have been tremendous improvements and innovations in the

design and development of pressure generating devices specifically for DACs. This has

propelled the detailed study of high pressure behaviour of condensed matter under

extreme conditions in combination with other thermodynamic parameters like high

temperature, low temperature, magnetic field, electric field etc. For further progress in

high pressure science it is advisable to use large volume samples without compromising

Pressure and temperature which demands for high strength anvil materials and larger

anvil sizes. This has resulted into quest for large CVD grown diamonds. Additionally

the third generation synchrotron sources, FELS and high power lasers are also going

to help in advancement of high pressure research on materials.

16

1.4. Crystallography under High Pressure

1.4 Crystallography under High Pressure

Structural studies of materials at ambient conditions using x-ray diffraction and /or

neutron diffraction are pertinent as the information of accurate structure sets the stage

for interpretation of why the materials are the way they are or in other words most of

the physical properties of materials can be understood by determining the structure of

the material and one can also engineer the materials of desired properties. Generally

crystal structure analysis includes the interpretation of observed diffraction pattern

(diffraction peaks with peak position and intensities) in terms of repeating unit i.e.

unit cell and the arrangement of atoms inside unit cell i.e. basis. The shape and size

of unit cell determines the diffraction peak positions while the intensity of these peaks

is determined by atomic arrangement in the unit cell. The variation of pressure adds

a new thermodynamic dimension to the crystal structure analyses. It may trigger new

chemical reactions or may bring about conformational and structural transformations

of molecules, polymerization, phase transitions, polymorphism affecting structure-

property relations. Essentially these studies opens up new fields like determination of

phase diagrams, polymorphism and dramatic changes in physical properties could lead

to a deeper understanding of matter at the atomic scale. In this section I will briefly

describe the salient features of high pressure crystallography. In case of high pressure

studies the crystal is under stress which may be either hydrostatic or nonhydrostatic.

In an opposed-anvil set up the stress state at the centre of the compressed sample is

given by

σij =

∣∣∣∣∣∣∣∣∣∣∣∣

σ11 0 0

0 σ22 0

0 0 σ33

∣∣∣∣∣∣∣∣∣∣∣∣=

∣∣∣∣∣∣∣∣∣∣∣∣

σp 0 0

0 σp 0

0 0 σp

∣∣∣∣∣∣∣∣∣∣∣∣+

∣∣∣∣∣∣∣∣∣∣∣∣

− t3

0 0

0 − t3

0

0 0 − t3

∣∣∣∣∣∣∣∣∣∣∣∣=σp +Dij(1.4)

Where σ11 and σ33 are radial and axial stress components respectively. σp is

17

1. Introduction

the mean normal stress which is equivalent to hydrostatic pressure. The uniaxial

stress component t=(σ33-σ33) and Dij is the deviatoric stress component. Thus for

hydrostatic compression the off diagonal stress components will be zero implying the

absence of any shear stress on the sample and the diagonal terms are equal to applied

pressure.

σkl = Pfork = l (1.5)

σkl = 0fork 6= l (1.6)

and hence for hydrostatic compression the stress strain relationship is given by

εij = PSijkk (1.7)

Here Sijkk is the elastic compliance tensor or elastic modulus tensor.

Therefore for crystal under stress the relative change of volume is given by the

sum of the diagonal term of the strain tensor,

∆V

V= Σεii = PΣSiikk (1.8)

The above equation implies that the isothermal volume compressibility is Siikk. Hence

the isothermal elastic compliances written out in matrix form can be related with the

isothermal bulk modulus K as

K = (S11 + S22 + S33 + 2S12 + 2S13 + 2S23)−1 (1.9)

which is true for all crystal systems. The relationship between individual elastic

compliances (Sijkk) and linear compressibilities (βl) of the axes can be obtained from

18


the fact that the linear compressibility, βl, in any direction in a crystal is defined by

its direction cosines li as βl = Sijkklilj [56] In case of non-hydrostatic environment

on the randomly oriented compressed polycrystalline sample the stress field can be

defined by principal stresses in the radial (σ1) and axial (σ3) directions as shown in

figure 1.3. Therefore the stress tensor can be written as σ = [σ1, σ1, σ3 as diagonal

Figure 1.3: For high pressure x-ray diffraction experiments the choice of diffraction ge-ometry for stress analysis. σ1 and σ3 are the principal stress axes. ψ is the angle betweenthe diffracting plane normal and the load direction.

elements]. The hydrostatic pressure is defined as the average of the three principal

stresses while the deviatoric stress component (t) is defined as the difference between

the two principal stresses i.e. radial and axial stresses.

P =2σ1 + σ3

3(1.10)

t = σ1 − σ3 (1.11)

As per anisotropic elasticity theory (σ1−σ3) is hkl dependent, however for all practical

purposes deviatoric stress represents the average differential stress for all hkl values.

It has been shown by AK Singh et al. [57] that dhkl in case of non-hydrostatic stresses

is a function of the angle ψ.

d(hkl) = dp(hkl)[1 + (1− 3 cos2 ψ)Q(hkl)] (1.12)

19

1. Introduction

where dp(hkl) is the d spacing under the hydrostatic pressure σp alone and Q(hkl) is

given by

Q(hkl) = (t/6)× [(α/GR) + ((1− α)/Gv)] (1.13)

Where GRand GV are the x-ray shear moduli calculated under the Reuss (iso-stress)

and Voigt (iso-strain) condition respectively. Here averaging is being done only over

the group of crystallites contributing to the diffracted intensity at the point of ob-

servation. Both the moduli are function of compliance coefficients, Sij. The nonzero

factor α which is less than 1 determines the relative weights of the strains calculated

under Reuss and Voight conditions. By plotting the equation (1.12) for several x-ray

diffraction peaks truly hydrostatic pressure dependence of the lattice parameters and

in turn the exact equation of state (EoS) can be determined.

With high pressure x-ray diffraction experiments the pressure induced variation of

unit-cell parameters of the sample are obtained and thereby the variation of volume

(or equivalently its density) with pressure is also deduced.

The pressure induced variation of volume of a solid is characterised by the bulk

modulus K = −V (∂P/∂V ). We generally parameterize the measured equations

of state in terms of the values of the bulk modulus and its pressure derivatives,

K’= ∂K/∂P and K”= ∂2K/∂P 2, determined at zero pressure. These zero pres-

sure (or almost room pressure) values are denoted by a subscript 0 thus : K0 =

−V0(∂P/∂V )(P=0), K0’= (∂K/∂P )(P=0)andK0”= (∂2K/∂P 2)(P=0) . The measured

variation of volume with pressure can be fitted with Murnaghan equation of state

[58] which can be derived from the assumption of linear variation of bulk modulus

with pressure.

V

V0

=

(1 +

K′P

K0

)−( 1

K′

)(1.14)

20


or as

P =K0

K ′

(V0

V

)K′

− 1

(1.15)

However the above equation of state is valid only for compressions up to 10% (i.e.

V/V0 > 0.9). Therefore to incorporate the higher compressions, Birch-Murnaghan

introduced a finite strain EoS, based upon the assumption [59] that the strain energy

of a compressed solid can be expressed as a Taylor series in the finite Eulerian strain,

fE =

[(V0

V )(2/3)

−1

]2

. By expanding the strain energy to the fourth order in strain we

get the following EoS.

P = 3K0fE (1 + 2fE)52

(1 +

3

2(K

′ − 4)fE +3

2

(K0K

” + (K′ − 4)(K

′ − 3) +35

9

)f 2E

)(1.16)

The third order truncation of strain energy where the coefficient of f 2E is set to

zero produces an EoS with three parameters as given below.

P = 3K0fE (1 + 2fE)52

(1 +

3

2(K

′ − 4)fE

)(1.17)

This equation fits the measured P-V data for compression up to 40 %. For V/V0

< 0.6 the finite strain EoS does not accurately represent the measured P-V data. For

simple solids under very high pressure Vinet EoS derived from a general inter-atomic

potential provides a more accurate fit to the pressure induced variation of volume.

P = 3K0(1− fV )

f 2V

exp(

3

2(K

′ − 1)(1− fV ))

(1.18)

Where fV =(VV0

) 13 The above equation (1.18) is also known as universal equation

of state which accurately describes the isothermal pressure-volume (P-V) relations

for a wide variety of materials.

21

1. Introduction

1.5 Phase Stability and High Pressure

Usually a phase transition means a transition between two equilibrium phases of mat-

ter whose signature is a singularity or discontinuity in some observable quantity which

characterises the phase of the matter. This may occur at a particular temperature or

pressure or by some other means such as by doping, or by applying electric and mag-

netic fields. In case of a structural phase transition, it is the crystal structure which is

altered abruptly. In such phase transition of solids, partial or complete rearrangement

of atoms, or only a slight rearrangement of their positions is required. Sometimes the

change may be quite small to be detected; but on the other hand dramatic changes

can also occur. It is important to realise that a crystal structure may be unstable

with respect to breaking of the symmetry (elastic instability), atomic motion (phonon

instability, displacive mode) or a combination of both. This can lead to phase trans-

formations in the materials. In terms of steric limit it has been shown by Sikka et al.

[60] that a crystal can go to the instability point under pressure when the distance

between the non-bonded atoms in the structure reaches a limiting value, called the

steric limit. This distance can be decreased either by direct bond compression or

by the bond angle bending during compression. In general it is understood that the

stability of a particular phase depends on its symmetry and the stiffness constants.

The most important physical quantity which determines the phase stability of

materials is Gibbs free energy given by

G = U + PV − TS (1.19)

Where U is the total internal energy, P is the pressure, T is the temperature, V is

the volume and S is the entropy of the system. For a phase to be thermodynamically

stable its Gibbs free energy has to be minimum. In real experiments pressure and

temperature are applied externally while internal energy, volume and entropy adjust

22

1.5. Phase Stability and High Pressure

to minimise the Gibbs free energy of the system. With the application of pressure

the phase transition can result as a crossover of Gibbs free energy of the system from

one phase to another phase. In case of isothermal pressure induced phase transitions

of first order the first derivative of Gibbs free energy G, for example volume V or

entropy S of the material changes discontinuously. Or in other words we can say

that ∆V 6= 0 and the P-V behaviour show hysteresis. In case of second order phase

transitions the first derivative of Gibbs free energy G for example volume and entropy

are continuous but the second derivative of G i.e. compressibility or specific heat

are discontinuous. Apart from equilibrium phase-boundaries of interest for a phase

transition, it is also interesting to understand detailed physical mechanisms causing

the structural changes including the kinetics of transformations. In case of 1st order

phase transition, the existence of a kinetic barrier prevents or delays transformation

to the equilibrium structure [61]. This leads to hysteresis in the transformation, i.e.,

progressive transformation of one distinct phase to another with phase coexistence

at constant pressure. But if there exists a third (metastable) structure having an

easier transformation path then the material may transform to the metastable phase.

Actually the name metastable phase is given to a state of a material in which the

material is in local and not in global free energy minimum. In strict sense there are no

metastable phases in classical thermodynamics, since any system should irreversibly

relax to the equilibrium state having least Gibbs free energy. However, long-lived

metastable solid phases exist whose life time at normal conditions exceeds the time

scale of the universe and hence their existence cannot be ignored.

Broadly the structural phase transitions can be classified into three types, recon-

structive, order-disorder, and displacive. A reconstructive phase transition is one in

which transition from one phase to another phase is brought about by bond breaking

and appropriate rejoining of bonds in the other phase such that the orientations of the

bonds in the two phases may be distinctly different or in other words the topological

23

1. Introduction

linkage pattern of the bonds in the two phases is drastically altered. Reconstructive

phase transitions are supposed to be slow (hours to seconds) in nature as atoms must

diffuse from one set of positions in one structure to different positions in another

structure so that a new set of bonds may be formed.

Order-disorder type of structural phase transitions can be divided in to two groups.

In a substitutional order-disorder phase transition both the parent and daughter

phases have very close orientation relations of the bonds. This type of phase transition

is also supposed to be sluggish. In an orientational order-disorder phase transition

small groups of atoms change their orientation by small amounts, and so they do not

alter the fundamental bonding in the material. Since in this type of phase transition

no long range diffusion is required, it is expected to occur relatively rapidly than

reconstructive phase transitions.

In a displacive phase transition bonds are not broken; instead the atoms are simply

displaced with respect to one another by small distances (compared to inter nuclear

distances). Therefore in these phase transitions the topology of the linkage pattern

in the two phases remains unaltered. Since the atomic movements are small, the

time required to complete this type of motion is ∼period of a phonon. Therefore

these types of phase transitions are faster (10−11 to 10−15 sec). Thus displacive

phase transitions usually involving relatively subtle changes in the crystal structure

may result in the interesting relationships between the two phases. This kind of

phase transition may take place continuously through a gradual change in the atomic

displacement, although the symmetry still changes abruptly at the transition point,

leading to a continuous or second order phase transition. On the other hand if there

exists a discontinuity in the volume of the crystal the transition is called first order.

In most cases, such transitions are related to soft mode. In order to observe and

stabilise the different phases under high pressure a lot of technological advances has

taken place which has been presented below.

24

1.6. High Pressure Generation and measurements

1.6 High Pressure Generation and measurements

1.6.1 High pressure Cells

As mentioned earlier in this chapter pressure is defined as force per unit area. Hence

in order to increase the pressure one can either increase the force or decrease the area.

Due to physical constraints, applied force cant be increased beyond a limit. Therefore

a trade off is established between applied force and area and one can generate a lot of

pressure with limited force applied on a very small area in contact. For high pressure

studies researchers in the initial years have used the first approach where they used

to apply as much force as possible using hydraulic press machines. But even with

cylinder of 5 mm diameter (for sample chamber) only moderate pressures of 5 GPa

have been achieved. These hydraulic presses are very bulky and could not be used

for most of the in-situ high pressure studies. In contrast diamond anvil cell (DAC)

based on the second approach. Using DACs one can generate pressure in the Mbar

range. In fact recently ∼ 6.4 Mbar static pressure has been generated using diamond

anvil cell [27]. This experiment had another innovation i.e. the usage of micro semi

balls made up of nano dimonds as second stage anvils in the conventional diamond

anvil cell. Using this device authors have studied the equation of state of rhenium up

to 640 GPa. Nowadays diamond anvil cells are basic work horses for generating very

high static pressure and for carrying out in-situ investigations of the high pressure

behaviour of materials.

1.6.2 Diamond anvil cell

A diamond cell essentially uses two flat parallel faces of two opposed diamond anvils,

as shown in figure 1.4. Force applied (as shown in figure 1.4) on these anvils pushes

these towards each other leading to the application of pressure on the sample loaded

into a metallic gasket. Depending on the way in which the force is generated and the

25

1. Introduction

mechanisms of the anvil-alignment there exist six different types of DACs. These are

named as NBS cell [20], Bassett cell [21], Mao-Bell cell [23], Syassen-Holzapfel cell

[22] membrane cell [24] and Panaromic cell [62]. During my research I have mostly

used Mao-Bell type of DACs.

Diamond being the hardest material is very useful in the application of pressure.

Brilliant-cut diamonds of gem quality are generally used as anvils. Diamonds are

transparent to visible, IR as well as hard x-rays, making it suitable for in-situ struc-

tural as well as spectroscopic investigations of materials under high pressure. The

Figure 1.4: Configuration of opposed diamond anvil, a pre indented metallic gasket witha hole is used as a sample chamber.

selection of diamonds and their size depends upon the type of DAC and the nature of

the studies. For example, diamonds with very low luminescence are used in the spec-

troscopic studies using light scattering [63]. These are known as type 1A diamonds.

On the other hand luminescent diamonds are not a problem for x-ray diffraction stud-

ies. Hence for these studies one can use type I or type II diamonds. The selection

of diamonds with low fluorescence level and without any internal or external crack is

26


very crucial as a starting step for preparation of anvil. The pointed culet of a diamond

is truncated into a flat face ranging from 300-500 µm for pressure ranging below 1

Mbar. Actually the pointed culet of gem quality diamond is removed by grinding on

a flat surface. The culet is shaped in octagonal or in hexadecagonal with typical area

of approximately 0.2− 0.4mm2 as shown in figure 1.5. The size of the diamond may

vary from 1/8 to 1/2 carat (1 carat=0.2 gm). Mostly anvil flats with similar area and

shape are used in a DAC.

Figure 1.5: The side and top view of a brilliant cut diamond.

The anvil flat is usually set parallel to the (100) or the (110) plane of the diamond.

The opposite side of the anvil flat with octagonal surface is referred to as the table

as shown in the figure 1.4 and has a typical diagonal distance of 3.5-4.5 mm in larger

diamonds.

27

1. Introduction

1.6.3 Background for high pressure experiments

1.6.3.1 Alignment of the DAC

The diamonds are mounted on to two metallic supports known as rocker and base

plate as shown in figure 1.6. One of the simplest methods of mounting the diamond

to backing plates is to glue them down with some kind of superglue. While mounting

the diamonds with glue one has to be careful otherwise the glue may close the conical

opening.

Figure 1.6: (a) Hemispherical rocker and (b) cylindrical base plate.

The metallic supports are helpful in linear and angular movement of anvils. The

rocker and the base plate work as bases for piston and cylinder devices respectively.

Both the rocker and base plate have conical opening in the centre at the position

of diamond. This allows the hindrance free access to incident as well scattered X-

rays and visible light. The alignment of diamond anvil cell is performed optically

with the help of a (stereo) microscope. In order to align the diamond anvil the culet

faces of both the diamonds have to be matched laterally by translation along X-Y

direction. The translational alignment is checked optically by viewing from the side

of the two anvils. The tilt alignment is achieved through radial/rotational alignment

by viewing through the two anvils and observing the interference fringes, arising from

the air wedge between the nonparallel culet faces. When the two culet faces tend to

be parallel, the thickness of the air wedge decreases and the number of interference

fringes reduce until a homogeneous grey indicates the disappearance of fringes and

thus achievement of perfect parallelism.

28


1.6.3.2 Choice of the gasket material

Before gasketed DAC, scientists performed high pressure experiments using piston

cylinder cell or large volume presses. Usage of metal gasket helps generation of

hydrostatic pressure employing fluid like substance inside the sample chamber. An

important role of the gasket is to provide mass support to the anvils. In this sense

gasket is one of the critical components of a diamond anvil cell. Alvin Van Valkenburg

was the first person to use metal gaskets [64]. The choice of gasket material and the

hole dimensions play a crucial role in determining the highest pressure a DAC can

achieve. Upon placing the metal gasket between the two diamonds the indented

portion of the gasket undergoes plastic deformation and the gasket material extrudes

outwards. The strain components within the gasket and its mechanical behavior

are governed by the frictional force (which is limited by the shear strength of the

metal) between the metal and the anvil. The pressure rises from the edge of the

culet towards the centre while the gradient is proportional to shear strength and

inversely proportional to the thickness of the gasket. A significant support is being

provided to the material between the diamonds by pre indented gaskets and this in

turn increases the pressure for a given gasket thickness by several GPa. The gasket

should always be sufficiently thin so that the sample hole contracts as the pressure

is raised. At higher pressure if the hole expands then one should terminate the run.

The sample chamber within the pre-indented gasket is prepared either by using spark

erosion or by mechanical drilling. The first technique is preferred over mechanical

drilling and is almost essential for the hardest materials such as tungsten and rhenium.

Depending upon the requirement of the experiment and the availability of material

a suitable metal sheet/foil (Inconel X750, tempered T301 stainless steel, waspalloy,

Cu-Be alloy, tungsten, rhenium, boron epoxy) is chosen as a gasket. The typical

initial thickness of the metal foil varies from 200 to 280 µm. Desirable thickness of

the pre indented portion is ∼30 to 100 µm depending upon the highest pressure to

29

1. Introduction

be achieved. Inconel or steel gaskets are quite suitable for the use in spectroscopic

(Raman experiments) and x-ray diffraction under high pressure. However for XRD

experiments at very high pressures using hard x-rays from synchrotron sources it is

preferable to use high Z metals like tungsten or rhenium as gaskets materials so as to

avoid the large background. For transport measurement like resistivity one prefers to

use non conducting gaskets like Al2O3 or MgO and for magnetic measurements under

high pressure since the gasket has to be nonmagnetic it is imperative to use Cu-Be

alloy. The amorphous boron mixed raisin epoxy in 4:1 ratio (by weight) is used in

case of high pressure experiments such as radial x-ray diffraction, nuclear resonant

inelastic scattering, inelastic x-ray scatterings and in laser heating experiments [65].

Due to high shear strength of amorphous boron, the thickness of sample chamber

can be maximised which in turn increases the pressure homogeneity. In addition to

this boron is also transparent to x-rays and so unwanted XRD peaks due to gaskets

are removed. Since amorphous boron is too porous to be used as a gasket material

directly, it is mixed with epoxy and thus obtained mixture is used for preparing gasket.

In order to prepare the amorphous boron gasket a hole slightly smaller than the anvil

culet dimension is drilled in a pre-indented metallic gasket and then it is filled with

boron epoxy mixture which is again compressed with anvil. In the compressed boron

part a hole is drilled of required dimension. Amorphous boron with boron nitride

seat has also been used to study the structure of amorphous iron up to 67 GPa

[66]. Use of amorphous boron gasket not only eliminates the XRD peaks from gasket

but also minimizes the x-ray absorption from it. In addition to this, experimenters

have also used bulk metallic glass gaskets for high pressure in-situ x-ray diffraction

experiments [67]. Amorphous metallic alloys lack long range order and exhibits very

good homogeneity and no microstructure discontinuities. Moreover these have higher

tensile fracture strength and hardness than those of crystalline counterparts. These

excellent physical properties make bulk metallic glasses good candidates as gaskets,

30


though many times lack of ductility might lead to fracture of diamonds.

1.6.3.3 Pressure transmitting medium

For high pressure experiments it is of utmost importance to ensure that the force

applied to the sample is homogeneous and the sample is free of any shear strains or

any differential stress. In order to achieve this, sample within the pressure chamber

must be immersed in a medium which displays hydrostatic behaviour, for example a

liquid, a gas or a soft solid having very low shear stresses. Non-hydrostatic stresses

lead to considerable broadening and shift in the position of the x-ray diffraction peaks

or in the positions of Raman peaks and thus it can lead to inaccurate determination of

lattice parameters or Raman modes behaviour. Sometimes non-hydrostatic stresses

can also suppress or facilitate the phase transitions and hence can change the phase

transition pressure or can even change the phase diagram.

The pressure transmitting medium should not support any shear stress. In addi-

tion to this the pressure transmitting medium should be chosen in such a way that

it does not dissolve or react with the sample. Additionally it should not propagate

inside the open structured or cage like structured compounds. These criteria have

resulted into the usages of large variety of pressure transmitting media like soft solids,

condensed gases, mixture of alcohols, fluorocarbons and inert silicone oil depending

upon the type of experiments one needs to carry out.

One of the most commonly used pressure transmitting medium for high pressure

studies is the 4:1 metanol:ethanol mixture, which is supposed to remain hydrostatic

up to its glass transition temperature i.e. at 10.4 GPa and quasi hydrostatic up to ∼20

GPa . The methanol, ethanol and water mixture (16:3:1) remains hydrostatic up to

14.3 GPa. But the later one can be only applied for non hygroscopic samples. Table

1.3 summarises the pressure media that are generally used for various high pressure

studies. It has been shown by Loubeyre et al. That hydrogen remains a very good

31

1. Introduction

hydrostatic medium even in the very high pressure (Mbar) regime. However there

are some drawbacks of hydrogen due to its high chemical reactivity and diffusion in

anvil and gasket. Liquid helium (He) is considered as the next most suitable pressure

transmitting medium due to its low freezing point. Though the liquid He freezes

at pressure beyond 0.5 GPa and below 39 K, but the pressure still remains quasi

hydrostatic as frozen helium is the softest solid known. Argon is found to be better

than methanol:ethanol mixture. But with reduction in temperature, the pressure also

reduces inside DAC. It has been observed that mixture of liquids remain hydrostatic

at pressures more than the freezing pressure of individual liquids. Actually with

increasing pressure the viscosity of these fluids increases and after a critical pressure

called as glass transition pressure the fluid transforms into glass and the pressure

in the sample chamber becomes inhomogeneous and differential (generally uni-axial)

stress and shear stresses appear. Among different solidified gasses Argon is the poorest

transmitting medium while helium is best. In the 0-10 GPa range nitrogen is equally

hydrostatic to neon despite its lower solidification pressure i.e. 2.4 GPa compared to

4.8 GPa of neon [68].

1.6.3.4 Pressure calibration

In case of high pressure experiments it is one of the most important tasks to measure

the accurate pressure at the sample. The pressure at the sample can be measured

using the primary /absolute or secondary scale. A primary scale is based on the

fundamental physical laws for example on laws of conservation of mass, momentum

and energy. Generally primary scale is used to pre-calibrate the secondary scale.

The primary/absolute scale can be determined by using the shock Hugoniot of a

material[79] , by using piston cylinder [80] or by directly measuring the density and

elasticity [81].

In first case, shock hugoniot of a material can be considered as a primary scale.

32


Table 1.3: Different pressure transmitting mediums with their range of application.

Medium Freezing pressure Quasi-hydrostatic Freezing temp (K) Refat RT (GPa) pressure range at at ambient pressure

RT(GPa)

Methanol:Ethanol 10.4 ∼ 20 160 [16, 69](M:E) (4:1)

Methanol:Ethanol:Water 14.5 ∼ 20 210 [70](M:E:W) (16:3:1)

Flourinert 1.8 ∼ 10 93 [71]Silicone oil 7 ∼ 15 250 [72, 73]

Daphne 2 ∼ 5 200 [74]Isopropyl alcohol ∼ 4.3 [30]

Pentane:isopentane (1:1) ∼ 7.4 [16]Hydrogen 5.7 ∼ 60 [75]Helium 11.8 ∼ 80 0.95 [76]Neon 4.7 ∼ 16 [76]Argon 1.2 ∼ 30 83 [76]Xenon ∼ 55 [77]

Nitrogen 2.4 ∼ 30 63 [78]

But due to increase in temperature at very high shock pressures one cannot compare

this pressure with static pressure. The low pressure data is fitted to determine the

equation of state of the material. Therefore by using the materials like gold (Au),

silver (Ag), copper (Cu), tungsten (W), Platinum (Pt) as the x-ray pressure marker

and by determining their unit cell volume, static pressure can be obtained. Hence

these materials are also called as secondary pressure gauges.

In the case of piston cylinder device the absolute pressure is measured by simply

measuring the force per unit area: from the loading of a piston of known area by a

known weight. This is a very accurate method for determination of low pressures. In

fact this method has an accuracy of ∼0.24% up to 2.6 GPa at the highest pressure,

while at higher pressures it is slightly inaccurate and has accuracy of 4% for pressure

between 2.5 GPa and 8 GPa.

Smith and Lawson et al. [82] proposed an idea to use a combination of volume V

33

1. Introduction

and compressibility (isothermal bulk modulus KT ) to extract the true thermodynamic

pressure by integration of KT .

P =∫ (

KT

V

)×(∂V

∂P

)(1.20)

The above pressure scale has an accuracy of ∼1%.

The inaccuracy in direct calculation of pressure from applied load increases for

higher pressures due to both internal friction and plastic or elastic deformation of

gasket which absorbs an unknown amount of the load. Hence to overcome this,

secondary scale method is used where some standard material is employed and by

utilizing its physical properties and characteristic relative changes with pressure one

can determine the pressure applied on the sample. Secondary pressure standards

can be of fixed or continuous type. The fixed pressure scales are usually used to

calibrate the large volume presses. Reproducible phase transitions of some materials

like Bismuth (Bi), Thallium (Tl), Barium (Ba) can be used to define the practical

pressure scale. The large changes in volume or electrical resistance at the phase

transition pressure can be used to calibrate the pressure.

One of the most convenient and commonly used methods for determination of

pressure is based on the laser induced fluorescence measurement. This method has

the advantage that the luminescent crystal such as ruby or rare earth element-doped

oxyhalogenides used for this measurement has to be used in very less amount and

hence a lot of volume of the sample chamber can be occupied by the sample as well as

pressure transmitting medium itself. The precision of the measurement is equivalent

to ∼ 0.01 GPa.

