Vibrational spectra and factor group analysis of Mn(0.5+x)Ti(2−2x)Cr2x(PO4)3 {0≤x≤0.50}

Accepted Manuscript

Title Vibrational spectra and factor-group analysis of doublearsenates of zirconium and alkali metal MZr2(AsO4)3 (M =LindashCs)

Author EYu Borovikova VS Kurazhkovskaya KNBoldyrev MV Sukhanov VI Petrsquokov SA Kokarev

PII S0924-2031(14)00103-9DOI httpdxdoiorgdoi101016jvibspec201406004Reference VIBSPE 2361

To appear in VIBSPE

Received date 5-12-2013Revised date 17-6-2014Accepted date 17-6-2014

Please cite this article as EYu Borovikova VS Kurazhkovskaya KN Boldyrev MVSukhanov VI Petrsquokov SA Kokarev Vibrational spectra and factor-group analysisof double arsenates of zirconium and alkali metal MZr2(AsO4)3 (M = LindashCs)Vibrational Spectroscopy (2014) httpdxdoiorg101016jvibspec201406004

This is a PDF file of an unedited manuscript that has been accepted for publicationAs a service to our customers we are providing this early version of the manuscriptThe manuscript will undergo copyediting typesetting and review of the resulting proofbefore it is published in its final form Please note that during the production processerrors may be discovered which could affect the content and all legal disclaimers thatapply to the journal pertain

of 19

Accep

ted

Man

uscr

ipt

1

Vibrational spectra and factor-group analysis of double arsenates of

zirconium and alkali metal MZr2(AsO4)3 (M = Li ndash Cs)

EYu Borovikovaa

VS Kurazhkovskayaa KN Boldyrev

b MV Sukhanov

c

VI Petrsquokovc SA Kokarev

a

a Department of Crystallography and Crystal Chemistry Moscow State University Moscow

119991 GSP-1 Russia

b Institute of Spectroscopy RAS Fizicheskaya st 5 Troitsk 142190 Moscow Russia

c Department of Chemistry Lobachevsky State University of Nizhni Novgorod pr Gagarina 23

603950 Nizhni Novgorod Russia

Abstract

Complex phosphates and arsenates of alkali metal and zirconium with NASICON and Sc(WO4)3

structures are fast ion conductors In this context double arsenates MZr2(AsO4)3 where M = Li

Na K Rb and Cs have been synthesised as powders through a precipitation method and

investigated by Raman and infrared spectroscopy in combination with factor-group analysis to

assign the bands The stretching and bending vibrations of the AsO43-

units and external modes

as well as the Zr4+

and M+ (Li ndash Cs) translations have been determined for these compounds

which crystallised in the cR3 (D3d6) and P1121n (C2h

5) space groups (LiZr2(AsO4)3) The

correlations between the spectra and the nature of the M+ cation are revealed Some external

modes were identified by studying mass effects (Zr ndash Hf Na ndash Cs) The bands for the

symmetrical bending vibrations of the AsO43-

units and some of the external modes shift toward

higher wavenumbers with the increasing size of the alkaline cations due to the predominant

direction of these vibrations and translations along the a axis the M+ cation size increases as

much as parameter a decreases The differences observed in the vibrational spectra of the

arsenates containing alkaline elements and zirconium with different space groups are caused by

the reduced symmetry

Keywords Raman and infrared spectra Factor group analysis NASICON

Corresponding author Tel +7(495)9392330 Fax +7(495)9395575

E-mail address amurrmailru (EYu Borovikova)

Page 2 of 19

Accep

ted

Man

uscr

ipt

2

1 Introduction

Complex orthophosphates of zirconium and alkali metal with the general formulae

MZr2(PO4)3 crystallise in a kosnarite (KZr2(PO4))-type structure [1] The synthetic analogue of

this mineral is sodium zirconium phosphate NaZr2(PO4)3 (NASICON ndash Na super ionic

conductor) [2] which has an ionic conductivity of σ300Cordm = 0210-1

(Ω cm)-1

[3] The NASICON-

type structure is built from (O3ZrO3M+(Na))O3ZrO3)infin columns along the c-axis that are

connected through PO4 tetrahedra along the a-axis These compounds generate considerable

interest due to their fast ion conduction [4-5] Studies involving their stability under extreme

conditions including high temperatures pressures radiation fields and aggressive chemical

media and the possibility of combining different useful properties in one compound are of

particular interest

The structures of lithium phosphate LiZr2(PO4)3 are related to two different structural

types NASICON ( cR3 space group) and Sc2(WO4)3 (P1121n space group) [6] The ionic

conductivities of these compounds are high in all cases (σ300Cordm = 1210-2

(Ω cm)-1

for the

rhombohedral phase and σ300Cordm = 510-4

(Ω cm)-1

) [6] The structural types of NASICON and

Sc2(WO4)3 are closely related they contain similar [Zr2(PO4)3]minus1

3infin frameworks However the

space orientation of the polyhedra changes relative to the symmetry of the phases

In contrast to the extensive studies of NASICON- and Sc2(WO4)3-type phosphates only a

few structural studies are reported for the arsenate analogues [7 8] The structure of

KZr2(AsO4)3 was determined from single-crystal X-ray diffraction data [7] and the structure of

NaZr2(AsO4)3 was solved using the Rietveld method [8] NaZr2(AsO4)3 has been studied using

vibrational spectroscopy [8]

The present paper reports the synthesis and investigation of arsenates with the general

formula of MZr2(AsO4)3 where M = Li Na K Rb or Cs through Raman and IR spectroscopy

using factor group analysis In general the exact vibrational bands assignment requires the

oriented single-crystal measurements or DFT calculations In this case double arsenates

MZr2(AsO4)3 were synthesised as powders For the crystal structures of these compounds it is

relatively difficult to do the DFT calculations because of the great number of atoms in the unit

cell The unit cell contains 108 atoms for the rhombohedral structure and 72 for monoclinic one

As for the factor group analysis it provides information on the number of bands and their

approximate location on the energy scale that is sufficient to identify the two structures and their

comparative analysis

2 Experimental

Page 3 of 19

Accep

ted

Man

uscr

ipt

3

The MZr2(AsO4)3 (M = Li Na K Rb or Cs) compounds were synthesised using a

precipitation method The reagents included MNO3 ZrOCl2middot8H2O and H3AsO4 Stoichiometric

amounts of aqueous 1 M MNO3 and zirconium oxychloride (ZrOCl2) were mixed Afterwards a

stoichiometric amount of 05 M arsenic acid was added with stirring and heating The arsenic

acid solution was prepared by dissolving elemental arsenic in a 11 mixture (by volume) of nitric

and hydrochloric acids with heating The reaction mixtures were dried at 90 and 270degC before

being thermally treated at 600 and 850minus950degC The thermal treatment stages were alternated

with careful grinding

The samples obtained were colourless polycrystalline powders The identity of the

desired compounds was confirmed on a Shimadzu XRD-6000 powder X-ray diffractometer over

a 2θ range of 10ndash60deg A Cu anode (30 mA and 30 kV) with filtered monochromatic Kα radiation

(λ = 154178 Aring) was used during the measurements The X-ray patterns of the samples contained

only reflections of the desired arsenates No reflections were assigned to the other compounds

The homogeneity and chemical composition of the samples were assessed through an

electron microprobe analysis on a CamScan MV-2300 device with a Link Inca Energy 200C

energy-dispersion detector operated at 200 kV revealing the homogeneity of the synthesised

samples The microprobe analysis confirmed that the stoichiometry of the samples was close to

the theoretical compositions

The infrared spectra of the synthesised compounds were obtained on an FSM 12011 FT-

IR spectrometer on KBr discs from 4000 to 400 cm-1

The spectral resolution was approximately

2 cm-1

The transmission spectra in the mid-IR were studied by forming a tablet with the sample

mixed with dry KBr powder The ratio of KBr to the sample was 5001 by weight (1 mg sample

to 500 mg KBr) The resulting powder was subsequently pressed at 5 tons in a Specac mould

(13-mm diameter) Concurrently the mould was heated to approximately 150degC to exclude

water The IR transmission spectra spanning 550ndash50 cm-1

were measured on an FT-IR

spectrometer (Bruker IFS 125 HR) with a spectral resolution up to 1 cm-1

For the far-infrared

measurements we used specially prepared pure polyethylene powder For the PE tablets we used

standard 13 mm press-form with the pressure of 2 tons at ambient conditions The ratio of PE to

the sample was 201 by weight (25 mg sample to 50 mg PE) Larger samples were used for the

measurements in the far-IR region due to the greater transparency of the sample in this spectral

region and the weaker phonon intensities

The Raman spectra of the powdered samples were obtained on a dispersive Raman

microscope (Bruker Senterra) with laser excitation at 532 nm The spectral resolution for the

Raman measurements was 3 cm-1

Page 4 of 19

Accep

ted

Man

uscr

ipt

4

3 Structural information

The sodium zirconium phosphate and arsenate form a hexagonal crystal structure with a

cR3 (Z = 6) space group [2 8] The crystal structure can be described as a network formed by

the corner sharing PO4 tetrahedra and ZrO6 octahedra The basic unit of the framework consists

of two ZrO6 octahedra joined by three PO4 tetrahedra These units are connected forming a

ribbon along the с axis The interstitial M1 (6b) sites are located between the two ZrO6 octahedra

along the c axis and have a distorted octahedral coordination The site symmetry is S6 ( 3 ) In

NaZr2(PO4)3 the Na ions fully occupy the M1 (6b) sites The structure of NaZr2(AsO4)3 is

similar to that of NaZr2(PO4)3 [8] The M2 sites are located between the ribbons in large cavities

with eight-fold coordination In NaZr2(AsO4)3 these positions are empty The arsenic atoms

occupy 18e sites and the site symmetry is C2 (2) The chemical formula of the crystals can be

written as follows [M1VI

][M2VIII

]3Zr2[XIV

]3O12 where X = P As

In the structure of the monoclinic modified LiZr2(PO4)3 the basic units of the framework

consist of two ZrO6 octahedra and three PO4 tetrahedra These fragments are similar to those

found in the NASICON-type structure but the arrangement of the units is different The

structure of LiZr2(PO4)3 with the P1121n space group contains alternating slabs with units

rotated on 71deg relative to each other The Li+ ions are tetrahedrally coordinated filling the voids

inside the structure and compensating for the negative charge Three distorted independent PO43-

tetrahedra can be observed in the LiZr2(PO4)3 structure with a P1121n space group The site

symmetry is C1 (1) for all of the polyhedra

4 Factor group analysis

Compounds with different space groups are expected to generate different types of

Raman- and infrared-active bands The vibrations of an isolated AsO43-

anion with a point

symmetry group Td include one A1 mode (ν1 ndash symmetrical stretching mode of AsO43-

unit) one

E mode (ν2 ndashsymmetrical bending mode of AsO43-

unit) and two F2 modes (ν3 ndashasymmetrical

stretching and ν4 ndash asymmetrical bending modes of AsO43-

unit) All of these signals are Raman-

active and only the ν3 and ν4 vibrations are infrared-active When assuming that the vibrations

are separated into internal and external modes a factor-group analysis generates six Raman-

active (ν1 ndash A1g + Eg ν3 - A1g + 3Eg) and six infrared-active (ν1 ndash Eu ν3 ndash 2A2u + 3Eu) stretching

vibrations for the AsO43-

unit as well as eight Raman-active (ν2 ndash 2A1g + 2Eg ν4 - A1g + 3Eg) and

seven infrared-active (ν2 ndash 2Eu ν4 ndash 2A2u + 3Eu) bending vibrations of the AsO43-

unit for

compounds with a NASICON-type structure ( cR3 space group factor group D3d) [9] (Table 1)

