STRUCTURE AND PHYSICAL PROPERTIES OF

SOFT MAGNETIC FeCo BASED ALLOYS

by

Aba Israel Cohen Persiano

July, 1986

A thesis submitted for the degree of of Philosophy of the University of

DoctorLondon

Department of Metallurgy and Materials Science Imperial College of Science and Technology

London, SW7

"’From a drop of water’, said the writer, ’a logician could infer the possibility of an Atlantic or a Niagara without having seen or heard of one or the other. So all life is a great chain, the nature of which is known whenever we are shown a single link of it. Like all other arts, the Science of Deduction and Analysis is one which can only be acquired by long and patient study, nor is life long enough to allow any mortal to attain the highest possible perfection in it’...n

A. Conan Doyle, A Study in Scarlet

ABSTRACT

The electrical and magnetic properties of nearly equiatomic FeCo alloys with small additions of V and Nb have been determined and correlated with the structure of the alloys. The effects of small additions of Ni, Cu, VNi, VCu and VW to the electrical resistivity of the same base alloy were also investigated.

The Mossbauer spectroscopy of FeCoV revealed that V atoms occupy preferentially the Fe sites in FeCo alloys. It was also found that the solubility limit of V and Nb in FeCo are respectively about 2 and 0.3 at%, above which the presence of solute-rich paramagnetic precipitates was observed. The correlation between volume fraction of such precipitates and magnetic properties of the alloys was successfully established, with the indication that martensite is ferromagnetic in FeCoV. The orientation of Hi „ t was also discussed.

A model to determine the electrical resistivity of quaternary alloys with two minor constituents was proposed based on the additivity of the effects of each minor element on the resistivity of the base alloy (FeCo). Such a model presents consistent results when applied to FeCoVW and FeCoVCu alloys.

A method for correlating parameters obtained from electrical resistivity and from x-ray diffractometry is presented and discussed in terms of the differing capabilities of these techniques to detect the major structural changes occurring in the FeCoNb alloys. The thermal component of the resistivity was interpreted in terms of the number of effective conduction electrons which was a function of the degree of long range order and the solute content of the matrix. The development of ordering, antiphase domains and precipitation, which change the relaxation time of the conduction electrons, have also been correlated with the resistivity measurements.

The x-ray results show that Nb produces an unprecedented reduction in the domain growth and ordering kinetics of nearly equiatomic FeCo. This has important consequences for the fabrication of FeCo based soft magnetic alloys.

CONTENTS

PAGECHAPTER 1 - INTRODUCTION....................................... 1

CHAPTER 2 - THE FeCo SYSTEM AND FeCo ALLOYS..................... 3

2.1 The FeCo Phase Diagram...................................3

2.2 Atomic Ordering......................................... 3

2.3 FeCo Based Alloys....................................... 7

2. 4 FeCoV A1 loys............................................72.4.1 Order-Disorder and APD Growth................ 82.4.2 Precipitation of Second Phase........................... 152.4.3 Recovery, Recrystallisation and Grain Growth...............202.4.4 Cold-Work Effects and Texture........................... 22

2,5 FeCoNb Alloys.......................................... 22

CHAPTER 3 - ELECTRICAL AND MAGNETIC PROPERTIES OF FeCoBASED ALLOYS...................................... 25

3.1 Electrical Resistivity..................................253.1.1 Ordering Effects....................................... 253.1.2 Other Scattering Effects................................ 273.1.3 Electrical Resistivity of FeCo and FeCo Based Alloys....... 28

3.2 Magnetic Properties of FeCo and FeCo Based Alloys......... 383.2.1 Ferromagnetism and FeCo Alloys.......................... 383.2.2 Other Magnetic Properties of FeCo Alloys................ .40

CHAPTER 4 - SOME APPLICATIONS OF MOSSBAUER SPECTROSCOPYAPPROPRIATE TO THE PRESENT INVESTIGATION............ 43

4.1 Detection of Magnetic Phases............................43

4.2 Quantitative Phase Analysis............................. 45

4.3 Measurement of Magnetic Parameters.......................45

4.4 Texture Effects....... 46

4.5 Ordered Alloys......................................... 46

4.6 Site Population............. 48

4.7 Lattice Defects........................................ 52

4.8 Mossbauer Spectroscopy of FeCo and FeCo Based Alloys....... 52

CHAPTER 5 - EXPERIMENTAL PROCEDURE AND TECHNIQUES...............58

5.1 Choice of Experimental Techniques........................58

5.2 Material............................................... 59

5.3 Differential Thermal Analysis........................... 59

5.4 Thermo-mechanical Treatments............................ 61

5.5 Microscopy............................................. 635.5.1 Light Microscopy....................................... 635.5.2 Scanning Electron Microscopy (SEM)............. 635.5.3 Transmission Electron Microscopy (TEM)................... 63

5.6 X-Ray Diffractometry....................................645.6.1 Determination of Degree of Long Range Order.............. 645.6.2 Determination of Antiphase Domain Size................... 665.6.3 Lattice Parameter Measurements.......................... 67

5.7 Mossbauer Spectroscopy.................................. 675.7.1 Detection of Phases Present............................. 685.7.2 Magnetic Properties on the atomic Scale.................. 685.7.3 Site Population........................................ 68

5.8 Electrical Resistivity.................................. 695.8.1 Dependence with Composition and State of Ordering....... .695.8.2 Electrical Resistivity Parameters and Structural Changes...695.8.3 A Computer Controlled Resistivity Rig.................... 71

5.9 Magnetic Measurements...................................72

CHAPTER 6 - RESULTS........................................ ...76

6.1 Phase Analysis......................................... 766.1.1 DTA Results............................................ 766.1.2 Microstructure.................................. . 78

6.2 Texture................................................ 89

6.3 Ordering of FeColNb...... ....,..,.906.3.1 Bragg-Wi 11 iams LRO Parameter (S).........................906.3.2 Lattice Parameter (a0).................................. 926.3.3 Antiphase Domain Size (D)............................... 95

6.4- Electrical Resistivity Results........... 956.4.1 Ternary Additions and Ordering Effects................... 956.4.2 Effects Due to Microstructural Changes................... 99

6.5 Magnetic Measurements Results.......................... 101

6.6 Some Parametric Changes with Ordering and Composition.....1086.6.1 Lattice Parameter......................................1086.6.2 Temperature Coefficient of the Electrical Resistivity....1106.6.3 Hyperfine Parameters................................... 110

CHAPTER 7 - DISCUSSION....................................... 116

7.1 A Statistical Analysis of the Site Populationof Low Vanadium in Equiatomic FeCo Alloys...............116

7.2 The Preferential Site for Vanadium in FeCo Alloys......... 121

7.3 Effects of Ternary Additions and Microstructura1 Changesto the Electrical Resistivity of FeCo Based Alloys....... 122

7.4 Microstructure and Electrical Resistivity of FeColNb..... 1307.4.1 Preliminary Comments................................... 1307.4.2 A New Empirical Function >(S,T).............. ........ 1317.4.3 A New Parameter (S’)................................... 1327.4.4 Application to the Quenched Material (Group 1)...........1347.4.5 Application to the Furnace-Cooled Material (Group 2)..... 143

7.5 Microstructure and Magnetic Properties.................. 1497.5.1 Correlation Between Bs and the Hyperfine Field...........1497.5.2 The Effect of Second Phase Particles on Bs and He........ 153

7.6 Texture and the Hyperfine Field.........................153

7.7 Ordering of FeCoNb Alloys.................... ........ 1577.7.1 LRO Parameter......................................... 1577.7.2 APD Growth............................................ 157

CHAPTER 8 - CONCLUSIONS AND SUGGESTIONS FOR FURTHER WORK....... 162

8.1 Conclusions........................................... 162

8.2 Suggestions for Further Work........................... 165

APPENDIX - THE MOSSBAUER EFFECT AND MOSSBAUER SPECTROSCOPY....... 166

ACKNOWLEDGEMENTS............................................. 173

REFERENCES...................................................174

CHAPTER 1

INTRODUCTION

Since 1912 the FeCo system has been reported to attain a magnetic moment per atom higher than its isolated constituent elements, and the composition Fe-35%Co was recognised to exhibit the highest magnetic saturation known for a binary metallic alloy (Weiss and Preuss-1912). In 1929 an American patent was granted to Elmen on the 50%Fe-50%Co composition, called Permendur, which was intended for the construction of small magnetic pole-pieces of sound recorders, loud speakers and earphones of deaf-aid sets. The equiatomic composition was found to present the lowest coercive force in the system, * higher permeability and slightly lower saturation magnetization than the observed for Fe-35%Co, being more suitable for many magnetic purposes. However, serious mechanical problems arose from the hardness and brittleness of this material and soon after attempts were made to overcome this problem by the addition of a third element to the equiatomic alloy.