Ruby fluorescence is a very important pressure gauge and is now commonly used

for pressure determination. Barnett et al. [83] and Piermarini et al. [84] calibrated

the shift in ruby fluorescence with the Dekker EOS of NaCl [85]. Ruby is Cr3+(0.05

34


at.%) doped α-Al2O3 which is known to be stable and does not undergo a phase

transition up to the Mbar pressures. Ruby crystal excited by a laser line (in the

visible region), undergoes a transition to the Y and U band and these de-excite by

non radiative decay to the metastable states 2E (E1/2 and E3/2). De-excitation from

these states to the ground state i.e. (2E→ 4A2) gives two strong luminescence lines R1

(E1/2 →4A2) and R2 (E3/2 →4A2) at 6942A (14402 cm−1) and 6928.2A (14432 cm−1)

respectively [86]. These fluorescence lines blue shift with application of pressure, thus

making the ruby fluorescence signal a suitable pressure calibrant.

Later on Piermarini et al. found that the hydrostatic pressure inside the cell varies

approximately linearly with shift of the R1 and R2 ruby luminescence lines up to 19.5

GPa and it was determined that Pressure (P, in kbar) is related to the wavelength

shift (∆λ, in A) by the relation

P (kbar) = 2.746∆λ(A) (1.21)

This linear relation is no longer valid for pressures beyond ∼ 30 GPa. The line

width and the distance between the two peaks can be used as an indicator for the

hydrostaticity of the stresses inside the cell [87]. Later on the ruby pressure scale

was extended to Mbar region under quasi hydrostatic conditions by Mao et al [88]

by calibrating it against Cu as x-ray pressure marker in argon (Ar) medium and

tungsten (W) as pressure marker in neon (Ne) medium and the pressure dependence

of the ruby line shift has been shown to obey the following relation

P (GPa) =1904

B

(1 +∆λ

694.24

)B− 1

(1.22)

Here pressure (P) is in GPa, ∆λ is the ruby R1 line wavelength shift is in nm and

parameter B = 7.665 and 5 for quasi-hydrostatic and non hydrostatic conditions

respectively.

35

1. Introduction

Ruby fluorescence technique has a drawback that intensity of luminescence peaks

decreases with pressure. This technique is useful only up to a pressure of ∼150 GPa.

Beyond this pressure, the fluorescence signal from diamond interferes with ruby peaks.

But due to fact that the diamond fluorescence and the ruby life times differ by several

orders of magnitude and hence by chopping the excitation source one can separate

out both the signals and pressure can still be determined. However, Xu et al., have

shown that beyond 280 GPa ruby fluorescence reappears due to diminishing diamond

fluorescence and using this technique it has been possible to measure pressure up to

550 GPa [89]. In addition to pressure measurement the ruby fluorescence is also useful

in many other ways, e.g. by observing the R1-R2 line separation one can speculate

about the hydrostatic nature of the pressure transmitting medium. For the truly

hydrostatic pressure the R1-R2 separation remains constant else it changes for the

non hydrostatic case. The R1-R2 separation increases for the ruby strained along

the a-axis whereas it decreases for ruby strained along the c-axis. The increase or

decrease in splitting is because of the movement of the R1 line as it has been found

to red shift remarkably for non hydrostatic stresses while R2 line is independent

of non hydrostatic stresses. Generally with non hydrostatic stresses the ruby lines

broaden primarily because of inhomogeneous stress distribution. One can anneal

at higher temperatures and cool slowly to remove the stresses in the ruby chips.

Since temperature produced a wavelength shift of the ruby lines by a mean value

of ∼6.2 ×10−3 nm/K. Vos and Schouten [90] gave an empirically derived third order

polynomial. Later on Syassen et al. [91] suggested that since the effect of Cr3+ doping,

temperature and pressure are independent of each other and hence the frequency shift

can be expressed as a superposition of these i.e.

∆ν = ∆ν(cw) + ∆ν(T ) + ∆ν(P ) (1.23)

36


here cw, T and P represents the Cr concentration, temperature and pressure respec-

tively.

For small ∆T the ∆ν(T ) can be written as

∆ν(T ) =

[(∂ν

∂V

)T

(∂V

∂T

)P

+

(∂ν

∂T

)V

](1.24)

here first part in the square bracket represents the contribution from thermal

expansion and second part is isochoric. For high pressure studies at elevated temper-

atures (HP-HT), ruby fluorescence technique is no more suitable because of the large

temperature induced frequency shifts of the ruby lines together with the broadening of

lines. Hence alternative fluorescence materials having small temperature dependent

shift and prominent pressure sensitivity are chosen to meet the requirement. One

such materials is Sm:YAG crystal (0.5 % Sm2+ concentration) with zero temperature

dependence and hence is used for pressure measurement in the HP-HT case [92] .

In addition to the above mentioned materials, Raman shifts of diamond 13C and of

cubic boron nitride, and Sm2+ fluorescence line shifts of SrB4O7: Sm2+ under high

pressures and high temperatures are also used to determine the pressure [up to P

∼100 GPa and T ∼850 K] [93, 94].

1.6.4 Synchrotron sources and diffraction technique

Synchrotron sources are electron accelerator based light sources with many more ad-

vantages over laboratory based x-ray tube sources such as rotating anode generator

type of x-ray sources etc. First and foremost thing is that their brightness is many

orders (∼104−10) higher compared to laboratory based x-ray sources. Hence incident

flux at the sample and diffracted intensity is excellent. The synchrotron radiation has

a wide energy (wavelength) range covering IR to hard x-rays and hence it is possible

to select a wavelength of choice and perform experiments. In addition to this the

37

1. Introduction

synchrotron radiation is a collimated beam (in vertical direction) with time structure

and plane polarised in the plane of the ring. In order to determine the crystal struc-

ture of a material x-ray diffraction, a ubiquitous technique, is most commonly used

and hence many more x-ray diffraction beam lines are operating at any synchrotron

facility.

1.6.4.1 Wavelength selection

Choice of the X-rays wavelength (λ) is another equally important factor in case of

high pressure x-ray diffraction experiments. Since this parameter directly affects the

range of d spacing and many other things hence it is of interest to discuss it briefly.

As we know that longer wavelengths produce stronger diffracted beams because the

scattering power of crystals varies as λ3 and the efficiency of most detector systems

also increases with larger wavelengths. But on the other hand the longer wavelengths

are quite strongly absorbed by both the samples and its surrounding like Be backing

plates, diamonds etc of DAC. In case of laboratory based sources, for example even

though the Cu (Kα)(λ = 1.5406A) radiation is of longer wavelength but it is un-

suitable for high pressure XRD experiments because the x-ray intensity transmission

through a pair of diamonds anvils each 1.5 mm thick will be only 0.9 %. Instead one

favours to use Mo(Kα)(λ = 0.7093) which has a transmission of ∼54 % under above

conditions. Although the Ag(Kα)(λ = 0.5594A) source has shorter wavelength than

Mo(Kα) and hence has better transmission with ∼67%under the above mentioned

conditions. But due to poor efficiency of many detectors at shorter wavelengths the

Ag x-ray tubes or Rotating anode generators based on Silver source are not prefer-

able. In addition to this the shorter wavelengths also generate higher background

and hence lower signal to noise ratios. With the use of monochromatic synchrotron

radiation one need not worry about the above discussed issues because at synchrotron

beam lines the incident as well as the diffracted intensity is generally more than suf-

38


ficient. Moreover due to quite low divergence of synchrotron beam the diffraction

from anvil is also minimised. Hence one prefers to go for the shorter wavelengths

at synchrotron sources for high pressure XRD experiments. However, for shorter

wavelengths the background intensity increases due to increased Compton scattering

from the DAC as well as reduced absorption by the gasket. Hence for high pressure

XRD experiments one generally favours to use tungsten (W) or Rhenium (Rh) as

gasket materials. Hence the choice of suitable radiation wavelength is a kind of trade

off. The wavelength ∼0.6888 A is generally used for monochromatic x-ray diffraction

studies at high pressure.

1.6.4.2 In-situ angle dispersive x-ray diffraction

X-ray diffraction is one of the most important techniques to be used for structural

studies of materials. X-rays of sub angstrom wavelengths are generally employed to

determine the structure of any material under extreme conditions. When the basic

condition for the diffraction i.e. Bragg equation is satisfied, one gets the constructive

interference among scattered x-rays.

2dhkl sin θhkl = nλ (1.25)

where dhkl is the interplanar spacing, θhkl is the angle of specular reflection corre-

sponding to lattice planes with miller indices hkl and λ is the wavelength of the x-rays

used. Diffraction angle which is defined as the angle between incident and diffracted

x-rays is equal to 2θhkl. In order to find out the crystal structure of a material one

can either use monochromatic x-rays or white x-rays. The x-ray diffraction method

in which one uses monochromatic x-rays and data is collected by scanning the angle

is known as angle dispersive x-ray diffraction. Another variant of x-ray diffraction

where one uses polychromatic x-rays is known as energy dispersive x-ray diffraction

(EDXRD) method which has been discussed in latter section. Angle dispersive x-ray

39

1. Introduction

diffraction (ADXRD) has better resolution (∆dd

= 10−3to10−4) than EDXRD method.

Nowadays with the use of area detectors like imaging plate the data in ADXRD can

be collected in large two theta range simultaneously. Variation of intensity of XRD

peaks with temperature is taken care by Debye Waller factor

Iα exp−2M (1.26)

Where 2M = 16π2 < u2 > sin2 θ/λ2 ; u is atomic displacement, 2θ is bragg angle

and λ is the wavelength of x-ray radiation. Therefore intensities of the observed XRD

peaks at higher angular values suffer because of increasing Debye Waller factor and

reducing form factor at higher angular values.

X-ray diffraction data can be collected from powder sample as well as single crys-

tals. Powder diffraction technique has several advantages in terms of data collection

as well as sample handling etc. However it has some drawbacks like; it is inherently

one dimensional; there will be overlap of XRD peaks with similar d spacings, num-

ber of crystallites actually diffracting are small and crystallites may have preferred

orientation at high pressures giving rise to texture effects. In order to circumvent all

these difficulties single crystal x-ray diffraction (SXD) can be used which gives more

information and higher resolution than polycrystalline XRD. In principle SXD can

provide accurate electron density distributions. The ambiguities observed in XRD

peak positions and intensities in powder XRD data due to overlapping peaks can

be easily avoided in SXD experiments. Thus for accurate determination of lattice

parameters and atomic positions SXD is better than powder x-ray diffraction. More-

over the SXD data gives three dimensional information. However SXD experiments

under high pressure have its own difficulties due to limited access of diffraction angle,

x-ray absorption by diamonds, non uniform background as well as XRD peaks due

to gasket.

For my high pressure XRD studies presented here I have used laboratory as well

40


as synchrotron sources. A typical schematic diagram of the geometry of our lab

based angle dispersive x-ray diffraction setup is shown in Figure 1.7. X-rays are

incident on the sample placed inside the sample chamber made up of metallic gasket

in side diamond anvil cell along its axis of force. The Debye-Scherer diffraction cones

obtained from powdered samples are detected by the imaging plate detector.

Figure 1.7: schematic diagram of a lab based XRD set up for high pressure XRD experi-ments.

The laboratory source is a 3-kW (point source configuration) rotating anode x-ray

generator (RAG), with molybdenum (Mo) target. The source is monochromatized

using highly oriented pyrolitic graphite (HOPG) (002) crystal. The monochromatic

(λ Mo (Kα) = 0.71069 A) x-ray beam is collimated using the exit and entrance slits of

the ionization chamber (beam intensity monitor) which is attached to the detector. A

pair of translational stages (YZ) stage is fixed on the base attached to the pre-aligned

MAR345 setup. We align the x-ray beam optics to get the maximum diffraction in-

tensity. The monochromator type and the slit sizes determine the intrinsic resolution

(instrument resolution) of the system.

Most of the synchrotron based XRD experiments presented in this thesis have

been carried out at Elettra, a 2.4 GeV, 150 mA synchrotron source operating in

top-up mode. Since for high pressure experiments the sample requirement is ∼pico

41

1. Introduction

litre hence one needs to use bright sources of x-rays. In case of BL 5.2R beamline at

Elettra synchrotron source, high flux x-ray is obtained from an insertion device which

is a hybrid multipole wiggler, composed of three sections for a total length of 4.5 m.

It has a fixed gap of 22mm with magnetic field strength B=1.6T. The white beam is

collimated in the vertical direction by a Pt coated cylindrical mirror with a radius of

curvature of 14.8 km. A Si (111) based double crystal monochromator (DCM) is used

to tune a specific wavelength and a bendable toroidal focusing mirror, with 55mm

and 9.3 km of sagittal and tangential radius, is used to focus the monochromatised

beam. Monochromatic x-rays of desired wavelength (typical, λ ∼ 0.6888 A), further

Figure 1.8: RAG based high pressure XRD set up at laboratory.

collimated through an 80 µm collimator, are incident on the sample inside DAC

and the diffracted x-rays are recorded either by Image plate detector or through

Pilatus detector. The collected x-ray diffraction data is in the form of two dimensional

image (powder rings). This 2-dimensional image is converted into one dimensional

diffraction profile using FIT2D [95] software. In order to calibrate or to find out

the tilt plane and rotation angle of image plate one needs to use a standard sample

like CeO2, LaB6 or NaCl before starting the high pressure experiments. With help of

42


these standard measurements the sample to detector distance is also calibrated. Thus

obtained diffraction profiles are carefully analysed for crystallographic parameters

with the help of Le Bail and Rietveld refinements as incorporated into GSAS [96]

or FULLPROF [97]. Le Bail refinement is a full pattern refinement method which

only refines the lattice parameters while Rietveld refinement is a method where entire

diffraction pattern is fitted at once and the integrated intensity of each peak is used

to refine the positions of the atoms in the cell. The details about these refinement

methods are given in appendix A.

1.6.4.3 In-situ energy dispersive x-ray diffraction

For energy dispersive x-ray diffraction (EDXRD) method [98] the white x-ray beam is

incident on the sample and the diffracted x-rays are energy analyzed through a high

purity germanium detector kept at a fixed angle. This technique is very useful in case

of measurements with constrained geometry, such as for samples at high pressures

and/or high temperatures. In addition to this it is also particularly suited for the

kinetic studies on the samples. Since the EDXRD method can produce data over

a larger Q(2π/d) range, defined by energy range of the white synchrotron radiation

and the collection angle (θ), this can provide better real space structural resolution.

The only limitation of this technique is that the HPGe detector has inherent resultion

∼10−2 and hence this technique has resolution (∆d/d)∼10−2 only. For EDXRD , the

Bragg condition can be written as

Ehkldhkl sin θ = 6.1999 (1.27)

where Ehkl is the energy of x-ray photons (in keV) which satisfy the Bragg condi-

tion for lattice planes with Miller indices hkl having inter-planer distance of dhkl (in )

at a diffraction angle θ [99]. From above relation it is understandable that the higher

the energy of the x-rays the smaller the d-values can be probed and hence one can

43

1. Introduction

probe larger Q range. Synchrotron has a very wide range of energy and hence fulfils

this requirement. The perfectly collimated x-rays through a pair of precision slits is

incident on the sample inside DAC. The DAC is aligned with respect to synchrotron

radiation beam with the help of seven axis sample positioning system. The diffracted

x-rays are collected by energy resolving liquid nitrogen cooled high purity germanium

detector. In order to define the diffraction lozenge i.e. sample volume from which

diffraction data is being collected one needs to collect the diffracted data through a

pair of precision slis. The data is collected through Multichannel analyser (MCA)

and signals of different energy are collected in different channels. Details about this

EDXRD beam line, data collection and a few studies have been presented in chapter

6.

1.6.5 Raman Spectroscopy

Raman spectroscopy is one of the most widely used and versatile techniques for studies

of materials under extreme conditions like high pressure [100]. It probes elementary

excitations in materials by utilising inelastic scattering processes using a near ul-

traviolet, visible and near infrared monochromatic light source (laser). The Raman

spectroscopy has an advantage that it provides a large amount of easily analyzable

information very rapidly. The recorded Raman spectra can be utilised to characterise

the vibrational, electronic and magnetic subsystems by observing the corresponding

elementary excitations. It can also be used as a finger-printing technique for analysing

the materials. By in situ Raman spectroscopy one can observe the changes in the

Raman spectra with the application of pressure. These changes may be in the form of

energy of vibrational excitations, phase transformations (including melting), chemical

reactivity and magnetic and electronic transitions.

Raman scattering is defined as an inelastic scattering of monochromatic light with

a material giving information about its vibrational states. In classical descriptions,

44


photons having energy h, where h is plancks constant and is frequency of the incident

radiation undergo collisions with molecules and if the collision is perfectly elastic, then

it will be deflected unchanged and is called Rayleigh scattering. In another case it

may also happen that energy is exchanged between photon and molecule during the

collision, being inelastic collision, the molecule may gain or lose amounts of energy

in accordance with the quantum laws. This is called Raman scattering. Out of the

scattered photon only a few photons (1 out of 106 incident photons) will be Raman

scattered. If the scattered photons have frequency less (creation of phonons) than the

incident photon then it is called stokes Raman scattering and if the scattered photon

have frequency more (absorption of phonons) than the incident photon frequency

then it is called anti stokes Raman scattering as shown in figure 1.9.

Figure 1.9: Depiction of stokes and antistokes Raman scattering.

Here the phonon is a quanta of vibrational energy corresponding to each of the

normal mode of vibration. During a vibrational motion, the charge distribution of

atoms in the unit cell changes. The incident electromagnetic radiation interacts with

various vibrational states of the material and this interaction is manifested in the

form of Raman scattering, IR absorption etc. If the dipole moment changes during a

vibration, then this mode is called infrared active mode. If the polarizability of the

45

1. Introduction

atoms in the unit cell is changed by the vibration, then the corresponding vibrational

mode is called Raman active mode. Within the harmonic approximation in a perfect

crystal, phonons of a given q have infinite lifetime. The corresponding first-order

Raman spectra should then be composed of δ-function-like peaks with a full width

at half maximum (FWHM) Γ determined by the spectrometer resolution. However

crystals are neither perfect nor exactly harmonic and hence there will be finite width

of the Raman peaks. The most natural imperfections are the mass fluctuations due

to the natural isotope abundances of the constituent atoms which gives rise to finite

lifetime of phonons. In addition to this another broadening mechanism is due to the

anharmonic decay of a given phonon into two phonons or more.

For recording Raman spectra under high pressure I have used indigenously devel-

oped confocal micro Raman set up in back-scattering geometry as shown in the figure

1.10. The micro Raman set up is built around a Jobin-Yvon HR 460 single stage

Figure 1.10: Micro Raman set up in confocal geometry for high pressure Raman scatteringmeasurement.

spectrograph with liquid nitrogen cooled charge coupled device (CCD). This spectro-

graph is of dispersive type having arrangements for an interchangeable dual grating

turret with gratings of groove density 1200 grooves/mm and 2400 grooves/mm in

Czerny-turner optical configuration. In this optical configuration two concave mir-

46


rors and one plano diffraction grating is used as shown in figure 1.11. The detector

is back thinned Spectrum One CCD where charges are stored in the depletion region

of metal-oxide semiconductor capacitors. Due to back thinning it provides a better

signal to noise ratio. It has two major advantages over its other counterparts like

PMT; one is its quantum efficiency is up to 90% which is higher than that of PMT

and another is that CCD is very fast in comparison to PMT as several frequencies

can be detected simultaneously.

Figure 1.11: Optical layout of dispersive Raman scattering set up.

For excitation we either use diode pumped solid state laser (Nd-YAG) with wave-

length 532nm or an Ar ion laser (457nm, 488 nm and 514.5 nm) which serve our pur-

pose of being monochromatic with narrow line width and capable of providing high

irradiance at the sample. Since the Raman scattered light is very weak (two to four

orders lower) in comparison to Rayleigh scattered light hence a suitable supernotch or

edge filter is used to stop the Rayleigh scattered light. Edge filters exhibit good trans-

mission only on one side of the Rayleigh line, but now the holographic notch filters

can provide good transmission in both the Stokes and anti-Stokes regions. Usually

only the stokes lines are measured, since the intensity of the anti-Stokes lines is much

lower than that of the Stokes lines at ambient temperature. However the intensity

of anti-Stokes lines increases at high temperatures. Therefore the anti-Stokes Raman

47

1. Introduction

scattering is well suited to the in situ investigation of samples at high temperatures.

Thus the anti stokes lines can also be used during HP-HT measurement to estimate

the temperature at the sample.

The main advantages of holographic notch filters are: high attenuation of the

Rayleigh line; narrow bandwidth; sharp spectral edges; good transmission outside

the band, even at low wavenumbers; high damage threshold and stability to the

environment.

Spectral purity, a very important parameter for Raman spectrometer, is defined as

its ability to distinguish radiation of the narrow wavenumber band ν ±∆ν, to which

it is set, from radiation of other wavenumbers. The ability of a monochromator to

distinguish between different wavenumbers depends upon factors like resolving power,

dispersion, and slit width.

1.7 Materials Studied

In this section the materials studied for my doctoral research work are summarized

along with the emphasis on motivation to study these materials.

1.7.1 Zircon Structured Materials

Zircon, an important mineral found in the earths crust, mainly in igneous rocks

and sediments. It has important geophysical implications as well as technological

applications in the field of solid state scintillators [101, 102], laser-host materials

[103], and in other optoelectronic devices like eye-safe Raman lasers [104, 105, 106]

etc. These materials have several advantages over other scintillating materials due to

its relatively large X-ray absorption coefficient and scintillation output. These are the

reasons that have made these materials very popular for detecting X-rays and γ−rays

in medical applications [107]. Zircon (ZrSiO4) crystallizes into tetragonal space group

48

1.7. Materials Studied

(I41/amd with four formula units) and under goes to a first order phase transition

from zircon to the reidite (scheelite) phase at ∼23 GPa. Several isostructural ABO4-

type compounds, such as vandates, chromates, germinates also crystallizes into zircon

structure. But it is not known how the nano crystalline zircon or scheelite structured

material will behave under pressure. The scheelite strucuted materials are known

to transform to many competing monoclinic phases or may show dissociation under

pressure followed by pressure induced amorphisation.

With the aim to understand the high pressure behavior and mechanism of phase

transiton I have studied the nano crystalline chromates (Y CrO4, HoCrO4) using x-

ray diffraction and Raman technique. In addition to this I have also investigated

a flouroscheelite compound, Lithium erbium fluoride (LiErF4) to understand the

sequence of phase transitions.

1.7.2 Pyrochlores

Pyrochlores are another class of compounds which have not only geophysical relevance

but also show interesting physical phenomenon. There is a lot of technological interest

in these compounds as high permittivity ceramics, thermistors, thick film resistors,

electrodes for solar cells etc. These compounds have geometrically frustrated mag-

netic structure and several competing interactions like near neighbor dipolar, crystal

field interactions and quantum fluctuations etc can lift the degeneracy which can

result in various complex ground states, at very low temperatures, e.g. spin-liquid,

spin-ice and spin-glass. It will be highly interesting to study such compounds under

pressure because high pressure may change delicate balance among various compet-

ing interactions leading to realization of different physical states. The pyrochlore

materials are also potentially useful in nuclear engineering as a result of their utility

for actinide rich nuclear waste immobilization. Hence it is imperative to study the

stability and high pressure behavior of these compounds.

49

1. Introduction

I have investigated the high pressure behavior of titanate pyrochlores i.e. ytter-

bium titanate (Y b2Ti2O7) and dysprosium titanate (Dy2Ti2O7) and determined that

Y b2Ti2O7 undergoes a reversible phase transition from cubic to monoclinic struc-

ture while the Dy2Ti2O7 shows a volume discontinuity around 9 GPa indicating an

instability in its lattice.

1.7.3 Perovskites

Perovskites are an important class of materials not only from basic physics point of

view but also due to their technological relevance as ferroelectrics, piezoelectrics, re-

laxors, multiferroic matierials etc. Under extreme temperature and pressure several of

them undergo phase transformations to the post perovskite structures or decompose

into their respective oxides, making them relevant to the understanding of geophys-

ical phenomenon. In particular the studies on silicates, oxides and fluorides suggest

that the transformation to the post perovskite structure could be responsible for the

seismic discontinuity at the earths lower mantle-core boundary. Hence it is of utmost

importance to study the high pressure behavior of materials with perovskite struc-

ture. Therefore, high pressure behavior of perovskites like BiFeO3, BaLiF3 and a

double perovskite Sr2MgWO6 have been studied using x-ray diffraction and Raman

scattering technique.

1.7.4 Phosphate material

The phosphate materials are well known for their geophysical importance. As these

materials are found within mantle and could be visualised as interlinked polyhedral

motif. The pressure may change the polyhedral motif by either affecting the inter

polyhedral linkages or by distorting the polyhedra by increasing the polyhedral coor-

dination. It is of interest to study the behaviour of these open framework structured

materials on application of pressure. U2O(PO4)2 is one such important material which

50

1.8. Plan of thesis

not only shows negative thermal expansion (NTE) behaviour but also has potential

applications in the field of nuclear waste disposal. Hence we have investigated the high

pressure behaviour of such a phosphate material i.e. U2O(PO4)2 employing Raman

scattering and x-ray diffraction technique up to ∼14 GPa and 6.5 GPa respectively.

1.8 Plan of thesis

The following chapters have been arranged as follows. The chapter two describes

about the high pressure investigation on zircon and scheelite structured materials

while the studies carried out on pyrochlore materials have been presented in chapter

3. Chapter 4 is about perovskite materials and their studies. In chapter 5, I have

presented the detailed investigations on U2O(PO4)2. The development of EDXRD

beam line along with a few studies have been described in chapter 6.

51

1. Introduction

52

2

Phase Transformation in Zircon

and scheelite Structured Materials

ABX4 type of structures known as ternary compounds have important geophysical

and geochemical relevance as these are common minerals in various kinds of igneous

rocks in the Earths upper mantle and crust, and have been also found in meteorite

impact debris [108]. In addition to this zircon is an important host mineral for heat

producing radioactive elements in the Earths crust. Zircon and scheelite type of com-

pounds are technologically important materials having very attractive luminescence

properties and hence are used in solid state scintillators [101, 102], laser-host materi-

als [103], and in other optoelectronic devices [104, 105, 106]. These materials show a

variety of phase transitions for example, materials with zircon structure are known to

undergo zircon to scheelite transition while scheelite structured materials may trans-

form to many competing monoclinic structures like wolframite or fergusonite or may

dissociate under high pressure. I have chosen to study the high pressure behaviour of

zircon structured chromates and scheelite structured fluoride. In particular, the inter-

est is in nano crystalline chromates as the high pressure behaviour of nano materials

may be distinct from their bulk counterparts. These studies have been described in

53

2. Phase Transformation in Zircon and scheelite Structured Materials

this chapter.

2.1 Zircon Structured Chromates

2.1.1 Structural Details

Zircon structured materials crystallise into tetragonal crystal system with space group

(S.G.) I41/amd (SG No=141) with four of formula units (Z=4) per unit cell. The

Chromate compounds (Y CrO4 and HoCrO4) are isostructural to zircon. These ma-

terials are made up of alternating edge sharing and corner sharing CrO4 tetrahedron

and YO8/HoO8 dodecahedron as shown in figure 2.1. The Y O8/HoO8 units are

connected to each other along the ’a’ axis through corner shared CrO4 tetrahedron.

Along the ’c’ axis, these are alternately linked with CrO4 tetrahedron by edge sharing.

A slight elongation is noted for CrO4 tetrahedra because the lengths of O-O edges

shared with Y O8 dodecahedron are shorter than those of unshared ones. However,

the Cr-O bond lengths are equal in CrO4 units.

Figure 2.1: Crystal structure of Y CrO4/HoCrO4 in tetragonal zircon phase.