Page 5 of 19

Accep

ted

Man

uscr

ipt

5

LiZr2(AsO4)3 has the P1121n space group and the C2h factor group the arsenic atoms occupy

sites with C1 symmetry (1) Therefore eight Raman-active (ν1 ndash Ag + Bg ν3 - 3Ag + 3Bg) and

eight infrared-active (ν1 ndash Au + Bu ν3 ndash 3Au + 3Bu) stretching vibrations are expected for the

AsO43-

unit For the bending vibrations of the AsO43-

unit ten Raman-active (ν2 ndash 2Ag + 2Bg ν4 -

3Ag + 3Bg) and ten infrared-active (ν2 ndash 2Au + 2Bu ν4 ndash 3Au + 3Bu) modes are expected (Table 1)

In the structure of LiZr2(AsO4)3 which has a P1121n space group the arsenic atoms occupy

three independent positions with C1 site symmetry (1) Consequently the amounts of Raman-

and infrared-active modes in each spectral region increase three-fold

The external modes include the translational modes of MI (M ndash Li ndash Cs) Zr and AsO4

3- ions

and the AsO43-

librations A group theoretical analysis leads to the following results

MZr2(AsO4)3 (factor group D3d)

AsO43-

translations Гт (AsO4) = A1g (Ra) + 2 A2g + 3 Eg (Ra) + A1u + 2 A2u (IR) + 3Eu (IR)

(position C2)

M+ translations Гт (M

+) = A1u + A2u (IR) + 2 Eu (IR) (position S6)

Zr4+

translations Гт (Zr4+

) = A1g (Ra) + 2 A2g + 2 Eg (Ra) + A1u + A2u (IR) + 2 Eu (IR)

(position C3)

AsO43-

librations Гlib = A1g (Ra) + 2 A2g + 3 Eg (Ra) + A1u + 2 A2u (IR) + 3Eu (IR)

The sum of the external modes (after subtracting the acoustical modes (A2u + Eu) Raman

active- 3 A1g + 8 Eg infrared active - 5 A2u + 9 Eu

LiZr2(AsO4)3 (factor group C2h)

AsO43-

translations Гт (AsO4) = 9 Ag + 9 Bg + 9 Au + 9 Bu (three positions C1)

M+ translations Гт (Li) = 3 Ag + 3 Bg + 3 Au + 3 Bu (position C1)

Zr4+


) = 6 Ag + 6 Bg + 6 Au + 6 Bu (two positions C1)

AsO43-

librations Гlib = 9 Ag + 9 Bg + 9 Au + 9 Bu (three positions C1)

After subtracting the acoustical modes (Au + Bu) the sum of the external modes is 27Ag +

27Bg (Raman active) and 26Au + 26 Bu (infrared active)

5 Results and discussion

51 AsO43-

stretching vibrations

Tables 2 and 3 lists the Raman and IR spectral assignments for the synthesised compounds

from 1080ndash50 cm-1

The spectra are shown in Figs 1minus3 Notably the wavenumbers of the ν3

vibrational bands in the Raman spectra are 980 and 950 cm-1

in the IR spectrum this value is

close to 1080 cm-1

Such high values are quite uncommon for arsenates In this case the

polarising nature of the metal ion (Zr4+

) may have generated this result A portion of the electron

density of the highly charged and small Zr4+

cation is localised in the AsndashO bond Consequently

Page 6 of 19

Accep

ted

Man

uscr

ipt

6

this bond is polarised therefore the force constants and the frequency increase [10] These bands

can be treated as AsndashOMndashO interaction bands

511 Raman spectra

Two slightly different types of Raman spectra are observed depending on the space group

of the compounds (Fig 1) The spectra of the arsenates with the cR3 space group remain

essentially the same regardless of the alkaline cation (Fig 1 a - e) In these spectra the AsO43-

stretching vibrations appear with two bands as the strongest signals (~860 and 850 cm-1

) two

weaker bands at higher wavenumbers (~980 and 950 cm-1

) and one weak band (~840 cm-1

)

Factor group analysis predicts generation of four ν3 and two ν1 Ramanndashactive stretching

vibrations by site and correlation splittings The asymmetrical stretching vibrations are observed

at higher wavenumbers relative to the symmetrical ones Therefore the bands at ~850 840 cm-1

are assigned to ν1 and the bands from 980minus860 cm-1

are assigned to components of the ν3

vibrations of the AsO43-

units Therefore the bands for the ν3 and ν1 vibrations overlap in the

region containing strong signals Their frequency is slightly lower in the spectrum for

CsZr2(AsO4)3 compared to the other spectra which is attributed to the larger size of the Cs+

When decreasing the ionic radius of the alkali metal cation two strong bands gradually approach

each other and in the Raman spectrum of LiZr2(AsO4)3 the band at 857 cm-1

becomes a

shoulder on the side of the band at 864 cm-1

The Raman spectrum of the monoclinic LiZr2(AsO4)3 differs from those of the phases

with the cR3 space group (Fig 1 f) The stretching vibrations for the AsO43-

units produce three

high frequency bands (976 953 and 938 cm-1

) two strong bands (869 and 854 cm-1

) two

shoulders (876 and 848 cm-1

) and two weak bands (820 and 805 cm-1

) The last four bands (854

848 820 and 805 cm-1

) from the six modes which are allowed by the group-theoretical analysis

for ν1 vibrations could arise from symmetrical stretching vibrations The bands from 980ndash860

cm-1

can be assigned to the components of ν3 Due to the proximity and partial overlap of

numerous stretching vibrations the observed number of the signals in this region is lower than is

allowed by the selection rules

512 Infrared spectra

The IR spectra of the compounds with the cR3 space group exhibit four to five bands

from the 1080ndash835 cm-1

region of the six predicted by group theory for the stretching vibrations

of these phases (Fig 2 a-e) The band with the lowest wavenumber (~850minus835 cm-1

) is related

to the symmetrical stretching vibrations of the AsO43-

unit Bands with higher wavenumbers

Page 7 of 19

Accep

ted

Man

uscr

ipt

7

were assigned to the components of ν3 In the high-frequency region of the IR spectra (1080 ndash

945 cm-1

) either two or three bands were observed that seemed to depend on the Zr4+

and M+

cations equally These bands shift toward lower wavenumbers when increasing the size of the

alkaline cation and the intensity of these bands decreases 956 (Li) rarr 946 cm-1

(Cs) 1018 (Li)

rarr 1005 cm-1

(Cs) The first band turns into a shoulder in the KZr2(AsO4)3 spectrum while the

second becomes a shoulder in the CsZr2(AsO4)3 spectrum The band with the highest frequency

(~1080 cm-1

) was observed in the LiZr2(AsO4)3 and KZr2(AsO4)3 spectra When increasing the

size of the alkaline cation the strong bands at 870 and 850 cm-1

for NaZr2(AsO4)3 shift toward

lower wavenumbers 870 rarr 851 cm-1

850 rarr 836 cm-1

(in IR spectra of CsZr2(AsO4)3)

In the infrared spectrum of LiZr2(AsO4)3 with a P1121n space group the stretching

vibrations of the AsO4 unit produce nine bands in the 1107ndash800 cm-1

region The number of

bands is increased relative to the rhombohedral LiZr2(AsO4)3 spectrum The high frequency

bands (1018 and 956 cm-1

) split into band doublets The three bands at 848 827 and 807 cm-1

might arise from the ν1 symmetrical stretching vibrations The theoretically predicted vibrations

with similar vibrational energies may appear very near one another Therefore fewer bands are

observed in the spectra than is expected from the factor-group analysis

52 AsO43-

bending vibrations

521 Raman spectra

The asymmetrical bending (ν4) vibrations of the AsO43-

units can be identified as two

bands in the 470ndash435 cm-1

region (Fig 1 a-e) by using the analogous Raman spectra for the

corresponding phosphates which show two weak bands for the ν4 vibrations of the PO43-

units


[9] One strong band and one or two weaker bands are observed from 380ndash

340 cm-1

These bands are components of ν2 (Fig 1 andashe) The general trend (that is the

frequency of the internal and external modes decreases when the cation ionic radius increases)

[11] is verified for the strong band (~340 cm-1

) in the NaZr(AsO4)3 spectrum which shifts

toward higher wavenumbers when increasing the ionic radius of the alkali metal cation 340 cm-1

(Na) rarr 358 cm-1

(K) rarr 370 cm-1

(Rb) rarr 383 cm-1

(Cs) For some other bands the progression

is as follows 359 cm-1

(Li) rarr 363 cm-1

(Na) rarr 381 cm-1

(K) 380 cm-1

(Li) rarr 389 cm-1

(Na)

Parameter c is highly sensitive toward increases in the size of the alkali metal cation Increase of

the alkali metal cation radii results in significant increase of parameter c and a slight decrease of

parameter a [2] The vibrations at 389 363 and 340 cm-1

in the Raman spectrum of

NaZr2(AsO4)3 are assumed to have a predominant component along the a axis In the Raman

spectra of MZr2(PO4)3 (M ndash Na ndash Cs) the bands for the ν2 vibrations of the PO43-

units

underwent a similar shift [9]

Page 8 of 19

Accep

ted

Man

uscr

ipt

8

The Raman spectrum of LiZr2(AsO4)3 with a P1121n (C2h5) space group does not differ

significantly from the spectrum of the rhombohedral phase (Fig 1 f)


The region between 490ndash350 cm-1

of the infrared spectra of the arsenates with the cR3

(D3d6) space group contains three to five signals that can be related to bending vibrations of the

AsO43-

unit (Fig 3 a - e) The low intensity of the ν2 vibrations is expected explaining why the

band at ~310 - 300 cm-1

cannot be a component of ν2 The frequency of the two bands at ~375ndash

350 cm-1

increases slightly with the size of M+ 369 cm

-1 (Na) rarr 371 cm

-1 (K) rarr 375 cm

-1

(Rb) rarr 377 cm-1

(Cs) 348 cm-1

(K) rarr 351 cm-1

(Rb) rarr 357 cm-1

(Cs) These vibrations are

assumed to have a predominant component along the a axis and to be related to ν2 These ν2

vibrations agree closely with those derived using the group theoretical analysis

The asymmetrical bending (ν4) vibrations can be identified through the two to three bands


of five modes predicted by the factor-group analysis This region in the

NaZr2(AsO4)3 spectrum contains one strong signal at 483 cm-1

and one weak band at 406 cm-1

In

the spectra of the arsenates with Li and large alkaline cations (K Rb Cs) doublets (494 467 cm-

1 (Li) 493 468 cm

-1 (K)) appear instead of one intense band For these two bands and the

additional band at 406 cm-1

(Na) a small decrease in the frequency is observed when the ionic

radius of the cation increases 494 cm-1

(Li) rarr 493 cm-1

(K) rarr 491 cm-1

(Rb) rarr 487 cm-1

(Cs)

467 cm-1

(Li) rarr 468 cm-1

(K) rarr 465 cm-1

(Rb)rarr 462 cm-1

(Cs) 406 cm-1

(Na) rarr 396 cm-1

(K) rarr 391 cm-1

(Rb)