In 1932, White and Wahl were granted an USA patent on the FeCo2%V called 2V-Permendur and, ever since, this third element has remained as the traditional ternary addition in soft magnetic materials, due to the fact that it gives good ductility without deteriorating significantly the magnetic properties of the material. Moreover, a few percentage of vanadium, as no other known addition, increases the electrical resistivity of the system by a factor of about 20, favouring the application of the alloy as a soft-magnetic material for a.c. purposes, as the eddy current losses are proportional to the electrical conductivity of the material.

By 1940 the application of high vanadium concentrations started when Nesbitt and Kelsall developed a machineable alloy named Vicalloy, designed for permanent magnet purposes and composed of 30-50%Fe, 36-62XCo and 6-16XV. The high-V Vicalloys 012% V) exibit a transformation of the retained paramagnetic phase into a ferromagnetic phase, induced by cold-work; these alloys are called Vicalloy II to differentiate them from the lower V alloys, named Vicalloy I.

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Some efforts in the past were made to partially substitute V by less expensive Cr in hard-magnetic materials. More recently many attempts to improve the properties of soft-magnetic FeCo alloys have been made, since it is still questionable whether vanadium is the best addition to the system, and the total substitution of vanadium or the addition of a fourth element to FeCoV such as FeCoVNi (e.g. Pitt-1980), FeCoCu, FeCoVCu, FeCoNi, FeCoSi, FeCoVSi, FeCoW, FeCoVW (e.g. Orrock-1986) have been investigated.

The understanding of the relationship between microstructure and physical properties of FeCo based alloys is of fundamental importance since both electrical and magnetic properties have marked dependence on microstructura1 features such as the presence of a second phase, changes in the degree of atomic order, development of antiphase domains and grain size as well as changes in the solute concentration in the matrix.

Only a few investigations have been performed with this objective and little is known about the correlation between, for instance, the presence of T2 precipitation or the solute content in the FeCo matrix and the alterations in the electrical and magnetic properties of the material. One of the purposes of the present investigation is to add to our knowledge on this subject, by studying the effects of the employment of additions such as Nb, V, Ni, Cu, VNi, VCu, and VW to the physical properties of nearly equiatomic FeCo.

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CHAPTER 2

THE FeCo SYSTEH AND FeCo ALLOYS

2.1 The FeCo Phase Diagram

A number of investigations have been made in order to determine the equilibrium phase diagram of FeCo alloys (eg. Ellis and Greiner- 1941, Lyashenko et al-1962, Normanton et al-1975) and reviewed in many publications (e.g, Hansen-1958, Elliot-1965, Shunk-1969,Riv1 in-1981). One of the most recent reviews, by Nishisawa and Ishida (1984) combined the information from many other investigators to produce the phase diagram shown in figure 2.1. The main features are the existence of a high temperature fee paramagnetic phase (I\ ) that at equiatomic composition transforms into ferromagnetic bcc phase («t ) at about 985*C; at lower temperatures andintermediate compositions the <xt phase undergoes atomic ordering to a B2 superlattice (a,’ phase) (see figure 2.2). The ordered structure has been found to be present at room temperature in the range between about 25 and 75 at* Co. For equiatomic composition the order/disorder transition takes place at about 730°C. Alloys quenched sufficiently rapidly from above this temperature are retained substantially in the disordered bcc state (Ellis and Greiner-1941). An interesting correlation between long range order, driven by pairwise interatomic forces, and ferromagnetism, given by Ising-type magnetic interactions, of FeCo alloys has been proposed by Moran-Lopez and Falicov (1980) in order to deduce the FeCo phase diagram in the composition range between 30 and 70 at* Co.

2.2 Atonic Ordering

The ordering of an equiatomic system of atoms A and B can be understood in terms of the interaction energy between two dissimilar atoms E(AB) compared with the average interaction energy between similar atoms CE(AA)+E(BB)3/2. The ordered structure is favoured if E(AB) < CE(AA)+E(BB)3/2.

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Fi gure 2.1 - The FeCo phase diagram, after Nishisawa and Ishida-1984

suetAnce B • = C o

Figure 2.2 - The B2 superlattice

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The Bragg-Wi11iams long range order parameter (S) for a binary AB alloy compares the probability Cp(A)1 of finding an atom A in the correct site with the fraction of atoms A in solution Cf(A)l and is given by:

S = Cp(A)-f(A)3/Ci-f(A)3 (2.1)

If AB has an equiatomic composition then the expression 2.1 reduces to:

S = 2p(A) - 1 (2.2)

Another important parameter in the study of atomic ordering is the short range order parameter (r) defined in terms of the observed average fraction Cq3 of dissimilar nearest neigbours compared with the expected fraction of dissimilar atoms in a fully disordered [q(d)3 and in a fully ordered [q(o)3 condition and is given by:

r = C q - q(d) ] / C q(o) - q(d)]

which in a B2 superlattice reduces to

r = (q - 4)/4

(2.3)

(2.4)

Ordered systems such as the FeCo alloys are stable at low temperatures but as the temperature increases the tendency to form pairs of dissimilar atoms is disturbed by the thermal energy that produces a continuous reduction of S. From a critical temperature (Tc) upwards the long range order parameter S is rigorously zero (see fig. 2.3). Nevertheless the short range order parameter decreases smoothly being different from zero even above Tc (Krivoglaz and Smirnov-1964).

In a real crystal some imperfections can occur in an ordered structure. The situation in which two like atoms are linked two-by-two over a surface is called an antiphase boundary (APB). The volume encapsulated by an APB is ordered and is called an antiphase domain (APD) (see fig. 2.4). The APB are high energy defects since they are formed by A-A or B-B bonds. At elevated temperatures the thermal energy provides enough atomic mobility for domain growth,

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Figure 2.3 - The variation in the long range order parameter, S, with temperature for FeCo - after Stoloff and Davies-1964.

APR

Otf fercnt crystals

w

Crystal boundary Oomain boundary

Figure 2.4 - Schematic representation of ordered domains in two different crystals with equal number of atoms A (black) and B (white)

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thus reducing the total area of APB and hence reducing the free energy of the system.

2.3 FeCo Based Alloys

The high saturation magnetization of FeCo alloys together with other magnetic characteristics discussed in section 3.2 confers to equiatomic FeCo the optimum conditions for a variety oftechnological applications as soft magnetic material used, for instance, in transformers and generators. Unfortunately the mechanical properties of these alloys are not very good since they tend to be brittle in the ordered condition. In addition, the electrical resistivity being low increases the losses due to eddy currents when the alloy is used as soft magnetic material in an a.c. application. To improve the strength, ductility and resistivity without degrading its magnetic qualities, it is common practice to add small amounts of one (e.g. vanadium) or perhaps two (e.g. vanadium and nickel) extra elements to nearly equiatomic FeCo (Clegg-1971, Josso-1973, Koylu et al- 1973, Pinnel et al-1976, Pitt and Rawlings-1981).

It has been found that various microstructura1 changes accompany the addition of ternary and quaternary elements. These changes play an important role in determining the properties of industrial interest. Some of the microstructura1 aspects that have been observed and are considered important to varying extents are the development of T2 precipitation, ordering, APD growth, recovery, recrystallization and grain growth. Among the ternary alloys the FeCoV system is the most widely used commercially and hence the most studied (e.g. English- 1966, Josso-1973, Mahajan et al-1974, Ashby et al-1978,Kawahara-1983 a and b). It is therefore appropriate to discuss the FeCoV system in more detail and this is done in the next section.

2.4 FeCoV Al1oys

This section deals mainly with FeCoV alloys but where appropriate, the quaternary systems FeCoVNi (e.g. Pitt-1980, Pitt and Rawlings- 1983), FeCoVCu, FeCoVSi and FeCoVW (e.g. Orrock-1986) or even other

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ternary systems with additions such as Nb, Al, Be, Cu, Au, Mn, Ag, Si, Ti, Zr, Ta, C, Cr, Mo, Al, Be, B, Cu, Au, Mn, Ag, Si, Ti, Zr, Ni and W (e.g. Kawahara-1983 c, Kawahara and Uehara-1984, Orrock-1986) are also referred to. Some aspects of FeCoNb alloys are discussed in section 2.5.