54

2.1. Zircon Structured Chromates

2.1.2 Introduction

Zircon (ZrSiO4) is known to undergo first order crystalline phase transition from the

zircon (S.G. I41/amd, Z = 4) to the reidite (scheelite I41/a, Z=4) form at 23 GPa

[108]. Several iso-structural ABO4 type compounds, such as the vanadates, chro-

mates, germanates, also undergo the same high pressure phase transition, displaying

a typical density increase of 10% [109, 110, 111, 112]. Static as well as shock ex-

periments on ZrSiO4 support the martensitic nature of this phase transformation

[113, 114].

There are a few important issues regarding these compounds such as mechanism

of phase transition, effect of nano crystalline particle size as well as possibility of

pressure induced amorphization. Kusaba et al. have suggested that zircon to scheel-

ite transformation may be brought about by shear deformations involving two pro-

cesses. According to this mechanism in the first process a simple shearing i.e. elonga-

tion/compression along the two equivalent (110) directions in the basal plane of the

zircon phase occurs leading to an increase in density by about 10% . In the second

process a small displacement of the atoms and rotation of the SiO4 tetrahedra [115] is

enough to establish a scheelite type of structure. However, based on the observations

of abrupt changes observed in frequencies of the Raman internal modes across this

transition, Jayaraman et al. have argued that the transformation path cannot be this

simplistic [111]. They felt that the Raman results indicate a substantial rearrange-

ment of the cations and the anions, both in length and angle. Recent theoretical

ab-initio and shell model calculations on ZrSiO4 by Smirnov et al. [116] predicted

this structure to be stable due to absence of any mechanical instability up to ∼ 70

GPa. Therefore they concluded that hydrostatic compression alone cannot be respon-

sible for this phase transition and instead it must be caused by anisotropic strains.

Energy barrier heights obtained through the first principles calculations by Florez et

al., indicate that transient states between zircon and scheelite phases are likely to be

55


monoclinic [117].

Though not of direct relevance in terms of mechanism, it is worth mentioning

here that a recent Raman investigation on zircon structured TbPO4 shows that it

transforms to a monazite structured monoclinic phase at high pressure [118]. Iso-

structural compounds like YCrO4 [119], LuVO4, YbVO4 [120, 121], YVO4 [110], also

transform to the scheelite phase at 3, 8, 5.9 and 8.5 GPa respectively. If this phase

transformation in the chromates and the vanadates is primarily due to shear strains, as

proposed by Smirnov et al., it is difficult to explain, why these compounds transformed

even though they were well within the hydrostatic limits of the pressure transmitting

media viz., methanol : ethanol :: 4:1 and nitrogen. All these results imply that the

zircon to scheelite phase transformation path is yet not fully understood, despite a

large number of studies on zircon and iso-structural compounds.

Another very important issue which needs to be understood in this set of com-

pounds is the dependence of their high pressure behaviour on particle size. For

example, whether the high pressure behaviour of the nano particles would be same

as that of the bulk material? Would they undergo the same phase transition as that

observed in the bulk or they would tend to amorphize at high pressure? Earlier, pres-

sure induced amorphization has been explained as a meta stable state obtained by the

frustration of a kinetically hindered phase during transformation to a higher density

phase [122]. Several tetrahedral coordinated materials have been shown to become

amorphous under pressure. However, there are several compounds like silicon, TiO2

etc. which are poor glass formers and do not amorphize in the bulk, but are known

to amorphize in the nano form [123]. Till date neither bulk zircon nor its iso struc-

tural compounds have been amorphized under pressure. It would be interesting to

see whether zircon structured compounds with smaller particle size would facilitate

amorphization.

In general, the thermodynamic properties of nano-crystalline materials may dif-

56


fer significantly from their bulk counterparts due to large surface to volume ratio

[108, 124, 125, 126]. In fact Tolbert et al. [123] showed that in nano-crystalline

CdSe the transformation pressure for wurtzite to rocksalt transformation increased

on decreasing the particle size. Further, the increase or decrease in the transformation

pressure of the nano-crystalline materials has been shown to depend on the ratio of the

volume collapse in bulk and nano crystalline samples at the transformation pressure

and the differences between surface and the internal energies [127]. The surface versus

bulk free energy contributions also affects the stability of the crystalline phases and a

whole new phase diagram can be assigned to the nano-crystalline materials [124]. It

is well known that zircon and zircon structured compounds in the bulk form, are poor

glass formers and have not yet been amorphized at high pressures. Recent studies

have shown that bulk ZrSiO4 can be amorphized at room pressure when irradiated

with heavy ions [128]. However, when bulk ZrSiO4 was simultaneously subjected to

high pressure and heavy ion irradiation, it fragmented into nano-particles and then

transformed to the scheelite phase at ∼14.5 GPa i.e., at much lower pressures than

the bulk [129]. In contrast, another study has shown that the transition pressure

for zircon-scheelite phase change is higher for nano-crystalline zircon [130] Therefore,

there is an ambiguity about the size and transformation-pressure correlation. The

understanding of this would have implications on the usage of reidite (scheelite phase

of zircon) as a peak pressure indicator in meteoric impacts [115]. With the aim to

understand the above mentioned issues it is important to carry out high pressure

investigations on some nano-crystalline zircon structured compounds, which in the

bulk show transformation to the scheelite phase at very low pressures. Since the bulk

forms of YCrO4 and HoCrO4 transform to the scheelite phase at P < 5 GPa i.e. well

within the hydrostatic pressure regime of most of the pressure transmitting media

employed in diamond anvil cells, we have investigated the structural behavior of the

nano-crystalline chromates at high pressures. Our results show that the transition

57


from the zircon to scheelite phase in these chromates proceeds via an intermediate

monoclinic phase and hence it is not a one step process. Moreover, this intermedi-

ate monoclinic structure is distinct from the monazite structure observed earlier in

TbPO4 [118] and has been observed for the first time in the zircon structured com-

pounds. We also observed a partial amorphization of the zircon structured chromates

at high pressure.

2.1.3 Experimental Details

Fully characterized nano-crystalline RECrO4 (RE = Y, Ho), synthesized by gel-

combustion process, were subjected to hydrostatic high pressure conditions in a di-

amond anvil cell. In different experiments the powder samples of yttrium chromate

and holmium chromate along with appropriate pressure markers (Cu) or ruby were

loaded into a 100 µm hole of a pre-indented tungsten gasket (70 µm) in the diamond

anvil cell. 16:3:1 methanol-ethanol-water mixture was used as a pressure transmitting

medium and the pressure was determined from the ruby fluorescence technique [131]

or the known equation of state of copper [132]. To ensure that the sample environ-

ment was truly hydrostatic we ensured that the sample does not directly bridge the

diamonds and the gasket hole has substantial amount of pressure transmitting fluid.

The average crystallite size of these nano-crystalline chromates, as deduced from the

Scherrers formula was 69 nm. The x-ray diffraction experiments were carried out at

BL10XU beamline at Spring8 (λ = 0.308 A) and at XRD1 beamline at Elletra (λ =

0.6702 A ) synchrotron source.

For Raman spectroscopic measurements the sample was loaded in 100 m hole of

pre-indented tungsten gaskets of thickness 50 µm in diamond anvil cell. In this

case we used 4:1 methanol-ethanol mixture as well as 16:3:1 water, methanol, ethanol

mixture as pressure transmitting mediums. The pressure was determined from the

well known ruby fluorescence method [131]. High pressure Raman experiments were

58


carried out on YCrO4 and HoCrO4 up to 32 GPa and 13 GPa respectively using

our confocal micro Raman set up developed around a single stage spectrograph with

liquid nitrogen cooled CCD. An edge filter is used to avoid the Rayleigh scattered

light. For the measurements presented here we used a diode pumped solid state laser

with wavelength 532 nm as an excitation source. Laser spot of size less than 10 µm

could be focused on the desired portion of the sample inside the gasket hole.

2.1.4 Results and Discussion

2.1.4.1 The Raman spectroscopic studies

The Raman modes at a few representative pressures can be seen in figure 2.2 and in

figure 2.3. The strongest Raman modes are the internal stretch modes of the CrO4

tetrahedra and all the other modes are very much weak. The mode assignments

were carried out in accordance with Long et al. (2006) [18]. The Raman modes are

observed at 816 cm−1 (ν3 ( Eg)), 863 cm−1 (ν1 (Ag)) for Y CrO4 and at 360 cm−1 (ν2

(Ag)), 775 cm−1 (ν3 (Bg)), 814 cm−1 (ν3 ( Eg)) , 860 cm−1 (ν1 (Ag)) for HoCrO4

and could be assigned to the internal modes of the CrO4 tetrahedra viz. symmetric

stretching ν1 (Ag), antisymmetric stretching ν3 (Bg and Eg), symmetric bending ν2

(Ag and Bg). At ambient pressure we did not observe the antisymmetric bending ν4

(Bg). Here we would like to mention that the antisymmetric bending mode of nano

YCrO4 lies close to the mode frequencies of isostructural bulk compounds. In both

HoCrO4 and YCrO4 we observed that at 8.3 and 9.1 GPa a new mode at 840 cm−1

arises and gains intensity at the cost of Raman modes of zircon structure.

The rest of the Raman modes were very weak and could not be discerned at high

pressure. These changes indicate a crystal to crystal phase transformation in these

nano chromates. We found that this transformation was sluggish and was complete

at 12 GPa and 10.5 GPa for Y CrO4, HOCrO4 respectively. The Raman modes

of the high pressure phase could be assigned to the scheelite structure of Y CrO4

59


Figure 2.2: Raman pattern of Y CrO4 at a few representative pressure.

in accordance with Long et al. [119]. These studies indicate that the pressure of

transformation from the zircon to the scheelite phase is higher than the transformation

pressure in bulk chromates. At still higher pressures of 32 GPa all the Raman modes

of Y CrO4 became too broad. This broadening could be due to pressure induced

structural disordering or due to nonhydrostaticity inside the sample chamber. On

release of pressure the two symmetric stretch modes of the chromate tetrahedra in

the scheelite phase were observed indicating that the transformation to the scheelite

phase was irreversible as observed in the bulk compounds.

The observed phonon frequencies of both the phases have been plotted as a func-

tion of pressure (figure 2.4). The pressure dependence of the ν1 mode in the nano

chromates (5.2 cm−1/GPa for Y CrO4 and 4.8 cm−1/GPa HoCrO4) are more than

that observed in bulk Y CrO4 (4.6 cm−1/GPa). This indicates that the rate of stiff-

60


Figure 2.3: Raman pattern of HoCrO4 at a few representative pressure.

ening of the symmetric mode is faster in the nano chromates.

The Raman spectroscopic results indicate that zircon structured nano chromates

transform to the scheelite phase at higher pressures than their bulk counterparts. At

high enough pressures the Raman modes become very weak and broad indicating that

there is some inherent disorder in the sample. It could also mean that the sample

had become partially amorphous at such high pressures. To ascertain the structure

of the high pressure phase we carried out angle dispersive x-ray diffraction studies on

these nano crystalline chromates.

61


Figure 2.4: Pressure induced variation of Raman shifts of (a) Y CrO4; triangle and circlerepresent the prominent Raman mode corresponding to zircon structure while the invertedtriangle and square represent the Raman modes for scheelite phase and (b) HoCrO4, squareand circle represent the main Raman mode corresponding to zircon and scheelite phaserespectively; here solid lines represent guide to an eye.

2.1.4.2 X-ray diffraction studies at Elettra

The diffraction data for both the nano chromates was collected at the Elettra syn-

chrotron source. The diffraction pattern of YCrO4 and HoCrO4 stacked at a few

representative pressures are shown in figure 2.5 and figure 2.6 respectively. The

diffraction patterns show that up to 10 GPa there is a monotonous shift and x-ray

diffraction peaks shift towards higher angular values for both the samples. Though

a small broad hump was observed at 12.8◦ which may correspond to two theta value

of the maximum intensity peak of the scheelite phase) at 11.8 GPa, it did not de-

velop into a discernible diffraction peak of the scheelite phase. The full width at half

maxima of the diffraction peaks from the zircon phase also show broadening with pres-

62


sure and beyond 10 GPa these diffraction peaks become very broad and are no longer

discernible, clearly indicating that the sample may have become disordered. These

diffraction patterns seem to suggest that the kinetics in nano crystalline samples is

such that the scheelite phase does not crystallize even up to ∼ 10 GPa. The diffraction

peaks which are visible at the highest pressure are from the pressure marker and from

the gasket material. Here we would like to mention that the FWHM of diffraction

peaks of copper (pressure marker) does not change much with pressure, indicating

that the pressure environment is quasi hydrostatic.

Figure 2.5: Diffraction pattern of YCrO4 at a few representative pressures.

These x-ray diffraction results seem to be contradicting our Raman spectroscopic

63


Figure 2.6: Diffraction pattern of HoCrO4 at a few representative pressures.

results. Our Raman studies indicate an irreversible crystal to crystal phase transfor-

mation whereas the x-ray diffraction experiments suggest the occurrence of pressure

induced amorphization. These contradicting results can be reconciled with an expla-

nation that the translational modes of the chromate tetrahedra are not observable

and the only new modes that are observable are weak and broad. Therefore we can

hypothesize that there is some sort of orientational disorder of the chromate tetra-

hedra which is leading to long range disorder as observed in the x-ray diffraction

experiments. As Raman spectra probes shorter length scales it is not surprising that

we could observe the internal modes of these tetrahedra. However, the second ex-

64


planation to these results could be that the new high pressure phase has a small

crystallite size due to multiple nucleation sites of new phase. It is known that when

solid- solid phase transitions are accompanied by a volume change, single crystals

fragment into much smaller crystallites [124].

However, these studies did not help us in ascertaining whether the high pres-

sure phase was disordered or poorly crystalline. To resolve this issue we carried out

experiments at a higher energy synchrotron source (Spring8).

2.1.4.3 X-ray diffraction studies at Spring8

The diffraction patterns of YCrO4 and HoCrO4 at a few representative pressures

are shown in figure 2.7 and in figure 2.8 respectively. The diffraction patterns from

both these compounds show that up to ∼6.5 GPa there is a monotonous shift in the

diffraction peaks towards higher two-theta values. On further raising the pressure

beyond 6.5 GPa, distinct new diffraction peaks were observed in the diffraction pat-

terns, as also indicated in figure 2.7 and figure 2.8. The diffraction patterns at these

pressures could be indexed to the tetragonal scheelite phase. As mentioned earlier

our Raman scattering measurements also establish the appearance of scheelite phase

beyond 6.5 GPa. Therefore clearly both these compounds do transform from zircon

to scheelite structure at high pressures unlike that observed in case of XRD data from

Elettra synchrotron soure. This may be due to fragmentation of larger nano particles

in to very small ones in high pressure phase resulting into non-observation of weak

diffraction peaks almost implying amorphization at low energy synchrotron source.

However the XRD peaks of zircon structure appeared to be broad. Earlier Tolbert

et al. [123] have established the shape changes of nano crystallites under pressure

and their role in the phase transformations [133, 134]. With this motivation I tried to

look into the FWHM of a few XRD peaks of zircon structured chromates. Figure 2.9

shows the FWHM of some of the diffraction peaks of the samples while their diffraction

65


Figure 2.7: The diffraction pattern of YCrO4 recorded at Spring8 at a few representativepressures. The ambient pressure data has been indexed with respect to the zircon structure.The diffraction peak marked as (112) at high pressure refers to the scheelite phase. It isapparent that background increases with pressure.

patterns can still be indexed as that of zircon phase. We find a large increase in the

FWHM of some of the diffraction peaks such as, (321), (312), (332) etc. whereas the

FWHM of the (101), (200), (202) diffraction peaks show relatively negligible change

from their ambient values. Earlier such variations have been ascribed to the shape

change of crystallites across a phase transformation.

To evaluate a similar possibility we note that zircon to scheelite phase transfor-

mation has been proposed to proceed through a shear in the basal plane such that

the angle of intersection between (100) and (010) direction changes from 90◦ to 115◦.

If this change is not abrupt, the intermediate state would not have a tetragonal sym-

metry and the unit cell would be essentially monoclinic. As mentioned earlier, recent

first principles calculations also suggests a similar transient intermediate monoclinic

phase [117].

On carrying out a Rietveld analysis of the diffraction pattern of YCrO4, at 4.6

66


Figure 2.8: The diffraction pattern of HoCrO4, recorded at Spring8 at a few representativepressures. The ambient pressure data has been indexed with respect to the zircon structure.The diffraction peaks of the high pressure phase have been indicated by arrows. The diffrac-tion peak marked as (112) at high pressure refers to the scheelite phase. The backgroundof the lowest pressure phase has been subtracted from all the subsequent pressure runs.

GPa we could fit the high pressure diffraction data to a monoclinic phase (SG: no.

15; I112/b, Z = 4, γ = 90.44◦) as shown in figure 2.10. In fact it was found that the

increased FWHM of some XRD peaks were because of overlapping XRD peaks from

monoclinic structure.

The structure of this monoclinic phase (MP) is similar to that of the zircon phase

(ZP) except for a slight rotation of the chromate tetrahedra as shown in figure 2.11

and a change in the gamma angle from 90◦ to 90.44◦. Similar monoclinic structure

also explains the results of HoCrO4 at 6.5 GPa. Thus the reduced symmetry of the

high pressure phase provides a rational explanation of unusual broadening of some of

the peaks as due to unresolved split peaks.

The existence of a monoclinic daughter phase has earlier been speculated, arising

possibly from softening of C66 shear elastic constant [135]. However, recent theoretical

67


Figure 2.9: The increase in FWHM of some of the diffraction peaks of (a) YCrO4 at 4.6GPa and (b) HoCrO4 at 6.5 GPa. The FWHM of the (200) diffraction peak did not increaseas the difference between the a and b cell constants in the monoclinic phase is 0.01 %.

calculations [116] have shown that this shear elastic constant is likely to soften only

at 70 GPa, making it a highly improbable cause of monoclinic distortion of the

parent tetragonal cell. The intermediate monoclinic phase determined by our Rietveld

analysis of XRD data is found to be energetically stable as per the first principles

calculations reported in [136]. This shows that in nano crystalline chromates the

observed monoclinic phase is not just an unstable transient phase but, has a range of

stability. The second high pressure phase i.e. scheelite was retained even on release

of pressure. For bulk YCrO4, an irreversible transformation to the scheelite phase at

∼ 3 GPa, has earlier been established through Raman measurements [119]. Though

there are no in-situ high pressure studies on bulk HoCrO4, the scheelite phase in this

compound too has been synthesized by subjecting its zircon phase to high temperature

(823 K) and pressure (4 GPa) in a belt type press [137]. Therefore, our results suggest

that the transformation to scheelite phase in nano-crystalline chromates occurs at

higher pressures than that observed in bulk. This is also consistent with the results

of M. Lang et al. on ZrSiO4 which shows only traces of reidite phase even at ∼ 36

GPa.

There are a few more useful features in the diffraction patterns shown in Figure

2.7 and figure 2.8 which are worth discussion. We note that the diffraction peaks of

68


Figure 2.10: Rietveld fits to the recorded diffraction pattern of YCrO4 at 4.6 GPa (red)in the monoclinic structure. The blue line shows the subtracted background and verticalbars give the expected positions of the diffraction peaks from the sample. The differencein the calculated and experimental diffraction pattern is given at the bottom of the graph(green).

the high pressure scheelite phase are very broad and are accompanied by an increasing

background. This could be due to small crystallite size (result of multiple nucleation

sites of new phase) of the new high pressure phase. In fact from the diffraction data

collected at Spring8 the calculated particle size of the high pressure phase is ∼7 nm

at 10 GPa. This is consistent with what is stated earlier in the section 2.1.4. (b),

that when solid- solid phase transitions are accompanied by a volume change, single

crystals fragment into much smaller crystallites [124]. Present experimental results

imply that at high pressure the chromate crystallites of ∼ 68 nm size have fragmented

into smaller nano particles and in this process some parts of the parent crystallites

may have become disordered leading to partial amorphization. This could be the

reason why amorphous like behaviour was observed with the lower flux synchrotron

69


Figure 2.11: The (a) zircon and (b) monoclinic structure of YCrO4 as determined fromthe diffraction data. The γ angle is 90.4◦. The chromium, Yttrium and oxygen atoms havebeen marked as Cr (grey), Y (blue) and O (red) respectively.

data.

Due to the lower symmetry of the intermediate phase, we also speculate, as pro-

posed by Toledano et al. [138], that the daughter phase may have multi domain

states. This could lead to structural mismatches of the sheared domains adjacent

to each other and finally result in fragmentation into still smaller nano particles.

Moreover, the fragmentation would not necessarily be of equal size and the smaller

nano-domains may significantly lose translational order due to relaxations of atoms

at the surfaces, contributing effectively to the observed increase in the background at

high pressure.

Hence our studies indicate that the zircon to scheelite phase transition in these

compounds may not be a one step process. Instead it is a two step process first

proceeding via a symmetry descent and then a symmetry ascent.

2.1.5 Conclusions

Our in-situ high pressure x-ray diffraction measurements and Raman scattering stud-

ies on zircon structured nano-crystalline chromates show that the structural phase

70


transformation from zircon to scheelite phase proceeds via an intermediate monoclinic

phase i.e. zircon → monoclinic → scheelite. Though there have been speculations

about zircon-scheelite phase transformation proceeding through an unstable transient

monoclinic phase in ZrSiO4, we have experimentally demonstrated the existence of a

similar intermediate stable state in a zircon structured compound for the first time.

For our nano-crystalline samples, the transformation pressure is found to be higher

than the bulk. This suggests that non-hydrostatic stresses or strains may not be

vital even in other iso-structural compounds where zircon-scheelite transformation

has been observed. However, in the present case, the intermediate monoclinic phase

(similar to the transient and hence unstable state proposed earlier [117] to delineate

the path of transformation) has been observed. This is similar to the case of the

B1-B2 phase transition in alkaline halides and oxides where an intermediate unsta-

ble monoclinic phase describes the transition pathway but is observed only in silver

chloride [139, 140]. We should also note that under certain thermodynamic condi-

tions, including the rate and step of the increase of pressure etc., it may be possible

to trap the intermediate transient structures - as was also observed in quartz [141].

However, in YCrO4, the observation of monoclinic phase in nano-crystalline samples

may purely be incidental, as theoretical results suggest the possibility of the same for

the bulk samples too, for which no in-situ x-ray diffraction investigations have been

carried out so far to the best of our knowledge.

The particle size of the scheelite phase has been found to be much smaller that the

parent phase, coexisting with a significant amorphous content. Also since reducing

particle size increases the transformation pressure in zircon structured compounds,

care must be taken when the pressures of meteoric impacts on radiation accumulated

zircon sites is determined from the presence of reidite.

71


2.2 Scheelite Structured Fluoride


In the earlier section 2.1 we described the zircon to scheelite phase transition in

chromates. For completeness we would like to mention that scheelite/reidite is the

name of a mineral calcium tungstate (CaWO4), which is used to describe the family of

all the minerals isostructural to it, like many tungstates, molybdates and fluorides etc.

Scheelite structured materials have tetragonal symmetry, appearing as dipyramidal

pseudo-octahedra and crystallise into space group (S.G.) I41/a (SG No = 88) with

four formula units (Z = 4) per unit cell. These materials posses distinct cleavage

planes and hence their single crystal can be cleaved very easily. The crystal structure

Figure 2.12: Crystal structure of LiErF4 in tetragonal scheelite phase.

of LiErF4 as shown in figure 2.12 can be visualised as made up of ErF8 dodecahedra

and LiF4 tetrahedra. The ErF8 dodecahedra are connected by edge shared ErF8

polyhedra and corner shared LiF4 tetrahedra in the a-c and a-b plane respectively.

72

2.2. Scheelite Structured Fluoride

2.2.2 Introduction

There is a lot of interest in the high pressure transitions of the scheelite struc-

tured compounds due to their possible geophysical implications. Several studies have

been carried out on the effects of pressure on the properties of scheelite structured

tungstates and molybdates [142, 143, 144, 145, 146, 147, 148, 149, 150] based on the

packing efficiency considerations, some of the earlier studies have predicted the wol-

framite to be one of preferred high pressure phase[151]. However some recent studies

have shown that these compounds may transform to any of the competing monoclinic

structures i.e. fergusonite or wolframite [152]. But till date very few studies [152, 153]

have been reported for scheelite structured fluoride compounds. These fluorides are

optically transparent insulators and hence find applications as important laser hosts,

scintillators and luminescence materials.

Lithium erbium fluoride belongs to the LiLnF4 (Ln = Eu - Lu) family which crys-

tallizes with the scheelite structure (I41/a, Z=4), a superstructure of fluorite CaF2

(Fm3m, Z=2). In this system the fluorine atoms are in a distorted simple cubic

arrangement as can be seen in Figure 2.12. Yttrium lithium fluoride an important

member of this family has been extensively studied by experimental as well as the-

oretical studies. These studies have shown that it undergoes two phase transitions

at high pressure [154]. LiLuF4 on the contrary has been shown to undergo only one

phase transition and LiGdF4 does not undergo any crystal to crystal phase transition

at high pressure, but progressively decomposes into a solid solution series [148, 155].

This behavior can be associated with the size of the Ln cation as we can see that

(R(Y) < R(Lu) < R(Gd)). Therefore we would expect the behavior of LiErF4 to lie

in between that of the end members LiYF4 and LiGdF4.

Another important aspect of these phase transitions in lanthanide fluorides, is the

structure of the first high pressure phase. Tungstate scheelites like CaWO4 trans-

forms from scheelite to wolframite (monoclinic) structure. The experiments and first

73


principles calculations indicate that the first high pressure phase in LiYF4 is simi-

lar to that of fergusonite (SG = I2/a) [156]. Molecular dynamical calculations show

that the structure is fergusonite like (SG =P21/c) [157]. In case of LiLuF4 the first

high pressure phase has been shown to be similar to that of fergusonite. It will be

interesting to see what happens in case of LiErF4 where Li-F is ionic in nature unlike

CaWO4 where W-O is predominantly covalent in nature.

We have carried out powder x-ray diffraction and Raman spectroscopic studies

on LiErF4, to ascertain whether its high pressure behavior is similar to that of the

lanthanide fluorides and to determine the structure of the first high pressure phase

and the nature of phase transition.

2.2.3 Experimental Methods

Lithium erbium fluoride has been prepared through the standard solid state route. AR

grade reactants, lithium fluoride and erbium fluoride, were mixed in stoichiometric

amounts. Well ground mixtures were heated in the pellet form at 1473 K for 36

hours. After this, the materials were reground, repelletized and heated at 1573 K

for 36 hours. In order to attain a better homogeneity, the products obtained after

second heating were again ground, pelletized and heated at 1673 K for 48 hours,

which was the final annealing temperature of all the specimens. The heating and

cooling was carried out at a rate of 2◦C per minute in a static air environment. The

compound thus formed has been characterized with the help of x-ray diffraction and

Raman spectroscopy. The lattice parameter of Lithium erbium fluoride is found to

be a = 5.159 ± 0.003 A, and c = 10.701 ± 0.002 A which is in good agreement

with the earlier reported value [158]. For x-ray diffraction experiments the powder

samples of Lithium erbium fluoride along with a few particles of gold ( pressure

markers) were loaded into a 100 µm hole of a pre-indented tungsten gasket (∼ 75

µm) in a diamond anvil cell. 4:1 methanol-ethanol mixture was used as a pressure

74


transmitting medium and the pressure was determined from the known equation of

state of gold [132]. These experiments were carried out at the XRD1 beamline of

the Elettra synchrotron source using the x-rays of wavelength 0.6702 A. The two

dimensional diffraction rings were converted to one dimensional diffraction patterns

using the FIT2D software [95]. The cell constants were determined by the Le Bail

method using the GSAS software [96]. The high pressure experiments were carried out

up to 28 GPa. For Raman measurements a single speck of a polycrystalline sample of

lithium erbium fluoride was loaded in a 100 µm hole of a pre-indented tungsten gasket

(∼ 75 µm) in a diamond anvil cell. In this case also we used 4:1 methanol-ethanol

mixture as a pressure transmitting medium and the pressure was determined from

the well known ruby fluorescence method [131]. Raman measurements under high

pressure were carried out up to ∼ 26 GPa using our confocal micro Raman system

which is already stated in chapter 1 Laser spot of size less than 10 µm could be focused

on the desired portion of the sample inside the gasket hole with the help of a viewing

system. This helps to reduce the background noise contributed by the diamond and

gasket substantially.