As expected from the correlation analysis the monoclinic phase generates a more

complex IR pattern than the rhombohedral ones (Fig 3f) The six bands from the 506ndash400 cm-1

region correspond to the asymmetrical bending vibrations of the AsO43-

unit The band at ~355

cm-1

and two shoulders (378 and 344 cm-1

) are the symmetrical bending vibration of AsO43-

53 External modes

531 MIV

translations

Authors [9] interpret Raman band at 265 cm-1

of KZr2(PO4)3 compound as translation

vibrations of Zr4+

Analogously we interpret weak bands at ~253 237 cm-1

in Raman spectra of

isostructural arsenates as related to Zr4+

translation (Fig 1 a - e) In the Raman spectrum of the

LiZr2(AsO4)3 with the P1121n space group three bands at ~269 256 and 230 cm-1

can be

related to Zr4+

translations

Page 9 of 19

Accep

ted

Man

uscr

ipt

9

The infrared spectra of the corresponding Zr and Hf compounds (NaZr2(AsO4)3 and

NaHf2(AsO4)3) show that the three bands (313 290 and 217 cm-1

) in the zirconium compound

spectrum exhibit an obvious Hf ndash Zr mass effect 313 rarr 309 290 rarr 280 217 rarr 199 cm-1

These bands can be assigned to Zr4+

translations (Figs 3 4)

532 M+ translations

The lowest lying bands in the infrared spectra are observed at 93 cm-1

for Na 71 cm-1

for

K 52 cm-1

for Rb and 49 cm-1

for Cs These bands exhibit an obvious Na ndash K ndash Rb ndash Cs mass

effect and must be assigned to translations of the monovalent cations The KZr2(AsO4)3 spectrum

shows three bands in these regions as predicted for M+ translations 84 cm

-1 (K) rarr 65 cm

-1

(Rb) 93 cm-1

(Na) rarr 71 cm-1

(K) rarr 52 cm-1

(Rb) rarr 49 cm-1

(Cs) and 75 cm-1

(Na) rarr 60 cm-1

(K) The wavenumber (93 cm-1

) for Li+ translations is too low because Li

+ occupies an atypically

large polyhedron M1 (6b) in the structure

533 AsO43-

translations and librations

These modes are characterised by their low frequency and lack of a mass effect for the

M4+

and M+ The detailed assignment of these modes is difficult due to the larger amount of

predicted modes compared to the low number of observed bands in the spectra The bands in the

infrared spectra from 220ndash90 cm-1

exhibit no Na ndash Cs and Zr ndash Hf mass effects and can be

assigned to a motion of the AsO43-

units

The band at 182 cm-1

in the IR spectrum of NaZr2(AsO4)3 shifts toward higher

wavenumbers when increasing the ionic radius of the M+ 182 cm

-1 (Na) rarr 189 cm

-1 (K) rarr 191

cm-1

(Rb) rarr 197 cm-1

(Cs) These vibrations are directed along the a axis which decreases when

the radius of the M+ cation increases

6 Conclusions

The double arsenates MZr2(AsO4)3 where M = Li Na K Rb or Cs with a structure

analogous to NASICON NaZr2(PO4)3 and LiZr2(AsO4)3 with a structure analogous to Sc2(WO4)3

were synthesised using a precipitation method and were characterised through Raman and

infrared spectroscopy A factor-group analysis for these compounds crystallising in the

cR3 (D3d6) and P1121n (C2h

5) space groups was performed The stretching and bending


units and external modes (Zr4+

and M+

translations) were assigned

The differences observed in the region containing the stretching vibrations in the infrared

and Raman spectra of the arsenates of alkaline elements and zirconium with different space

groups have been explained by a reduction in symmetry Five vibrational stretching modes for

Page 10 of 19

Accep

ted

Man

uscr

ipt

10

AsO43-

units in the Raman and IR spectra of the arsenates with cR3 (D3d6) space groups

are

observed of the six predicted by factor-group analysis The number of the bands increases to nine

in the Raman and IR spectra of the monoclinic phase The bands at 1018 and 950 cm-1

split into

two bands in the IR spectrum of LiZr2AsO4 with a P1121n (C2h5) space group Three ν1 bands

for the AsO43-

units appear in this spectrum

Two asymmetrical bending vibrations for AsO43-

units are observed in the Raman spectra

of the rhombohedral compounds of the five allowed by the selection rules and three bands are

apparent for the ν4 vibrations of AsO43-

units in the IR spectra of the five predicted by factor-

group analysis The number of symmetrical bending vibrational modes in the Raman spectra of

the arsenates with the cR3 (D3d6) space group increases to four These modes correspond well to

those derived by group theoretical analysis In the infrared spectra two bands for the ν2

vibrations are observed of the four that are allowed by the correlation analysis In the IR spectra

three Zr4+

and three M

+ (Li ndash Cs) translational bands are observed in accordance with the

predictions of factor-group analysis

The frequency of the ν2 vibrational bands of the AsO43-

units in the Raman and IR

spectra of one band corresponding to Zr4+

translation and one AsO43-

external mode in the IR

spectra increases when increasing the radius of the ionic alkali metal These vibrations and

translations have a predominant component along the a axis which decreases when the c axis

stretches

Acknowledgements

This work was carried out with the financial support of the Russian Foundation for Basic

Research (Project No 11-03-00032) Moscow Russia

Page 11 of 19

Accep

ted

Man

uscr

ipt

11

References

[1] M E Brownfield E E Food S J Sutley T Botinelly Am Min 78 (1993) 653

[2] HY-P Hong Mater Res Bull 11 (1976) 173

[3] J B Goodenough HYP Hong JA Kafales Mat Res Bull 11 (1976) 203

[4] C Delmas A Nadiri JL Soubeyroux Solid State Ionics 28 ndash 30 (1988) 419

[5] P Padma Kumar S Yashonath Journal of Chemical Sciences 118 (2006) 135

[6] F Sudreau D Petit and J P Boilot Solid State Chem 83 (1989) 78

[7] M El Brahimi J Durand Z Anorg Allg Chem 584 (1990) 178

[8] M Chakir A El Jazouli D De Wall Mat Res Bull 38 (2003) 1773

[9] P Tarte A Rulmont C Merckaert-Ansay Spectrochim Acta 42A (1986) 1009

[10] M Sugantha U V Varadaraju GV Subba Rao J Solid State Chem 111 (1994) 33

[11] VS Farmer (Ed) Infrared Spectra of Minerals Mineral Society London Adlard and Son

Ltd 1974 pp 278-279

Page 12 of 19

Accep

ted

Man

uscr

ipt

12

Figure captions

Fig 1 Raman spectra of MZr2(AsO4)3 (a) M = Cs (b) M = Rb (c) M = K (d) M = Na (e) M =

Li ( cR3 (D3d6) space group) (f) M = Li (P1121n (C2h

5) space group)

Fig 2 Mid-infrared absorption spectra of MZr2(AsO4)3 (a) M = Cs (b) M = Rb (c) M = K (d)

M = Na (e) M = Li ( cR3 (D3d6) space group) (f) M = Li (P1121n (C2h

5) space group)

Fig 3 Far-infrared absorption spectra of MZr2(AsO4)3 (a) M = Cs (b) M = Rb (c) M = K (d)


5) space group)

Fig 4 Far-infrared absorption spectrum of NaHf2(AsO4)3

Page 13 of 19

Accep

ted

Man

uscr

ipt

Table 1 Internal modes of tetrahedral ion AsO43-

in M+ Zr2(AsO4)3 where M

+ - Li - Cs with

space groups cR3 (D3d6) Z = 6 and P1121n (C2h

5) Z = 4 for LiZr2(AsO4)3

Vibrations AsO 3

4 unit Point group Td Site group C2 Factor group D3d

1 A1 A A1g + Eg + A1u + Eu

2 E 2A 2A1g + 2Eg + 2A1u + 2Eu

3 4 F2 A + 2B A1g + 2A2g + 3Eg +

A1u + 2A2u +3Eu

Vibrations AsO 3

4 unit Point group Td Site group C1 Factor group C2h

1 A1 A Ag + Bg + Au + Bu

2 E 2A 2Ag + 2Bg + 2Au + 2Bu

3 4 F2 3A 3Ag + 3Bg + 3Au + 3Bu

Tables 1-3

Page 14 of 19

Accep

ted

Man

uscr

ipt

Table 2 The assignments of vibrational modes of MZr2(AsO4)3 where M = Li minus Cs with the

space group cR3 (D3d6)

Assignment Wavenumber cm-1

Li Na K Rb Cs

Ra IR Ra IR Ra IR Ra IR Ra IR

ν3 1084 1080

979 1018 979 1017 982 1017 981 1011 977 1005

951 956 948 955 949 954 sh 948 951 sh 943 946 sh

864 870 863 872 862 868 862 859 859 851

ν1 857 849 856 852 857 847 853 845 846 836

838 837 842 842 837

ν4 494 483 493 491 487

473 467 472 468 468 471 465 471 462

445 446 437 435 434

406 396 391

ν2 380 377 389

359 359 363 369 381 371 375 377

346

333 340 358 348 370 351 383 357

TZr4+

310 313 308 303 298

290 288

253 256 255 255 254

241 217 237 223 238 231 237 238

TAsO4

+

Lib AsO4

189 187 182 189 191 197

176 173

158 141

129 129 133 129 131

119

96

89

TM+ 84 65

93 93 71 52 49

75 60

Page 15 of 19

Accep

ted

Man

uscr

ipt

Table 3 The assignments of vibrational modes of LiZr2(AsO4)3 with the space group P1121n

(C2h5)

Assignment Wavenumber (cm-1

) Assignment

Wavenumber (cm-1

)

Ra IR Ra IR

ν3 1107 ν2 388

1027 364 378

1006 354 354

976 344

953 954 336

938 935 TZr4+

+

TAsO4

297

876 286

869 883 269

ν1 854 256

848 848 230 241

820 827

805 807 TAsO4

+

Lib AsO4

194

ν4 506 178

496 126

474 476

455

430 434

400

Page 16 of 19

Accep

ted

Man

uscr

ipt

Figure 1

Page 17 of 19

Accep

ted

Man

uscr

ipt

Figure 2 edited

Page 18 of 19

Accep

ted

Man

uscr

ipt

Figure 3

Page 19 of 19

Accep

ted

Man

uscr

ipt

Figure 4

of 19

Accep

ted

Man

uscr

ipt

1

Vibrational spectra and factor-group analysis of double arsenates of

zirconium and alkali metal MZr2(AsO4)3 (M = Li ndash Cs)

EYu Borovikovaa

VS Kurazhkovskayaa KN Boldyrev

b MV Sukhanov

c

VI Petrsquokovc SA Kokarev

a

a Department of Crystallography and Crystal Chemistry Moscow State University Moscow

119991 GSP-1 Russia

b Institute of Spectroscopy RAS Fizicheskaya st 5 Troitsk 142190 Moscow Russia

c Department of Chemistry Lobachevsky State University of Nizhni Novgorod pr Gagarina 23

603950 Nizhni Novgorod Russia

Abstract

Complex phosphates and arsenates of alkali metal and zirconium with NASICON and Sc(WO4)3

structures are fast ion conductors In this context double arsenates MZr2(AsO4)3 where M = Li

Na K Rb and Cs have been synthesised as powders through a precipitation method and

investigated by Raman and infrared spectroscopy in combination with factor-group analysis to

assign the bands The stretching and bending vibrations of the AsO43-

units and external modes

as well as the Zr4+

and M+ (Li ndash Cs) translations have been determined for these compounds

which crystallised in the cR3 (D3d6) and P1121n (C2h

5) space groups (LiZr2(AsO4)3) The

correlations between the spectra and the nature of the M+ cation are revealed Some external

modes were identified by studying mass effects (Zr ndash Hf Na ndash Cs) The bands for the

symmetrical bending vibrations of the AsO43-

units and some of the external modes shift toward

higher wavenumbers with the increasing size of the alkaline cations due to the predominant

direction of these vibrations and translations along the a axis the M+ cation size increases as

much as parameter a decreases The differences observed in the vibrational spectra of the

arsenates containing alkaline elements and zirconium with different space groups are caused by

the reduced symmetry

Keywords Raman and infrared spectra Factor group analysis NASICON

Corresponding author Tel +7(495)9392330 Fax +7(495)9395575

E-mail address amurrmailru (EYu Borovikova)

of 19

Accep

ted

Man

uscr

ipt

2

1 Introduction





(Ω cm)-1

[3] The NASICON-






particular interest




(Ω cm)-1

for the


(Ω cm)-1




















2 Experimental

Page 3 of 19

Accep

ted

Man

uscr

ipt

3






















2 cm-1

















Page 4 of 19

Accep

ted

Man

uscr

ipt

4













][M2VIII

]3Zr2[XIV













anion with a point


unit) one











unit for


Page 5 of 19

Accep

ted

Man

uscr

ipt

5




AsO43-








3- ions

and the AsO43-



AsO43-


(position C2)