Figures 2.5 and 2.6 show the combined results obtained respectively by Koster and Lang (1938) and Ellis and Greiner (1941) or by Martin and Geisler (1952) and Koster and Schmid (1955) (reviewed by Raynor and Rivlin-1983) for the vertical section of the low vanadium end of approximately equiatomic FeCo phase diagram. The common points, with the solution of some controversies by more recent works, are:

a) The existence of a high temperature phase with Ai (fee) structure designated Tt.

b) The r\ phase transforms into a low temperature phase with structure A2 (bcc) designated oct • The phase diagrams differ somewhat in the position of the a,+Ti phase field. For FeCo2V the upper and lower limits are in the ranges 937-1000°C and 789-895°C respectively. More recently Ashby et al (1977) put these limits at 900-950“C and 850-875°C respectively. The consensus of opinions is that the T, phase transforms martens itically, on quenching, into a non-equilibrium A2 (bcc) phase designated a2 , as reported by Ashby (1975).

c) The ai phase undergoes a disorder/order transformation near 700°C to the B2 superiattice structure designated a,’.

d) The precipitation of a low temperature r2 phase in the <xt ’ matrix. Ashby et al (1977) have shown that r2 is vanadium rich and has the Ll2 ordered structure. This transformation is fully reviewed by Pitt (1980).

2.4.1 Order-disorder and APD Growth

A full understanding of the order-disorder transformation is of considerable importance since ordered FeCo and based alloys are

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Figure 2.5 - The FeCo-V phase diagram (vertical section) after Ellis and Greiner-1941 (E+G) and Koster and Lang-1938 (K+L).

containing V content (full lines), after Martin lines show ri/n+al and n + ai/ocl

Coequiatomic FeCo as function of and Geis1er-1952. The broken boundaries under equilibrium conditions for alloys with constant (52%); after Koster and Schmid-1955, apud Raynor and Rivlin-1983.

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brittle. In contrast however, the disordered structure has enough ductility to be mechanically worked (Stoloff and Davies-1964, Clegg-1971, Koylu et al 1973, Pinnel et al-1976, Kawahara- 1983c), In addition, other parameters such as the electrical resistivity (discussed in chapter 3) and the magnetic hyperfine field (discussed in chapter 4) change with ordering.

Critical Temperature

The order/disorder transition temperature (Tc) of equiatomic FeCo is around 730*C (Seehra and Si I insky-1976, Rossiter-1981) and may vary in FeCo based alloys depending on the ternary or quaternary addition employed, as reported by several workers (e.g. Martin and Geisler- 1952, Greist et al-1955, Hagiwara and Suzuki-1976, Urushihara and Sato-1978, Orrock-1986). Table 2.1 shows the effects produced by ternary/ quaternary additions to the value of Tc. The general trend shows that elements such as W, Si and Al tend to increase Tc while V, Ni, Cr and Cu tend to decrease Tc. A good review on the critical temperature of FeCo based alloys is presented by Orrock-1985.

Ordering and Lattice parameter Changes

A small but significant difference between the lattice parameter (aQ) of ordered and disordered FeCo or FeCo based alloys has been reported (Fine and Ellis-1952, Clegg-1971, Orrock-1986). In allcases the value corresponding to the ordered structure is bigger than that for the disordered structure. According to Fine and Ellis such a difference in a0 is due to the smaller coeficient of thermal expansion observed for the ordered structure.

OClegg (1971) observed an almost constant difference of about 0.0020A between the two structural conditions in FeCo, FeCo(0.35at%)Nb, FeCo(0.35at%)Cr and FeCo(0.4-5.2at%)V. He also noticed that a0 increases with the addition of Nb and increasing additions of V as shown in figure 2.7. Orrock (1986) observed similar changes and

Oreports a little higher difference (about 0.0030A) between a0 of ordered and disordered nearly equiatomic FeCo with small additions

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TABLE 2.1

Dependence of Tc in FeCo based alloys with ternary or quaternary additions

REFERENCE MATERIAL TECHNIQUE COMMENTS

Martin and Geis1er-1952 FeCol.8V x-ray Tc=700°C

Greist et al 1955

FeCoSi FeCoA1

th.analysis

Both Si and Al increase Tc at about 40°C/at%

Stoloff and Davies-1962 FeCo2V x-ray Tc=720°C

Clegg and Buck 1ey-1973 FeCoV

Mag. sat. x-ray V decreases Tc by li°C/at%

Hagiwaraand

Suzuki-1976

FeCoWFeCoCrFeCoV

DTAW increases Tc by 8®C/atX Cr decreases Tc by 5°C/at* V decreases Tc by ll*C/at%

Urushi hara and

Sato - 1978FeCoW DTA

Tc increases up to 755°C with 0.2at% W and then decreases

Orrock-1985

several FeCo and FeCoV based a 11oys

DTA

=========in FeCo:==========Si increases Tc by 19°C/wt% W decreases Tc by 6°C/wt% Cu decreases Tc by li*C/wt% V decreases Tc by 14"C/wt% Ni decreases Tc by 30°C/wt%========in FeCo2V:=========Si increases Tc by 30°C/wt% Mn increases Tc by 18°C/wt% W decreases Tc by 6®C/wt% Cu decreases Tc by llaC/wt%

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FeC o 2

D iso rdered

o F eC o-V• FeC o—Nb■ FeCo—C r

t i3 4

a t 'A

Figure 2.7 - additions of

The change in lattice parameter of FeCo with vanadium, chromium and niobium, after Clegg-i97i

JL5

var i ous

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of W, Cu, Ni, V and Si (figure 2.8-a) or VW, VCu and VSi (figure 2.8-b). Both authors associated varying degrees of long range order with intermediate values of a0. Orrock used this method to correlate successfully the obtained S to the cold-workability of 2.5mm thick specimens in the quenched condition. He observed that all the specimens with LRO below a limit of about S=0.3 are Tollable; some of the specimens containing V have this limit extended to S=0.5; above this limit no specimen was Tollable.

Mechanism of Ordering

Buckley (1975) observed that equiatomic FeCo and FeCo0.4XCr present two distinct mechanisms of ordering: i) grain boundary nucleation and growth of the fully ordered structure in the range 250-430°C and ii) homogeneous ordering followed by APD coalescence above 500°C. On the other hand he observed only the homogeneous process in FeCo2.5XV at all ordering temperatures. Rogers, Flower and Rawlings (1975), however, found evidences of the grain boundary mechanism in FeCo2%V but not to the same extent as in the binary alloy which showed a wider temperature range for this mechanism than that reported by Buck 1ey.

Kinetics of Ordering

On quenching FeCo and FeCo based alloys from above Tc it is commonly observed that the thickness is not small enough to permit a quench rate sufficiently rapid to avoid the ordering (English-1966, Ashby et al-1977). This occurs because of the extremely rapid ordering transformation that surpasses the cooling rate of a relatively thick sample. Kadykova and Selissky (1960) estimated quench rates to retain disorder as great as 6000°C/s. On the other hand Clegg and Buckley (1973) refer to cooling rates of about 3000°C/s and this necessitates thicknesses of 0.7 mm (or lower) for quenchings from 800°C into iced brine.

Although it is often assumed that vanadium is responsible for the lowering of the ordering kinetics, and hence facilitating the retention of disorder, the work of Clegg and Buckley casts doubts on

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(a)

a t ’/. Addition

(b)Fi KV-Lg., 2* 8 “ The variation of lattice parameter a0 with alloy addition to (a) FeCo and (b) FeCoV in the ordered (open symbols) and disordered conditions (full symbols) after Qrrock 1986.

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this role for vanadium (see fig. 2.9). However the more recent work of Orrock (1986) has demonstrated that V, as well as W, Ni and Cu additions, retard the ordering kinetics whereas Si increases the rate of ordering. Smith and Rawlings (1976) observed by neutron diffraction technique that cold working retards the ordering kinetics of FeCol.8V but has little effect on the activation energy for ordering which they determined as 256 KJ/mol. This compares favourably with the value of 247 KJ/mol for atomic diffusion in disordered FeCo (Hirano and Cohen-1972). Fishman et al (1970) also report similar activation energies for diffusion in disordered FeCo (228 KJ/mol for Fe and 250 KJ/mol for Co), while the reported values for diffusion in an ordered matrix are much higher (553 KJ/mol) for both Fe and Co.