2.2.4.1 Structural Effects

X-ray diffraction pattern stacked at a few representative pressures are shown in figure

2.13. It has been observed that up to 10.7 GPa there is a monotonous shift of

the x-ray diffraction peaks towards higher two theta values. Beyond this pressure

the appearance of new x-ray diffraction peaks clearly indicates a structural phase

transition. At 15 GPa new x-ray diffraction peaks shown with arrow marks emerge

which implies the occurrence of second phase transition at this pressure. On further

pressurizing most of the x-ray diffraction peaks of LiErF4 disappear except two broad

humps at 7.5◦ and 12.5◦. This implies the loss of long range ordering at 25 GPa.

75


The complete pressure induced amorphization occurs across 28 GPa. We have also

Figure 2.13: X-ray diffraction patterns of lithium erbium fluoride stacked at a few repre-sentative pressures.

observed that the initial phase is retrieved when pressure is released from 15 GPa.

However, when it is released from 28 GPa the disordered phase is retained. The

pressure induced amorphization in this compound may be kinetically hindered as

observed in lithium gadolinium fluoride [155] beyond 11 GPa. Although the Mo-O

is covalent, the BaMoO4 transform from scheelite to monoclinic (fergusonite) phase.

Hence I have compared the variation of lattice parameters of LiErF4 with BaMoO4

with pressure.

The pressure induced variation of lattice parameters a and c of LiErF4 and

BaMoO4 are shown in figure 2.14. From the above figure we can note that the

rate of change of c lattice parameter of BaMoO4 is more than that of LiErF4 while

the rate of change of lattice parameter a is almost same in both the cases. The linear

axial compressibility of LiErF4 is determined to be 4.8 x 10−3 and 2.2 x10−3 /GPa

for a axis and c axis respectively while that for BaMoO4 is 5.4 x 10−3 and 8.4 x10−3

76


Figure 2.14: Pressure induced variation of c and a lattice parameters of LiErF4 andBaMoO4 in scheelite phase. Symbols and lines represent observed data and linear fit tothese data respectively. The data for BaMoO4 has been taken from Panchal et al. 2006

/GPa for a axis and c axis respectively. Figure 2.15 presents the pressure dependence

of the c/a ratio in the scheelite phase of LiErF4, LiYF4 and BaMoO4. The c/a ra-

tio of fluoro scheelite compounds increases with pressure while that of oxy scheelite

compounds decreases with pressure. Here we can note that the MoO4/WO4 tetrahe-

dra are rigid in comparison to LiF4 tetrahedra; Mo-O/W-O being covalent and Li-F

ionic. Therefore LiF4 tetrahedra may see larger changes compared to MoO4/WO4.

On the other hand the compression of Er-F (Ba-O) will be smaller (greater) com-

pared to Mo-O (W-O) bond compression in the same pressure range. Compression

leads to reduced interatomic distances and cation sizes which in turn increases the

cation-cation repulsive forces. As per Errandonea et al. [151] the reduction of anion

sizes due to compression increases the packing efficiency of anions in the cationic sub

lattice. The increase in the anionic packing efficiency increases the c/a ratio and leads

to different cationic coordination. While the increase in cationic repulsion decreases

77


Figure 2.15: Pressure dependence of c/a ratio in the scheelite structure of LiErF4, LiYF4,BaMoO4 and CaWO4. The data for LiErF4 are from present study and LiYF4, BaMoO4

and CaWO4 data are taken from references (Grzechnik et al. 2002, Panchal et al. 2006 andErrandonea et al. 2005) respectively.

the c/a ratio and leads to equal cation coordination. That is why the oxy fluorites

may transform to wolframite structure with cation coordination (6-6). While the flu-

oroscheelite compounds may transform to fergusonite structure with different cation

coordination (8-4) and (8-6). The observed x-ray diffraction pattern at each pressure

has been analyzed using Rietveld analysis and the lattice parameters have been de-

duced. Our Rietveld analysis indicates that the structure of the first high pressure

phase is similar to that of fergusonite phase. The diffraction pattern at 13.7 GPa as

shown in figure 2.13 has been indexed to the fergusonite structure. This structure is

a distorted and compressed version of scheelite structure and is obtained by a small

78


distortion of the cation matrix with significant displacements of the anions. This

Figure 2.16: The high pressure fergusonite structure of LiErF4 obtained from the scheelitestructure.

can be visualized from figure 2.16. Some reports indicate that the post fergusonite

phase under high pressure may be a phase isostructural to baddeleyite structure (SG:

P21/c) [157] or to the wolframite type of structure [159]. But these phases do not fit

to our post fergusonite diffraction pattern observed at 15 GPa. This leaves further

scope for structure determination of this new high pressure phase.

The pressure induced variation of volume of unit cell of scheelite and fergusonite

phase has been shown in figure 2.17. It can be clearly seen from this figure that within

experimental uncertainties there is no discontinuity in the volume at the first phase

transition. This behavior is similar to the x-ray diffraction results of YLiF4 [154].

In rare earth niobates, tantalates and tungstates, it is debatable whether this phase

transition is first order or second order. The earlier theoretical studies add to the

confusion as first principles calculations show that there is a 0.5% volume collapse in

YLiF4 whereas molecular dynamical calculations do not observe any discontinuity in

the volume across the transition pressure [156, 157]. In fact the P-V curve of LiLuF4

shows that the first phase transition has a tricritical nature [154]. Our studies suggest

79


Figure 2.17: Pressure versus volume of LiErF4. The circles and squares represent thedifferent experimental runs of the scheelite phase and the triangles represent the fergusonitephase. The red line represents B-M fit for the scheelite phase.

that this phase transition may be second order in nature.

The third order Birch Murnaghan equation of state was fitted to the pressure

volume data of the scheelite phase. The bulk modulus at zero pressure was determined

to be K = 81 GPa, with its pressure derivative K′ = 6.4. It is well known that the

compressibility of the scheelite and zircon structured compounds depend upon the

valence of the two different cations. It can be clearly seen from the table shown

below that it increases when the difference between the valence of the two cations

increases (table 2.2) and the valence of the tetrahedral cation is closer to the value 4.

We can see that the bulk modulus of LiErF4 does lie in between the (2, 6) and (3, 5)

compounds.

2.2.4.2 Spectroscopic effects

As stated earlier LiErF4 has body centered unit cell consisting of a pair of formula

units per basis point. Hence a primitive cell can be chosen with two numbers of

formula units per unit cell. This results into 36 vibrational modes at the centre of

the brillouin zone which are distributed among the irreducible representation of point

80


Table 2.1: Bulk Modulus of different ABO4 compounds.

ABO4 Formal charge of the cations Bulk Modulus(GPa)A B

AgReO4 1+ 7+ 31KReO4 1+ 7+ 18

BaMoO4 2+ 6+ 56BaWO4 2+ 6+ 57PbWO4 2+ 6+ 69PbMoO4 2+ 6+ 71LiErF4 3+ 1+ 81

LaNbO4 3+ 5+ 111YVO4 3+ 5+ 138

ZrGeO4 4+ 4+ 238HfGeO4 4+ 4+ 242ThGeO4 4+ 4+ 223ZrSiO4 4+ 4+ 301

group C4h as given below.

Γvib = 3Ag + 5Au + 5Bg + 3Bu + 5Eg + 5Eu (2.1)

Here one Au and one Eu mode corresponds to rigid translations of the whole crystal.

The other Au, Buand Eu modes are infrared active while the Ag, Bg and Eg modes

are Raman active. Thus it will have thirteen Raman-active modes: ΓRaman = 3 Ag+

5 Bg + 5 Eg. Figure 2.18 shows the observed Raman spectra of LiErF4 in the spectral

region 200-1000 cm−1.

We have observed five Raman modes for this compound. The observed Raman

modes given in table 2.3 have been tentatively assigned as per S. Salun et al. [153].

The peaks marked with * are fluorescence along with Raman modes observed

in this measurement. The broad bands in the region 500-800 cm−1 are fluorescence

corresponding to transition from 4S3/2 to 4I5/2. Figure 2.19 shows the observed Raman

81


Figure 2.18: Raman spectra of lithium erbium fluoride stacked at ambient conditions.The asterisk (*) presents the fluorescence for LiErF4.

Table 2.2: Tentative assignment of Raman modes of LiErF4.

Raman modescm−1 Tentative assignment [51]

325 Bg

335 Eg

362 Bg

380 Bg

418 Ag

spectra of LiErF4 stacked at a few representative pressures.

The Raman mode at 325 cm−1 disappears at 10.8 GPa and discontinuous changes

are observed in the Raman mode frequencies observed at 335, 362, 380 and 418 cm−1

across this pressure. The Raman modes at 335 and 362 cm−1 soften beyond 10.8 GPa

while the other two modes at 380 and 418 cm−1 show steep hardening as shown in

figure 2.20. The relative intensity of Raman mode at 418 cm−1 drastically reduces

beyond 13.5 GPa while the relative intensity of Raman mode at 380 cm−1 picks up

intensity. At ∼ 18 GPa all the Raman modes become broad. At this pressure even the

fluorescence lines broaden too much. Beyond 20 GPa the Raman spectra indicates the

82


Figure 2.19: Raman spectra of lithium erbium fluoride stacked at a few representativepressures.

loss of long range ordering. The above changes in the Raman spectra are in accordance

with our observation in x-ray diffraction investigation where the scheelite structure

changes to fergusonite beyond 10 GPa and it undergoes another structural phase

transition around 15 GPa followed by pressure induce amorphization beyond 20 GPa.

It has been observed by Errandonea et al. [151] that in the scheelite compounds one

external mode in the scheelite phase softens and then stiffens in the fergusonite high

pressure phase. However other scheelite compounds which do not undergo scheelite

to fergusonite transition under high pressure do not show softening. In LiErF4 we

have observed that one of the Eg symmetry mode at 335 cm−1 softens and then

stiffens in the fergusonite phase. The softening of the Eg symmetry mode, one of

the translational mode, involves a rotation of the LiF4 tetrahedra in the a-b plane as

has been explained by Errandonea et al. for LiYF4. Actually with compression the

Li-F distance decreases till the LiF4 tetrahedra become rigid. At further compression

83


Figure 2.20: Variation of Raman shifts of LiErF4 with pressure. Solid lines are guide toeye.

the stiffening of the Li-F bond and continuous decrease in the a lattice parameter

forces the LiF4 tetrahedra to rotate around tetragonal c axis. This suggests that the

scheelite to fergusonite phase transition in LiErF4 is second order in nature. This is

in accordance with no volume drop observed across this phase transition in our x-ray

diffraction studies.

2.2.5 Conclusion

Our synchrotron based powder x-ray diffraction and Raman spectroscopic studies

show that LiErF4 undergoes two structural phase transitions from Scheelite to fergu-

sonite and from fergusonite to another high pressure phase beyond 10 GPa and at 15

GPa respectively. Pressure induced amorphization is observed at 28 GPa. Softening

of Eg mode is observed during the scheelite to fergusonite phase transition. No vol-

ume drop across this transition and mode softening implies the first phase transition

to be of second order in nature. The bulk modulus of LiErF4 in scheelite phase is

84


determined to be 81 GPa with its pressure derivative as 6.4. Our studies also show

that the high pressure behavior of lithium erbium fluoride does lie in between the end

members LiYF4 and LiGdF4. These studies indicate that as the size of the octahedral

cation increased the pressure of amorphization was lowered.

85


86

3

Structural Transition in Frustrated

Titanate Pyrochlores

The compounds with general formula A2B2O7 (where A and B are metallic cations)

known as ternary metallic oxides represent a family of phases iso structural to a

mineral pyrochlore, (NaCa)(NbTa)O6F/(OH). These minerals occur in pegmatites

associated with carbonatites alkali rocks. Its name is derived from the Greek as pyro

means fire and Khloros means green, the colour to which the mineral usually turns

on ignition. A large number of these compounds are invariably of cubic structure

and of ionic nature. In these compounds the B cation can be a transition metal

with variable oxidation state or a post transition metal and the A cation can be

a rare earth (Ln) or an element with inert lone-pair of electrons. This is why the

pyrochlores can exhibit a large variety of interesting physical properties. These can

be insulators, semiconductor or metallic. Many of its phases where A and B are in

highest oxidation state show promising dielectric, piezo-and ferro-electric behavior.

The pyrochlores with 3d transition element at B site and /or a rare earth at A site

also exhibit magnetic behaviour ranging from para- to ferro- to antiferro-magnetism

at and below 77 K. Apart from this, these materials have a variety of applications

87

3. Structural Transition in Frustrated Titanate Pyrochlores

ranging from refractory to high permittivity ceramics, switching elements, thick film

resistors, electrodes etc [160]. Pyrochlores are also useful in the disposal of radioactive

waste due to their enhanced resistance threshold to radiation damage [161, 162, 163].

High pressure can lift the delicate balance between various competing interactions

in pyrochlore compounds. As a result it can show very interesting new physical

phenomenon and stabilization of new phases. To unravel this I have carried out high

pressure studies on titanate pyrochlores, ytterbium titanate and dysprosium titanate

and the same has been presented in this chapter.

3.1 Structural details

The pyrochlores with general formula A2B2O6O′ crsyatllise in to space group Fd3m

with eight molecules per unit cell (Z = 8) and have four crystallographically nonequiv-

alent atoms. The structure is composed of two types of cation coordination polyhe-

dron as shown in figure 3.1 below. The larger A cations are eight coordinated and

are located within scalenohedra (distorted cubes) which contain six equally spaced

anions (O′-atoms) at a slightly shorter distance from the central cations while the

smaller B cations are six coordinated and are located within trigonal antiprisms with

all the six anions at equal distance. The pyrochlore structure has only one refinable

positional parameter which is oxygen x fractional coordinate. The A and B cations

are located at 16d and 16c Wyckoff sites respectively while the anions are located at

48f and 8b sites. The pyrochlore structure can also be visualized based on a fluorite

type cell where the cations A and B form a face centered cubic array and the anions

are located in the tetrahedral interstices of the cationic array. There exist three kinds

of tetrahedral interstices for anions: 48f positions having two A and two B cations as

their near neighbors, 8a positions having four B cations as their near neighbors and

8b positions having four A cations as near neighbors. In pyrochlore structures the 8a

88

3.2. Introduction

(a)

(b)

Figure 3.1: (a)Polyhedra of Yb/Dy and Ti and (b)Crystal structure of Yb2Ti2O7/Dy2Ti2O7 in the cubic phase.

positions are vacant.

3.2 Introduction

Most of the pyrochlore oxides which crystallize in to Kagome lattice and have mag-

netic A+ or B+cations are geometrically frustrated antiferromagnets [164]. Figure

3.2 (a) and (b) depicts the geometrical frustration in case of triangular and tetra-

hedral arrangement of spins where the spin marked with question mark ? is frus-

trated. In these geometrically frustrated magnets, frustration of spins to order and

minimize their exchange energies leads to a macroscopically degenerate ground state

[165]. However, competing interactions like near neighbor dipolar and crystal field

interactions and quantum fluctuations etc. can lift the degeneracy resulting into var-

ious complex ground states at very low temperatures, e.g., spin-liquid, spin-ice and

spin-glass. Subjecting such interesting compounds to high pressures can change the

delicate balance between the various competing interactions and may lead to the re-

alization of different physical states. For example, Tb2Ti2O7 is the only member of

the pyrochlore titanates that remains in spin-liquid state down to 70 mK[166]. How-

89


Figure 3.2: Geometrical frustration in (a) triangular and (b) tetrahedral spin lattices. (c)represents the spin ice behavior; a pair of spin pointing inward and another pair of spinpointing outward.

ever, under external pressure of ∼ 8.6 GPa, Tb2Ti2O7 transforms into a mixed phase

of spin-liquid and spin-solid at 1.5 K, as revealed by neutron scattering experiments

[167]. Earlier, a structural transition has been observed in spin-liquid Tb2Ti2O7 [168]

and Gd2Ti2O7 [169], linking to the proposed broken symmetry [170] and cubic-to-

tetragonal structural fluctuations below 20 K [171]; thus attributing the structural

instability of Tb2Ti2O7 to its unique spin-liquid state [172]. In the high pressure

regime, experimental measurements reveal that Sm2Ti2O7 and GD2Ti2O7 pick up

anion disorder at ∼ 40 GPa [173] Interestingly in all these pressure induced changes,

the cubic structure of the pyrochlore is retained, implying its inherent stability even

under quite high pressures. Previous high pressure x-ray diffraction study has revealed

cubic to monoclinic phase transition in Ho2Ti2O7, Y2Ti2O7 and Tb2Ti2O7 near 37,

42 and 39 GPa, respectively [174]. In an earlier study, the transition pressure for

Tb2Ti2O7 is reported to be ∼ 51 GPa [175]. In this work, I have studied high pres-

sure behavior of Yb2Ti2O7 and Dy2Ti2O7 by employing x-ray diffraction and Raman

scattering measurements.

Yb2Ti2O7, an insulator, crystallizes into the pyrochlore structure [1, 17] with a lat-

tice parameter of 10.074 A at room temperature. Though early studies on the specific

heat of Yb2Ti2O7 reported a magnetically ordered state near ∼ 200 mK [176], Hodges

90

3.3. Experimental Details

et al [177]concluded that the Yb3+ spin fluctuations slow down at low temperatures

by more than 3 order of magnitude without freezing completely. A polarized neutron

study by Gardner et al [178] ruled out a frozen magnetic ground state and confirmed

that the majority of the spins continue to fluctuate even below the 240 mK, while

a small amount of magnetic scattering was observed at (111) Bragg position at 90

mK. The absence of a long range order in Yb2Ti2O7 down to 90 mK (as in Tb2Ti2O7

up to 70 mK) owing to a structural instability motivated us for the present study on

Yb2Ti2O7 .

Dy2Ti2O7 also crystallizes into the pyrochlore structure with lattice parameter

10.109 A at room temperature. The Dy2Ti2O7 [179] and Ho2Ti2O7 [180] exhibit the

spin ice like ground state known as dipolar spin ice, a unique properties among all

the known titanate pyrochlores, at very low temperature. The spin ice ground state

is analogous to ordering of protons in ordinary water ice [181]. In this case a pair of

spins point in on an elementary tetrahedron and another pair of spins point out as

shown in figure 3.2c. The reported existence of magnetic monopoles in Dy2Ti2O7 has

also made it more interesting [182] to study.

In this study, using x-ray diffraction and Raman experiments at high pressures,

we show that the spin frustrated pyrochlore Yb2Ti2O7 undergoes a reversible cubic

to monoclinic phase transition at ∼ 28.6 GPa and the monoclinic phase picks up an

anion disorder at ∼ 46 GPa. While our studies on the spin ice Dy2Ti2O7 show a

structural distortion at ∼ 9 GPa with a possible lattice instability at this pressure.

3.3 Experimental Details

Stoichiometric amounts of Yb2O3 / Dy2O3 (99.99%) and TiO2 (99.99%) were mixed

thoroughly and heated at 1200 ◦C for about 15 hours. The resulting mixture was well

ground and isostatically pressed into rods of about 6 cm long and 5 mm diameter.

91


These rods were sintered at 1400 ◦C in air for about 72 hours. This procedure

was repeated until the compound Yb2Ti2O7 / Dy2Ti2O7 was formed, as revealed

by powder x-ray diffraction analysis, with no traces of any secondary phase. These

rods were then subjected to single-crystal growth by the floating-zone method in

an infrared image furnace under flowing oxygen. X-ray diffraction measurements,

carried out on the powder obtained by crushing a part of the single crystalline sample

and energy dispersive x-ray analysis carried out in a scanning electron microscope

confirmed the formation of a pure pyrochlore Yb2Ti2O7 / Dy2Ti2O7 phase. For high

pressure x-ray diffraction experiments, the finely powdered,Yb2Ti2O7 / Dy2Ti2O7 was

loaded (along with a few particles of Cu) in a hole of ∼ 100 µm diameter drilled in a

pre-indented (∼ 70 micron thick) tungsten gasket of a Mao-Bell type of diamond-anvil

cell (DAC). A methanol:ethanol (4:1) mixture was used as a pressure transmitting

medium. The pressure was determined from the known equation of state of copper

[132]. High-pressure angle dispersive x-ray-diffraction experiments were carried out

up to ∼ 40.4 / 34 GPa on powder samples of Yb2Ti2O7 / Dy2Ti2O7 at the 5.2R

(XRD1) beamline of Elettra Synchrotron source employing monochromatized x-rays

(λ = 0.68881 A). The diffraction patterns were recorded using a MAR345 imaging

plate detector kept at a distance of ∼ 20 cm from the sample. The diffraction profiles

were obtained by the radial integration of the two dimensional diffraction rings using

the FIT2D software [95]. High pressure Raman experiments were carried out upto

∼ 50 / 29 GPa using a confocal micro Raman set up in back-scattering geometry.

A tiny single crystalline Yb2Ti2O7 / Dy2Ti2O7 sample was loaded in a pre-indented

tungsten gasket. Methanol:ethanol (4:1) mixture was used as pressure transmitting

medium. A tiny ruby chip (∼ 20 µm) was also loaded in the gasket hole to monitor

the pressure. Raman spectra were recorded using 532 nm laser radiation from a diode

pumped solid state laser. The calibration (and any possible drift) of the spectrometer

was monitored using standard spectral neon lines.

92

3.4. Results and Discussion

3.4 Results and Discussion

3.4.1 Yb2Ti2O7

3.4.1.1 X-ray diffraction measurements

Figure 3.3 shows the x-ray diffraction patterns of Yb2Ti2O7 at a few representative

pressures. The diffraction peaks marked as Cu correspond to the copper pressure

marker and the peaks marked as W are due to the tungsten gasket. The diffrac-

tion pattern of Yb2Ti2O7 at ambient conditions has been indexed using cubic space

group Fd3m. Upon increasing the pressure, the x-ray diffraction pattern shows that

Yb2Ti2O7 remains in the cubic structure up to ∼ 27 GPa. At about 28.6 GPa, two

new diffraction peaks start emerging at 2θ ∼ 7.4◦and 14.7◦. On further increasing

the pressure up to ∼ 30.5 GPa, these diffraction peaks gained intensity and more

diffraction peaks emerged at 2θ ∼ 12.1◦, 12.7◦, 16.1◦, 20.6◦ and 25.7◦, as shown with

arrows in Figure 3.3. The intensity of these peaks increased with increasing pressure.

Using crysfire indexing package, most of the new features of the observed diffraction

pattern beyond ∼ 30.5 GPa could be indexed with a monoclinic structure (space group

P21/c). The observed P-V variation fitted with 3rd order Birch- Murnaghan (B-M)

equation of state for Yb2Ti2O7 pyrochlore and high pressure monoclinic phase. The

red solid line is B-M fit of the experimentally observed P-V data while the blue dashed

line represents the pressure induced volume variation obtained by the first principles

calculations [183]. Upper inset shows the variation of the x-position parameter of the

O48f atoms at various pressures. Lower inset shows the crystal structure of the high

pressure monoclinic phase.

Incidentally this phase is similar to that of the high pressure phase of Gd2Zr2O7

[184]. The x-ray diffraction patterns, recorded up to ∼ 40.4 GPa, show that the

ambient pyrochlore phase coexists with the high pressure monoclinic phase up to the

highest recorded pressure. The coexistence of the high pressure phase with the cubic

93


Figure 3.3: X-ray diffraction profiles of Yb2Ti2O7 at a few representative pressures. Ar-rows indicate the x-ray diffraction peaks due to monoclinic phase at high pressure.

pyrochlore structure up to the highest pressure of our studies suggests a substantial

kinetic barrier for this transformation. This also suggests that the high pressure phase

is formed very slowly and the cations disordering in the high pressure phase may not

be complete even at highest pressure of our studies. However the phase fraction

analysis indicates that the fraction of monoclinic phase increases with pressure

All the diffraction patterns were analyzed using Rietveld refinement as imple-

mented in the GSAS [96]. Below ∼ 29 GPa, our refined coordinates imply that the

x-value of oxygen (O) at the 48f position increases with pressure (upper inset of figure

3.4).We have refined the lattice parameters as well as the atomic coordinates of the

new high pressure phase. The resulting fit is shown in figure 3.5 and the determined

structural parameters are listed in Table 3.1. It is well known that the pyrochlore

structure becomes an ideal fluorite structure when the x-value of the oxygen at 48f

94


Figure 3.4: The observed P-V variation fitted with 3rd order Birch- Murnaghan (B-M)equation of state for Yb2Ti2O7 pyrochlore and high pressure monoclinic phase. The red solidline is B-M fit of the experimentally observed P-V data while the blue dashed line representsthe pressure induced volume variation obtained by the first principles calculations (Mishraet al. 2012). Upper inset shows the variation of the x-position parameter of the O48f atomsat various pressures. Lower inset shows the crystal structure of the high pressure monoclinicphase.

Wyckoff site equals 0.375. Figure. 3.4 (upper inset) indicates that the pyrochlore

Yb2Ti2O7 may adopt a disordered-fluorite structure beyond ∼ 29 GPa. The new high

pressure monoclinic phase is shown in the lower inset of figure 3.4. It may be noted

from Table 3.1 that the new structure is a disordered structure having equal occu-

pancies for Yb and Ti atoms i.e. either one of these atoms occupy the two equivalent

sites. It may be noted here that recently it has been shown in Bi2Te3 that at high

pressures, either of two constituent atoms could occupy the bcc lattice sites [185].

Our results, though not implying indistinguishability of Yb and Ti, are similar in

terms of occupancies.The deduced variation of volume/formula unit with pressure is

given in Figure 3.4.

The observed volume drop of ∼ 14% at the transition pressure implies that the

95


Figure 3.5: Rietveld refinement of diffraction pattern of Yb2Ti2O7 at 40.4 GPa. Thediffraction pattern consists of contributions from pyrochlore phase, high pressure monoclinicphase, tungsten gasket and Cu pressure marker.

transformation to the monoclinic phase is of first order, consistent with the observa-

tion of co-existence of phases at higher pressures. The experimental pressure-volume

variation was fitted using third order Birch-Murnaghan equation of state [59] which

gives the bulk modulus B = 219 ± 6 GPa and its pressure derivative B′ = 3.2 ± 0.5.

The fit of the P-V data beyond 28.6 GPa give B = 355.7 ± 28 GPa and B′ = 0.03 ±

1.22 for the high pressure monoclinic phase. Relatively larger errors in the respective

values in the monoclinic phase are due to the limited number of data points. On

release of pressure, the high pressure phase reverts back to the pyrochlore structure

completely.

96


Table 3.1: The refined atomic coordinates of the high pressure monoclinic phase ofYb2Ti2O7 at 30.5 GPa (Space Group: P21/c , lattice parameters being a=5.544 A, b=3.963A, c=4.578 A and γ=104.663◦).

Atom Wyckoff x/a y/b z/c Occupancy

Yb 4e 0.218 0.0310 0.200 0.5Ti 4e 0.218 0.0310 0.200 0.5O1 4e 0.0705 0.3327 0.3447 0.75O2 4e 0.4499 0.7588 0.4793 1.0

3.4.1.2 Raman spectra at high pressures

According to group theoretical analysis, a pyrochlore structure have optical modes

given by the following representation

Γopt = A1g(R) + Eg(R) + 2F1g + 4F2g + 3A2u + 3E2u + 7F1u(IR) + 4F2u (3.1)

Out of which six are Raman (R) active modes and seven are infrared (IR) active

[186, 187].

Raman spectrum of Yb2Ti2O7 at ambient conditions, shown in the Figure 3.6,

exhibits eight Raman bands, marked as pk1 to pk8: pk1 = 212 cm−1, pk2 = 302

cm−1, pk3 = 329 cm−1, pk4 = 525 cm−1, pk5 = 539 cm−1, pk6 = 608 cm−1, pk7 =

715 cm−1 and pk8 = 750 cm−1.