Zr4+



(position C3)

AsO43-





AsO43-



Zr4+



AsO43-





51 AsO43-







close to 1080 cm-1






Page 6 of 19

Accep

ted

Man

uscr

ipt

6



511 Raman spectra





) two



)












becomes a




units produce three



) two




848 820 and 805 cm-1



cm-1









) is related



Page 7 of 19

Accep

ted

Man

uscr

ipt

7


945 cm-1


and M+



(Cs) 1018 (Li)

rarr 1005 cm-1



(~1080 cm-1





850 rarr 836 cm-1











52 AsO43-

bending vibrations

521 Raman spectra






units



340 cm-1






(Na) rarr 358 cm-1

(K) rarr 370 cm-1

(Rb) rarr 383 cm-1



(Li) rarr 363 cm-1

(Na) rarr 381 cm-1

(K) 380 cm-1

(Li) rarr 389 cm-1

(Na)







units


Page 8 of 19

Accep

ted

Man

uscr

ipt

8







AsO43-


band at ~310 - 300 cm-1


350 cm-1


-1 (Na) rarr 371 cm

-1 (K) rarr 375 cm

-1

(Rb) rarr 377 cm-1

(Cs) 348 cm-1

(K) rarr 351 cm-1

(Rb) rarr 357 cm-1









In


1 (Li) 493 468 cm





(Li) rarr 493 cm-1

(K) rarr 491 cm-1

(Rb) rarr 487 cm-1

(Cs)

467 cm-1

(Li) rarr 468 cm-1

(K) rarr 465 cm-1

(Rb)rarr 462 cm-1

(Cs) 406 cm-1

(Na) rarr 396 cm-1

(K) rarr 391 cm-1

(Rb)





cm-1



53 External modes

531 MIV

translations



vibrations of Zr4+


in Raman spectra of




can be

related to Zr4+

translations

Page 9 of 19

Accep

ted

Man

uscr

ipt

9







532 M+ translations


for Na 71 cm-1

for

K 52 cm-1

for Rb and 49 cm-1




-1 (K) rarr 65 cm

-1

(Rb) 93 cm-1

(Na) rarr 71 cm-1

(K) rarr 52 cm-1

(Rb) rarr 49 cm-1

(Cs) and 75 cm-1

(Na) rarr 60 cm-1





533 AsO43-



M4+






units




-1 (Na) rarr 189 cm

-1 (K) rarr 191

cm-1

(Rb) rarr 197 cm-1



6 Conclusions









and M+





Page 10 of 19

Accep

ted

Man

uscr

ipt

10

AsO43-


are



split into


for the AsO43-











three Zr4+

and three M










stretches

Acknowledgements



Page 11 of 19

Accep

ted

Man

uscr

ipt

11

References












Ltd 1974 pp 278-279

Page 12 of 19

Accep

ted

Man

uscr

ipt

12

Figure captions



5) space group)



5) space group)



5) space group)


Page 13 of 19

Accep

ted

Man

uscr

ipt



+ - Li - Cs with



Vibrations AsO 3


1 A1 A A1g + Eg + A1u + Eu

2 E 2A 2A1g + 2Eg + 2A1u + 2Eu

3 4 F2 A + 2B A1g + 2A2g + 3Eg +

A1u + 2A2u +3Eu

Vibrations AsO 3



2 E 2A 2Ag + 2Bg + 2Au + 2Bu

3 4 F2 3A 3Ag + 3Bg + 3Au + 3Bu

Tables 1-3

Page 14 of 19

Accep

ted

Man

uscr

ipt




Li Na K Rb Cs


ν3 1084 1080

979 1018 979 1017 982 1017 981 1011 977 1005

951 956 948 955 949 954 sh 948 951 sh 943 946 sh

864 870 863 872 862 868 862 859 859 851

ν1 857 849 856 852 857 847 853 845 846 836

838 837 842 842 837

ν4 494 483 493 491 487

473 467 472 468 468 471 465 471 462

445 446 437 435 434

406 396 391

ν2 380 377 389

359 359 363 369 381 371 375 377

346

333 340 358 348 370 351 383 357

TZr4+

310 313 308 303 298

290 288

253 256 255 255 254

241 217 237 223 238 231 237 238

TAsO4

+

Lib AsO4

189 187 182 189 191 197

176 173

158 141

129 129 133 129 131

119

96

89

TM+ 84 65

93 93 71 52 49

75 60

Page 15 of 19

Accep

ted

Man

uscr

ipt


(C2h5)


) Assignment

Wavenumber (cm-1

)

Ra IR Ra IR

ν3 1107 ν2 388

1027 364 378

1006 354 354

976 344

953 954 336

938 935 TZr4+

+

TAsO4

297

876 286

869 883 269

ν1 854 256

848 848 230 241

820 827

805 807 TAsO4

+

Lib AsO4

194

ν4 506 178

496 126

474 476

455

430 434

400

Page 16 of 19

Accep

ted

Man

uscr

ipt

Figure 1

Page 17 of 19

Accep

ted

Man

uscr

ipt

Figure 2 edited

Page 18 of 19

Accep

ted

Man

uscr

ipt

Figure 3

Page 19 of 19

Accep

ted

Man

uscr

ipt

Figure 4

of 19

Accep

ted

Man

uscr

ipt

2

1 Introduction





(Ω cm)-1

[3] The NASICON-






particular interest




(Ω cm)-1

for the


(Ω cm)-1




















2 Experimental

of 19

Accep

ted

Man

uscr

ipt

3






















2 cm-1

















Page 4 of 19

Accep

ted

Man

uscr

ipt

4













][M2VIII

]3Zr2[XIV













anion with a point


unit) one











unit for


Page 5 of 19

Accep

ted

Man

uscr

ipt

5




AsO43-








3- ions

and the AsO43-



AsO43-


(position C2)



Zr4+



(position C3)

AsO43-





AsO43-



Zr4+



AsO43-





51 AsO43-







close to 1080 cm-1






Page 6 of 19

Accep

ted

Man

uscr

ipt

6



511 Raman spectra





) two



)












becomes a




units produce three



) two




848 820 and 805 cm-1



cm-1









) is related



Page 7 of 19

Accep

ted

Man

uscr

ipt

7


945 cm-1


and M+



(Cs) 1018 (Li)

rarr 1005 cm-1



(~1080 cm-1





850 rarr 836 cm-1











52 AsO43-

bending vibrations

521 Raman spectra






units



340 cm-1






(Na) rarr 358 cm-1

(K) rarr 370 cm-1

(Rb) rarr 383 cm-1



(Li) rarr 363 cm-1

(Na) rarr 381 cm-1

(K) 380 cm-1

(Li) rarr 389 cm-1

(Na)







units


Page 8 of 19

Accep

ted

Man

uscr

ipt

8







AsO43-


band at ~310 - 300 cm-1


350 cm-1


-1 (Na) rarr 371 cm

-1 (K) rarr 375 cm

-1

(Rb) rarr 377 cm-1

(Cs) 348 cm-1

(K) rarr 351 cm-1

(Rb) rarr 357 cm-1









In


1 (Li) 493 468 cm





(Li) rarr 493 cm-1

(K) rarr 491 cm-1

(Rb) rarr 487 cm-1

(Cs)

467 cm-1

(Li) rarr 468 cm-1

(K) rarr 465 cm-1

(Rb)rarr 462 cm-1

(Cs) 406 cm-1

(Na) rarr 396 cm-1

(K) rarr 391 cm-1

(Rb)





cm-1



53 External modes

531 MIV

translations



vibrations of Zr4+


in Raman spectra of




can be

related to Zr4+

translations

Page 9 of 19

Accep

ted

Man

uscr

ipt

9







532 M+ translations


for Na 71 cm-1

for

K 52 cm-1

for Rb and 49 cm-1




-1 (K) rarr 65 cm

-1

(Rb) 93 cm-1

(Na) rarr 71 cm-1

(K) rarr 52 cm-1

(Rb) rarr 49 cm-1

(Cs) and 75 cm-1

(Na) rarr 60 cm-1





533 AsO43-



M4+






units




-1 (Na) rarr 189 cm

-1 (K) rarr 191

cm-1

(Rb) rarr 197 cm-1



6 Conclusions









and M+





Page 10 of 19

Accep

ted

Man

uscr

ipt

10

AsO43-


are



split into


for the AsO43-











three Zr4+

and three M










stretches

Acknowledgements



Page 11 of 19

Accep

ted

Man

uscr

ipt

11

References












Ltd 1974 pp 278-279

Page 12 of 19

Accep

ted

Man

uscr

ipt

12

Figure captions



5) space group)



5) space group)



5) space group)


Page 13 of 19

Accep

ted

Man

uscr

ipt



+ - Li - Cs with



Vibrations AsO 3


1 A1 A A1g + Eg + A1u + Eu

2 E 2A 2A1g + 2Eg + 2A1u + 2Eu

3 4 F2 A + 2B A1g + 2A2g + 3Eg +

A1u + 2A2u +3Eu

Vibrations AsO 3



2 E 2A 2Ag + 2Bg + 2Au + 2Bu

3 4 F2 3A 3Ag + 3Bg + 3Au + 3Bu

Tables 1-3

Page 14 of 19

Accep

ted

Man

uscr

ipt




Li Na K Rb Cs


ν3 1084 1080

979 1018 979 1017 982 1017 981 1011 977 1005

951 956 948 955 949 954 sh 948 951 sh 943 946 sh

864 870 863 872 862 868 862 859 859 851

ν1 857 849 856 852 857 847 853 845 846 836

838 837 842 842 837

ν4 494 483 493 491 487

473 467 472 468 468 471 465 471 462

445 446 437 435 434

406 396 391

ν2 380 377 389

359 359 363 369 381 371 375 377

346

333 340 358 348 370 351 383 357

TZr4+

310 313 308 303 298

290 288

253 256 255 255 254

241 217 237 223 238 231 237 238

TAsO4

+

Lib AsO4

189 187 182 189 191 197

176 173

158 141

129 129 133 129 131

119

96

89

TM+ 84 65

93 93 71 52 49

75 60

Page 15 of 19

Accep

ted

Man

uscr

ipt


(C2h5)


) Assignment

Wavenumber (cm-1

)

Ra IR Ra IR

ν3 1107 ν2 388

1027 364 378

1006 354 354

976 344

953 954 336

938 935 TZr4+

+

TAsO4

297

876 286

869 883 269

ν1 854 256

848 848 230 241

820 827

805 807 TAsO4

+

Lib AsO4

194

ν4 506 178

496 126

474 476

455

430 434

400

Page 16 of 19

Accep

ted

Man

uscr

ipt

Figure 1

Page 17 of 19

Accep

ted

Man

uscr

ipt

Figure 2 edited

Page 18 of 19

Accep

ted

Man

uscr

ipt

Figure 3

Page 19 of 19

Accep

ted

Man

uscr

ipt

Figure 4

of 19

Accep

ted

Man

uscr

ipt

3






















2 cm-1

















of 19

Accep

ted

Man

uscr

ipt

4













][M2VIII

]3Zr2[XIV













anion with a point


unit) one











unit for


Page 5 of 19

Accep

ted

Man

uscr

ipt

5




AsO43-








3- ions

and the AsO43-



AsO43-


(position C2)