Kinetics of Domain Growth

Many workers have noticed that the APD size of FeCoV alloys is proportional to the root square of the annealing time (e.g. English- 1966, Clegg and Buck 1ey-1973, Rogers et al-1975). The same proportionality is also observed in some binary alloys such as FeCo and Cu3Au and coincides with the grain growth exponent of recrystallized materials. Nevertheless this is not the general rule as described in the review by Brown (1978) on the ordering of binary alloys. The activation energy for antiphase domain growth in FeCo2V alloys was found to be in the range 178-377 KJ/mol . The most reliable results show a constant value of about 255 KJ/mol in the temperature range 473-650*C which is consistent with APD coarsening by atora/vacancy interchanges in the mainly disordered APBs as reported by Ashby (1975).

2.4.2 Precipitation of Second Phase

Some previous workers have reported the presence of vanadium-rich precipitates after annealing FeCoV alloys in the temperature range 600-700°C (Davies and Sto1 off-1966, Fiedler and Davis-1970, Mahajan et al-1974, Pinnel et al-1976). The most relevant information from these works refer to very small particles (smaller than 1 pm diameter) with a composition of about 22%V, 65%Co, 13%Fe and a

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Figure 2.9 - Isothermal ordering curves for FeCo (a) and FeCo2.5V (b), after Clegg and Buckley-1973.

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lattice parameter of 3.5669 ± 0.0005 A (according to Fiedler and Davis) that are formed more easily in cold-worked specimens.

In the last ten years more detailed studies of this precipitation process have been carried out using techniques such as transmission electron microscopy.

Ashby et al (1978) reported the presence of a vanadium-rich r2 precipitate with an Ll2 superlattice structure after annealing cold-worked FeCo2V for 6.5 x 103s at 550°C. On the other hand, undeformed samples of FeCo2V annealed in the range 500-550°C ordered more slowly and vanadium segregation at the APBs was detected prior to precipitation, which took place after very long times (10‘s). The most favoured precipitation sites were the grain boundaries. Within the grains precipitation occurred at the dislocations for thecold-worked material, inhibiting their movement, and on the APBs for the undeformed material. A transport-controlled mechanism for the formation of such precipitates, rather than a nuc1 eation-contro11ed mechanism, was suggested. The precipitates were found to have a lath morphology with the long axis along the <i11> directions and to be twinned and faulted on the (111) planes. Figure 2.10 shows the TTT curves for T2 formation in cold-worked and in annealed FeCo2V.

iPitt and Rawlings (1981) observed a significant increase in theproportions of T2 precipitation on adding 3.5 to 7.4 wt% Ni to the ternary FeCo (0.7 to 1.5 vit%) V. Figure 2.11 shows the TTT curve for annealed FeCoV3.5Ni. The same figure displays the TTT curve obtainedby Ashby and co-workers for FeCoV under similar conditions. Acomparison between the two materials shows that the position of the "nose" of the TTT curve changes from about T=550°C and t=104 s in FeCoV to about T=650*C and t=103s in FeCoVNi. The precipitates are reported to be rich in V and Ni. The small grain sizes in the quaternary recrystallized alloys are attributed to the presence of r2 particles restricting primary grain growth. Pitt (1980) also studied the effects of up to 3% Mn addition to FeCoV but unlike for Ni, no significant increase in precipitation was observed. In the publication of this work the author also presents a good review on gamma precipitation in FeCo based alloys up to 1980.

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F i gure 2.10 - TTT curves for annealed and cold worked FeCo2V, after Ashby, Flower and Rawlings-1978.

Figure 2.11 - TTT curve for annealed FeCoV3.5Ni alloy after Pitt and Rawlings-1981, compared with that reported by Ashby et al-1978 for FeCo2V.

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Kawahara (1983a and b) studied the mechanisms for the improvement of ductility in the alloy due to small additions of several elements to equiatomic FeCo and suggested that C, V, Cr, Ni, Nb, Mo, Ta and W have a potential to combine with Co to form a Co3X type compound. Such compounds by withdrawing Co atoms from the matrix, inhibit the formation of B2 ordered FeCo and, consequently, are reported to be responsible for the formation of local concentration disordered zones (LCD zones). Thus these elements are effective in improving the ductility of the respective alloys. On the other hand according to Kawahara Al, Be, B, Cu, Au, Mn, Ag, Si, Ti and Zr do not form such compounds and LCD zones and hence do not improve the ductility of the a 11oys.

Orrock (1986) observed the presence of fine second phase particles (diameter less than 0.5 jim) in FeCo2V(l-5 wt%)Cu, FeCo2V(l-5 wt%)W and FeCo(l-5 wt%)Ni. The particles were identified as r2 with a lattice parameter of about 3.6 X and were responsible for marked grain refinement. In contrast, the addition of 1 to 3 wt% Si to FeCo or FeCo2V did not cause significant changes to the microstructure. The only ternary systems which could be rolled were the FeCo2V and FeCoSNi but most quaternary systems containing 2%V were Tollable.

Precipitation and Changes in the Lattice Parameter (aa)

It has been known for some time that the lattice parameter varies nearly linearly with the addition of solute elements to a primary solid solution due to the expansion or contraction of the lattice produced by a larger or smaller solute atom. This fact, known as Vegard’s law, has been extended to changes in solute concentration due to precipitation or pre-precipitation processes (e.g. Wilkes and Barrand-1968 in a study of the pre-precipitation in CuBe alloys).

The changes observed by Orrock (1986) in the lattice parameter of FeCoX alloys as function of V, W, Ni, Cu and Si contents (figure 2.8-a) were correlated with the atomic radius of the additional element by assuming that Vegard’s law is reasonably valid for small additions of a third/fourth element to nearly equiatomic FeCo. The same argument, together with microstructural considerations, were

- 1 9 -

used to explain the changes in a0 due to the additions or W up to1.5at%, Cu up to 4.5at% and Si up to 6at% to FeCo(2.2at%)V (figure 2.8-b). Saturations of a0 as observed in FeCoVW or the maximum observed in FeCoVSi were associated with the solubility limits of the respective quaternary additions and confirmed by the presence of precipitates in the corresponding specimens. In the case of FeCoVSi it was suggested that there was a possible depletion of V atoms from the matrix during the precipitation process at compositions above 2at%Si.

The main points on the precipitation process in FeCo alloys are summarized in table 2.2.

2.4.3 Recovery, Recrystallisation and Grain Growth

The electron microscopy and electrical resistivity investigation of Ashby et al (1978) detected recovery of FeCo2V cold-rolled (25-50% R.A.) at temperatures as low as 500°C. Recrystallisation and grain growth were detected in cold-worked FeCoV alloys after annealing the material for 2 hours at temperatures just below the order-disorder transition (Davies and Stoloff-1966, Fiedler and Davis-i970). On the other hand Buckley (1976) has reported that recrystallisation can occur below 600°C but the time to recrysta11ise the material is excessively long.

The influence of alloying elements is important whether they remain in solution or form precipitates. For example Buckley observed a two stage recrystallisation in FeCo0.4Cr when the Cr is in solution: between 250 and 475°C (recrystallisation driven by ordering) and above 600°C (normal recrystal 1isationj. On the other hand many other workers have reported that second phase particles produced by alloying additions can affect both recrystallisation and grain growth. This is exemplified by the work of Branson et al (1980). They suggested that about 5% by volume or T2 present in some FeCoVNi alloys is responsible for the enhancement in the recrystallisation as well as the restriction observed in the grain growth; however the small amount of gamma (less than 1% in volume) in FeCoV is thought to be insurficient to greatly afreet the recrystailisat ion or the

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TABLE 2.2

Precipitation of second phase in FeCo based alloys

REFERENCE MATERIAL INFORMATION

very small (<lpm) solute richSeveral authors particles with about 22%V,up to 1976 FeCoV 65%Co and 13%Fe. Formed more

easily in deformed material.

V rich particles; lath shape;FeCo2V L12 structure; in previously

annealed material tend to precipitate on the grain

undeformed boundaries and APBs after 10*s; in cold-worked material

Ashby et al-1978 or tend to precipitate in the grains and sub-grains after 103s. A transport controlled

co1d-worked mechanism is suggested; TTT*• curve has "nose" at 550°C.