The position and relative intensities of these bands are in agreement with the

earlier reports[168, 186, 188, 189]. On the basis of an earlier work [163] the Raman

modes Pk2, Pk5 and Pk6 are identified as F2g; Pk3 as Eg and Pk4 as A1g modes. The

fourth F2g mode, which is usually located near 450 cm−1 in the rare-earth titanates

(as discussed in the ref. [190, 191], could not be seen because of poor signal to noise

ratio. In the pyrochlore structure, all the Raman active modes involve the movement

of oxygen atoms. As discussed in the publication [168], pk1 is a disorder-induced

97


Figure 3.6: Raman spectrum of Yb2Ti2O7 pyrochlore at ambient pressure. The differentraman modes have been labeled as pk1 to pk8.

Raman active mode involving vibration of Ti4+ atoms that form a tetrahedral network

with vacant 8b-sites at the center of each tetrahedron. The Raman bands observed at

715 cm−1 (pk7) and 750 cm−1 (pk8) can be assigned to second order Raman spectra

[168, 189]. In addition, we have also observed two weak broad bands at ∼ 887 cm−1

and 1049 cm−1, which can also be second order Raman modes. Figure 3.7 shows

the Raman spectra of Yb2Ti2O7 at a few representative pressures. These data were

recorded under quasi hydrostatic conditions up to ∼ 50 GPa on compression as well

as on release of pressure. The corresponding pressure-induced changes in the Raman

frequencies, deduced from the spectra by fitting a sum of Lorentzian functions are

shown in figure 3.8. The intensity of the pk1 Raman mode is too weak and hence was

not followed at high pressures. On increase of pressure, the observed Raman modes

shift towards higher wave numbers. Using the bulk modulus of the ambient phase

the Grneisen parameters for these modes were calculated (Table 3.2).

The pk5 Raman mode disappears beyond 25 GPa. Most of the observed modes

show a slope change at ∼ 29.7 GPa, implying a phase transition at this pressure,

in agreement with our x-ray diffraction results. On increasing the pressure beyond

29.7 GPa, the observed Raman modes stiffen and broaden. Beyond 41.4 GPa the

98


Figure 3.7: The evolution of the Raman modes of Yb2Ti2O7 at a few representativepressures (R stands for Release).

Raman modes (for example one at 750 cm−1) corresponding to the monoclinic phase

gain intensity at the cost of Raman modes of pyrochlore phase. The two strong

Raman modes pk2 and pk4 corresponding to parent phase loose intensity drastically

beyond this pressure. This also implies the coexistence of pyrochlore phase with high

pressure monoclinic phase as observed in case x-ray diffraction results. At ∼ 45 GPa

the strong pk2 and pk4 modes almost disappear and a broad band emerges in place of

these modes. The broadening of the Raman modes could be understood because of the

presence of different types of defects like cation antisite defect formation. The analysis

of ruby R-lines does not suggest abnormally high non-uniform stresses but at the same

time it is difficult to completely rule out the contribution of inhomogeneous stress

distribution towards broadening of Raman peaks. Therefore, we tend to presume

that these changes in the Raman spectra may indicate onset of anionic disorder, also

99


Figure 3.8: Pressure induced variation of Raman mode frequencies of Yb2Ti2O7 .

observed earlier in other pyrochlore compounds. Upon decompression, the broad

bands shift towards lower wave numbers up to ∼ 31 GPa. At this pressure the Raman

modes of the pyrochlore structure start re-appearing. On complete release of pressure,

all the Raman modes of the pyrochlore structure are fully recovered confirming the

reversibility of structural changes

3.4.1.3 Conclusions

Our in-situ x-ray diffraction and Raman measurements on pyrochlore Yb2Ti2O7 show

that it undergoes a structural phase transition from cubic (Fd3m) pyrochlore to a

monoclinic phase (P21/c) at ∼ 28.6 GPa. Interestingly, analysis of the x-ray data

suggests this high pressure phase to be substitutionally disordered, analogous to a

pressure induced disordered phase observed in Bi2Te3. The observed phase transition

is first order in nature. These results are shown to be consistent with our Raman

100


Table 3.2: Mode Gruneisen parameter of Raman modes.

Frequency (ω (cm−1)) dω/dP (cm−1 / GPa) Gruneisen parameter (γ)

302 2.2 1.6329 3.1 2.1525 2.2 0.9540 2.6 1.1608 3.9 1.4715 2.8 0.8750 2.2 0.6

scattering measurements. On release of the pressure, the initial structure is fully

recovered implying the reversibility of the phase transition. In the cubic phase the

bulk modulus of Yb2Ti2O7 is found to be 219 6 ± GPa and it increases substantially

to 355.7 ± 28 GPa across the phase transition to the monoclinic phase. New high

pressure phase is found to have structural occupancy disorder observed also in other

compounds recently.

3.4.2 Dy2Ti2O7

3.4.2.1 Structural effects by XRD

Figure 3.9 represents the stacked x-ray diffraction pattern of Dy2Ti2O7 at few repre-

sentative pressures. The x-ray diffraction pattern of Dy2Ti2O7 at ambient conditions

could be indexed with cubic structure in space group Fd3m.

The diffraction pattern at ambient conditions is Rietveld refined to determine the

lattice parameter as 10.109 (5)A which is in close agreement with the earlier reported

values for Dy2Ti2O7 [192]. The various (hkl) values for Dy2Ti2O7 have been written

along the x-ray diffraction peaks at ambient conditions. The x-ray diffraction peaks

corresponding to pressure marker copper (Cu) and gasket (W) has been written as Cu

(hkl) and W (hkl) respectively. The x-ray diffraction peaks from impurity phase has

101


Figure 3.9: Diffraction pattern of Dy2Ti2O7 pyrochlore stacked at a few representativepressures

been marked with asterisk (*). On compression the observed x-ray diffraction peaks

shift toward higher angular values. Beyond ∼15 GPa the x-ray diffraction peaks of the

sample broaden significantly, especially the (400) and (222) x-ray diffraction peaks as

shown in figure 3.10. While the XRD peak (111) of pressure marker Cu shows little

variation in its FWHM. This implies that sample is under quasi hydrostatic

environment and the broadening observed in the x-ray diffraction peaks of sample

is primarily because of inherent disorder or it may be due to transformation to low

symmetry phase having multiple peaks. The diffraction pattern corresponding to

each pressure has been refined using Le Bail and Rietveld refinement as incorporated

into GSAS package [96]. Figure 3.11 represents the variation of different dhkls with

respect to pressure. For better presentation purpose different dhkl have been plotted

in separate layers. A change in slope of dhkls is observed ∼9 GPa which implies a

102


Figure 3.10: Full width at half maximum for different x-ray diffraction peaks of Dy2Ti2O7

at various pressures.

subtle discontinuity in dhkl, around this pressure. At the same pressure we have

also observed discontinuity in variation of volume and lattice parameter as shown in

figure 3.12 and figure 3.13 respectively. The closed symbol in figure 3.12 represents

the observed data while the solid line is Birch-Murnaghan (B-M) fit to the observed

P-V data. The P-V data fitted with third order B-M equation of state determines the

bulk modulus and its pressure derivative as 201.5 GPa and 0.3 respectively while the

P-V data beyond 9 GPa fitted with third order B-M equation of state produces the

bulk modulus as 359.9 GPa with its pressure derivative fixed as 4 for high pressure

phase. The value of bulk modulus for ambient phase is comparable to that of the other

pyrochlores [183]. The new high pressure phase seems to be quite incompressible. The

subtle discontinuity observed around 9 GPa is intrinsic to the sample and is related

with its structural instability as it is well within the hydrostatic limit of pressure

transmitting medium (metahnol:ethanol :: 4:1). The inset in figure 3.12 shows the

pressure induced variation of lone refinable parameter i.e. x-coordinate of oxygen 48f.

The inset shows that this fractional coordinate undergoes a sudden changes at ∼9 GPa

implying a rearrangement of TiO6 octahedra. It might also explain the changes in

103


Figure 3.11: Pressure induced variation of different dhkl values.

the compressibility of Dy2Ti2O7 around this pressure.

3.4.2.2 Raman Spectroscopic effect

As mentioned in the section 3.4.1 B a pyrochlore structure should have six Raman

optical modes Γopt =A1g+ Eg+ 4F2g.

Here, since cations occupy sites with inversion symmetry, therefore only O and O

anion atoms are responsile for Raman-active modes. The Raman spectra at ambient

conditions has been shown in the figure 3.14 and different Raman modes observed at

ambient conditions has been denoted with p1, p2 to p11. Different sections of the

Raman spectrum has been zoomed (written as X1, X2 etc in figure 3.14) appropriately

to show the Raman modes observed at ambient conditions. Assignment of various

observed Raman modes have been done following the earlier reported work works

[173, 190].

The Position and relative intensities of these Raman modes agree with the earlier

104


Figure 3.12: Pressure induced variation of volume per unit cell. The black dot symbolsrepresent the observed data while the red solid line is obtained from fitting the third orderBirch-Murnaghan equation of state to the observed variation of volume with pressure.

reported values as shown in table 3.3[190]. The five Raman active modes are marked

as P4 (309 cm−1, F2g), P5 (335cm −1, Eg), P6 (522 cm−1, A1g), P7 (548 cm−1, F2g)

and (P8, 694 cm−1, F2g) as shown in the figure 3.15. The Raman mode at 450 cm−1

(F2g) observed by Saha et al. is too weak to be observed. The additional Raman

modes at higher wave numbers (P9, P10 and P11) may be due to second order Raman

scattering and the modes at lower wave number (P1, P2) can be assigned to crystal

field transitions of Dy3+ in Dy2Ti2O7 .

Figure 3.15 represents the stacked Raman spectra of Dy2Ti2O7 at a few repre-

sentative pressures up to 29 GPa under compression and decompression both. The

Raman peaks observed below 308 cm−1 become too weak and broad to be observed

with pressure. Hence, here we have followed the intense modes for unambiguous re-

sults. The Raman modes observed at ∼308 cm−1 and ∼520 cm−1 stiffen with pressure

and lose their intensity beyond 25 GPa. Figure 3.16 represents the variation of Ra-

man shifts of modes observed at ∼308 cm−1, 520 cm−1, 551 cm−1 and 703 cm−1 with

105


Figure 3.13: Pressure induced variation of lattice parameter of pyrochlore phase.

Figure 3.14: Raman spectrum of Dy2Ti2O7 pyrochlore at ambient pressure. The differentraman modes have been labeled as P1 to P11.

pressure. Here the closed and open symbols represent the data during compression

and decompression respectively. It is noted from figure 3.16 that the Raman modes

observed at 551 cm−1 and 703 cm−1 show discontinuity around 9 GPa. This is in

accordance with changes observed in our x-ray diffraction based investigations.

Using the bulk modulus of ambient phase and slope of Raman shift, the Gruneisen

parameter of observed Raman modes has been deduced and the same has been shown

106


Table 3.3: Assignment of Raman modes of Dy2Ti2O7. The origin of modes with (phonon)assignment has been discussed in text.

Normal modes ν(cm−1)(this Expt.) ν(cm−1)(Saha etal.) Assignment

P1 137 126 phononP2 213 194 phononP3 273 287 phononP4 309 312 phononF2g

P5 335 330 phonon E2g

P6 522 515 phononA1g

P7 548 563 phononF2g

P8 694 680 phonon E2g

P9 718 712 overtoneP10 875 867 overtoneP11 1000 overtone

Figure 3.15: Raman spectra of Dy2Ti2O7 pyrochlore stacked at a few representativepressures.

107


Figure 3.16: Variation of Raman shift of different modes with pressure.

in table 3.4.

The maximum value of Gruneisen parameter (3.0) observed for the Raman mode

at 703 cm−1 signifies its maximum contribution towards specific of this compound

while lowest Gruneisen parameter (0.95) is observed for mode at 521 cm−1 implies

that the contribution of this mode towards specific heat is minimum. The low temper-

ature Raman spectroscopic studies carried out by Saha et al. [190] on this compound

indicated the appearance of a new Raman band at ∼287 cm−1 below 110 K. They

Table 3.4: Raman mode frequencies (ν), their pressure dependence (dν/dP) and corre-sponding Grneisen parameters (γ) in the cubic pyrochlore phase of Dy2Ti2O7 .

Frequency (ν (cm−1)) dν/dP (cm−1 / GPa) Gruneisen parameter (γ)

309 2.74 1.79521 2.45 0.96552 5.32 1.94703 10.48 3.0

108


attributed this to a Raman inactive phonon mode which becomes Raman active due

to site symmetry lowering as a result of local structural deformation below 110 K.

Based on the anomalous softening of this new band with low temperature they sug-

gested that spin-phonon coupling is not responsible for this behavior rather it is

strong phonon-phonon anharmonic interaction which leads to this anomalous behav-

ior. Later on Maczka et al. [193] argued that crystal field splitting is responsible

for the origin of Raman mode at low temperatures. They also suggested that the

anomalous behavior of the Raman modes may be because of combination of many

factors like strong bond bending character, stronger second-neighbor force constant

of O-O and availability of free x-co-ordinate of oxygen which affects the distortion of

TiO6 octahedra. The elastic constant studies by Nakanishi et al. also show a possible

lattice distortion. From our powder x-ray diffraction studies we have also observed a

volume discontinuity around 9 GPa. This can be related with a possible structural

distortion concomitant with lattice instability around this pressure. Since the cations

in Dy2Ti2O7 occupy the Wyckoff sites with inversion symmetry and the anions i.e

oxygen atoms participate in the Raman active modes. Hence, we speculate that a

subtle structural instability occurs due to deformation in the anionic sublattice of

Dy2Ti2O7 across 9 GPa.

3.4.2.3 Conclusions

Angle dispersive powder x-ray diffraction and Raman scattering studies have been

carried out on geometrically frustrated spin ice pyrochlore Dy2Ti2O7 up to ∼ 34.3

GPa and ∼ 29GPa repectively on compression and decompression. At ∼9 GPa a subtle

structural distortion is observed in the P-V diagram which shows the possibility of

lattice distortion at this pressure. This is in accordance with our results obtained

from Raman sacttering measurement. The observed pressure induced variation of

volume fitted with third order Birch-Murnaghan equation of state determines the

109


bulk modulus to be 201.5 ± 6.9 GPa with its pressure derivative as 0.3 ± 1.9.

110

4

Structural Investigation of

perovskites

The perovskite structure with general chemical formula ABX3 owes its name to miner-

alogist Lev. Aleksevich von Perovski. Its archetypal compound is CaTiO3 which was

first discovered by Gustav Rose in 1839 from samples found in the Ural mountains

in Russia [194]. Studies on perovskites are important not only from basic physics

point of view but also due to their technological applications [195]. Under extreme

temperature and pressure several of them undergo phase transformations to the post

perovskite structures or decompose into their respective oxides making them relevant

to the understanding of geophysical phenomena [196, 2]. In particular, the studies on

silicates, germanates, oxides and fluorides suggest that the transformation to the post

perovskite structure could be responsible for the seismic discontinuity at the earths

lower mantle-core boundary [197, 198, 199] . Since these perovskites are made up of

a network of corner linked polyhedra, tilt or distortion of the polyhedra, at low/high

temperatures or on application of pressure, plays a crucial role in their stability.

Based on empirical formulation Ross et al. have shown that the tilt of the octahedra

at high pressures is related to the compressibility of the constituent polyhedra [200].

111

4. Structural Investigation of perovskites

Perovskite materials exhibit many interesting and intriguing properties from appli-

cation point of view such as ferroelectricity, superconductivity, charge ordering, spin

dependent transport and the interplay of structural, magnetic electrical and trans-

port properties. These compounds having many technological applications are used

as sensors, switches, and catalyst electrodes in certain types of fuel cells etc [201]. The

perovskites can accommodate variety of elements as cations and anions exhibiting a

wide spectrum of physical properties. These compounds with transition metal cations

on the B site show a variety of intriguing electronic and/or magnetic properties. In

addition to the above mentioned chemical flexibility, the wide range of physical prop-

erties are mainly related to the complex character that transition metal cations play

in certain coordinations with oxygen or halides as anions [10]. While magnetism and

electronic correlations are usually related to unfilled 3d electron shells of the tran-

sition metal, pronounced dielectric properties are connected with filled 3d electron

shells. Multiferrocity, a coexistence of spontaneous ferroelectric and ferromagnetic

moments, has also been reported for perovskite type of compounds. These novel

properties are exploited in the usage of these materials in the field of data storage,

microelectronic devices, spintronics etc [202, 203]. Under compression the ideal cubic

perovskites become distorted perovskites having reduced symmetry, which is impor-

tant for their electric and magnetic properties. Cubic perovskites undergo structural

phase transitions by distortion/rotation of octahedral and/or movement of the central

cation, driven by Jahn-Teller distortions. Several of these also display ferroelectric

or ferroelastic instabilities leading to multiferroicity. The distortions are expected to

diminish on increase of temperature, as the structure tends towards the parent per-

ovskite form [204]. Effects of pressure on structure, however, are difficult to predict

due to the complex changes in the inter-ionic interactions coupled with the interplay

of several degrees of freedom such as distortion/rotation of octahedra, displacement

of ions etc. As mentioned above the perovskite structure with general stoichiometry

112

4.1. Crystallography of the Perovskite structure

ABX3, can have a variety of compositions possible as different A and B cations and X

as anions. Some of these can be ideal cubic perovskite, distorted perovskite, double

perovskites or inverse perovskite. I have chosen to study a multiferroic oxide distorted

perovskite BiFeO3, a double perovskite Sr2MgWO6 and an inverse perovskite BaLiF3

to understand the polymorphism and high pressure behavior of these compounds.

4.1 Crystallography of the Perovskite structure

The structure of an ideal cubic perovskite is shown in Figure 4.1 where the A cations

are shown at the corners of the cube, and the B cations in the centre with oxygen

ions in the face- centred positions. The space group for cubic perovskite is Pm3m (S.

G. No = 221). The atomic positions are shown in table 4.1.

Figure 4.1: Unit cell of cubic perovskite. Gray, green and red spheres represent the Acations, B cations and oxygen anions respectively. B cation with oxygen atoms forms anoctahedra.

Table 4.1: Atomic positions in the cubic perovskite

Atom site Wyckoff site Co-ordinates

A cation (1b) (0, 0, 0)B cation (1a) (0.5, 0.5, 0.5)X anion (3c) (0.5, 0.5, 0.0); (0.5, 0, 0.5); (0, 0.5, 0.5)

The distortion of cubic perovskite structure generate orthorhombic structures with

Pnma or Pbnm space group as well as rhombohedral structure with space groups R3c,

R3c etc. The rhombohedral structure is shown in figure 4.2.

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Figure 4.2: Distorted cubic perovskite structure of BiFeO3 in R3c space group. The greycolored spheres are bismuth atoms, the yellow colored are iron atoms while the one withred colors represent oxygen atoms.

Another way of describing the perfect cubic perovskite structure is to consider

it as made up of corner shared BO6 octahedra with interstitial A cations. If one

considers the atoms as rigid spheres then for an idealized cubic perovskite structure

each cation has to be in contact with an oxygen anion; the radii of the ions can be

related:

RA+RO =√

2× (RB +RO) (4.1)

Where RA, RB and RO are the ionic radii of A, B cations and the oxygen ion

respectively. However, with reducing A cation size, a point will come where the

cations will be too small to remain in contact with the anions in the cubic structure.

Hence the B-O-B links will bend a little bit to allow the tilting of BO6 octahedra which

will bring in some anions into contact with A cations. To allow for this distortion, a

constant t is introduced into the above equation, therefore

RA+RO = t×√

2× (RB +RO) (4.2)

The constant t is known as tolerance factor which is a measure of the degree of

distortion of a perovskite from ideal cubic structure. The closer the value of t to unity

the closer it will be to ideal cubic structure.

114

4.2. Phase transitions in multiferroic BiFeO3

4.2 Phase transitions in multiferroic BiFeO3

4.2.1 Introduction

Bismuth ferrite (BiFeO3) is a multiferroic in which the ferroelectricity arises due to

the 6s lone pair electrons of bismuth, [205, 206, 207] and the partially filled d orbitals

of Fe generate the magnetic ordering. At room temperature BiFeO3 crystallizes into

rhombohedrally distorted perovskites with space group R3c [208, 209] having 6 for-

mula units per unit cell (Z = 6). This structure is derived from cubic Pm3m structure

by displacement of Fe3+ and Bi3+ cations from their centro-symmetric positions along

[111] pseudo cubic direction and an antiphase tilting of the adjacent FeO6 octahedra.

It is one of the few perovskites which exhibits both the displacement of the cations

from their centro-symmetric position as well as the tilt of the octahedra.

The high pressure behavior of BiFeO3 has earlier been investigated by several

groups and has led to a multitude of, sometimes contradictory, observations [210, 211,

212, 213, 214, 215, 216, 217]. In one of the earliest studies, using Raman scattering and

Ar as pressure transmitting medium (PTM), Haumont et al [210] reported two high

pressure phase transitions at ∼3.5 GPa and ∼10 GPa to C2/m and Pnma respectively.

These were later confirmed by them with x-ray diffraction (XRD) measurements

employing a more hydrostatic (hydrogen) PTM [211]. However, XRD experiments

by Gavriliuk et al. [212] , using PTM like hydrogen and helium, did not show any

transition till 50 GPa, at which pressure BiFeO3 underwent a Mott transition to a

metallic phase. Subsequent XRD experiments [213] reported a single transition, but

at 10 GPa. In contrast Belik et al. [214] claimed the observation of three structural

transitions (using the 16:4:1 methanol:ethanol:water (M:E:W) mixture as PTM) viz.,

R3c→ orthorhombic1→ orthorhombic2→ Pnma. In fact Belik et al. also discussed

the presence of an Orthorhombic3 phase on release of pressure. However, it should

be noted that the samples used by these authors had impurities arising from the

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unreacted and intermediate reaction products. Measurements carried out on single

crystals of BiFeO3 by Guenno et al. [215] suggest that under hydrostatic conditions

there are two intermediate phases while under non-hydrostatic conditions there are

three phases. However, these authors did not report the crystal structures of the high

pressure phases.

Theoretical results are also similarly diverse: ab-initio calculations by Ravindran

et al. [216] indicated that BiFeO3 transforms to the Pnma phase at 10 GPa. However,

corroborating the results of Gavriliuk et al., ab initio calculations of Vazquez et al.

[217] also showed that BiFeO3 undergoes a first order phase transition from a high

spin (Fe3+) state phase to a low spin (Fe3+) state phase at 36 GPa. Recently, using

first principles methods, Dieguez et al. [218] have performed a systematic search

for the potentially stable phases of BiFeO3 and found a large number of possibly

competing structures.

Hence to determine the structure of the intermediate phase of BiFeO3 I have

carried out high pressure x-ray diffraction studies in detail. The first principles ab-

initio study on BiFeO3 as reported in Ref. [219] has helped to determine the accurate

fractional coordinates of the intermediate high pressure phase.

4.2.2 Methods

Equimolar amounts of Bi(NO3)3 and Fe(NO3)3 were dissolved in 2N HNO3 along

with tartaric acid in 1:1 molar ratio with respect to the metal ion. This solution was

heated under constant stirring at 200 ◦C till all the liquids evaporated. Finally this

dry powder was calcined at 500 ◦C for about half an hour to yield BiFeO3. This sample

was characterized with the help of x-ray diffraction. Rietveld refinement of this data

confirms the formation of rhombohedral (S.G. R3c) BiFeO3 and a small amount of (2

% in weight) Bi2Fe4O9 impurity. The unit-cell parameters were determined to be a

= 5.571(1) A and c = 13.827 (3) A (hexagonal setting), which are in good agreement

116


with the earlier reported lattice constants of BiFeO3 [209, 220].

For high pressure experiments finely powdered sample of BiFeO3 was loaded along

with a few specs of copper in a hole, of ∼100 µm diameter, drilled in a pre indented (∼

70 micron thick) tungsten gasket of a diamond-anvil cell (DAC). Methanol: ethanol

(4:1) mixture was used as pressure transmitting medium. The pressure was deter-

mined from the known equation of state of copper [132]. High-pressure angle dis-

persive x-ray-diffraction experiments (λ = 0.68881 A), were carried out up to ∼ 27.0

GPa at the 5.2 R (XRD1) beamline of Elettra Synchrotron source. The diffraction

patterns were recorded using MAR345 imaging plate detector kept at a distance of ∼

20 cm from the sample. Two-dimensional x-ray diffraction patterns were transformed

to one-dimensional diffraction profiles by the radial integration of diffraction rings

using the FIT2D software [95].


The x-ray diffraction pattern of BiFeO3 at a few representative pressures is shown in

Figure 4.3.

The impurity peaks are very weak and have been marked with an asterisk (*)

. These peaks can be followed up to 3 GPa beyond which they are not discernible.

The appearance of new weak peaks in the diffraction pattern at 4.1 GPa indicate

that BiFeO3 has undergone a structural phase transition to a lower symmetry phase.

Inset shows that these new peaks are distinct from the impurity peaks. The diffraction

pattern appears to be similar to the first high pressure phase observed by Haumont

et al [211]. On comparing the 7.5 GPa diffraction pattern of Gavriliuk et al.[212]

we find that very weak diffraction peaks ignored by these authors actually have d

spacings ( at 5.21A, 3.1 A, 2.61 A) similar to those of the new peaks observed by us

and Haumont et al. [211]. Since the new diffraction peaks are very weak the authors

might have missed these new peaks, concluding the absence of any phase change upto

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Figure 4.3: X-ray diffraction pattern of BiFeO3 at a few representative pressures. X-raydiffraction peaks marked with the star are from impurity while the peaks marked withsolid and dotted arrows are from the new high pressure phases with space group P2221 andPnma respectively. The inset shows the zoomed view of diffraction pattern at 4.1 GPa andhighlights the fact that the new XRD peaks of P2221 phase are distinct from the impuritypeaks.

50 GPa. We have observed that in our studies these diffraction peaks remain weak

over the entire range of existence implying that the first high pressure phase may not

be very different from the initial phase and could be obtained by a slight distortion of

the R3C structure. On further increase of pressure new weak diffraction peaks start

appearing at 6.4 GPa indicating the onset of a second phase transition. By 11 GPa the

transformation seems to be complete as the new peaks become stronger and some of

the diffraction peaks of the first high pressure phase have disappeared. Coexistence of

both the high pressure phases over this pressure range implies the first order nature

of this transformation. On release of pressure the diffraction pattern of the initial

phase was retrieved indicating the reversibility of both the phase transitions.

The structure of the second high pressure phase at 11 GPa was found to be

118


similar to that reported in earlier experiments (orthorhombic non-polar Pnma) and

its fractional coordinates at 11 GPa are given in table 4.2. However, to determine

the structure of the first high pressure phase observed at 4.1GPa we fitted all the

diffraction peaks and determined their peak positions. Eighteen XRD peaks were

used to determine the structure of the new phase with the help of the CRYSFIRE

package [221]. An orthorhombic cell was fitted with a figure of merit 6.1. Using the

extinction conditions in CHECKCELL the most probable space group of the first high

pressure phase was determined to be P2221 (S.G. no.17). From density considerations

this first high pressure phase should have at least 8 formula units, compared to 6 in

the ambient R3C phase. Using the reverse Monte Carlo method (FOX software) an

approximate structure was determined for the first high pressure phase. Using the

information so derived, we carried out Rietveld analysis using the GSAS software.

The goodness of fit parameters were Rwp = 6.5%, Rp = 4.8 % with a reduced Chi2

= 0.413. However, after the final refinement we found that the structure was very

strained with some of the Fe-O distances as short as 1.696 A compared to 2.1 A and

1.9 A at ambient pressures.

Table 4.2: Fractional coordinates of orthorhombic phase (Pnma) at 11 GPa (2nd highpressure phase) a=5.531 A, b=7.687 A, c=5.359 A with Z= 4

Atoms x y z

Bi 0.55360 0.25000 0.51140Fe 0.00000 0.00000 0.50000O 0.53341 0.25000 0.10360O 0.20000 0.95400 0.19450

In addition to orthorhombic (P2221) we have also considered monoclinic (C2/m)

structure of Ref [211] as a possible candidate. The monoclinic structure consists

of 12 formula units per units cell and even for this structure a large variation in

the Bi-O (1.76 A 2.5 A) and Fe-O (1.24 A -2.13 A) bond lengths was observed.