Zr4+



(position C3)

AsO43-





AsO43-



Zr4+



AsO43-





51 AsO43-







close to 1080 cm-1






Page 6 of 19

Accep

ted

Man

uscr

ipt

6



511 Raman spectra





) two



)












becomes a




units produce three



) two




848 820 and 805 cm-1



cm-1









) is related



Page 7 of 19

Accep

ted

Man

uscr

ipt

7


945 cm-1


and M+



(Cs) 1018 (Li)

rarr 1005 cm-1



(~1080 cm-1





850 rarr 836 cm-1











52 AsO43-

bending vibrations

521 Raman spectra






units



340 cm-1






(Na) rarr 358 cm-1

(K) rarr 370 cm-1

(Rb) rarr 383 cm-1



(Li) rarr 363 cm-1

(Na) rarr 381 cm-1

(K) 380 cm-1

(Li) rarr 389 cm-1

(Na)







units


Page 8 of 19

Accep

ted

Man

uscr

ipt

8







AsO43-


band at ~310 - 300 cm-1


350 cm-1


-1 (Na) rarr 371 cm

-1 (K) rarr 375 cm

-1

(Rb) rarr 377 cm-1

(Cs) 348 cm-1

(K) rarr 351 cm-1

(Rb) rarr 357 cm-1









In


1 (Li) 493 468 cm





(Li) rarr 493 cm-1

(K) rarr 491 cm-1

(Rb) rarr 487 cm-1

(Cs)

467 cm-1

(Li) rarr 468 cm-1

(K) rarr 465 cm-1

(Rb)rarr 462 cm-1

(Cs) 406 cm-1

(Na) rarr 396 cm-1

(K) rarr 391 cm-1

(Rb)





cm-1



53 External modes

531 MIV

translations



vibrations of Zr4+


in Raman spectra of




can be

related to Zr4+

translations

Page 9 of 19

Accep

ted

Man

uscr

ipt

9







532 M+ translations


for Na 71 cm-1

for

K 52 cm-1

for Rb and 49 cm-1




-1 (K) rarr 65 cm

-1

(Rb) 93 cm-1

(Na) rarr 71 cm-1

(K) rarr 52 cm-1

(Rb) rarr 49 cm-1

(Cs) and 75 cm-1

(Na) rarr 60 cm-1





533 AsO43-



M4+






units




-1 (Na) rarr 189 cm

-1 (K) rarr 191

cm-1

(Rb) rarr 197 cm-1



6 Conclusions









and M+





Page 10 of 19

Accep

ted

Man

uscr

ipt

10

AsO43-


are



split into


for the AsO43-











three Zr4+

and three M










stretches

Acknowledgements



Page 11 of 19

Accep

ted

Man

uscr

ipt

11

References












Ltd 1974 pp 278-279

Page 12 of 19

Accep

ted

Man

uscr

ipt

12

Figure captions



5) space group)



5) space group)



5) space group)


Page 13 of 19

Accep

ted

Man

uscr

ipt



+ - Li - Cs with



Vibrations AsO 3


1 A1 A A1g + Eg + A1u + Eu

2 E 2A 2A1g + 2Eg + 2A1u + 2Eu

3 4 F2 A + 2B A1g + 2A2g + 3Eg +

A1u + 2A2u +3Eu

Vibrations AsO 3



2 E 2A 2Ag + 2Bg + 2Au + 2Bu

3 4 F2 3A 3Ag + 3Bg + 3Au + 3Bu

Tables 1-3

Page 14 of 19

Accep

ted

Man

uscr

ipt




Li Na K Rb Cs


ν3 1084 1080

979 1018 979 1017 982 1017 981 1011 977 1005

951 956 948 955 949 954 sh 948 951 sh 943 946 sh

864 870 863 872 862 868 862 859 859 851

ν1 857 849 856 852 857 847 853 845 846 836

838 837 842 842 837

ν4 494 483 493 491 487

473 467 472 468 468 471 465 471 462

445 446 437 435 434

406 396 391

ν2 380 377 389

359 359 363 369 381 371 375 377

346

333 340 358 348 370 351 383 357

TZr4+

310 313 308 303 298

290 288

253 256 255 255 254

241 217 237 223 238 231 237 238

TAsO4

+

Lib AsO4

189 187 182 189 191 197

176 173

158 141

129 129 133 129 131

119

96

89

TM+ 84 65

93 93 71 52 49

75 60

Page 15 of 19

Accep

ted

Man

uscr

ipt


(C2h5)


) Assignment

Wavenumber (cm-1

)

Ra IR Ra IR

ν3 1107 ν2 388

1027 364 378

1006 354 354

976 344

953 954 336

938 935 TZr4+

+

TAsO4

297

876 286

869 883 269

ν1 854 256

848 848 230 241

820 827

805 807 TAsO4

+

Lib AsO4

194

ν4 506 178

496 126

474 476

455

430 434

400

Page 16 of 19

Accep

ted

Man

uscr

ipt

Figure 1

Page 17 of 19

Accep

ted

Man

uscr

ipt

Figure 2 edited

Page 18 of 19

Accep

ted

Man

uscr

ipt

Figure 3

Page 19 of 19

Accep

ted

Man

uscr

ipt

Figure 4

of 19

Accep

ted

Man

uscr

ipt

4













][M2VIII

]3Zr2[XIV













anion with a point


unit) one











unit for


of 19

Accep

ted

Man

uscr

ipt

5




AsO43-








3- ions

and the AsO43-



AsO43-


(position C2)



Zr4+



(position C3)

AsO43-





AsO43-



Zr4+



AsO43-





51 AsO43-







close to 1080 cm-1






Page 6 of 19

Accep

ted

Man

uscr

ipt

6



511 Raman spectra





) two



)












becomes a




units produce three



) two




848 820 and 805 cm-1



cm-1









) is related



Page 7 of 19

Accep

ted

Man

uscr

ipt

7


945 cm-1


and M+



(Cs) 1018 (Li)

rarr 1005 cm-1



(~1080 cm-1





850 rarr 836 cm-1











52 AsO43-

bending vibrations

521 Raman spectra






units



340 cm-1






(Na) rarr 358 cm-1

(K) rarr 370 cm-1

(Rb) rarr 383 cm-1



(Li) rarr 363 cm-1

(Na) rarr 381 cm-1

(K) 380 cm-1

(Li) rarr 389 cm-1

(Na)







units


Page 8 of 19

Accep

ted

Man

uscr

ipt

8







AsO43-


band at ~310 - 300 cm-1


350 cm-1


-1 (Na) rarr 371 cm

-1 (K) rarr 375 cm

-1

(Rb) rarr 377 cm-1

(Cs) 348 cm-1

(K) rarr 351 cm-1

(Rb) rarr 357 cm-1









In


1 (Li) 493 468 cm





(Li) rarr 493 cm-1

(K) rarr 491 cm-1

(Rb) rarr 487 cm-1

(Cs)

467 cm-1

(Li) rarr 468 cm-1

(K) rarr 465 cm-1

(Rb)rarr 462 cm-1

(Cs) 406 cm-1

(Na) rarr 396 cm-1

(K) rarr 391 cm-1

(Rb)





cm-1



53 External modes

531 MIV

translations



vibrations of Zr4+


in Raman spectra of




can be

related to Zr4+

translations

Page 9 of 19

Accep

ted

Man

uscr

ipt

9







532 M+ translations


for Na 71 cm-1

for

K 52 cm-1

for Rb and 49 cm-1




-1 (K) rarr 65 cm

-1

(Rb) 93 cm-1

(Na) rarr 71 cm-1

(K) rarr 52 cm-1

(Rb) rarr 49 cm-1

(Cs) and 75 cm-1

(Na) rarr 60 cm-1





533 AsO43-



M4+






units




-1 (Na) rarr 189 cm

-1 (K) rarr 191

cm-1

(Rb) rarr 197 cm-1



6 Conclusions









and M+





Page 10 of 19

Accep

ted

Man

uscr

ipt

10

AsO43-


are



split into


for the AsO43-











three Zr4+

and three M










stretches

Acknowledgements



Page 11 of 19

Accep

ted

Man

uscr

ipt

11

References












Ltd 1974 pp 278-279

Page 12 of 19

Accep

ted

Man

uscr

ipt

12

Figure captions



5) space group)



5) space group)



5) space group)


Page 13 of 19

Accep

ted

Man

uscr

ipt



+ - Li - Cs with



Vibrations AsO 3


1 A1 A A1g + Eg + A1u + Eu

2 E 2A 2A1g + 2Eg + 2A1u + 2Eu

3 4 F2 A + 2B A1g + 2A2g + 3Eg +

A1u + 2A2u +3Eu

Vibrations AsO 3



2 E 2A 2Ag + 2Bg + 2Au + 2Bu

3 4 F2 3A 3Ag + 3Bg + 3Au + 3Bu

Tables 1-3

Page 14 of 19

Accep

ted

Man

uscr

ipt




Li Na K Rb Cs


ν3 1084 1080

979 1018 979 1017 982 1017 981 1011 977 1005

951 956 948 955 949 954 sh 948 951 sh 943 946 sh

864 870 863 872 862 868 862 859 859 851

ν1 857 849 856 852 857 847 853 845 846 836

838 837 842 842 837

ν4 494 483 493 491 487

473 467 472 468 468 471 465 471 462

445 446 437 435 434

406 396 391

ν2 380 377 389

359 359 363 369 381 371 375 377

346

333 340 358 348 370 351 383 357

TZr4+

310 313 308 303 298

290 288

253 256 255 255 254

241 217 237 223 238 231 237 238

TAsO4

+

Lib AsO4

189 187 182 189 191 197

176 173

158 141

129 129 133 129 131

119

96

89

TM+ 84 65

93 93 71 52 49

75 60

Page 15 of 19

Accep

ted

Man

uscr

ipt


(C2h5)


) Assignment

Wavenumber (cm-1

)

Ra IR Ra IR

ν3 1107 ν2 388

1027 364 378

1006 354 354

976 344

953 954 336

938 935 TZr4+

+

TAsO4

297

876 286

869 883 269

ν1 854 256

848 848 230 241

820 827

805 807 TAsO4

+

Lib AsO4

194

ν4 506 178

496 126

474 476

455

430 434

400

Page 16 of 19

Accep

ted

Man

uscr

ipt

Figure 1

Page 17 of 19

Accep

ted

Man

uscr

ipt

Figure 2 edited

Page 18 of 19

Accep

ted

Man

uscr

ipt

Figure 3

Page 19 of 19

Accep

ted

Man

uscr

ipt

Figure 4

of 19

Accep

ted

Man

uscr

ipt

5




AsO43-








3- ions

and the AsO43-



AsO43-


(position C2)



Zr4+



(position C3)

AsO43-





AsO43-



Zr4+



AsO43-





51 AsO43-







close to 1080 cm-1






of 19

Accep

ted

Man

uscr

ipt

6



511 Raman spectra





) two



)












becomes a




units produce three



) two




848 820 and 805 cm-1



cm-1









) is related



Page 7 of 19

Accep

ted

Man

uscr

ipt

7


945 cm-1


and M+



(Cs) 1018 (Li)

rarr 1005 cm-1



(~1080 cm-1





850 rarr 836 cm-1











52 AsO43-

bending vibrations

521 Raman spectra






units



340 cm-1






(Na) rarr 358 cm-1

(K) rarr 370 cm-1

(Rb) rarr 383 cm-1



(Li) rarr 363 cm-1

(Na) rarr 381 cm-1

(K) 380 cm-1

(Li) rarr 389 cm-1

(Na)







units


Page 8 of 19

Accep

ted

Man

uscr

ipt

8







AsO43-


band at ~310 - 300 cm-1


350 cm-1


-1 (Na) rarr 371 cm

-1 (K) rarr 375 cm

-1

(Rb) rarr 377 cm-1

(Cs) 348 cm-1

(K) rarr 351 cm-1

(Rb) rarr 357 cm-1









In


1 (Li) 493 468 cm





(Li) rarr 493 cm-1

(K) rarr 491 cm-1

(Rb) rarr 487 cm-1

(Cs)