Ni enhances r2 formation butPitt-1980

FeCoVNino precipitate was observed after slow cooling from 750°C

and(V=0.7-1.5%)

if Ni content is 1.8% or less. TTT curve for undeformed alloy has the "nose" at lower

Pitt & (Ni=l.8-7.4%) times and higher temperaturesRawlings-1981 when compared to FeCoV. Small

grains are due to T2 present.

If Co3X compounds are presentSevera1 the alloy is ductile. The

reason is attributed to LCDternary zones that, being deficient

in Co, do not permit theKawahara-1983a&b FeCoX formation of B 2 (ordered)

volumes. Some Co3 X effectivea 11oys elements are: C,V,Cr,Ni,Nb,Mo

Ta and W; ineffective are: B,(X=0.01-4at%) A1, Be, Cu,Au,Mn,Ti,Si, and Zr.

r2 particles with diameterFeCo2VCu less than 0.5 pm and latticeFeCo2VW parameter 3.6 X; cause grain

Orrock-1985 FeCoNi refinement in FeCoVCu, FeCoVWFeCoSi & FeCoNi; no microstructura1

(X=l,3,5 wt%) change was observed in FeCoSi.

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grain growth of the ternary alloy and, consequently the recrystallised grain size is much larger. This effect has been confirmed for other FeCo based systems by Orrock (1985) as mentioned in the last sub-section.

2.4.4 Cold Work Effects and Texture

Orrock (1985) found that an effective method of controlling the grain size in FeCo based alloys is by changing the degree of cold-work prior to the final anneal: the smaller the % cold-work the larger the grain size. The same author reported a (001)[llO] texture for heavily rolled FeCoV while the recrystallised texture was (11DC211]. On the other hand, a light deformation (<30%) shows a (112H110] texture that changes principally to (112)Cll0] on recrystallisation. Material given a two-stage treatment (heavy initial roll, intermediate anneal and quench, and final light roll) exhibits a (111)C2113 texture while the recrystallised texture is a duplex (111)C211] and (112)C1103.

2.5 FeCoNb Alloys

In the last few years the advantages of employing niobium as substitute of vanadium in special steels (e.g. Souza et al-1984), as a ternary element in FeCo magnetic alloys (e.g. Kawahara-1983 c, Kawahara and Uehara-1984) or in amorphous magnetic FeCo based systems (e.g. Morita et al-1985) has been pointed out. Apart from the latter and a few other papers, the FeCoNb system has received very little attention and no phase diagram was found in the specialised literature. This section presents some previous results and discusses the potential that niobium exhibits as a third element in soft-magnetic FeCo alloys.

Clegg and Buckley (1973) observed that a small amount of niobium (0.37 at%) can retard the ordering kinetics of FeCo by about one order of magnitude at temperatures about 450°C. Even at 550°C a reasonable delay was observed for the ordering of FeCoNb when compared with the other alloys investigated (FeCo, FeCoV and FeCoCr) see f igure 2.12.

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Figure 2.12 - TTT curves for isothermal ordering in FeCo and some FeCo based alloys. Open symbols indicate relative degree of order = 0.5, full symbols indicate relative degree of order = 0.95, after Clegg and Buckley-1973.

Fisure 2.13 - Darken-Gurry plot used for obtaining a rough estimate of the solubility of elements in each other. The larger the distance between two points of the plot, the smaller the solubility of the corresponding elements. Inside the small circle easily soluble elements are found in Fe or Co, the space between the two circles contains elements that are somewat less soluble in Fe or Co, while the solubility outside the larger circle is frequently quite small.

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The Canadian patent No 934 990 issued on October 1973 refers to a magnetic alloy composed of 0.5-2.5% V, 45-52% Co, 0.02-0.5% Nb,0.07-0.3% Zr (balance Fe). This system is reported to be ductile, with the Nb being one of the most significant elements to achieve this effect.

Kawahara (1983-c) and Kawahara and Uehara (1984) in studies on the mechanical and magnetic properties of several ternary FeCo based alloys confirm the good ductility of FeCo alloys containing 0.5-2% Nb and attributed this to the reported LCD zones near Co3Nb compounds as discussed in the last section. The reported magnetic parameters exhibited by FeCo0.5Nb quenched from 1200oC and 90% cold-rolled are: saturation magnetization (Bs)=2.33 T and coercive force (Hc)=2200 A/m. On the other hand FeCo2Nb quenched from 1100*C and 90% cold-rolled gave Bs=2.16 T and Hc=3300 A/m.

Some other considerations can also be drawn: niobium is the first element below vanadium in group V-A and therefore there are similarities in their electronic structures. Since vanadium is traditionally the best element to be added to FeCo in order to improve its physical properties, one can suppose that Nb may also do the same, as has been partially confirmed from the mechanical properties viewpoint. Some of the resemblances that can be pointed out are: both elements have common structure (bcc), valency (5), electronegativity (1.6). The solubility of Nb in FeCo must be also considered: according to the Darken-Gurry diagram (figure 2.13) while V is in the first circle around Fe and Co (which corresponds high solubility in FeCo) Nb is located in the second circle (Darken and Gurry-1953). This means that niobium has intermediate solubility in the binary system while the elements outside this area have remote chances of forming a solid solution. Another important argument favouring the substitution of V for Nb is that of economics, since commercially pure Nb costs about 20% less than commercially pure V.

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CHAPTER 3

ELECTRICAL AND MAGNETIC PROPERTIES OF FeCo BASED ALLOYS

3.1 Electrical Resistivity

The understanding and control of the electrical resistivity (f>) of soft magnetic materials is important since the eddy current losses in AC core materials are proportional to their conductivity. Many of the typical microstructura1 features that can affect the resistivity of FeCo based alloys such as ordering, APB or precipitation are discussed in sections 3.1.1 and 3.1.2. Section 3.1.3 presents some previous resistivity results from FeCo and FeCo based alloys.

3.1.1 Ordering Effects

The electrical resistivity of a disordered substitutional binary alloy with unlimited mutual solubility should present a strong dependence with the atomic fraction (c). The addition of atoms B to pure metal A or vice-versa, disturbs the regularity of the crystal lattice, increasing the residual resistivity of the pure metal (theoretically zero). If both metals have similar electronic structure the simplest random model predicts a free electrons scattering factor proportional to c(l-c) and a maximum in the residual resistivity at the equiatoraic composition is expected (Krivoglaz and Smirnov-1964). This is indeed the case for alloys such as quenched (disordered) CuAu (see fig. 3.1 - curve A). The onset of ordering and the consequent increase of the lattice periodicity is responsible for the drop of the residual resistivity as evidenced by the minima observed in the resistivity of annealed CuAu alloys at the Au contents c=0.25 and c=0.5 (fig 3.1 - curve B).

A more specific treatment can be carried out in terms of changes or creation of new energy gaps due to the interactions of the Fermi surface with different Brillouin zone boundaries produced in an ordering system. The presence of new possible Bragg reflections of the conduction electrons changes their density of states N(E) which

- 2 5 -

F i gure 3.1 - The variation of electrical resistivity with composition for the Cu-Au system in the quenched from 650*C condition (curve A) and in the annealed at 200°C condition (curve B) Ordering is present in the alloys annealed but not in those quenched

-2 6 -

reduces the Fermi energy and consequent 1y stabi1izes thesuper lattice (Nicholas-1953) . This change is respons ib1e foralterations of the effective number of conduction e1ectrons, Neff,and/or its effective mass, m* (Rossiter 1980-a).

An expression for the electrical resistivity of a binary alloy as function of the Bragg-Wi11iams LRO parameter (S) and the absolute temperature (T) has been proposed by Rossiter (1980-a), who used the simple relaxation time approximation (p=ra* / (Neff e2 t ) where e is the electrons charge and t their relaxation time) and took into account the effects of ordering on the effective number of conduction electrons [Neff a (1-AS2)] and on the relaxation time C(1/t ) a (i-S2)]. The proposed expression for p(S,T) for a material whose Debye temperature is both below Tc and independent of S is:

p(S, T) = tpo(O) (i-S2) + (B/n,) T ] / (1-AS2) (3.1)

where p0(0) is the residual resistivity of the fully disordered alloy and B/n„ and A are appropriate constants dependent on the material. An important step in the deduction of expression 3.1 was to consider (1/Neff) oc (Sp/ST) (Coles-1960) thus enabling changes in Neff to be determined through the variations in the temperature coefficient of the electrical resistivity. Good agreement between the theoretical values obtained from equation 3.1 and the experimental data for Cu3 Au and Fe3Al was reported by Rossiter (1980-a).