This type of a bond length distribution appears to be unphysical for this compound.

119


On refinement we found that despite the larger number of refinable parameters, the

measures of goodness of fit were poorer (Rwp = 10 %, Rp = 7 % with reduced Chi2

= 1.1) compared to those of P2221. Although fit with the orthorhombic structure is

better than the monoclinic, both structures are significantly strained at the end of

refinement. The first principles based structural optimization technique was used to

let the atomic coordinates evolve to minimize the local forces as mentioned in the Ref

[211]. Accordingly, starting from the experimentally obtained structural parameters,

coordinates in R3c, P2221 and C2/m phases at different volumes were optimized.

As expected, at higher volumes (or lower pressures), the rhombohedral R3c phase is

found to be energetically stable. The initial orthorhombic (P2221) and monoclinic

(C2/m) structure were also relaxed using first principles calculations. For comparison

I have presented here the structure and the nature of changes brought about by these

simulations [219] on both the structures in Figure 4.4.

Figure 4.4: Rietveld refined monoclinic (C2/m) structure (from reference Haumont et al.2009). (b) Relaxed monoclinic structure after theoretical structural optimization (Mishra etal. 2013). The resulting bond lengths for Bi-O and Fe-O changed from 2.22A to 2.44A and1.86A to 1.89A respectively (c) Rietveld refined orthorhombic (P2221) structure (presentstudy, without relaxation). (d) Relaxed orthorhombic (P2221) structure after theoreticalstructural optimization (Mishra et al. 2013)

I have used both of these optimized structures for the final Rietveld refinement.

The fit was found to be much better in the case of the P2221 phase and has been

shown in Figure 4.5. The goodness of fit parameters were found to be Rwp = 6.1%,

Rp = 4.4%, and reduced Chi2 = 0.414. As mentioned above, even with the relaxed

coordinates the fit of the C2/m phase was poorer than that of the P2221 phase with

120


goodness of fit parameters, Rwp = 8.7%, Rp = 6.4%, and reduced Chi2 = 0.85.

Hence, we conclude that the first high pressure phase belongs to P2221 orthorhombic

structure. The fractional coordinates of the refined P2221 phase have been given in

table 4.3.

Table 4.3: Fractional coordinates of orthorhombic phase (P2221) at 4.1 GPa (First highpressure phase) a=5.4858 A, b=5.5577 A and c=14.4582 A with Z= 8

Atoms x y z

Bi 0 0.46262 1/4Bi 1/2 0.02891 1/4Bi 1/2 0 0Bi 0.95900 1/2 0Fe -0.01780 -0.01470 0.37770Fe 0.51640 0.50110 0.37830O1 0.67370 0.82600 0.62610O2 0.18640 0.72040 0.61790O3 0.72720 0.76430 0.10100O4 0.80220 0.68800 0.35900O5 0 0.03860 1/4O6 1/2 0.43490 1/4O7 0.06450 0 0O8 0.45380 1/2 0

Since the main diffraction peaks of all the phases from R3C to Pnma are similar we

would expect small distortions and tilts to bring about these phase transitions. This

can be clearly seen from Figure 4.6 where we have plotted all the three structures.

It can be seen that on increase of pressure the octahedra rotate about b axis of the

ambient phase, with a slight shift of the Fe atoms towards the centre of symmetry.

Our studies along with the earlier reports suggest that irrespective of the PTM at

least one high pressure phase is observed between the ambient and the Pnma phase.

4.2.4 Bulk Modulus

The pressure induced variation of volume per formula unit of the three phases is

shown in Figure 4.7. On fitting the third order Birch Murnaghan equation of state

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Figure 4.5: Rietveld refined diffraction pattern of BiFeO3 at three different pressures(ambient, 5.0 GPa and 15.0 GPa) representing Rhombohedral (R3c), Orthorhombic (P2221)and (Pnma) symmetries respectively. For Rietveld refinement three contributions viz. fromBiFeO3, tungsten (gasket) and copper (the pressure marker) were used at each pressure. Thered, green and blue solid lines represent the calculated intensity, background and differencefrom observed data respectively while the black dots represent the experimental data.

[59] to all the three phases we found that the bulk moduli are as follows: R3c —

105.9±1.2 GPa, P2221— 110.5 ± 3.1 GPa, Pnma — 305.4±5.8 GPa. The pressure

derivative was fixed to be 4 in all the three cases. From these results we can see that

the R3c and P2221 phases have similar compressibility in contrast to the non polar

Pnma phase which is relatively incompressible. The bulk modulus of the R3c phase

is in close agreement with earlier determined values of 111 GPa [211] and 97 GPa

[213] respectively. However, using the PV data up to 40 GPa, Gavriliuk et al [212]

determined the bulk modulus of the R3c phase to be 75.5 GPa. Bulk modulus of

Pnma phase determined by us is in agreement with earlier studies [212, 213]. The

enhanced bulk modulus of Pnma phase is indicative of change in the nature of bonding

of BiFeO3 under pressure.

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Figure 4.6: (a) Crystal structure of BiFeO3 at ambient conditions. (b) The structureof the first high pressure phase (P2221). (c) Structure of the second high pressure phase(Pnma).

Figure 4.7: Observed variation in the volume (per formula unit) of BiFeO3 as a function ofpressure. Symbols represent the experimentally observed data while solid lines are obtainedfrom fitting the P-V data with third order Birch-Murnaghan equation of state.

4.2.5 Conclusion

Using synchrotron based angle dispersive x-ray diffraction measurements we have

studied the high pressure behavior of pervoskite BiFeO3. We report two structural

phase transitions under pressure viz, at ∼ 4.1 and ∼ 6.4 GPa. The Rietveld refinement

of the diffraction data suggest that both the high pressure phases are orthorhombic,

the first being P2221 and the second phase belonging to the space group Pnma. These

123


results are in contrast to the previous studies such as the observation of monoclinic

phase below 10 GPa. The first high pressure phase has compressibility similar to

that of the ambient phase while the second high pressure phase becomes significantly

less compressible. Theoretical structural optimization in combination with Rietveld

refinement has helped to determine the accurate structure of the intermediate high

pressure phase.

4.3 Structural evolution of Sr2MgWO6


Sr2MgWO6 crystallizes into tetragonal crystal system with space group I4/m having

two number of formula units (Z=2) per unit cell. Its structure is made up of corner

sharing MgO6 and WO6 octahedra as shown in Figure 4.8. Along c axis these corner

sharing octahedra are linearly arranged while in the a-b plane these octahedra have

a particular tilt angle. Its lattice parameter at ambient conditions are a = 5.5791 A,

and c =7.9381 A.

4.3.2 Introduction

Sr2MgWO6, a double perovskite, is an analog compound to Sr2FeMoO6 which display

interesting coincident magnetic ordering, metal-insulator and a structural transfor-

mation [222, 223, 224, 225, 226]. Various compounds in this family are found to

have monoclinic, tetragonal and cubic structures and some of the compounds display

this sequence on increase of temperature. For example, Sr2MgWO6 transforms from

tetragonal to cubic structure (Fm3m) at high temperature. In contrast, Ca2MgWO6

and Sr2CaWO6 crystallize in the monoclinic structure (P21/n) at ambient conditions,

which transform first to the tetragonal structure (I4/m) and then to cubic structure

(Fm3m) on increase of temperature. It would be interesting to investigate whether

124

4.3. Structural evolution of Sr2MgWO6

Figure 4.8: Tetragonal crystal structure of Sr2MgWO6 at ambient conditions (Space groupI4/m).

these transformations are driven entirely by the changes in the inter-atomic distances,

which can also be easily brought about by subjecting the compounds to high pres-

sures. High pressure studies on Sr2CoWO6 shows favorable trend as it undergoes a

transition from tetragonal to monoclinic at 2.2 GPa. This has prompted us to inves-

tigate structural evolution of one of the simpler compounds of this double perovskite

family viz, without magnetic interactions, such as Sr2MgWO6. The results of the

experimental, synchrotron based x-ray diffraction and micro-Raman studies in this

compound are in accordance with first principles density functional reported in [227].

4.3.3 Methods

To synthesize Sr2MgWO6 appropriate amounts of SrCO3, MgO and WO3 were thor-

oughly homogenized and then heated at 1123 K for 24 h in a platinum boat. The

product obtained was further ground and pelletized (12 mm diameter and 810 mm

height) and heated at 1473 K for 30 h. The final product was characterized by pow-

der x-ray diffraction and it showed crystalline Sr2MgWO6 with a small amount of the

125


SrWO4 impurity. The ambient structure of Sr2MgWO6 was confirmed to be tetrago-

nal (space group I4/m, Z=2) with lattice parameters, a = 5.5791 A and c = 7.9381 A

which compare well with the earlier reported values of a = 5.5876 A and c= 7.9490

A [228, 229].

For high pressure experiments finely powdered sample of Sr2MgWO6 was loaded

along with a few specs of copper in hole of ∼100 µm diameter drilled in a pre in-

dented (∼ 80 micron thick) tungsten gasket of a diamond-anvil cell (DAC). Methanol:

ethanol (4:1) mixture was used as pressure transmitting medium. The pressure was

determined from the known equation of state of copper[132]. High-pressure angle

dispersive x-ray-diffraction experiments, were carried out up to ∼ 28.0 GPa at the

5.2 R (XRD1) beamline of Elettra Synchrotron source with monochromatized x-rays

of λ = 0.68881 A. The diffraction patterns were recorded using MAR345 imaging

plate detector kept at a distance of ∼ 20 cm from the sample. Two-dimensional x-ray

diffraction patterns were transformed to one-dimensional diffraction profiles by the

radial integration of diffraction rings using the FIT2D software [95]. The Raman

spectra were recorded up to ∼ 40 GPa using our confocal micro Raman set up as

mentioned in chapter1.


Figure 4.9 shows the x-ray diffraction patterns of Sr2MgWO6 at a few representative

pressures. The ambient diffraction pattern has been indexed with respect to tetrag-

onal phase and the x-ray diffraction peaks marked as Cu and W represent the peaks

due to copper (the pressure marker) and tungsten (gasket) respectively.

Due to the fact that c ∼√

2a, several diffractions peaks coincidentally overlap and

in these cases only the dominant (hkl) is indicated. On application of pressure up

to ∼10 GPa all the x-ray diffraction peaks shift towards higher two-theta values. On

further raising the pressure the pairs of coincidentally overlapping diffraction peaks

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Figure 4.9: Diffraction pattern of Sr2MgWO6 at a few representative pressures. Peaksmarked as (hkl), W and Cu are from the sample, gasket and pressure marker respectively.Asterisk (*) represents the impurity peak.

viz., (002), (110), (103), (121), (004), (220) and (204), (312), observed at ∼ 9.9◦,

16.5◦, 20◦ and 24.6◦, show increasing separation. No other significant changes were

observed in the diffraction pattern up to ∼28 GPa. The structural evolution was

determined by carrying out Rietveld refinement using GSAS [96] on all the recorded

diffraction patterns. For this the diffraction profiles were analyzed using three phases

viz., tetragonal Sr2MgWO6, copper (pressure marker) and tungsten (gasket). Refine-

ment showed excellent fitting, e.g., RP=2.7%, RWP=4.1 % and RF2=9.9 % at the

ambient pressure. Figure 4.10 shows the Rietveld refinement of diffraction pattern

recorded at ambient conditions.

Figure 4.11 shows the variation of normalized lattice parameters i.e. a/a0 and c/c0

with pressure, establishing that the increased splitting of coincidentally overlapping

127


Figure 4.10: Rietveld refinement of diffraction pattern at ambient conditions. The diffrac-tion pattern consists of contributions from Sr2MgWO6, tungsten gasket and Cu pressuremarker.

peaks is due to different compressibility along of a and c axes.

The anisotropic compressibility can in principle bring about significant electronic

properties changes, as observed in the Sr2FeMoO6 by Zhao et al [230]. However the

density of states (DOS) calculation on this compound as reported in [227]does not

show any appreciable change up to 100 GPa. On release of pressure all the results

display reversibility. Figure 4.12 shows the observed variation of V/V0 with pressure,

which when fitted to the third order Birch-Murnaghan equation of state gives the bulk

modulus and its pressure derivative to be 128 ± 4 GPa and 7.74±0.7 respectively.

The experimentally determined lattice parameters and volume are in agreement

with that obtained from computed one [227]. The experimentally determined bulk

modulus is also in agreement with the one obtained by fitting the energy-volume Birch

Murnaghan equation of state i.e. 132.6 GPa. Figure 4.13 shows the observed pressure

induced variations of two prominent Raman active modes of Sr2MgWO6 (viz., at 452

cm−1 and 857 cm−1, which correspond to bending and W-O stretching modes respec-

128


Figure 4.11: Variation of normalized lattice parameters with pressure. Symbols representthe experimental data and the solid lines represent the computed data taken from Mishraet al. 2010

tively [231]. The Raman scattering measurements were carried out up to 40 GPa and

show no unusual change indicative of a transformation. Using the observed value of

the bulk modulus (i.e., 128 GPa) the Grneisen parameters [γ =[(B/ω)*(dω/dp)]] are

determined to be 0.56 and 0.73 for the modes mentioned above.

The structure of Sr2MgWO6 is made up of alternate corner shared octahedral

i.e. WO6 and MgO6. In a-b plane these octahedra are connected through O1 atoms

(ambient fractional co-ordinates (0.7709, 0.7117, 0.0)) and along the c-axis these are

connected by O2 atoms (ambient fractional co-ordinates (0.0, 0.0, 0.2548)). Due to

the special positions occupied by the Mg, O2 and W atoms along the c-axis, the bond

angle Mg-O2-W is constrained to remain 180◦. In contrast the calculated Mg-O1-W

129


Figure 4.12: The observed P-V variation fitted with Birch- Murnaghan (B.M.) equationof state (red) for Sr2MgWO6. Symbols represent the observe data. Dash-dot line representsthe results of our first principles calculations taken from Mishra et al. 2010 for comparison.

bond angle at the ambient conditions is 163.3◦. Therefore, one may expect that

compression of Mg-O2 and W-O2 bonds may be more than Mg-O1 and W-O1 bonds,

as some compression may be accommodated by further bending of Mg-O1-W angle.

This is in accordance with the first principles calculations [227]. It has been shown

that this angle reduces slightly, to 154.7◦ at ∼ 100 GPa. However, the computed

variation of different cation-oxygen (i.e. Mg-O1, Mg-O2; W-O1, W-O2) bond lengths

shows that the Mg-O2 and W-O2 bonds are less compressible compared to Mg-O1

and W-O1 bonds, as shown in Ref. (SrMg paper) [227]. We speculate that the two

bonds formed by oxygen atom in the linear geometry are less compressible because

the presence of lone pair of oxygen atom heightens the repulsion on compression.

130


Figure 4.13: Variation of the frequencies of two prominent Raman active mode ofSr2MgWO6 with pressure.

In contrast, the two bonds formed by oxygen atom in the bent geometry in the a-b

plane are more compressible due to less repulsion by lone pair electrons of oxygen

atom under compression.

4.3.5 Conclusion

Angle dispersive x-ray diffraction and Raman scattering studies have been carried out

on Sr2MgWO6 up to ∼28 GPa and ∼40 GPa respectively. This compound is found

to be structurally stable up to the highest pressure in this study. Bulk modulus of

ambient phase is determined to be 128 ± 3.9 GPa which is in close agreement with

the theoretical value of bulk modulus, 132 GPa, reported in ref. [227]. These results

suggest that the temperature or pressure induced phase transformations in double

perovskites are not entirely due to the associated volume changes. Unusual higher

compression of bonds in basal plane compared to those along c axis are ascribed to

131


the presence of lone pair of electrons of oxygen. In contrast to this the compound

Sr2CaWO6 undergoes a phase transition on application of pressure [231]. It is inter-

esting to note that the smaller size of the cation Mg2+ with respect to Ca2+ may be

playing a role in the behavior of this material under high pressure.

4.4 Structural stability of BaLiF3

4.4.1 Introduction

BaLiF3 crystallizes in the cubic inverse perovskite structure. The high pressure struc-

tural stability of some group I-II flouro perovskites have been investigated, but there

is no experimental study on the structural stability of the I-II fluorides with the

inverse-perovskite structure. In the only high pressure study (limited to 20 GPa)

on BaLiF3, Korba et al. have calculated its electronic structure, density of states

and optical properties using density functional theory based on FP-LAPW method

[232]. With the help of their calculations they predicted that the valence band width

of BaLiF3 increases monotonically with pressure. Recent experiments and ab-initio

calculations on perovskite structured KMgF3 [48] and CsCdF3 [233] show that they

are structurally stable upto 40 and 60 GPa respectively and their pressure induced

band gap variation is similar to that of BaLiF3 [232]. In BaLiF3 the centre of the F−

octahedron is occupied by the small Li+ ion compared to the other cubic perovskites

where this position is occupied by the bigger B+2 cation. The smaller size of the

Li+ ion in the F− octahedral cage results in a larger anharmonicity of the Li+ ion.

Phase transitions in non-cubic NaMgF3 have been attributed to the anharmonicity

of the F− ion. Hence it is possible that even BaLiF3 may become structurally un-

stable at pressures higher than 20 GPa. Recently Xiao et al [234] have shown that

cubic perovskite PbCrO3 transforms to an iso-structural cubic form at ∼ 1.6 GPa.

This transition may be attributed to the presence of the transition metal ion at the

132

4.4. Structural stability of BaLiF3

centre of the octahedron. Hence to determine and compare the structural stability of

the cubic inverse-perovskite fluoride with the perovskite structured fluorides I have

carried out high pressure x-ray diffraction experiments up to 50 GPa.

4.4.2 Methods

Stoichiometric amounts of dried LiF (Riedel de Haen, 99 %) and BaF2 (Alfa 99.9%)

were homogenized and pelletized in an inert atmosphere. The pellets were wrapped

in a platinum foil and were sealed in a fused quartz tube in argon atmosphere and

were heated at 750 ◦C for 4 hrs. The heating and cooling was carried out very slowly

(5◦C/min). BaLiF3 thus obtained was characterized using powder x-ray diffraction.

In agreement with earlier studies its structure was found to be cubic inverse-perovskite

with (Space group No = 221, Pm3m) lattice parameter a = 3.995 A [52].

For the high pressure experiments, finely powdered sample of BaLiF3 along with a

few specs of copper was loaded in a hole of ∼100 µm diameter drilled in a pre-indented

(∼ 80 micron thick) tungsten gasket of a diamond-anvil cell (DAC). Methanol: ethanol

(4:1) mixture was used as a pressure transmitting medium. The pressure was deter-

mined from the known equation of state of copper [132]. High-pressure angle dis-

persive x-ray-diffraction experiments were carried out up to ∼ 50 GPa at the 5.2 R

(XRD1) beamline of Elettra Synchrotron source using monochromatized x-rays of

λ = 0.6888 A. The diffraction patterns were recorded using the MAR345 imaging

plate detector kept at a distance of ∼ 20 cm from the sample. Two-dimensional x-ray

diffraction patterns were transformed to one-dimensional diffraction profiles by the

radial integration of diffraction rings using the FIT2D software [95].

133



4.4.3.1 X-ray diffraction

Figure 4.14 shows the x-ray diffraction patterns of BaLiF3 at a few representative

pressures. There is a monotonous shift in the diffraction peaks towards higher 2θ

values up to 20 GPa. Beyond ∼ 27 GPa it appears as if the (111) and (211) XRD peaks

have split transforming the higher symmetry cubic structure to a lower symmetry one.

However, careful Rietveld analysis (using GSAS [96]) indicates that this peak splitting

is due to the separation of overlapping peaks of sample and the gasket and BaLiF3

remains cubic up to 50 GPa.

Figure 4.14: Diffraction patterns of BaLiF3 at a few representative pressures. The gasketand copper pressure marker peaks have been marked as W and Cu respectively. Thediffraction patterns of the released runs have been marked with r.

The linear compressibility, (1/l)(dl/dP) of Ba-Ba and Ba-Li at low pressures is

3.17x10−3 /GPa and is similar to that of Li-F and Ba-F which implies that the con-

stituent polyhedra do not get distorted with pressure. Linear compressibilities of

134


different cation-anion bonds in the cubic perovskite CsCdF3 were also found to be

equal (2.6 x10−3/GPa) indicating that the cation-anion bonds of the perovskites and

inverse-perovskites have similar compressibilities. On the basis of relative compress-

ibilities of the AX12 and BX6 polyhedra Ross et al [200] have formulated some general

rules for predicting phase transitions in oxide perovskites. Assuming that the addi-

tional valence sum mismatch induced by pressure at both the A and B cation sites is

same they have stated that if

βA / βB= MB/MA >1 the tilt angle of polyherda are reduced and perovskite struc-

ture becomes more symmetric

< 1 the tilt angle of polyherda increases resulting in symmetry lowering phase tran-

sitions

=1 the degree of distortion of the structure would not change with pressure (4.3)

(where β respresents the compressibility of the two polyhedra and M- represents the

variation of the bond valence sum at the cation of the polyhedra, due to change in

the average bond distance ).

While making these formulations they [235] have assumed that the additional sum

mismatch induced by pressure is same at both the A and B cation sites and therefore

βA/βB = MB/MA. However, as βA/βB for both compounds is equal to 1, but MA/MB

is ∼2.828 and ∼ 0.7 for BaLiF3 and CsCdF3 respectively, the relation βA/βB = MB/MA

does not hold for this class of compounds. Also, as seen in Figure 4.15 the additional

valence sum mismatch ∆Vi (i = A, B) due to application of pressure is not equal

at both the cation sites for BaLiF3 (Here Mi = (-Ri (dVi/dRi) ; Ri is average bond

distance, <Vi> is the total bond valence sum at the central cation I calculated on

135


the basis of the average bond length). This indicates that the assumptions made by

Zhao et al [235] (i.e. the additional valence sum mismatch induced by pressure is

the same at both the A and B cation sites) cannot be extended to the perovskites

and inverse-perovskites crystallizing with the cubic structure and hence the ratio of

MA/MB cannot be used as a reliable predictor of their compression behavior.

Figure 4.15: The additional valence sum mismatch at both (Ba, Li) cation sites (∆Vi (i= A, B) as a function of pressure.

The bulk modulus K0 = 75.9 ± 1.3 GPa and its pressure derivative K′ = 5.35±

0.15 were determined by fitting the third order Birch-Murnaghan equation of state

[59] to the observed pressure induced variation of volume [Figure 4.16]. Using the

elastic constants measured by Shimamura et al. [236] the bulk modulus is calculated

to be K0 ∼ 74.3 GPa, close to our experimental value.

4.4.3.2 Bulk modulus by empirical methods

The bulk modulus of a material depends on the bulk moduli of the constituent poly-

hedra and the network structure linking these polyhedra. In the case of corner linked

structures the bulk moduli are known to be significantly less than their constituent

polyhedra because of the bending of linkages and not due to compression of the poly-

136


hedra. However, in spinels and garnets where there is extensive edge sharing of the

polyhedra, the bulk modulus of the minerals is similar to those of the constituent

polyhedra. As in BaLiF3 constituent polyhedra are face sharing, it is understandable

that the bulk moduli of the constituent octahedra and dodecahedra are similar to

that of the compound.

Figure 4.16: The observed P-V variation fitted with third order Birch-Murnaghan equa-tion of state for BaLiF3. The closed and open circles represent the compression and decom-pression data respectively, while the red solid line is the fitted curve with B-M equation ofstate. The dot-dashed blue colour line shows the EOS obtained from ab-initio calculationsof Mishra et al. 2011

On plotting the V/V0 of the dodecahedra of different fluoro perovskites [237, 238]

(Figure 4.17) we find that irrespective of whether the centre of the dodecahedra is a

group I or II element (i.e. K or Ba) the compressibility of these dodecahedra are the

same.

However, the dodecahedra are less compressible if an atom of transition metals,

such as Co occupies its central position. This difference in compressibility could be

137


Figure 4.17: Pressure induced variation of normalized volume of KF12 and BaF12 poly-hedra for several fluoro-perovskites. For KZnF3 and KMgF3 the data are from referenceAguado et al. 2008 while for KCoF3 data was taken from Aguado et al. 2009. BaLiF3 datais from the present high pressure x-ray diffraction experiments.

due to the presence of d electron bonding in the Co-F bond.

Hazen et al derived a semi-empirical formula (using the data for several metal

oxides and silicates) for estimating the bulk moduli of polyhedral compounds [239]

by relating it to the cation charge density of its constituent polyhedra. For these

compounds the polyhedral compressibilities are proportional to the average polyhe-

dral volumes divided by the formal charges of the cations. Hazen et al [239] found

that K0 (in GPa) is (750 *Zi ) /d3, where Zi is the cationic formal charge and d is the

mean cationanion distance (in A). However, fitting the experimentally determined

bulk moduli of several scheelite-structured compounds as a function of the A cationic

charge per unit volume of the AO8 polyhedra, Errandonea et al found that K0 (GPa)

is (610 *Zi) /d3 [240]. The difference in coefficients of the above two formulations

arose because Errandonea et al included only scheelite and scheelite-like structures

while Hazen et al included a more diverse set of compounds. In both these formula-

tions the more compressible polyhedron was used for determining the bulk modulus.

Since the fluoro-perovskites also are made up of a network of polyhedra we tried to

138


Table 4.4: Bulk Modulii of various fluoro-perovskites determined from x-ray diffractiondata as well as from the known elastic constants of these compounds. Bulk moduli calculatedusing semi-empirical formulation of Hazen et al and Errandonea et al are shown. Since boththe octahedra and dodecahedra have the same compressibilities the bulk modulii have beencalculated using the polyhedral cation formal charge and mean cationanion distance (inA) of both the polyhedra (shown in column 7-10 of this table). It can be seen that thebulk moduli calculated from our fit to the Scotts formulation 60 K0=(Y-Zλ)(V0)n where n= 0.1387, Y = 25.28 and Z = - 42.57 gives the closest agreement with the experimentalvalues.

Material Lattice K0 K0 ’ Bulk Bulk K0 K0 K0 K0

parameter (exp) modulia modulib (Octa (Octa (dodeca (dodeca(A) hedra)c hedra)d hedra)c hedra)d

CsCdF3 4.4669 79 3.8 62.9 74.7 13.5 110 67 55KMgF3 3.989 71.2 4.7 70.4 75.3 189 154 95 77BaLiF3 3.995 e 75.9e 5.4 74.3 75.4 94.9 77.2 67 54KZnF3 4.053 77 79.9 75.8 180 147 90 73

NaMgF3 3.833 75 f 74.1 213 173 107 87RbCaF3 4.455 50.4 78.7 135 110 68 55CsCaF3 4.526 50.8 79.2 129 105 23 19KMnF3 4.182 64.7 76.7 164 133 29 24KFeF3 4.120 f 76.3 172 140 30 25KCoF3 4.071 78.7 75.9 178 145 31 26KNiF3 4.012 85.1 75.9 186 151 33 27

determine the bulk modulus of barium lithium fluoride using the formulation of both

Errandonea et al and Hazen et al. As both the polyhedral units of this compound

have the same compressibility, bulk modulus determined using either of the polyhe-

dra should give us the same result. However, as can be seen from table 4.4, the bulk

modulus calculated using the octahedra is very different from that determined from

the experiments.

These results imply that we cannot use the semi-empirical formulation of Hazen

[239] and Errandonea [240] to predict the bulk moduli of flouro perovskites. Hence

ain (GPa)From elastic constantsbCalculated using out fit to Scotts’s formulationcCalculated as per Hazen et al.dCalculated as per Errandonea et al.eFrom Mishra et al. 2011(BaliF3)findicates unavailability of elastic constants data.