467 cm-1

(Li) rarr 468 cm-1

(K) rarr 465 cm-1

(Rb)rarr 462 cm-1

(Cs) 406 cm-1

(Na) rarr 396 cm-1

(K) rarr 391 cm-1

(Rb)





cm-1



53 External modes

531 MIV

translations



vibrations of Zr4+


in Raman spectra of




can be

related to Zr4+

translations

Page 9 of 19

Accep

ted

Man

uscr

ipt

9







532 M+ translations


for Na 71 cm-1

for

K 52 cm-1

for Rb and 49 cm-1




-1 (K) rarr 65 cm

-1

(Rb) 93 cm-1

(Na) rarr 71 cm-1

(K) rarr 52 cm-1

(Rb) rarr 49 cm-1

(Cs) and 75 cm-1

(Na) rarr 60 cm-1





533 AsO43-



M4+






units




-1 (Na) rarr 189 cm

-1 (K) rarr 191

cm-1

(Rb) rarr 197 cm-1



6 Conclusions









and M+





Page 10 of 19

Accep

ted

Man

uscr

ipt

10

AsO43-


are



split into


for the AsO43-











three Zr4+

and three M










stretches

Acknowledgements



Page 11 of 19

Accep

ted

Man

uscr

ipt

11

References












Ltd 1974 pp 278-279

Page 12 of 19

Accep

ted

Man

uscr

ipt

12

Figure captions



5) space group)



5) space group)



5) space group)


Page 13 of 19

Accep

ted

Man

uscr

ipt



+ - Li - Cs with



Vibrations AsO 3


1 A1 A A1g + Eg + A1u + Eu

2 E 2A 2A1g + 2Eg + 2A1u + 2Eu

3 4 F2 A + 2B A1g + 2A2g + 3Eg +

A1u + 2A2u +3Eu

Vibrations AsO 3



2 E 2A 2Ag + 2Bg + 2Au + 2Bu

3 4 F2 3A 3Ag + 3Bg + 3Au + 3Bu

Tables 1-3

Page 14 of 19

Accep

ted

Man

uscr

ipt




Li Na K Rb Cs


ν3 1084 1080

979 1018 979 1017 982 1017 981 1011 977 1005

951 956 948 955 949 954 sh 948 951 sh 943 946 sh

864 870 863 872 862 868 862 859 859 851

ν1 857 849 856 852 857 847 853 845 846 836

838 837 842 842 837

ν4 494 483 493 491 487

473 467 472 468 468 471 465 471 462

445 446 437 435 434

406 396 391

ν2 380 377 389

359 359 363 369 381 371 375 377

346

333 340 358 348 370 351 383 357

TZr4+

310 313 308 303 298

290 288

253 256 255 255 254

241 217 237 223 238 231 237 238

TAsO4

+

Lib AsO4

189 187 182 189 191 197

176 173

158 141

129 129 133 129 131

119

96

89

TM+ 84 65

93 93 71 52 49

75 60

Page 15 of 19

Accep

ted

Man

uscr

ipt


(C2h5)


) Assignment

Wavenumber (cm-1

)

Ra IR Ra IR

ν3 1107 ν2 388

1027 364 378

1006 354 354

976 344

953 954 336

938 935 TZr4+

+

TAsO4

297

876 286

869 883 269

ν1 854 256

848 848 230 241

820 827

805 807 TAsO4

+

Lib AsO4

194

ν4 506 178

496 126

474 476

455

430 434

400

Page 16 of 19

Accep

ted

Man

uscr

ipt

Figure 1

Page 17 of 19

Accep

ted

Man

uscr

ipt

Figure 2 edited

Page 18 of 19

Accep

ted

Man

uscr

ipt

Figure 3

Page 19 of 19

Accep

ted

Man

uscr

ipt

Figure 4

of 19

Accep

ted

Man

uscr

ipt

6



511 Raman spectra





) two



)












becomes a




units produce three



) two




848 820 and 805 cm-1



cm-1









) is related



of 19

Accep

ted

Man

uscr

ipt

7


945 cm-1


and M+



(Cs) 1018 (Li)

rarr 1005 cm-1



(~1080 cm-1





850 rarr 836 cm-1











52 AsO43-

bending vibrations

521 Raman spectra






units



340 cm-1






(Na) rarr 358 cm-1

(K) rarr 370 cm-1

(Rb) rarr 383 cm-1



(Li) rarr 363 cm-1

(Na) rarr 381 cm-1

(K) 380 cm-1

(Li) rarr 389 cm-1

(Na)







units


Page 8 of 19

Accep

ted

Man

uscr

ipt

8







AsO43-


band at ~310 - 300 cm-1


350 cm-1


-1 (Na) rarr 371 cm

-1 (K) rarr 375 cm

-1

(Rb) rarr 377 cm-1

(Cs) 348 cm-1

(K) rarr 351 cm-1

(Rb) rarr 357 cm-1









In


1 (Li) 493 468 cm





(Li) rarr 493 cm-1

(K) rarr 491 cm-1

(Rb) rarr 487 cm-1

(Cs)

467 cm-1

(Li) rarr 468 cm-1

(K) rarr 465 cm-1

(Rb)rarr 462 cm-1

(Cs) 406 cm-1

(Na) rarr 396 cm-1

(K) rarr 391 cm-1

(Rb)





cm-1



53 External modes

531 MIV

translations



vibrations of Zr4+


in Raman spectra of




can be

related to Zr4+

translations

Page 9 of 19

Accep

ted

Man

uscr

ipt

9







532 M+ translations


for Na 71 cm-1

for

K 52 cm-1

for Rb and 49 cm-1




-1 (K) rarr 65 cm

-1

(Rb) 93 cm-1

(Na) rarr 71 cm-1

(K) rarr 52 cm-1

(Rb) rarr 49 cm-1

(Cs) and 75 cm-1

(Na) rarr 60 cm-1





533 AsO43-



M4+






units




-1 (Na) rarr 189 cm

-1 (K) rarr 191

cm-1

(Rb) rarr 197 cm-1



6 Conclusions









and M+





Page 10 of 19

Accep

ted

Man

uscr

ipt

10

AsO43-


are



split into


for the AsO43-











three Zr4+

and three M










stretches

Acknowledgements



Page 11 of 19

Accep

ted

Man

uscr

ipt

11

References












Ltd 1974 pp 278-279

Page 12 of 19

Accep

ted

Man

uscr

ipt

12

Figure captions



5) space group)



5) space group)



5) space group)


Page 13 of 19

Accep

ted

Man

uscr

ipt



+ - Li - Cs with



Vibrations AsO 3


1 A1 A A1g + Eg + A1u + Eu

2 E 2A 2A1g + 2Eg + 2A1u + 2Eu

3 4 F2 A + 2B A1g + 2A2g + 3Eg +

A1u + 2A2u +3Eu

Vibrations AsO 3



2 E 2A 2Ag + 2Bg + 2Au + 2Bu

3 4 F2 3A 3Ag + 3Bg + 3Au + 3Bu

Tables 1-3

Page 14 of 19

Accep

ted

Man

uscr

ipt




Li Na K Rb Cs


ν3 1084 1080

979 1018 979 1017 982 1017 981 1011 977 1005

951 956 948 955 949 954 sh 948 951 sh 943 946 sh

864 870 863 872 862 868 862 859 859 851

ν1 857 849 856 852 857 847 853 845 846 836

838 837 842 842 837

ν4 494 483 493 491 487

473 467 472 468 468 471 465 471 462

445 446 437 435 434

406 396 391

ν2 380 377 389

359 359 363 369 381 371 375 377

346

333 340 358 348 370 351 383 357

TZr4+

310 313 308 303 298

290 288

253 256 255 255 254

241 217 237 223 238 231 237 238

TAsO4

+

Lib AsO4

189 187 182 189 191 197

176 173

158 141

129 129 133 129 131

119

96

89

TM+ 84 65

93 93 71 52 49

75 60

Page 15 of 19

Accep

ted

Man

uscr

ipt


(C2h5)


) Assignment

Wavenumber (cm-1

)

Ra IR Ra IR

ν3 1107 ν2 388

1027 364 378

1006 354 354

976 344

953 954 336

938 935 TZr4+

+

TAsO4

297

876 286

869 883 269

ν1 854 256

848 848 230 241

820 827

805 807 TAsO4

+

Lib AsO4

194

ν4 506 178

496 126

474 476

455

430 434

400

Page 16 of 19

Accep

ted

Man

uscr

ipt

Figure 1

Page 17 of 19

Accep

ted

Man

uscr

ipt

Figure 2 edited

Page 18 of 19

Accep

ted

Man

uscr

ipt

Figure 3

Page 19 of 19

Accep

ted

Man

uscr

ipt

Figure 4

of 19

Accep

ted

Man

uscr

ipt

7


945 cm-1


and M+



(Cs) 1018 (Li)

rarr 1005 cm-1



(~1080 cm-1





850 rarr 836 cm-1











52 AsO43-

bending vibrations

521 Raman spectra






units



340 cm-1






(Na) rarr 358 cm-1

(K) rarr 370 cm-1

(Rb) rarr 383 cm-1



(Li) rarr 363 cm-1

(Na) rarr 381 cm-1

(K) 380 cm-1

(Li) rarr 389 cm-1

(Na)







units


of 19

Accep

ted

Man

uscr

ipt

8







AsO43-


band at ~310 - 300 cm-1


350 cm-1


-1 (Na) rarr 371 cm

-1 (K) rarr 375 cm

-1

(Rb) rarr 377 cm-1

(Cs) 348 cm-1

(K) rarr 351 cm-1

(Rb) rarr 357 cm-1









In


1 (Li) 493 468 cm





(Li) rarr 493 cm-1

(K) rarr 491 cm-1

(Rb) rarr 487 cm-1

(Cs)

467 cm-1

(Li) rarr 468 cm-1

(K) rarr 465 cm-1

(Rb)rarr 462 cm-1

(Cs) 406 cm-1

(Na) rarr 396 cm-1

(K) rarr 391 cm-1

(Rb)





cm-1



53 External modes

531 MIV

translations



vibrations of Zr4+


in Raman spectra of




can be

related to Zr4+

translations

Page 9 of 19

Accep

ted

Man

uscr

ipt

9







532 M+ translations


for Na 71 cm-1

for

K 52 cm-1

for Rb and 49 cm-1




-1 (K) rarr 65 cm

-1

(Rb) 93 cm-1

(Na) rarr 71 cm-1

(K) rarr 52 cm-1

(Rb) rarr 49 cm-1

(Cs) and 75 cm-1

(Na) rarr 60 cm-1





533 AsO43-



M4+






units




-1 (Na) rarr 189 cm

-1 (K) rarr 191

cm-1

(Rb) rarr 197 cm-1



6 Conclusions









and M+





Page 10 of 19

Accep

ted

Man

uscr

ipt

10

AsO43-


are



split into


for the AsO43-











three Zr4+

and three M










stretches

Acknowledgements



Page 11 of 19

Accep

ted

Man

uscr

ipt

11

References












Ltd 1974 pp 278-279

Page 12 of 19

Accep

ted

Man

uscr

ipt

12

Figure captions



5) space group)