3.1.2 Other Scattering Effects

Jones and Sykes (1938) studied the scattering effects of antiphase domains on the electrical resistivity of Cu3Au. Their expression for p using the wave theory in terras of the domain size (D) is:

P = (h/e2)(3/nN2)l'2[(1/A )+(r/D)] (3.2)

where h is Plank’s constant, N the number of conduction electrons per unity volume, A is the free electrons mean free path and r the probability of an electron being reflected at the APB. Rossiter and

- 2 7 -

Bykovek (1978) showed in a study of the resistivity of Cu3 Au that the maximum in p is observed for small domain sizes comparable to A.

Other sorts of scattering of the conduction electrons as in short-range ordering (eg Jones et al 1971), or pre-precipitation stages of either Guinier-Preston zone (GP zone) (eg Smugeresky et al 1969) or spinodal decomposition (eg Delafond et ai 1975) can also increase the electrical resistivity. In the cases of pre-precipitation processes the scattering effect, which tends to increase j>, competes with the effect of a more solute-free matrix which tends to decrease p due to less interference to the electrons' movement. In these circumstances, if the material is subjected to a heat treatment where the scattering effect is transient, the overall result corresponds to a maximum in the resistivity at a particular time and temperature and a subsequent drop below the initial value as shown in figure 3.2.

Rossiter and Wells (1971 a,b) proposed a GP zone scattering model in which the conduction electrons are described as free wave functions. Such a model predicts a maximum of the resistivity for zone sizes of the order of the mean free path (A ) of the conduction electrons. Hillel et al (1975) developed a similar model considering the zones morphology. Their findings show that peak resistivity is much more affected by ageing temperature and solute concentration for flat clusters than for spherical clusters.

3.1.3 Electrical Resistivity of FeCo and FeCo Based Alloys

FeCo alloys:

At temperature electrical resistivity of nearly equiatomic FeCo was determined by Seehra and Si 1 insky (1976) in the range 227-1077*C. The major features of this investigation are concerned with the behaviour of p(T) below Tc and around the order/disorder and <xi/<xl+ri transitions. The former transition, as described later, ischaracterized by a noticeable change in £p/ST near Tc while thelatter transition produces a sharp increase of p of about 20%, that suggests a first order transition, and a hysteresis of about 12°C around 962°C (see fig 3.3).

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P t 10* ( I I cm J

1.8 “V 1

| 7 s * \ A I-5 .3 o(.%2n.. s * . \ Xi '. - IO * C

1.6c>' * : \ • 7 7 #K *

1.5

14

1.3

12UJ r0 O'

\\

o' 10* 10*It (m in) —►

10*

Figure 3.2 - Resistivity data for Al-5.3at&Zn alloy versus ageing time at -10°C, after Smugeresky et al-1969.

Figure 3.3 - The electrical resistivity of Fe-46.29at%Co as function of the test temperature, after Seehra and Silinsky-1976.

-2 9 -

f

In the ordered state Seehra and Silinsky observed that j>(T) shows a good fit with a second-order polynomial. The same parabolic behaviour was observed by Rossiter (1981) in annealed and/or quenched equiatomic FeCo in the range 4.2-272 K (-268.8 to -1*0. This behaviour, also observed in other metals such as Ni (Potter 1937), is characteristic of transition ferromagnetic metals and can be associated with s-d exchange interactions: as temperature rises the incoherent scattering of the conduction s-electrons by the increasingly disordered spins of localized d-electrons produces an extra increase of the resistivity that should be added to the phonons component (Ziman-1962); another approach involves concepts such as ’spin mixing’ which considers changes in the spin orientation of the conduction electrons (spins flip) with increasing temperature and a consequent change in their scattering probability (Dugda1e-1977).

Seehra and Silinsky (1976) also found a specific-heat X-type anomaly in Sp/ST near Tc (about 733*0 followed by the parameter’s stabilization in the disordered state. The proportionality between Sp/ST and the specific heat near Tc was established. A similar anomaly has been reported in other systems such as 0-brass (Simons and Salamon-1974) for which no extra energy gap appears on the Fermi surface which nearly fills the Brillouin zone and the correlations between nearest neighbours, hence the atomic order, dominate the scattering of the conduction electrons.

Rossiter (1981) reported that the residual resistivity of quenched equiatomic FeCo drops from about 2.7 to 1.6 jiftcm when the alloy changes from disordered to the ordered equilibrium condition at about 530“C (fig 3.4-A). Other changes observed in the same range of quenching temperatures show that both Sp/ST (fig 3.4-B) and Cpo/(£p/ST)] (fig 3.4-C) drop on ordering due to increasing Neff and t respectively. The cusp-like anomaly observed in Cpa/(Sp/ST)3 near Tc could be associated with the effects of short and long-range order on Neff and t as discussed by Rossiter (1980-b).

-30-

Figure 3.4 - Residual resistivity &of FeCo (A) and the associated parameters (Sf/ST) (BJL and CJ>0 / (£f/£T) 3 (CJ_ taken at 250 K, as function of the quench temperature, after Rossiter-1981.

-3 1 -

FeCo based a l lo y s

Although data on the effect of various ternary additions to the electrical resistivity of FeCo can be found in the literature (Chen- 1962, Chen-1963, Bozorth-1964, Dinhut et al-1977), thesepublications suffer from a lack of essential microstructural information. Only for FeCoV alloys has the resistivity beenadequately correlated with thermo-mechanical history and hence raicrostructure (Dzhavadov and Selisskiy-1963, Josso-1973, Pinnel et al-1976, Ashby et al-1978).

Figure 3.5 after Bozorth (1964) shows how the resistivity of many alloys containing equal proportions of Fe and Co and small amounts of a third element changes with the ternary content. These materials were heat treated at 1000°C but it is not stated whether the heat treatment was followed by furnace cooling or quenching. Theinversion in the curves for Mo and W is thought to reflect the respective solid solubility limits. The most impressive increase of p (by a factor of about 6) is observed by the addition of about 4% V

Chen (1962) studied the effects produced by the addition of less than 5 at% of Ni, Cu, Ti, V, Cr and Mn to the mean saturation moment and the electrical resistivity of equiatomic FeCo. The general trend shows an increase of p with the ternary addition (see fig. 3.6). Despite some small discrepancies between the data from Bozorth (fig 3.5) and Chen (fig 3.6) there is reasonable agreement in the classification of which elements are more or less effective in increasing p of FeCo. According to Chen the average increment in p is 0.3, 0.5, 1.3, 13, 16 and 22 pQcm per atomic percent of Cu, Ni, Mn, Ti, V and Cr respectively. From the magnetic and electrical data he concluded that Ti, V, Mn and Cr donate electrons to and Ni accepts electrons from the matrix. The insignificant changes in p due to the addition of Cu in FeCo was associated with its full d-shell that stays unchanged. Among the attempts to explain the large increase of p due to the addition of Ti, V and Cr into FeCo the most plausible was that discussed in terms of Friedel’s theory (Friedel-1958) and using concepts such as virtual bound states (VBS). The same treatment was employed by Dinhut et al (1977) and similar

- 3 2 -

Figure 3.5 - The effect of various alloy additions on the electrical resistivity of FeCo, after Bozorth-1964.

Figure 3.6 - Increase of residual resistivity of FeCo with a third element, after Chen-1962.

-3 3 -

conclusions were drawn, namely that the changes in the density of states of d-electrons, due to the appearence of VBSs in FeCoTi, FeCoV and FeCoCr were responsible for the large increases in p.

Dinhut et al also used Friedel’s model to explain the alterations of p due to ordering of FeCo and FeCo alloys with additions of 2 at% V, Ti, Cr and Mn. They observed that the onset of order produces a drop in the resistivity Cat 77K) of FeCo, FeCoMn and FeCoCr while FeCoV and FeCoTi have the resistivity increased on ordering. The reason for such a behaviour was attributed to features of the respective VBSs. If the VBSs are more than half empty (FeCoV and FeCoTi) the onset of ordering fills up the virtual bound states increasing the density of states of spins-up localized d-electrons which causes the observed increase of p; the opposite is observed if the VBSs are more than half full (FeCoCr) or if no VBS is present (FeCo and FeCoMn). Figure 3.7 (after Dinhut et al-1977) shows the changes in p of FeCo and some FeCo based alloys quenched from various temperatures. The only approach used to explain these curves was related to the electronic structure of the material. As mentioned before, no reference to the microstructure of the material was made.