139


in order to predict the correct bulk modulus with the help of a semi-empirical for-

mulation we used the fact that the bulk moduli can be related to the ambient pres-

sure molar volume as suggested by Ming et al [241]. Using this correlation and

semi-theoretical formulation of Scott et al [242], we have fitted the relation K0 =

(Y-Zλ)(V0)n where λ is the Cohen polarization factor [243], V0 is the molar volume

(cm3mol−1), and Y, Z and n are the parameters obtained by fitting the known ex-

perimental values of different fluoro-perovskites. The fitted values of n,Y and Z are

0.1387, 25.28 and -42.57 respectively. Using our fitted values we have calculated the

bulk moduli of several fluoro-perovskites (tabulated in the sixth column of table 4.4).

The values of bulk moduli appear to be in agreement with the earlier experimentally

observed values. Till date the bulk moduli of a few fluoro-perovskites have been de-

termined using the equation of state. However, since the elastic constants of several

of these compounds were known [244] we calculated their bulk moduli, which are

shown in column 5 of table 4.4. From this table we can see that though there is

a large difference (25%) in the bulk moduli, determined from elastic constants and

equation of state for CsCdF3 the difference from our calculated value is small i.e.,

∼ 5%. This gives us the confidence that we can predict the bulk moduli of differ-

ent fluoro-perovskites using our fit to Scotts semi-empirical formulation [242]. Since

there is a large discrepancy in the bulk moduli of CsCaF3 and RbCaF3 (table 4.4) we

feel that x-ray diffraction experiments should be carried out on these compounds to

determine their bulk moduli..

4.4.3.3 Comparison with calculations

The experimentally determined bulk modulus (75.9 GPa) of BaLiF3 by our studies is

in close agreement with that obtained from elastic constants (73.9 GPa). It is also in

agreement with the one obtained from fitting the third order B-M equation of state

to computed E-V data (69.4 GPa) as reported in [245]. I have also compared the

140


Table 4.5: Ambient pressure elastic constants and moduli of ALiF3 (A= Ba, Sr, Ca) deter-mined from GGA ab-initio computations. For comparison the experimentally determinedelastic constants of BaLiF3 from Boumriche1994 have also been tabulated.

Material K0=1/3 EOSa C11 C12 C44 C12/C44 G K/G(C11+2C12) (GPa) (GPa) (GPa) (GPa)

(GPa)

BaLiF3 73.9 69.4 136.4 42.8 47.1 0.91 47.02 1.57130b 46.5b 48.7b

CaLiF3 85.31 75.9 179.5 38.2 45.8 0.83 54.55 1.56SrLiF3 72.07 68.1 157.2 38.5 48 0.80 52.2 1.49

results from isostructural compounds SrLiF3 and CaLiF3. Table 4.5 indicate that all

the three inverse perovskites have similar compressibility.

The Variation in the elastic constants under pressure can provide useful informa-

tion about changes in the stability and stiffness of material. Cubic lattices have only

three independent constants, namely C11, C12 and C44. Calculated values at ambient

pressure are given in Table 4.5. It can be seen that for BaLiF3 these are in close

agreement with experimentally determined values [232]. For all the three compounds

the ratio C12/C44 is almost close to unity as predicted by the Cauchys law and this

indicates that the short range potentials are almost spherically symmetric.

Table 5.6 shows that the calculated elastic constants for the perovskite fluorides

are found to obey the modified stability criterion [247] (given below) for cubic crystals

under finite strain corresponding to pressures of ∼ 84 GPa i.e.,

M1 = (C11 + 2C12)/3 + P/3 > 0 (4.4)

M2 = C44 − P > 0 (4.5)

M3 = (C11 − C12)/2− P > 0 (4.6)

aimplies Bulk modulus determined from EOS obtained by ab-initio density functional calculationsas reported in A. K. Mishra et al. [245]

bshows that elastic constants taken from experimental data of reference [246]K is bulk and G isshear modulus

141


Table 4.6: Derived elastic constants characterizing mechanical stability (Mi eqs. 1-3)of BaLiF3 at different pressures, calculated from GGA ab-initio computations reported inMishra et al. 2011

Pressure (GPa) K/G M1 M2 M3

0.0 1.57 73.9 47.13 46.791.74 1.65 79.94 46.67 45.539.09 1.59 100.56 53.49 50.8620.52 1.66 141.16 62.55 57.6738.58 1.73 201.03 74.45 63.9448.55 1.75 231.75 80.13 66.8667.74 1.79 290.98 90.03 71.7484.24 1.82 340.75 97.51 74.36

The angular character of atomic bonding can be described by the Cauchy pressure

(C12-C44). If this pressure is negative then the material is nonmetallic with directional

bonding and if it is positive then the material is expected to be metallic [248]. This

has been verified for ductile materials like Nickel and Aluminium and also for brittle

materials like Silicon. The fluorides that we have studied have a negative Cauchy

pressure at ambient condition, which increases towards positive values on application

of pressure.

Although the large bandgap of BaLiF3 at high pressures shows that it is still an

insulator, this change in sign of the Cauchy pressure could be indicative of reduction

in the angular character of the bonding. In fact for BaLiF3 we have observed that its

sign changes around 21 GPa where the increase in the band gap is very gentle and

then beyond 38 GPa the band gap starts decreasing, as mentioned in [245].

The plastic properties of materials can be linked by their elastic moduli using

pugh indicator (K/G). The shear modulus (G) of materials represents the resistance

to plastic deformation [249]. K/G ratio greater than 1.75 and poissons ratio greater

than 0.33 are associated with ductility of a material [250]. Our studies show that

Cauchy pressure, K/G and poissons ratio (ν) (Table 4.6) of BaLiF3 increases with

pressure indicating that application of pressure reduces the brittleness and angular

142


nature of bonding of BaLiF3. Our studies also indicate that brittleness of BaLiF3 <

CaLiF3∼ SrLiF3.

4.4.4 Conclusions

High pressure x-ray diffraction studies on inverse-perovskite BaLiF3 show that this

compound is structurally stable up to ∼ 50 GPa. The bulk modulus of BaLiF3 is

determined to be 75.9 GPa which is in close agreement with that determined from semi

empirical formulation. Amongst the three alkaline earth fluoro perovskites (ALiF3,

A=Ba, Ca, Sr) which crystallize in the inverse -perovskite structures, BaLiF3 is the

least brittle at ambient conditions and also the degree of brittleness decreases at high

pressures. Since these fluorides do not undergo any structural phase transitions at

high pressures they can be used as an alternative pressure marker. By fitting the

observed pressure induced variation of volume with the third order Birch-Murnaghan

equation of state K0 and K′ were determined to be ∼75.9 ± 1.3 GPa and 5.35± 0.15

respectively. It has been shown that the compressibility of the perovskite and inverse-

perovskite fluorides is similar. The behavior of the elastic constants at high pressure

with apparent reduction in the band gap as reported in [245] indicates a decrease

in the directional nature of the bonding. Our studies also indicate that the ratio of

MA/MB cannot be used as a reliable predictor of the compressional behavior of cubic

inverse perovskites.

143


144

5

Pressure induced phase

transformation in U2O(PO4)2

The phosphate materials having open framework structures and interlinked polyhe-

dral motif are well known for their geophysical importance. Under compression such

open structures may collapse which result in the rotation and/or distortion of con-

stituent polyhedral units. The high pressure structural investigations of these open

framework materials are therefore of interest from the point of view of basic material

research. U2O(PO4)2 is an important material with the potential applications in the

field of nuclear waste disposal [251]. In this chapter I have presented the high pressure

investigations on this material.

5.1 Introduction

The materials having framework structures display a large number of phase tran-

sitions due to different compressibilities of the constituent polyhedra and also due

to ease of bending across the polyhedral linkages. Prominent among this class of

materials are α-SiO2 (quartz), α-AlPO4, α-GaPO4, α-GeO2, etc., which are re-

ported to undergo pressure-induced phase transitions to higher coordinated structures

145

5. Pressure induced phase transformation in U2O(PO4)2

[252, 253, 254, 255] . Among these, the compounds having PO4 tetrahedra are found

to show interesting structural changes. For example, in α-AlPO4, AlO4 tetrahedra

are more easily transformed to octahedrally coordinated AlO6 resulting in the trans-

formation to orthorhombic Cmcm phase at ∼ 12 GPa. In contrast, the more rigid

PO4 retains its tretrahedral coordination to quite high pressures i.e. upto ∼ 70 GPa

[254, 255].

Diuranium oxide phosphate (U2O(PO4)2) belongs to a family of tetravalent metal

oxide phosphate which are represented by M2O(PO4)2 (where M=U, Zr, Th, etc.).

These compounds are used as thermal-shock resistant ceramics, composites and are

also considered as potential candidates for the long-term storage of nuclear waste due

to their low solubility in water [251, 256]. These materials are also of interest in

areas of ion exchange [257, 258] and protonic conduction [259, 260]. Due to the open

framework structure, these compounds can also provide some zeolitic features, such as

accessible open spaces, rigid frameworks, chemical/thermal stability, size and shape

selectivity and catalytically active sites [261, 262]. In particular, diuranium oxide

phosphate, iso-structural to Zr2O(PO4)2 (an ultra-low expansion ceramic), shows a

continuous thermal contraction [263].

At ambient conditions, U2O(PO4)2 exists in the orthorhombic structure with space

group Cmca (space group no.= 64) [264]. Earlier studies on its sintered rods implies

that U2O(PO4)2 has macroscopic negative thermal expansion (NTE) in the temper-

ature range 20-1000◦C [263]. However, subsequent studies [265] showed that it has

anisotropic thermal expansion behaviour; positive thermal expansion in [100] and

[001] directions and negative thermal expansion in [010] direction. Recent neutron

diffraction as well as x-ray diffraction studies have shown that its negative thermal

expansion behavior results mainly from a polyhedra rocking mechanism, somewhat

similar to what is now believed to be the cause of NTE in monodentate framework

structures such as α-ZrP2O7 [266] and ZrW2O8 [267].

146

5.2. Structural Details

In the recent years, the behaviour of several compounds which display nega-

tive thermal expansion such as Al2(WO4)3 [268], Sc2(WO4)3 [269], Y2(WO4)3 [270] ,

Zr(WO4)2 and Hf(WO4)2 [271, 272, 273] etc. has been investigated under pressure.

These studies suggest that for these compounds K′ (derivative of bulk modulus) is

either negative or very small [274]. These compounds also show many interesting

intermediate structural phase transformations before eventual amorphization at high

pressures.

As U2O(PO4)2, a NTE material, is made up of UO7 polyhedra and PO4 tetrahedra

it would be interesting to explore the nature of structural changes resulting from the

relative compressibilities of polyhedra under pressure. Our high pressure Raman and

x-ray diffraction studies on this compound up to 14 GPa and 6.5 GPa respectively

indeed reveal new high pressure phases of this compound.

5.2 Structural Details

Figure 5.1: Edge Shared UO7 (pentagonal bipyramids) and PO4 (tetrahedra) as inU2O(PO4)2.

The diuranium oxide phosphate crystallises into orthorhombic symmetry with

space group Cmca (space group no., 64). In this structure, distorted UO7 pentagonal

bi-pyramids share an O(1)-O(1) edge with three equivalent PO4 tetrahedra as shown

in Figure 5.1 and Figure 5.2 These pentagonal bi-pyramids are tightly connected as

147


Figure 5.2: The parent orthorhombic structure as viewed along [100].

pairs in the (100) plane by strong U-O(3)-U bridging and form infinite zigzag chains

along [100] by sharing O(1)-O(1) edges. The PO4 tetrahedra also share corners with

UO7 polyhedra.

5.3 Methods

5.3.1 Synthesis

The diuranium oxide phosphate has been synthesized using wet chemical route, as

given in reference [264]. To begin with, uranium metal is dissolved in 6M HCl to make

a concentrated solution of tetravalent uranium. This solution is then mixed with con-

centrated phosphoric acid (5M H3PO4), at room temperature. This mixture is evap-

orated and annealed under argon flow. Annealing under argon environment prohibits

the oxidation of U2O(PO4)2 and consequent formation of triclinic UIV (UV IO2)(PO4)2,

which otherwise takes place in air at ≥ 300 ◦C [275]. Thus prepared sample has been

characterised using x-rays of wavelength 0.71069 A obtained from rotating anode

generator x-ray source with molybdenum target in our laboratory. The sample was

found to crystallize into orthorhombic crystal structure. The unit cell parameters of

U2O(PO4)2 are determined to be a = 7.052 ± 0.003 A, b = 8.991 ± 0.004 A and c

= 12.673 ± 0.004 A as deduced from the observed powder x-ray diffraction pattern

148

5.3. Methods

of the above prepared sample. These values are in close agreement with the unit cell

parameters (a = 7.087 A, b = 9.036 A, c = 12.702 A) published earlier [264].

5.3.2 Experiemntal Details

The powdered sample of U2O(PO4)2 was loaded in a hole of ∼130 m diameter of a

tungsten gasket which was pre-indented to a thickness of 80 µm in a MaoBell type of

diamond anvil cell [76]. Raman scattering experiments have been carried out under

quasi-hydrostatic as well as non-hydrostatic pressures. For quasi-hydrostatic mea-

surements, 4:1 methanolethanol mixture was used as a pressure transmitting medium.

In the Raman experiments ruby R-lines were used for the pressure calibration [131],

whereas for the x-ray diffraction experiments platinum was used as a pressure marker.

In the latter case, the pressure on the sample was deduced using the equation of state

of platinum [132].

For Raman measurements, we have used our indigenous micro Raman system with

confocal optics. The Raman scattered light from the sample, which is excited by 532

nm laser line of the diode-pumped solid state laser, is collected using a CCD based

single stage spectrograph and a super-notch filter. The Raman modes in the spectral

range 180-1200 cm1 have been recorded as a function of pressure up to 14 GPa. Neon

(Ne) and Mercury (Hg) lines were used for calibration purpose.

Angle dispersive x-ray diffraction measurements have been carried out using Mo

(Kα) monochromatized x-rays (λ= 0.71069 A) from a Rigaku rotating anode x-ray

generator. The x-rays are collimated to ∼100 µm and the two dimensional diffraction

rings, collected on a MAR345 imaging plate, are converted to one dimensional diffrac-

tion profiles using the FIT2D software [95]. The cell parameters were determined

using Le Bail analysis as incorporated in the GSAS software [96]. The diffraction

pattern was recorded up to ∼ 7 GPa and on release of pressure.

149


5.4 Results and Discussion

5.4.1 Raman Spectroscopy

5.4.1.1 Raman modes under ambient conditions

As mentioned above, at ambient conditions, U2O(PO4)2 has orthorhombic structure

(space group Cmca, point group mmm (D2h) with four formula units per unit cell).

Its factor group is isomorphous to the point group D2h and its order is g = 8.

As the conventional unit cell is C face centered, a primitive unit cell having two

formula units can be chosen which would have 26 atoms. Thus U2O(PO4)2 has

75 fundamental vibrational modes, which can be classified in terms of irreducible

representations as follows

ΓU2O(PO4)2 = 11Ag + 7B1g + 7B2g + 11B3g + 8Au + 12B1u + 12B2u + 7B3u. (5.1)

The polyhedral molecules (PO4)3− and UO7 occupy the site symmetry Cs (C1h).

Figure 5.3: Correlation diagram of internal modes of U2O(PO4)2 based on PO4 smme-try group. The known frequencies of the isolated (PO4)3− tetrahedron are given in theparenthesis.

One of the oxygen occupies site symmetry C2h and another occupies C1. The cor-

relation diagrams, given in Figure 5.3 and Figure 5.4 show factor group splitting of

150


Figure 5.4: Correlation diagram of internal vibrations of U2O(PO4)2 based on UO7 sm-metry group.

Table 5.1: Tentative assignment of observed Raman modes of diuranium oxide phosphate.

Frequencies(cm−1) Tentative assignment

207 External modes and/or U-O stretch mode247, 266 U-O stretch

433 δs(P-O) (symmetric bending mode)and/or Eg U-O stretch

629 δas (P-O) (asymmetric bending mode)and/or overtone of U-O stretch

881 Unassigned1002 νs (P-O)

1030, 1087 νas (P-O)

various modes of PO4 and UO7 in the orthorhombic system of U2O(PO4)2. Figure 5.5

and Figure 5.6 shows the observed Raman spectrum of this compound in the spectral

region 180-800 cm−1 and 800-1200 cm−1 respectively. As lattice dynamical calcula-

tions are not available in the literature for this compound, the mode assignments has

been carried out following the earlier infrared and Raman studies on various struc-

tural modifications of uranium phosphate [276, 277]. Thus the assignments for the

observed Raman modes, given in table 5.1, should be viewed as tentative.

151


Figure 5.5: Raman spectrum of U2O(PO4)2 at ambient conditions in the spectral region180-800 cm−1; * indicates unidentified peaks.

Figure 5.6: Raman spectrum of U2O(PO4)2 at ambient conditions in the spectral region800-1300 cm−1.

5.4.1.2 High Pressure Raman studies

The Raman modes of U2O(PO4)2, recorded in the spectral region 180-1200 cm−1,

under quasi-hydrostatic and non-hydrostatic pressures are shown in Figures 5.7, 5.8

and 5.10 respectively. The corresponding pressure induced changes in the positions

of Raman modes are shown in Figures 5.9 and 5.11 respectively.

In the case of hydrostatic pressures, all the observed modes were found to display

a monotonic stiffening with pressure up to 2 GPa. The Raman mode observed at

152


Figure 5.7: Raman spectra of U2O(PO4)2 under quasi hydrostatic conditions in the spec-tral region 180-800 cm−1.

Figure 5.8: Raman spectra of U2O(PO4)2 under quasi hydrostatic conditions in the spec-tral region 800-1300 cm−1.

207 cm−1 (U-O stretch) shows broadening at very low pressures (∼ 2 GPa), while

the modes at 247 cm−1 and 266 cm−1 (U-O stretch) show significant broadening at

somewhat higher pressure (∼ 3.6 GPa).The band observed at 433 cm−1 shows splitting

beyond 2 GPa. As this band is tentatively assigned to δs(P-O) and Eg (U-O) stretch

153


Figure 5.9: Variation of Raman mode frequencies with pressure under hydrostatic condi-tions. (Error bars are larger beyond 6 GPa due to broad Raman peaks).

modes, it is possible that these modes separate out at higher pressures. At the same

pressure, the PO4 asymmetric stretch mode at 1030 cm−1 (νas (P-O)) shows increase

in the relative intensity with respect to the mode at 1002 cm−1 (νs (P-O)).

The relative intensity of the U-O stretch mode observed at 207 cm−1 with the

respect to PO4 stretching modes reduces significantly at pressures above 6 GPa. We

also find that beyond 6.7 GPa, various Raman modes of the initial structure are

replaced by broad bands in the region 300-700 cm−1 and the intense mode νas (P-

O) observed at 629 cm−1 under ambient conditions becomes almost unobservable

beyond this pressure. The vanishing of intensity of this mode beyond 6.7 GPa is

found to be rather abrupt. At the same pressure, the Raman mode observed at 881

cm−1 ((νs (P-O)) is found to pick up intensity. Above 7 GPa, the sharper peaks

corresponding to PO4 modes are replaced by a red shifted broad band at ∼ 981 cm−1

around the asymmetric stretching mode. All the features mentioned above suggest

that the structure becomes increasingly disordered as the pressure is increased.

The results under non hydrostatic conditions do not display any significant intensity

redistribution amongst the internal PO4 modes, unlike under hydrostatic pressures.

154


Figure 5.10: Raman spectra of U2O(PO4)2 under non-hydrostatic conditions in the spec-tral region (a) 180-800 cm−1 and (b) 800-1300 cm−1.

Figure 5.11: Variation of Raman mode frequencies with respect to pressure under non-hydrostatic conditions.

In addition, we found that the modes at 1002 cm−1 (νs (P-O)), 1030 cm−1 and 1087

cm−1 (νas(P-O)), continue to exist up to ∼ 8 GPa and beyond this pressure all these

modes merged into a single broad band. We note that this broad band is also red-

shifted compared to the centroid of the earlier peaks.

We should also point out that this feature is somewhat different from the results

155


under hydrostatic pressures, where we observed two bands, i.e. one corresponding to

the centroid of the evolving peaks and another one that is red-shifted with respect to

these (marked with arrow in Figure 5.8). This suggests that the kinetics of pressure

induced transformation is different for hydrostatic and non hydrostatic conditions.

The emergence of these red-shifted broad bands is similar to what has also been

reported earlier for Sc2(WO4)3 [269] where these were ascribed to the emergence

of higher coordinated disordered state. In general, as in the hydrostatic case, the

observed pressure induced broadening of the Raman modes of PO4 as well as UO7

polyhedra suggest that U2O(PO4)2 becomes progressively more disordered at higher

pressures.

To summarize, the overall evolution of the Raman modes and existence of a struc-

tural transition are common to both hydrostatic and non-hydrostatic conditions.

However, the transition pressure for the non-hydrostatic conditions (∼ 8 GPa) is

slightly higher than that for the hydrostatic pressures (∼ 6 GPa). Due to the fact

that non-hydrostatic pressures in a DAC also imply heterogeneous stress distribution,

one generally observes broadening of the peaks at lower pressures. In this sense the

loss of sharp Raman features at a higher pressure under non-hydrostatic conditions

is counter-intuitive and hence interesting which may encourage further work.

Earlier investigations on many negative thermal expansion materials have at-

tempted to interpret the observed negative thermal expansion using the Grneisen

parameters [265]. There has been varied opinions about the contribution of various

energy modes to negative thermal expansion and in earlier studies mostly the low

energy modes ( ≤10 meV) have been shown to be of relevance. We have given in

table 6.1, the slope of change of the Raman modes with pressure (dν/dP) and mode

Gruneisen parameters of all the observed modes of U2O(PO4)2. Among the observed

modes, the Raman mode observed at 207 cm−1 (∼ 25 mev) which is tentatively as-

signed to U-O stretching mode shows negative grneisen parameter. It is of interest

156


Table 5.2: Raman active mode frequencies (ω), their pressure dependence (dω/dP) andcorresponding Gruneisen parameters (γ) of the Orthorhombic Cmca phase of U2O(PO4)2 .

ω(cm−1) dω/dP (cm−1GPa1) γ

207 -1.37 -0.41247 1.65 0.41266 1.15 0.26433 0.71 0.10629 1.54 0.15881 3.79 0.261002 3.29 0.201030 3.71 0.221087 5.99 0.34

to note that in the high temperature study of U2O(PO4)2 one of the U-O bonds was

found to show negative thermal expansion coefficient [265]. Lattice dynamical calcu-

lations may throw more light on rigid unit modes (RUM) i.e. correlated polyhedral

rotations and its role in the NTE of this compound.

As shown in Figure 5.12 , Raman spectra on release of pressure are similar for

hydrostatic as well as non-hydrostatic conditions. However an interesting feature in

these spectra is the emergence of a new mode at ∼ 870 cm−1 .When the retrieved

sample from the hydrostatic experiments was coincidentally investigated after one

month, it showed that 870 cm−1 mode gains intensity and in addition the broad band

at ∼ 1000 cm−1 is replaced by some of the sharper modes. This observed Raman

spectrum closely resembles the spectrum of the U(UO2)(PO4)2, a mixed-valence phase

of uranium orthophosphate [278]. In this compound uranium exists in 4+ and 6+

state as evidenced by the observation of two types of binding energy for U(IV) and

U(VI) by P. Benard et al [278]. On compression there exists a possibility of charge

transfer from uranyl ion (U4+) to (UO2) 2+ and thus facilitating the conversion of

U2O(PO4)2 into mixed valence U(UO2)(PO4)2.

157


Figure 5.12: Raman spectra of U2O(PO4)2 on release of pressure (h) denotes from hy-drostatic and (nh) denotes from non-hydrostatic conditions.

5.4.2 X-ray diffraction studies

Figure 5.13 shows the x-ray diffraction profiles of U2O(PO4)2 at a few representative

pressures. The observed variations of the d-spacing with pressure are given in Figure

5.14. The diffraction peaks of the pressure marker (platinum) and gasket (tungsten)

are marked as Pt (hkl) and W (hkl) respectively. Our data show [Figure 5.13 ] that

with the increase of pressure many of the diffraction peaks of the ambient phase

lose intensity and by ∼ 5.5 GPa the diffraction pattern becomes quite weak and has

broad features. On further increase of pressure, the diffraction peaks of U2O(PO4)2

broadened substantially, while the diffraction peaks from the pressure marker and

gasket continue to be sharp. Across 5.5 GPa, we also observe discontinuous changes

in the d spacings of the diffraction peaks indicating a structural phase transition at

158


Figure 5.13: X-ray diffraction patterns of U2O(PO4)2 at a few representative pressures.

this pressure.

From the diffraction pattern at ∼ 6 GPa, we find that the remnant diffraction peaks

lie close to the known diffraction peaks of the lower symmetry triclinic phase of mixed

valence uranium orthophosphate U(UO2)(PO4)2. Consistent with our Raman results,

Le Bail fit to the diffraction data at ∼ 6 GPa as shown in Figure 5.16 indicates it to

be a mixture of initial orthorhombic and a new triclinic phase with cell parameters

as a = 8.795 ± 0.003 A, b = 9.302 ± 0.002 A, c = 5.483 ± 0.002 A, α = 102.810 ±

0.00030, β = 97.000 ± 0.00040, γ =102.040 ± 0.00050.

These values are reasonably close to the earlier reported cell parameters of the

mixed valence phase i.e., a = 8.8212 A, b = 9.2173 A, c = 5.4772 A, α = 102.6220, β

159


Figure 5.14: Pressure induced variation of dhkl.

= 97.7480, γ = 102.4590 [278]. However, the quality of the diffraction data beyond ∼

6 GPa is not sufficient for the Rietveld analysis and hence more detailed information

about the structure of the daughter phase can not be deduced. For the parent phase,

our P-V data (up to ∼ 6 GPa) when fitted to Birch-Murnaghan equation of state

[59] , gives the bulk modulus and its derivative to be ∼ 61 ± 8 GPa and ∼1.4 ± 3.1

respectively.

Our Raman and x-ray diffraction data at high pressures suggest that the abun-

dance of the disordered parent phase increases with the increase of pressure and the

new phase, similar to the mixed valence phase of uranium, is also poorly crystallized.

These results suggest that the transformation to the daughter phase is kinetically

frustrated giving rise to the increasing abundance of disorder [122] .

160


Figure 5.15: Le Bail fit to the diffraction pattern at 6 GPa; both the parent orthorhombicand high pressure triclinic phase have been fitted.

Figure 5.16: V/V0 versus pressure for the orthorhombic phase. The solid line is fit toBirch-Murnaghan equation of state.

161


5.5 Conclusion

We have investigated the high pressure behaviour of U2O(PO4)2 employing Raman

scattering and x-ray diffraction technique up to ∼14 and 6.5 GPa respectively. The ob-

served changes in the Raman spectra as well as the x-ray diffraction patterns suggest

that U2O(PO4)2undergoes a phase transition at ∼ 6 GPa to a mixture of a disordered

ambient pressure phase and a new high pressure phase. The new phase resembles

the triclinic mixed-valence phase of uranium orthophosphate (U(UO2)(PO4)2). On

release of pressure the initial phase is not retrieved implying the irreversibility of the

phase transition. Our Raman data also suggests the increase in abundance of the

triclinic phase with time.

162

6

Development of EDXRD Beamline

6.1 Introduction

For high pressure X-ray diffraction experiments employing diamond anvil cell the re-

quirement of small amount of samples (∼ pico litre) necessitates the use of brighter

x-ray sources. Moreover for mega bar experiments this requirement become more

stringent due to further reduction in sample volume. The XRD data from laboratory

based rotating anode x-ray sources or x-ray tubes have limited reliability in terms of

usefulness of data for detail structural refinement. The advent of synchrotron sources

is boon for material scientist especially for high pressure community because these

sources provide synchrotron beam (Infrared to hard X-rays) of high flux and of col-

limated nature with a particular time structure. In addition the synchrotron beam

is linearly polarized in the plane of ring and elliptically polarized out of this plane.