5) space group)



5) space group)


Page 13 of 19

Accep

ted

Man

uscr

ipt



+ - Li - Cs with



Vibrations AsO 3


1 A1 A A1g + Eg + A1u + Eu

2 E 2A 2A1g + 2Eg + 2A1u + 2Eu

3 4 F2 A + 2B A1g + 2A2g + 3Eg +

A1u + 2A2u +3Eu

Vibrations AsO 3



2 E 2A 2Ag + 2Bg + 2Au + 2Bu

3 4 F2 3A 3Ag + 3Bg + 3Au + 3Bu

Tables 1-3

Page 14 of 19

Accep

ted

Man

uscr

ipt




Li Na K Rb Cs


ν3 1084 1080

979 1018 979 1017 982 1017 981 1011 977 1005

951 956 948 955 949 954 sh 948 951 sh 943 946 sh

864 870 863 872 862 868 862 859 859 851

ν1 857 849 856 852 857 847 853 845 846 836

838 837 842 842 837

ν4 494 483 493 491 487

473 467 472 468 468 471 465 471 462

445 446 437 435 434

406 396 391

ν2 380 377 389

359 359 363 369 381 371 375 377

346

333 340 358 348 370 351 383 357

TZr4+

310 313 308 303 298

290 288

253 256 255 255 254

241 217 237 223 238 231 237 238

TAsO4

+

Lib AsO4

189 187 182 189 191 197

176 173

158 141

129 129 133 129 131

119

96

89

TM+ 84 65

93 93 71 52 49

75 60

Page 15 of 19

Accep

ted

Man

uscr

ipt


(C2h5)


) Assignment

Wavenumber (cm-1

)

Ra IR Ra IR

ν3 1107 ν2 388

1027 364 378

1006 354 354

976 344

953 954 336

938 935 TZr4+

+

TAsO4

297

876 286

869 883 269

ν1 854 256

848 848 230 241

820 827

805 807 TAsO4

+

Lib AsO4

194

ν4 506 178

496 126

474 476

455

430 434

400

Page 16 of 19

Accep

ted

Man

uscr

ipt

Figure 1

Page 17 of 19

Accep

ted

Man

uscr

ipt

Figure 2 edited

Page 18 of 19

Accep

ted

Man

uscr

ipt

Figure 3

Page 19 of 19

Accep

ted

Man

uscr

ipt

Figure 4

of 19

Accep

ted

Man

uscr

ipt

8







AsO43-


band at ~310 - 300 cm-1


350 cm-1


-1 (Na) rarr 371 cm

-1 (K) rarr 375 cm

-1

(Rb) rarr 377 cm-1

(Cs) 348 cm-1

(K) rarr 351 cm-1

(Rb) rarr 357 cm-1









In


1 (Li) 493 468 cm





(Li) rarr 493 cm-1

(K) rarr 491 cm-1

(Rb) rarr 487 cm-1

(Cs)

467 cm-1

(Li) rarr 468 cm-1

(K) rarr 465 cm-1

(Rb)rarr 462 cm-1

(Cs) 406 cm-1

(Na) rarr 396 cm-1

(K) rarr 391 cm-1

(Rb)





cm-1



53 External modes

531 MIV

translations



vibrations of Zr4+


in Raman spectra of




can be

related to Zr4+

translations

of 19

Accep

ted

Man

uscr

ipt

9







532 M+ translations


for Na 71 cm-1

for

K 52 cm-1

for Rb and 49 cm-1




-1 (K) rarr 65 cm

-1

(Rb) 93 cm-1

(Na) rarr 71 cm-1

(K) rarr 52 cm-1

(Rb) rarr 49 cm-1

(Cs) and 75 cm-1

(Na) rarr 60 cm-1





533 AsO43-



M4+






units




-1 (Na) rarr 189 cm

-1 (K) rarr 191

cm-1

(Rb) rarr 197 cm-1



6 Conclusions









and M+





Page 10 of 19

Accep

ted

Man

uscr

ipt

10

AsO43-


are



split into


for the AsO43-











three Zr4+

and three M










stretches

Acknowledgements



Page 11 of 19

Accep

ted

Man

uscr

ipt

11

References












Ltd 1974 pp 278-279

Page 12 of 19

Accep

ted

Man

uscr

ipt

12

Figure captions



5) space group)



5) space group)



5) space group)


Page 13 of 19

Accep

ted

Man

uscr

ipt



+ - Li - Cs with



Vibrations AsO 3


1 A1 A A1g + Eg + A1u + Eu

2 E 2A 2A1g + 2Eg + 2A1u + 2Eu

3 4 F2 A + 2B A1g + 2A2g + 3Eg +

A1u + 2A2u +3Eu

Vibrations AsO 3



2 E 2A 2Ag + 2Bg + 2Au + 2Bu

3 4 F2 3A 3Ag + 3Bg + 3Au + 3Bu

Tables 1-3

Page 14 of 19

Accep

ted

Man

uscr

ipt




Li Na K Rb Cs


ν3 1084 1080

979 1018 979 1017 982 1017 981 1011 977 1005

951 956 948 955 949 954 sh 948 951 sh 943 946 sh

864 870 863 872 862 868 862 859 859 851

ν1 857 849 856 852 857 847 853 845 846 836

838 837 842 842 837

ν4 494 483 493 491 487

473 467 472 468 468 471 465 471 462

445 446 437 435 434

406 396 391

ν2 380 377 389

359 359 363 369 381 371 375 377

346

333 340 358 348 370 351 383 357

TZr4+

310 313 308 303 298

290 288

253 256 255 255 254

241 217 237 223 238 231 237 238

TAsO4

+

Lib AsO4

189 187 182 189 191 197

176 173

158 141

129 129 133 129 131

119

96

89

TM+ 84 65

93 93 71 52 49

75 60

Page 15 of 19

Accep

ted

Man

uscr

ipt


(C2h5)


) Assignment

Wavenumber (cm-1

)

Ra IR Ra IR

ν3 1107 ν2 388

1027 364 378

1006 354 354

976 344

953 954 336

938 935 TZr4+

+

TAsO4

297

876 286

869 883 269

ν1 854 256

848 848 230 241

820 827

805 807 TAsO4

+

Lib AsO4

194

ν4 506 178

496 126

474 476

455

430 434

400

Page 16 of 19

Accep

ted

Man

uscr

ipt

Figure 1

Page 17 of 19

Accep

ted

Man

uscr

ipt

Figure 2 edited

Page 18 of 19

Accep

ted

Man

uscr

ipt

Figure 3

Page 19 of 19

Accep

ted

Man

uscr

ipt

Figure 4

of 19

Accep

ted

Man

uscr

ipt

9







532 M+ translations


for Na 71 cm-1

for

K 52 cm-1

for Rb and 49 cm-1




-1 (K) rarr 65 cm

-1

(Rb) 93 cm-1

(Na) rarr 71 cm-1

(K) rarr 52 cm-1

(Rb) rarr 49 cm-1

(Cs) and 75 cm-1

(Na) rarr 60 cm-1





533 AsO43-



M4+






units




-1 (Na) rarr 189 cm

-1 (K) rarr 191

cm-1

(Rb) rarr 197 cm-1



6 Conclusions









and M+





of 19

Accep

ted

Man

uscr

ipt

10

AsO43-


are



split into


for the AsO43-











three Zr4+

and three M










stretches

Acknowledgements



Page 11 of 19

Accep

ted

Man

uscr

ipt

11

References












Ltd 1974 pp 278-279

Page 12 of 19

Accep

ted

Man

uscr

ipt

12

Figure captions



5) space group)



5) space group)



5) space group)


Page 13 of 19

Accep

ted

Man

uscr

ipt



+ - Li - Cs with



Vibrations AsO 3


1 A1 A A1g + Eg + A1u + Eu

2 E 2A 2A1g + 2Eg + 2A1u + 2Eu

3 4 F2 A + 2B A1g + 2A2g + 3Eg +

A1u + 2A2u +3Eu

Vibrations AsO 3



2 E 2A 2Ag + 2Bg + 2Au + 2Bu

3 4 F2 3A 3Ag + 3Bg + 3Au + 3Bu

Tables 1-3

Page 14 of 19

Accep

ted

Man

uscr

ipt




Li Na K Rb Cs


ν3 1084 1080

979 1018 979 1017 982 1017 981 1011 977 1005

951 956 948 955 949 954 sh 948 951 sh 943 946 sh

864 870 863 872 862 868 862 859 859 851

ν1 857 849 856 852 857 847 853 845 846 836

838 837 842 842 837

ν4 494 483 493 491 487

473 467 472 468 468 471 465 471 462

445 446 437 435 434

406 396 391

ν2 380 377 389

359 359 363 369 381 371 375 377

346

333 340 358 348 370 351 383 357

TZr4+

310 313 308 303 298

290 288

253 256 255 255 254

241 217 237 223 238 231 237 238

TAsO4

+

Lib AsO4

189 187 182 189 191 197

176 173

158 141

129 129 133 129 131

119

96

89

TM+ 84 65

93 93 71 52 49

75 60

Page 15 of 19

Accep

ted

Man

uscr

ipt


(C2h5)


) Assignment

Wavenumber (cm-1

)

Ra IR Ra IR

ν3 1107 ν2 388

1027 364 378

1006 354 354

976 344

953 954 336

938 935 TZr4+

+

TAsO4

297

876 286

869 883 269

ν1 854 256

848 848 230 241

820 827

805 807 TAsO4

+

Lib AsO4

194

ν4 506 178

496 126

474 476

455

430 434

400

Page 16 of 19

Accep

ted

Man

uscr

ipt

Figure 1

Page 17 of 19

Accep

ted

Man

uscr

ipt

Figure 2 edited

Page 18 of 19

Accep

ted

Man

uscr

ipt

Figure 3

Page 19 of 19

Accep

ted

Man

uscr

ipt

Figure 4

of 19

Accep

ted

Man

uscr

ipt

10

AsO43-


are



split into


for the AsO43-











three Zr4+

and three M










stretches

Acknowledgements



of 19

Accep

ted

Man

uscr

ipt

11

References












Ltd 1974 pp 278-279

Page 12 of 19

Accep

ted

Man

uscr

ipt

12

Figure captions



5) space group)



5) space group)



5) space group)


Page 13 of 19

Accep

ted

Man

uscr

ipt



+ - Li - Cs with



Vibrations AsO 3


1 A1 A A1g + Eg + A1u + Eu

2 E 2A 2A1g + 2Eg + 2A1u + 2Eu

3 4 F2 A + 2B A1g + 2A2g + 3Eg +

A1u + 2A2u +3Eu

Vibrations AsO 3



2 E 2A 2Ag + 2Bg + 2Au + 2Bu

3 4 F2 3A 3Ag + 3Bg + 3Au + 3Bu

Tables 1-3

Page 14 of 19

Accep

ted

Man

uscr

ipt




Li Na K Rb Cs


ν3 1084 1080

979 1018 979 1017 982 1017 981 1011 977 1005

951 956 948 955 949 954 sh 948 951 sh 943 946 sh

864 870 863 872 862 868 862 859 859 851

ν1 857 849 856 852 857 847 853 845 846 836

838 837 842 842 837

ν4 494 483 493 491 487

473 467 472 468 468 471 465 471 462

445 446 437 435 434

406 396 391

ν2 380 377 389

359 359 363 369 381 371 375 377

346

333 340 358 348 370 351 383 357

TZr4+

310 313 308 303 298

290 288

253 256 255 255 254

241 217 237 223 238 231 237 238

TAsO4

+

Lib AsO4

189 187 182 189 191 197

176 173

158 141

129 129 133 129 131

119

96

89

TM+ 84 65

93 93 71 52 49

75 60

Page 15 of 19

Accep

ted

Man

uscr

ipt


(C2h5)