Dzhavadov and Selisskiy (1962) observed that isothermal annealing of cold rolled (90% RA) FeCo (0.25 - 1.9 wt% V) results in p initially increasing to a peak value and then subsequently dropping below the initial value. With the exception of the 1.9V alloy, neither the initially quenched FeCoV nor the cold-rolled or quenched FeCo exhibited this behaviour. The resistivity peak in the cold-worked material was attributed to vanadium clustering effects prior to precipitation. Unfortunately the lack of knowledge on the structural features did not permit a more detailed interpretation of the data. Figure 3.8 shows the relative changes in p of cold rolled FeCoV alloys aged at 525°C as function of ageing time. It is interesting to note that the sample with the lowest V content (0.25 wt%) gave an initial drop in p prior to the resistivity peak and that the curve for the binary alloy presented a sharp drop and stabilization at about 30% below the initial value.

Ashby, Flower and Rawlings (1978) correlated resistivity and

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Figure 3.7 - Resistivity of FeCoX alloys (X=Ti, V, Cr and Mn) as function of quenching temperature, after Dinhut et al - 1977.

Figure 3.9 - Relative change in the resistivity of FeCo and FeCoV alloys initially cold rolled (90% RA) and annealed at 525°C, as function of time. After Dzhavadov and Selisskiy (1962).

- 3 5 -

microstructure of aged FeCo2V previously disordered or disordered and cold-rolled. The initially disordered material showed aresistivity peak, similar to that observed by Dzhavadov and Selisskiy, which increased in magnitude and was attained at shorter times with increasing ageing temperatures (see fig* 3.9-A). The initially disordered and cold-worked material showed a greater increment of p followed by a continuous drop in value (seefig.3.9-B). In both cases the reason for the initial increase in p was attributed to the electronic scattering due to very smallordered nuclei (APD sizes much less than 400 X) in a disordered matrix. Increasing the degree of long-range order and the domainsize leads to the subsequent drop in p. The final increase in p in the undeformed alloy was associated with clustering of the vanadium at the APBs, while the continuous drop of p in the cold-workedmaterial was attributed to recovery and gamma precipitation. Some of the electrical resistivity values for FeCo and FeCoV alloys reported in the literature are presented in table 3.1.

TABLE 3.1

Electrical resistivity of some FeCo Alloys at 77K

author material condition p (}iQcm)

Rossi ter 1981

FeCoordered 1.9

disordered 3.1

Dinhut et al 1977

FeCoordered 1.83

disordered 2.60

FeCo2Vordered 38.9

disordered 32.0

Ashby1975

FeCo2Vordered 21

disordered 39

- 3 6 -

(A) (B)Figure 3.9 - The Percentage change in resistivity with time, on ageing FeCo2V (A) initial ly disordered and aged at the indicated temperatures and (B) initially quenched and cold rolled (50 and 25% RA) or simply quenched (0%) and aged at 550°C. After Ashby et al-1978).

- 3 7 -

3.2 Magnetic Properties of FeCo and FeCo Based Alloys

3.2.1 Ferromagnetism and FeCo Alloys

According to the quantum mechanical extension of the molecular fieldtheory any ferromagnetic system fulfils two necessary preconditionsi) the existence of an atomic magnetic moment (p) - whose naturalunit is the Bohr magneton (jiB = eh/47tmc= 9.27 x 10*2 4 Am where e isthe electron’s charge, m its mass, h Planck’s constant and c thevelocity of light in vacuum) and ii) a special electron exchangeinteraction of electrostatic origin (measured through the exchangeintegral J) promoting the parallelism of adjacent spins. The firstcondition depends on the electronic structure for which the 3dtransition elements exhibit specially favourable circumstances; thesecond involves some geometrical parameters and is favourable whenthe ratio between the lattice parameter (an) and the 3d shelldiameter (d) is higher than 1.5. Figure 3.10 shows the exchangeintegral as function of the ratio a0/d for transition elements inthe iron group. If J>0, the ferromagnetic configuration (parallelspins) is stable since the exchange energy (Utt ) betweenadjacent spins St and Sj (given by the Heisenberg model

^ ^Uit = -2J Si.Sj) is negative and thus less than that for noninteracting atoms.

Ferromagnetism is retained when the exchange energy is high enough to outweigh the thermal energy that tends to neutralize the parallelism of the spins. The temperature for which the spontaneous magnetization vanishes is termed the Curie temperature. Above that temperature the magnetically disordered system becomes paramagnetic.

Since ji depends on the electronic structure, different elements show different values of the parameter. Among the 3d transition elements the Fe atom has the highest atomic moment (2.2 jiB) followed by Co (1.7 pB). All oying changes the electronic configurations and thus p and in some cases it is possible to produce an average moment higher than the pure base elements. This is oberved in a range of FeCo alloys (e.g. p=2.4pB at 35%Co) as shown in the S1ater-Pau1ing curve (figure 3.11). This is probably the most noticeable characteristic

-3 8 -

J Co

c r - F c y ^ 0 ^p : a/i.

0 / IJ> r - F c A

AM n

Figure 3.10 - Dependence of the exchange integral (J) on the ratio between the lattice parameter (a0) and the 3d shell diameter vd) in transition elements of the iron group.

Figure 3.11 - Slater-Pauling curve: Average atomic momentfunction of the electron concentration. After Bozorth-1964.

as

-3 9 -

of this alloy and that value corresponds to the highest known moment per atom achieved by a binary system (Bozorth-1964).

3.2.2 Other Magnetic properties of FeCo Alloys

In addition to the magnetic moment, some other characteristics must be considered when designing a soft magnetic material. Theequiatomic composition has shown higher permeabilities at high flux densities and anisotropy constant close to the ideal value (zero) with saturation only slightly lower than the maximum at 35%Co. The combination of these factors gives to the equiatomic FeCo the optimum magnetic properties for a wide variety of purposes (Oron et al-1969). The addition of a third or even a fourth element to FeCo is made more for the improvement of the mechanical and electrical properties rather than the magnetic, which usually decline after the additions. Nevertheless some atomic and raicrostructura1 parameters can be controlled in order to keep the magnetic properties at good levels (Chen-1963, Josso-1974, Smith and Rawlings-1976, Pinnel and Bennet-1974, Kawahara and Uehara-1984, Orrock-1986).

From the atomic viewpoint it is worth mentioning the rise in the mean saturation moment for some FeCoMn alloys. Chen (1963) correlated this increase with the atomic occupancy of localized d-electrons of Mn atoms in the band structure of the system forcompositions Co:Fe > 1. He also reports the effects of otheradditions (Ti, V, Cr, Ni and Cu) to the mean saturation moment ofFeCo (see fig. 3.12). On the other hand, Smith and Rawlings (1976)observed that the atomic moments of the constituent elements Fe and Co (respectively 2.99 ± 0.2 and 1.65 ± 0.2 jiB) in FeCol.8V arelittle affected by the presence of vanadium, since the reported values for the parameter in equiatomic FeCo are in the ranges2.9-3.0 and 1.7-1.9 pB respectively.

Some microstrutura1 features such as atomic order, grain size and the presence of paramagnetic phases have considerable influence on the magnetic properties of a material (Bozorth 1964). In the present case the basic constituent elements are ferromagnetic and an increase of only 4% is observed in the saturation magnetization on

- 4 0 -

Fisure 3.12 - The mean saturation moment per atom in ternary FeCo alloys with concentration of various solute elements, after Chen-1963

Yd ( cm” )

Fi gure 3,13 - The coercive force as function of the reciprocal of the grain diameter for FeCoV rolled to give predominantly (112)ClT03 (open symbols) and (111H211] textures (full symbols), after Qrrock- 1986.

-4 1 -

ordering FeCo (Smoluchowsky-1951). Pfeifer and Radeloff (1980) observed an inverse relationship between grain size (d) and coercive force (He) of FeCo2V: He a 1/d, this has been partially confirmed by Orrock (1985) who found the relationship He = (A/d) + B for the same alloy; A and B are constants which are dependent on the material’s texture (see fig 3.13).