These qualities of the synchrotron beam widen the use of synchrotron sources in many

interesting areas including material research. With the availability of insertion de-

vices like wavelength shifter, wigglers and undulators at third generation synchrotron

sources the flux of the synchrotron beam further increases. Hence to harness the capa-

bility of synchrotron source, we have developed an Energy dispersive x-ray diffraction

163

6. Development of EDXRD Beamline

Table 6.1: Salient designed parameters of Indus-2 synchrotron source.

Parameters Values

Electron beam energy 2.5 GeVBeam emittance-horizontal 5.81E-08 m. rad

Beam emittance-vertical 5.81E-09 m. radElectron beam size σx 0.215 mm

σy 0.243 mmσx′ 0.352 mradσy′ 0.062 mrad

Dipole magnetic field 1.5 TCritical wavelength 1.986

Beam life time 24 HrsPower loss 186.6 KW

Bunch length 2.23 cmMaximum current 300 mA

Circumference 172.4743 mRevolution frequency 1.738 MHz

RF frequency 505.812 MHzHarmonic number 291

(EDXRD) beam line at a bending magnet port of 2.0/2.5 GeV Indus-2 synchrotron

source at RRCAT, Indore. Proposed design parameters of Indus-2 are listed in table

I, though presently it is operating at 2.5 GeV, ∼120mA maximum injected current

with a beam life time of nearly ∼ 7 hours. As, discussed in chapter1, for energy dis-

persive x-ray powder diffraction all the diffraction peaks are collected simultaneously

at a fixed scattering angle 2θ, therefore this technique is particularly useful for studies

of materials under extreme conditions such as high pressure and/or high temperature

which require constrained geometry. This technique is also suited for studying the

rapid phase transitions and kinetics of the sample. The availability of larger Q (2π/d)

range at synchrotron sources implies more reliable structural determination.

EDXRD beam line has been designed, developed, installed and commissioned [98]

at bending magnet port BL-11 of Indus-2, synchrotron source at RRCAT Indore.

This beam line utilizes white synchrotron radiation (SR) from a bending magnet,

164

6.2. Basic Principle

filtered through 200 µm thick water cooled Be window and collimated using precision

slits. The diffracted x-rays from the sample are analyzed using energy resolving high

purity germanium (HPGe) detector. Generally we can obtain white SR beam from

bending magnet up to 70 keV having good intensity. With the availability of a wide

range of 2θ angle (± 25◦), the diffraction data can be collected over a large Q range

(up to 15 A−1

) using this beamline.

6.2 Basic Principle

The basic principle of energy dispersive x-ray diffraction is Braggs law expressed in

energy space

Edhkl sin θ = C (6.1)

where E is the energy of the photons scattered at the fixed angle 2θ by the planes

with interplanar spacing dhkl. C is a constant equal to 6.19926 keV A [279].

Here, all the diffraction peaks are recorded simultaneously by an energy sensitive

detector and their profile is convolution of the detector resolution and broadening

due to the beam divergence. Assuming these contributions as Gaussian the width of

a diffraction peak ∆E is given by

∆E =[(∆ED)2 + (∆Eθ)

2]1/2

(6.2)

The broadening due to detector, at energy E, is given by

∆ED =[(∆Eamp)

2 + 2.35× (1/2)FεE]1/2

(6.3)

where ∆E amp is due to noise in the detector and preamplifier, F is Fano factor and

165


ε is energy required for e−-hole pair generation.

∆Eθ = E cot θ∆Θ (6.4)

For simplicity the equation (6.2) can be written as

∆E =[k2

1 + k2E + (k3E)2]1/2

(6.5)

or

∆E/E =[k2

1/E2 + k2/E + (k3)2

]1/2(6.6)

Where k1, k2 are the constants of detector system and k3 is geometric constant

cot θ∆θ, ∆θ represents the total equatorial divergence of the incident The above

equation (6.5) implies that the relative energy width of a diffraction peak (∆E/E)

decreases with energy. It is observed that resolution is essentially detector limited

due to low divergence of synchrotron beam. For improved resolution one needs to

record the diffraction data at higher energies. Equation (6.1) implies that for peaks

at higher energies one needs to work at lower scattering angles. Form the variation of

resolution with scattering angle it is observed that resolution improves with decreas-

ing 2θ until cot θ shoots up and causes a rapid degradation of the resolution. Thus, a

trade off is established among various parameters like energy range, scattering angle,

sample thickness, d spacing of interest etc to optimize the resolution and intensity of

energy dispersive powder x-ray diffraction pattern.

166

6.3. EDXRD Beamline at Indus-2

6.3 EDXRD Beamline at Indus-2

6.3.1 Design and Description

The EDXRD beamline has been designed to collect the diffraction data in plane of the

ring by changing the scattering angle. The key parameters which play an important

role in the design of this beam line are the geometric resolution, detector resolution

and the divergence of the synchrotron beam. For Indus-2 the γ=m/m0, where m

and m0 are relativistic mass and rest mass of electron, is ∼5000, hence the vertical

divergence of the synchrotron beam which is proportional to 1/γ is 0.2 mrad and

horizontal divergence is defined by the first slit across the sweep of the synchrotron

beam.

Schematic layout of EDXRD beam line is shown in figure1. It comprises of water

cooled Be window, water cooled pneumatic copper beam stopper, Primary slit system,

Evacuation chamber with vacuum pumps, Precision slits systems etc. A Carefully

designed state of the art sample maneuvering system with eight axis goniometer is

an integral part of our experimental station. The diffracted data is collected after

passing through a pair of precision slits by an energy resolving High purity germanium

detector (Canberra Model) in multichannel analyzer mode. A mechanical layout of

Figure 6.1: Schematic layout of EDXRD beamline.

EDXRD beam line in top view is shown in figure 6.2 and the photograph of beam

167


line viewed from inside and outside as installed is shown in Figure 6.3 (a) and Figure

6.3 (b) respectively. The synchrotron radiation is transported from storage ring to

beyond the concrete wall (Biological shield) through the front end optics. The

Figure 6.2: Mechanical layout of EDXRD beamline in top view.

Figure 6.3: Photograph of EDXRD beam line installed at port no BL 11 at Indus-2 from(a) inside (b) outside.

synchrotron beam is transported to the experimental station by collimating through

a few slits beyond the Be window of front end.

For EDXRD beamline the first slit is called the primary slit. Being the first

component of the beamline all the slit baldes are water cooled to avoid any heating

due to the heat load of synchrotron beam which is ∼30W/mrad. This slit system is at

∼16 m from the tangent point of the synchrotron source therefore for 0.2 mrad vertical

divergence, the slit opening is ∼ 3.2mm. The synchrotron radiation being of guasian

168

6.3. EDXRD Beamline at Indus-2

profile the high energy intense x-rays are in the central part of beam. Therefore we

select the synchrotron beam in the central region and further cut it down through

the independent movement of 4 tungsten carbide blades mounted in the vertical and

horizontal jaws. The movement range of these vertical and horizontal jaws are in the

range of -2 mm to 15 mm and from -2 mm to 30 mm respectively.

Using this slit an aperture for ∼ 0.5 mm2 synchrotron beam is selected out of

larger beam. This beam is further collimated through a pair of precision slits made

of ∼ 4 mm thick WC blades. In future we have planned to install a focusing optics,

such as Kirkpatrick-Baez mirror system, for focusing the white x-ray beam just before

the sample stage. This will provide the synchrotron beam ∼40 µm2 with an order

of improvement in the incident flux at the sample. This will increase the signal to

noise ratio. Especially in case of high pressure measurements the signal from gasket

peak can be avoided without compromising the flux. The sample is mounted on a

goniometric sample stage, capable of supporting and aligning a diamond anvil cell

for the high pressure studies. This is followed by point slits (which also define the

scattering angle 2θ) and HPGe detector, placed just behind the last point slit.

6.3.2 Sample Stage

For diffraction experiments especially under diamond anvil cell it is very important

to align the sample accurately with respect to synchrotron radiation. The diffracting

volume also known as the diffracting lozenge is defined by the slit system as the

volume of sample irradiated by the direct beam which is collected by the HPGe

detector. Therefore it is lozenge shaped volume of intersection of the incident beam

with the detector line of sight as shown in figure 6.4. For alignment of samples we have

designed the sample stage, shown in figure 6.5, which consists of linear translational

stages and rotational stages having resolution of micron level and millidegree level

respectively. At the bottom there is a pair of linear translational XY stages on which

169


Figure 6.4: Diffracting lozenge as defined by incident and diffracted beam.

a rotational 2θ stage is mounted. This rotational 2θ stage has a detector arm attached

to it on which a pair of precision slit is mounted along with HPGe detector. The 2θ

arm is rotated with help of air pads. It is used to fix the scattering angle. On top

of this stage another θ rotational stage is mounted whose axis coincides with the 2θ

stage. The exact coincidence of 2θ and θ axis is necessary for accurate alignment of

the sample in EDXRD geometry. A set of linear translational stage i.e. xyz mounted

on top of the θ stage is used to maneuver the sample with respect to synchrotron

beam. For our high pressure experiments the diamond anvil cell is mounted on this

xyz stage. We have a provision for another rotational stage known as φ stage mounted

on top of xyz stage to align the single crystal samples in case of Laue x-ray diffraction.

Various components of EDXRD beamline has been aligned and the x-ray spot size at

the sample is kept at ∼ 100/200 µm depending upon the requirement. Using these

settings, and with Indus-2 operating at ∼ 2 GeV and 10 mA, we have recorded first set

of powder diffraction patterns of a few elemental metals for benchmarking purpose.

Some of these are shown in Figure 6.6. The energy resolution (∆E/E) of the detector

used, as reflected through the FWHM of the recorded fluorescence peaks, is 0.021 for

Au(Lα1) at 9.713 keV and 0.019 for Cu (Kα1) at 8.047 keV. These results show an

excellent signal to noise ratio of the recorded diffraction peaks.

170

6.4. A few studies at high pressures

Figure 6.5: Sample stage with DAC mounted on it.

6.4 A few studies at high pressures

Having aligned the beamline with respect to synchrotron radiation we have adopted

this beamline for high pressure studies using diamond anvil cell. For pressure mea-

surement we have developed an off line fluorescence based ruby pressure measurement

set up. In the following section I have presented a few high pressure studies carried

out on this beam line.

6.4.1 Natural uranium

Natural uranium is a very important reactor fuel material. Knowledge of its com-

pressibility behavior helps in designing the reactor fuel composition. It has also been

speculated to be a source of internal heating of our planets [280]. It crystallizes in

the orthorhombic structure (α-U) with space group Cmcm. We have performed high

pressure EDXRD experiments on natural uranium up to 25 GPa. For this, natural

171


(a) (b)

Figure 6.6: First diffraction pattern of (a) gold and (b)copper.

uranium sample along with a few specs of gold as a pressure marker was loaded in to a

pre indented tungsten gasket of thickness 80 µm with a hole diameter of 100 µm. Fig-

ure 6.7a represents the stacked diffraction pattern at a few representative pressures.

Its lattice parameter at ambient conditions a = 2.856 A, b = 5.876 A and c = 4.955

A are in excellent agreement with the earlier reported one [281]. Our measurements

show that α phase is stable up to the highest pressure studied and the observed P-V

data, fitted with third order B-M equation of state as shown in figure 6.8 gives its

bulk modulus and its derivatives as B0= 108 GPa and B′0= 6.2 respectively. These

values are in close agreement with the earlier reported experimental value [281].

6.4.2 Sesquioxides

The rare earth sesquioxides (RE2O3) are important materials from technological as

well as from basic physics point of view. These materials are applied in the fields

like data storage, cement additives, paints, coatings etc. From the physics point of

view their structural stability with pressure is still controversial. These materials

crystallize into three polymorphs with hexagonal (P3m1), monoclinic (C2/m) and

cubic (Ia3) structures. These are also known as A-type, B-type and C-type structures

172

6.4. A few studies at high pressures

(a)

(b)

Figure 6.7: (a) Stacked diffraction pattern of natural uranium at a few pressures; (b)equation of state of natural uranium, symbol represents the observed data and red line isB-M fit as per A. Lindbaum et al.

respectively [282].

The relative stabilities of these phases are understood in terms of the cationic

and anionic radius ratios [283]. A type phase is found to be stable from Lantahanum

(La) to Neodymium (Nd), B type from samaraium (Sm) to Gadolinium (Gd) and

C type phase for other rare earth sesquioxides. The decrease in molar volume has

been observed for sequence C to B to A. Earlier studies on Yb2O3 show discrepancies

about its transition from C to A [284]. To resolve this I have carried out high pressure

EDXRD studies on Yb2O3 up to ∼24 GPa. Figure 6.8 (a) shows the energy disper-

sive x-ray diffraction pattern of Yb2O3 stacked at few representative pressures. The

r letter in bracket alongside few pressures represents the diffraction pattern during

decompression. The x-ray diffraction peaks at ambient conditions marked as (hkl)

has been indexed to C-type cubic phase. The lattice parameter at ambient conditions

has been determined to be 10.433 A which is in close agreement with earlier reported

173


(a)

(b)

Figure 6.8: (a) EDXRD pattern of Yb2O3 at few representative pressures; (b) Pressureinduced variation of volume of phase A and phase C.

values. Up to 15.9 GPa the x-ray diffraction peaks shift towards higher energy values

values. Beyond this pressure new x-ray diffraction peaks appear indicating the emer-

gence of a new phase. At 24.1 GPa this phase could be indexed to A-type hexagonal

phase (P3m1)

The observed P-V variation was fitted with third order B-M equation of state for

C - phase and A - phase as shown in Figure 6.8 (b) where symbols represent the

observed data and solid lines are obtained from B-M fit.

6.5 Adaptation for high temperature studies

This beam line has been adapted for carrying out EDXRD studies at high tempera-

tures. A high temperature set up as shown in figure 6.9 has been mounted with help

of proper adapter plate on top of xyz stage of experimental station.

It has been installed an aligned with respect to synchrotron beam for carrying

out in-situ energy dispersive x-ray diffraction measurements by varying temperature.

174

6.5. Adaptation for high temperature studies

Figure 6.9: High temperature furnace installed at EDXRD beamline.

This set up consists of graphite heating element with the provision for mounting and

rotating the sample filled capillary inside evacuated/inert environment.

The heating element is mounted from the top lid of the water cooled chamber.

Sample is filled in quartz capillaries for temperature up to 800 ◦C and for higher tem-

peratures it is mounted on platinum wires. Temperature is controlled by Eurotherm

temperature controller. The temperature at the sample is monitored through K type

thermocouple. High temperature studies on standard samples like quartz has been

carried out to calibrate the high temperature set up.

175


176

Appendix A

Structure Determination

The basic principle of structure determination from XRD pattern has already been

introduced in chapter 1. Although single crystal XRD is more preferable for structure

determination of materials at ambient condition, however due to practical limitations

of this technique in case of experiments under high pressure and/or due to non avail-

ability of single crystal materials, the powder XRD becomes a preferred technique for

determination of crystal structure under high pressure. A powder x-ray diffraction

pattern contains a wealth of information to be extracted from it. Broadly speaking

a powder diffraction pattern constitutes two parts, one is background and another

is reflections/diffraction peaks. The background contains information about local

structure, amorphous fraction and lattice dynamics [285] along with Compton scat-

tering contribution to it. The diffraction peaks constitutes mainly three parts, its

position, intensity and profile which contain information about unit cell shape and

size, arrangement of atoms within unit cell and instrument broadening convoluted

with sample broadening respectively. Since the crystal structure determines diffrac-

tion pattern. Therefore it should be possible to go in the reverse direction and deduce

the structure with a given diffraction pattern.

The determination of an unknown crystal structure is accomplished in three major

177

Appendix A. Structure Determination

steps.

1. The shape and size of a unit cell is deduced from the positions of the diffraction

peaks. By making an assumption as to which of the seven crystal system the

unknown structure belongs to, the Miller indices are assigned and thus the

shape and size of the unit cell is deduced form the diffraction peaks. This step

is known as Indexing which has been discussed in detail in A1.

2. The number of atoms per unit cell is then calculated from the shape and size

of the unit cell, chemical formula unit of the sample and its measured density.

3. At last the positions of the atoms in the unit cell are deduced from the relative

intensities of the diffraction peaks

A.1 Indexing

For indexing a diffraction pattern the first step is to find out the accurate 2θ values

from it and then index the crystal system and unit cell dimensions. Each of the

diffraction peaks of a particular phase corresponds to reflection from a set of Brag

planes denoted by Miller indices (hkl). These are defined as set of integers inversely

proportional to the intercepts of crystal plane along the crystal axes. The interplanar

spacing dhkl measured at right angles to the planes is function of the plane indices

and the lattice constants (a, b, c, α, β, γ) and thus it depends on the crystal system

(shown in table A.1) involved. The dhkl’s for different crystal systems are given below.

Cubic1

d2=h2 + k2 + l2

a2(A.1)

Tetragonal1

d2=h2 + k2

a2+l2

c2(A.2)

178

A.1. Indexing

Table A.1: Lattice parameters for the seven crystal systems

Crystal System Lattice paramters

Triclinic a 6= b 6= c α 6= β 6= γMonoclinic a 6= b 6= c α = γ =90◦ 6= β

Orthorhombic a 6= b 6= c α = β = γ =90◦

Tetragonal a = b 6= c α = β = γ =90◦

Cubic a = b = c α = β = γ =90◦

Rhombohedral a = b = c α = β = γ 6= 90◦

Hexagonal a = b 6= c α = β =90◦, γ =120◦

Orthorhombic1

d2=h2

a2+k2

b2+l2

c2(A.3)

Hexagonal1

d2=

4

3

(h2 + hk + k2

a2

)+l2

c2(A.4)

Rhombohedral1

d2=

(h2 + k2 + l2) sin2 α + 2(hk + kl + hl) cos2 α− cosα

a20(1− 3 cos2 α + 2 cos3 α)

(A.5)

Monoclinic1

d2=

1

sin2 β

(h2

a2+k2 sin2 β

b2+l2

c2− 2hl cos β

ac

)(A.6)

Now consider the simplest case i.e. of cubic system Combining the Bragg equation

2dsinθ = λ with plane spacing equation A.1 we get

sin2 θ

h2 + k2 + l2=

sin2 θ

s=

λ2

4a2(A.7)

Since the sum (h2 + k2 + l2) is always integral and λ2/4a2 is a constant for any

pattern, hence the problem of indexing the pattern of a cubic material is equivalent

to finding a set of integers ’s’ such that these give constant quotient upon dividing

the various sin2θ values. Once the proper integers ’s’ are determined one can get the

set of h k l values such that sum of square of these numbers is equal to ’s’. For more

179


complex systems the computer algorithms with auto indexing program must be used.

There are many indexing programs available from http://www.ccp14.ac.uk such as

Dicovl91, Crysfire or Checkcell. One can input the peak positions and wavelength into

these programs and these will generate cell parameters. Subsequently, best possible

space group is chosen based on the extinction conditions observed.

A.2 Rietveld Refinement

In principle the powder XRD peaks should appear as delta function peaks for an ideal

crystal diffracted with perfectly collimated x-ray beam. Therefore one can accurately

determine the position and intensity of diffraction peaks. However, in practice these

peaks are broadened and shifted slightly due to other effects such as finite instru-

ment resolution, crystallite size, thermal motion, stress, strain, preferred orientation,

stacking faults and other imperfections. In order to determine the correct structure

these effects should be deconvoluted.

The intensity of a diffraction peak is proportional to the square of the structure

factor (Fhkl), defined as

Fhkl =N∑j=1

fj exp[2πi(hxj + kyj + lzj)] (A.8)

Where fj is atomic scattering factor of atom j and (xj, yj, zj) is its fractional coordi-

nates.

Rietveld refinement is a whole pattern fitting where least square method is used

to minimise the sum of square of the differences of observed and calculated intensities

over all data points in the diffraction pattern [286].

S =∑

w(Io − Ic)2 (A.9)

180

A.2. Rietveld Refinement

Here Io and Ic are observed and calculated intensities respectively while w is weight

factor per data point. I have used GSAS program [96] with a graphical interface called

EXPGUI [287] for Rietveld refinement of the diffraction pattern. As per this program

the calculated intensity of a diffraction peak is given by

Ic = Ib + Id + Sh∑

SphYph] (A.10)

Where Ib represents the contribution from the background and is modelled as an

empirical function, Id is an additional contribution to the background due to diffuse

scattering, Sh and Sph are scaling factors for a particular XRD powder profile (called

a histogram) and for a particular phase within that profile respectively. Yph is the

intensity of the bragg peak which is related with the square of the structure factor

given in equation (A.8)

Yph = |Fph|2H(T − Tph)Kph (A.11)

Where Fph = Fhkl is the structure factor for a particular reflection, H(T-Tph) is a

profile peak shape function and Kph is a product of various geometric and other

correction factors. It is given by

Kph =EphAhOphMpL

Vp(A.12)

Where Eph, Ah, Oph, Mp, L and Vp are extinction correction, absorption correction,

preferred orientation correction, reflection multiplicity, Lorentz polarisation correction

and unit cell volume for the phase respectively. The Oph becomes especially useful in

the analysis of high pressure powder diffraction data.

In order to extract the observed structure factor (Fo) from an experimental diffrac-

tion profile we use the LeBail method [288]. This is performed by setting all the

calculated structure factors Fc=1 and running the least square algorithm to extract

Fo. The set of Fo′s from the first cycle are then used as the Fc

′s for the next cycle

181


until a very good fit is observed. The lattice parameters and profile shape parameters

may also be refined at each step in this process, as these are not dependent on the

structure factor. The Le Bail method does not require detailed atomic arrangement

but only the knowledge of lattice parameters and space group which can be obtained

from indexing. The structure factors thus generated are then used in the Rietveld

refinement.

There are several possible profile function incorporated into GSAS. But we use

pseudo-voight [289] to describe the line shapes. It is a combination of Gaussian and

Lorentzian components having options for many refinable coefficients to adjust the

full width half maximum (FWHM), asymmetry parameters, Gaussian and lorentzian

fractions etc. For high pressure x-ray diffraction patterns it is advised not to use

many refinable parameters due to limited 2θ range of the pattern as well as large

background due to Compton scattering from diamond. In this case only the FWHM

of Gaussian and lorentzian components are refinable profile parameters.

Having done a good Le Bail refinement, the precise crystal structure is refined

using the Rietveld method. For fitting background scattering I have used Chebyshev

polynomial incorporated into GSAS program. These polynomials are a sequence of

orthogonal polynomials which are related to de Moivres formula. These provide an

approximation that is close to the polynomial of best approximation to a continuous

function and hence are useful for modelling the background function more robustly

in comparison to other functions.The atomic positions, fractional coordinates and

thermal motions can be refined using Rietveld refinement. The fraction of each phase

contributing to the diffraction pattern as well preferred orientation can also be refined

using Rietveld refinement method.

Finally the quality of the refined fit can be judged by visual inspection at the first

sight. In addition to this the agreement between the observed and calculated powder

182

A.2. Rietveld Refinement

patterns is judged by several indicators. The R-profile factors,

Rp =

∑ |Io − Ic|∑Io

andRwp =

√S∑WI2

o

(A.13)

characterise the adjustment between observed and calculated profiles at each in-

tensity steps. Rwp is one of the most important factors. The quality of the refined

structure model is better estimated with the R-structure factors, RB and RF , based

on the integrated intensity and structure factor amplitude of the reflections, respec-

tively. The factor RF is comparable to the R factor derived in structure determination

from single crystal diffraction.

RF =

∑ |Fo − Fc|∑Fo

andRwp =

√S∑WI2

o

(A.14)

Another parameter is Rexp =√

n−p∑WI2o

where n and p are number of data points

and number of variable parameters respectively. Another important parameter which

is used in GSAS is χ2 = (Rwp / Rexp)2. The χ2 should be close to unity for correct

refined model while its diverging values indicate the incorrect model and one has to

modify the initial model itself.

183


184

Appendix B

List of Publications

1. A.K. Mishra, Nandini Garg, K.K. Pandey, K.V. Shanavas, A.K. Tyagi and

Surinder M Sharma Zircon- monoclinic-scheelite transformation in nanocrys-

talline chroamtes, Phys. Rev. B 81, 104109, 2010.

2. A. K. Mishra, Shanavas K. V., Nandini Garg, H. K. Poswal Balaji Mandal and

surinder M. Sharma Pressure induced phase transitions in BiFeO3, Solid

State Commun.154, 72-76, 2013.

3. A. K. Mishra, H. K. Poswal, Surinder M Sharma, Surajit Saha, D. V. S.

Muthu, Surjeet Singh, R. Suryanarayanan, A. Revcolevschi, and A. K. Sood

The study of pressure induced structural phase transition in spin-

frustrated Yb2Ti2O7 pyrochlore, J. Appl. Phys. 111, 033509, 2012.

4. A.K. Mishra, Nandini Garg, K.V. Shanavas, S.N. Achary, A. K. Tyagi and

Surinder M. SharmaHigh pressure structural stability of BaLiF3, J. Appl.

Phys. 110, 123505, 2011.

5. A.K. Mishra, H.K. Poswal,S.N. Acharya, A.K. Tyagi and S.M. Sharma Struc-

tural evolution of double perovskites Sr2MgWO6 under high pressure,

Phys. Sattus Solidi B 247 (7), 1773-1777, 2010.

185

Appendix B. List of Publications

6. K.K. Pandey, H.K. Poswal, A.K. Mishra, Abhilash Dwivedi, R. Vasanthi, Nan-

dini Garg and Surinder M. Sharma Energy dispersive x-ray diffraction

beam line at Indus-2 Synchrotron source, Pramana 80, 607-619, 2013.

7. A.K. Mishra, Chitra Murli, A. Singhal and Surinder M. Sharma Pressure

induced phase transformation in U2O(PO4)2, J. Solid Chem. 181(5),

1240-1248, 2008.

8. Pallavi S Mallavi, S Karmakar, Debjani Karmakar, A. K. Mishra, H. Bhatt

,N. N. Patel, and Surinder M. Sharma High pressure structural and vibra-

tional properties of the spin-gap system Cu2PO4 (OH) J.Phys.:Condens

Matter 25, 045402, 2013.

9. Chitra Murli, A. K. Mishra, Susy Thomas and Surinder M. Sharma Ring open-

ing polymerization in carnosine under pressure, J. Phys. Chem. B 116,

4671-4676, 2012.

10. A.K. Mishra, Chitra Murli, Nandini Garg, R. Chitra and Surinder M Sharma

Pressure induced structural transformations in Bis (glycinium) ox-

alate,J. Phys. Chem. B 114, 17084-17091, 2010.

11. A. K Mishra, Chitra Murli and Surinder M SharmaHigh Pressure Raman

spectroscopic study of deuterated γ- glycine, J. Phys. Chem. B 112(49),

15867-15874 , 2008.

12. A.K. Mishra, Nandini Garg, K.K. Pandey, Vineet Singh and Surinder M Sharma

Effect of the surfactant CTAB on the high pressure behavior of CdS

nano particles, J. Phys. : Conference Series 377, 012012, 2012.

13. K. K. Pandey, Nandini Garg, A. K. Mishra and Surimder M. Sharma High

pressure phase transition in Nd2O3, J. Phys. : Conference Series 377,

012006, 2012.

186

14. A. K. Mishra, Chitra Murli, Ashok K. Verma, Yango Song, M. R. Suresh Ku-

mar,and Surinder M. Sharma Conformation and hydrogen bond assisted

polymerisation in glycine lithium sulphate, C ommunicated to J. Phys.

Chem B.

15. A. K. Mishra, H. K. Poswal, Surinder M. Sharma and A. Revcolevschi and A

K Sood Lattice instability in Dy2Ti2O7 at high pressures, to be commu-

nicated to J. Phys.:Condens Matter.

16. A. K. Mishra, Nandini Garg, A. K. Tyagi and Surinder M. Sharma Structural

phase transitions in LiErF4, to be communicated to Phys. Rev. B.

187

Appendix B. List of Publications

188

References

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