) Assignment

Wavenumber (cm-1

)

Ra IR Ra IR

ν3 1107 ν2 388

1027 364 378

1006 354 354

976 344

953 954 336

938 935 TZr4+

+

TAsO4

297

876 286

869 883 269

ν1 854 256

848 848 230 241

820 827

805 807 TAsO4

+

Lib AsO4

194

ν4 506 178

496 126

474 476

455

430 434

400

Page 16 of 19

Accep

ted

Man

uscr

ipt

Figure 1

Page 17 of 19

Accep

ted

Man

uscr

ipt

Figure 2 edited

Page 18 of 19

Accep

ted

Man

uscr

ipt

Figure 3

Page 19 of 19

Accep

ted

Man

uscr

ipt

Figure 4

of 19

Accep

ted

Man

uscr

ipt

11

References












Ltd 1974 pp 278-279

of 19

Accep

ted

Man

uscr

ipt

12

Figure captions



5) space group)



5) space group)



5) space group)


Page 13 of 19

Accep

ted

Man

uscr

ipt



+ - Li - Cs with



Vibrations AsO 3


1 A1 A A1g + Eg + A1u + Eu

2 E 2A 2A1g + 2Eg + 2A1u + 2Eu

3 4 F2 A + 2B A1g + 2A2g + 3Eg +

A1u + 2A2u +3Eu

Vibrations AsO 3



2 E 2A 2Ag + 2Bg + 2Au + 2Bu

3 4 F2 3A 3Ag + 3Bg + 3Au + 3Bu

Tables 1-3

Page 14 of 19

Accep

ted

Man

uscr

ipt




Li Na K Rb Cs


ν3 1084 1080

979 1018 979 1017 982 1017 981 1011 977 1005

951 956 948 955 949 954 sh 948 951 sh 943 946 sh

864 870 863 872 862 868 862 859 859 851

ν1 857 849 856 852 857 847 853 845 846 836

838 837 842 842 837

ν4 494 483 493 491 487

473 467 472 468 468 471 465 471 462

445 446 437 435 434

406 396 391

ν2 380 377 389

359 359 363 369 381 371 375 377

346

333 340 358 348 370 351 383 357

TZr4+

310 313 308 303 298

290 288

253 256 255 255 254

241 217 237 223 238 231 237 238

TAsO4

+

Lib AsO4

189 187 182 189 191 197

176 173

158 141

129 129 133 129 131

119

96

89

TM+ 84 65

93 93 71 52 49

75 60

Page 15 of 19

Accep

ted

Man

uscr

ipt


(C2h5)


) Assignment

Wavenumber (cm-1

)

Ra IR Ra IR

ν3 1107 ν2 388

1027 364 378

1006 354 354

976 344

953 954 336

938 935 TZr4+

+

TAsO4

297

876 286

869 883 269

ν1 854 256

848 848 230 241

820 827

805 807 TAsO4

+

Lib AsO4

194

ν4 506 178

496 126

474 476

455

430 434

400

Page 16 of 19

Accep

ted

Man

uscr

ipt

Figure 1

Page 17 of 19

Accep

ted

Man

uscr

ipt

Figure 2 edited

Page 18 of 19

Accep

ted

Man

uscr

ipt

Figure 3

Page 19 of 19

Accep

ted

Man

uscr

ipt

Figure 4

of 19

Accep

ted

Man

uscr

ipt

12

Figure captions



5) space group)



5) space group)



5) space group)


of 19

Accep

ted

Man

uscr

ipt



+ - Li - Cs with



Vibrations AsO 3


1 A1 A A1g + Eg + A1u + Eu

2 E 2A 2A1g + 2Eg + 2A1u + 2Eu

3 4 F2 A + 2B A1g + 2A2g + 3Eg +

A1u + 2A2u +3Eu

Vibrations AsO 3



2 E 2A 2Ag + 2Bg + 2Au + 2Bu

3 4 F2 3A 3Ag + 3Bg + 3Au + 3Bu

Tables 1-3

Page 14 of 19

Accep

ted

Man

uscr

ipt




Li Na K Rb Cs


ν3 1084 1080

979 1018 979 1017 982 1017 981 1011 977 1005

951 956 948 955 949 954 sh 948 951 sh 943 946 sh

864 870 863 872 862 868 862 859 859 851

ν1 857 849 856 852 857 847 853 845 846 836

838 837 842 842 837

ν4 494 483 493 491 487

473 467 472 468 468 471 465 471 462

445 446 437 435 434

406 396 391

ν2 380 377 389

359 359 363 369 381 371 375 377

346

333 340 358 348 370 351 383 357

TZr4+

310 313 308 303 298

290 288

253 256 255 255 254

241 217 237 223 238 231 237 238

TAsO4

+

Lib AsO4

189 187 182 189 191 197

176 173

158 141

129 129 133 129 131

119

96

89

TM+ 84 65

93 93 71 52 49

75 60

Page 15 of 19

Accep

ted

Man

uscr

ipt


(C2h5)


) Assignment

Wavenumber (cm-1

)

Ra IR Ra IR

ν3 1107 ν2 388

1027 364 378

1006 354 354

976 344

953 954 336

938 935 TZr4+

+

TAsO4

297

876 286

869 883 269

ν1 854 256

848 848 230 241

820 827

805 807 TAsO4

+

Lib AsO4

194

ν4 506 178

496 126

474 476

455

430 434

400

Page 16 of 19

Accep

ted

Man

uscr

ipt

Figure 1

Page 17 of 19

Accep

ted

Man

uscr

ipt

Figure 2 edited

Page 18 of 19

Accep

ted

Man

uscr

ipt

Figure 3

Page 19 of 19

Accep

ted

Man

uscr

ipt

Figure 4

of 19

Accep

ted

Man

uscr

ipt



+ - Li - Cs with



Vibrations AsO 3


1 A1 A A1g + Eg + A1u + Eu

2 E 2A 2A1g + 2Eg + 2A1u + 2Eu

3 4 F2 A + 2B A1g + 2A2g + 3Eg +

A1u + 2A2u +3Eu

Vibrations AsO 3



2 E 2A 2Ag + 2Bg + 2Au + 2Bu

3 4 F2 3A 3Ag + 3Bg + 3Au + 3Bu

Tables 1-3

of 19

Accep

ted

Man

uscr

ipt




Li Na K Rb Cs


ν3 1084 1080

979 1018 979 1017 982 1017 981 1011 977 1005

951 956 948 955 949 954 sh 948 951 sh 943 946 sh

864 870 863 872 862 868 862 859 859 851

ν1 857 849 856 852 857 847 853 845 846 836

838 837 842 842 837

ν4 494 483 493 491 487

473 467 472 468 468 471 465 471 462

445 446 437 435 434

406 396 391

ν2 380 377 389

359 359 363 369 381 371 375 377

346

333 340 358 348 370 351 383 357

TZr4+

310 313 308 303 298

290 288

253 256 255 255 254

241 217 237 223 238 231 237 238

TAsO4

+

Lib AsO4

189 187 182 189 191 197

176 173

158 141

129 129 133 129 131

119

96

89

TM+ 84 65

93 93 71 52 49

75 60

Page 15 of 19

Accep

ted

Man

uscr

ipt


(C2h5)


) Assignment

Wavenumber (cm-1

)

Ra IR Ra IR

ν3 1107 ν2 388

1027 364 378

1006 354 354

976 344

953 954 336

938 935 TZr4+

+

TAsO4

297

876 286

869 883 269

ν1 854 256

848 848 230 241

820 827

805 807 TAsO4

+

Lib AsO4

194

ν4 506 178

496 126

474 476

455

430 434

400

Page 16 of 19

Accep

ted

Man

uscr

ipt

Figure 1

Page 17 of 19

Accep

ted

Man

uscr

ipt

Figure 2 edited

Page 18 of 19

Accep

ted

Man

uscr

ipt

Figure 3

Page 19 of 19

Accep

ted

Man

uscr

ipt

Figure 4

of 19

Accep

ted

Man

uscr

ipt




Li Na K Rb Cs


ν3 1084 1080

979 1018 979 1017 982 1017 981 1011 977 1005

951 956 948 955 949 954 sh 948 951 sh 943 946 sh

864 870 863 872 862 868 862 859 859 851

ν1 857 849 856 852 857 847 853 845 846 836

838 837 842 842 837

ν4 494 483 493 491 487

473 467 472 468 468 471 465 471 462

445 446 437 435 434

406 396 391

ν2 380 377 389

359 359 363 369 381 371 375 377

346

333 340 358 348 370 351 383 357

TZr4+

310 313 308 303 298

290 288

253 256 255 255 254

241 217 237 223 238 231 237 238

TAsO4

+

Lib AsO4

189 187 182 189 191 197

176 173

158 141

129 129 133 129 131

119

96

89

TM+ 84 65

93 93 71 52 49

75 60

of 19

Accep

ted

Man

uscr

ipt


(C2h5)


) Assignment

Wavenumber (cm-1

)

Ra IR Ra IR

ν3 1107 ν2 388

1027 364 378

1006 354 354

976 344

953 954 336

938 935 TZr4+

+

TAsO4

297

876 286

869 883 269

ν1 854 256

848 848 230 241

820 827

805 807 TAsO4

+

Lib AsO4

194

ν4 506 178

496 126

474 476

455

430 434

400

Page 16 of 19

Accep

ted

Man

uscr

ipt

Figure 1

Page 17 of 19

Accep

ted

Man

uscr

ipt

Figure 2 edited

Page 18 of 19

Accep

ted

Man

uscr

ipt

Figure 3

Page 19 of 19

Accep

ted

Man

uscr

ipt

Figure 4

of 19

Accep

ted

Man

uscr

ipt


(C2h5)


) Assignment

Wavenumber (cm-1

)

Ra IR Ra IR

ν3 1107 ν2 388

1027 364 378

1006 354 354

976 344

953 954 336

938 935 TZr4+

+

TAsO4

297

876 286

869 883 269

ν1 854 256

848 848 230 241

820 827

805 807 TAsO4

+

Lib AsO4

194

ν4 506 178

496 126

474 476

455

430 434

400

of 19

Accep

ted

Man

uscr

ipt

Figure 1

Page 17 of 19

Accep

ted

Man

uscr

ipt

Figure 2 edited

Page 18 of 19

Accep

ted

Man

uscr

ipt

Figure 3

Page 19 of 19

Accep

ted

Man

uscr

ipt

Figure 4

of 19

Accep

ted

Man

uscr

ipt

Figure 1

of 19

Accep

ted

Man

uscr

ipt

Figure 2 edited

Page 18 of 19

Accep

ted

Man

uscr

ipt

Figure 3

Page 19 of 19

Accep

ted

Man

uscr

ipt

Figure 4

of 19

Accep

ted

Man

uscr

ipt

Figure 2 edited

of 19

Accep

ted

Man

uscr

ipt

Figure 3

Page 19 of 19

Accep

ted

Man

uscr

ipt

Figure 4

of 19

Accep

ted

Man

uscr

ipt

Figure 3

of 19

Accep

ted

Man

uscr

ipt

Figure 4

of 19

Accep

ted

Man

uscr

ipt

Figure 4

Vibrational spectra and factor group analysis of Mn(0.5+x)Ti(2−2x)Cr2x(PO4)3 {0≤x≤0.50}

Documents

Transcript of Vibrational spectra and factor group analysis of Mn(0.5+x)Ti(2−2x)Cr2x(PO4)3 {0≤x≤0.50}