The presence of paramagnetic second phase particles is usually responsible for an increase in He and remanence and a reduction in the saturation induction (Bs) (Pinnel and Bennett-1975, Orrock- 1985), although in some cases the occurrence of precipitation leads to an increase of Bs as observed by Branson et al (1980) after annealing FeCoVNi alloys; this anomaly was attributed to the removal of V from the matrix which out-weighed the usual effects caused by the presence of the paramagnetic particles.

Some other aspects on the magnetic properties of FeCo alloys on the atomic scale are discussed in the next chapter.

-4 2 -

CHAPTER 4

SOHE APPLICATIONS OF HQSSBAUER SPECTROSCOPY APPROPRIATE TO THE PRESENT INVESTIGATION

This chapter deals with the information of relevance to the present study, that may be obtained from Mossbauer spectroscopy. Sections 4.1 to 4.7 present interesting uses of the technique in diverse alloys exhibiting similar properties to FeCo based alloys. These examples give only a brief idea of the power of Mossbauer spectroscopy in this specific situation. More general and detailed applications on ferrous metallurgy can be obtained in reviews such as Gonser (1968), Jones (1973) and Schwartz (1976). The results from the limited amount of previous work on FeCo based alloys are reported in section 4.8. The theoretical foundations and some other practical aspects of Mossbauer spectroscopy are presented in appendix 1.

4.1 Detection of Magnetic Phases

The nuclear Zeeman effect is a powerful tool in the identification of magnetic phases or in the study of magnetic properties of metals and alloys. The split of the nuclear energy level due to the presence of a magnetic field in the nucleus site creates a number of different resonant conditions and consequently a multi-line spectrum is observed, eg the allowed transitions in ferromagnetic iron or iron rich alloys produce a characteristic set of six lines (sextet) as shown in figure 4.1. In contrast, a paramagnetic structure usually produces a single line, although it is possible for a single paramagnetic phase to give, for instance, two distinct peaks that can be interpreted either in terms of different sites of the resonant atom or the presence of an electric field gradient in a single site as in the intermeta11ic iron-zinc £, phase (see fig 4.2 after Jones and Denner 1974).

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Figure 4.1 - Typical Mossbauer spectra for metaJJic iron at different temperatures up to the Curie temperature, after Preston et al-1962.

Figure 4.2 - The Mossbauer spectrum of an iron-zinc intermetallic compound (Si phase); the two peaks may arise from two distinct sites or from the effect produced by an electrical field gradient in a single site; another possibility may be that two different forms of SI phase are present. After Jones and Denner-1974.

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4.2 Quantitative Phase Analysis

The quantitative analysis of the Mossbauer spectrum of a two-phase mixture is usually difficult and many corrections are necessary, involving such details as the sample’s thickness, texture and other polarization effects, nature and composition of the phases present.

Nevertheless some approximations can be used, for example, when a small fraction of paramagnetic phase is present in a ferromagnetic matrix, the area of the paramagnetic peak can be compared to the area of the two weak innermost lines of the ferromagnetic spectrum. Actually it is never strictly correct to compare the total area of the six ferromagnetic lines to that of the paramagnetic line. Even in the extreme example of equal mixtures of para and ferromagnetic powders the ratio between the respective areas (A ferro/ A para) is i.9 which corresponds to an error of about 90% if one takes the relative area of the peaks as the relative volume fraction (Schwartz-1976).

Sometimes the content of the Mossbauer active element is so low that some details of the absorption spectrum virtually vanish. In that case it is necessary to enrich the sample with a content of the Mossbauer isotope higher than its natural abundance (e-g. Jones and Denner - 1974, Nicholls and Rawlings 1977).

4.3 Measurement of Magnetic Parameters

The separation between the nuclear energy levels due to the Zeeman effect is proportional to the nuclear moment (ji) and the internal (or external) magnetic field (H) at the resonant nucleus site. This nuclear separation can be measured through the splitting of the corresponding spectrum lines (Preston et al - 1962) and an example of this effect in Vicalloy is reported in section 4.8.

Marshall (1958) has shown that the magnetic internal field (or magnetic hyperfine field) in a pure ferromagnetic metal should be proportional to its magnetization. This has been closely, but not exactly, confirmed experimentally for iron and cobalt respectively

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by Nagle et al (i960) and Portis and Gossard (1960). Johnson et al(1961) extended the study to varying compositions of binary FeCo and FeNi alloys assuming the proportionality between ji and H in the Fe nucleus. A general similarity in form between their results and the Slater-Pauling curve for saturation moments was observed (fig 4.3), but no strict proportionality was established.

4.4 Texture Effects

The spatial spin orientation can be determined by the analysis of the relative intensities. For instance, in the 14.4 KeV transition of the 37Fe isotope, the relative intensities of peaks 1, 2,...6are It sla :1s = U t l a t U = C3( 1+cos2 9) / 4 ] : tsin293 : [(1+cos29)/4]where 9 is the angle between H and the propagation direction of the gamma radiation (Cohen-1976). Thus the relative intensities of the peaks are affected by the presence of any preferred orientation of H in the specimens.

If for instance H is normal to the the sample’s surface, 9 is 0 and lines 2 and 5 vanish giving the ratio I, : I2 : Is : U : Is : U = 3:0:1:1:0:3; on the other hand, if H lies parallel to the sample’s surface 9=90° and the ratio is 3:4:1:1:4:3. These two extremes of behaviour are shown in fig. 4.4 (A) and (B) for Fe2 0 3 at two different temperatures. In both cases the direction of the gamma radiation was parallel to the <111> direction and the spins were respective 1ly parallel or antiparallel to the <111> crystallographic direction (T=80K; spectrum a) or normal to that direction (T=300K; spectrum b) (after Gonser - 1968).

4.5 Ordered Alloys

Differences in the local environment of the Mossbauer produce some interesting effects such as the peculiarities spectrum of ordered Fe3Al exemplified below. Since these usually involve the close neighbourhood of thenucleus, they are sensitive to ordering.

isotope of the effects resonant

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Figure 4.3 - The changes in the hyperfine field of Fe-X alloys relative to that of metallic Fe, as function of the number of electrons per atom. The broken line corresponds to reported brittle Fe-Co samples, most probably in the ordered condition. After Johnson et al- 1961.

Figure 4.4 - Mossbauer spectra of Fe2 0 3 with (A) H normal and (B) H parallel to the sample’s surface.

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Figure 4.5 (after Ono et al -1962 apud Jones- 1973) shows the Mossbauer spectrum of ordered Fe3Al. In this condition the overlap of two ferromagnetic spectra is observed, generated by Fe atoms in sites type A, where each Fe atom has 8 Fe nearest neighbours, and insites type D, where each Fe atom has 4 Al and 4 Fe nearestneighbours - see figure 4.5. The A sites, having much largerhyperfine field (299 KOe) than the D sites (229 KOe) have a largersplit of the peaks. This difference in H shows how the presence ofnon-magnetic elements in the first coordination shell of the Fe atom affect the magnetic properties of the material. In fact, when all the nearest neighbours of the Fe atom are Al, a paramagnetic peak is observed as reported by Huffman and Fisher (1967).

In FeCo based alloys both base elements are ferromagnetic and ordering or the presence of small quantities of a non ferromagnetic ternary element cannot produce such a marked change. Nevertheless, some differences in the hyperfine parameters of FeCo based alloys in the ordered or disordered conditions can be noticed and are discussed in section 4.8.

4.6 Site Population

The examples mentioned in the last section show how the magnetic properties of iron are affected by the presence of a non-magnetic element (also treated here as an "impurity") in the neighbourhood of the 57Fe atom in a bcc structure. These disturbances, produced by changes in both spin and charge density of s-like itinerant electrons at the resonant nucleus alter the hyperfine field (H) and the isomer shift (S ) of the sextet structure and can be used to deduce the atomic distribution in the close coordination spheres of the resonant atom (e.g. Dubiel and Zinn -1983).

Wertheim et al (1964) studied the influence on the hyperfine field of Fe of small additions of several elements (Ti, V, Cr, Mn, Co, Ru, Al, Ga and Sn). The FeV alloys were studied in the greatest detail and the effect of vanadium up to 16 at% was described in terms of the binomial distribution of V atoms in the 8 sites of the first or

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Figure 4.5 - Structure of Fe3Al showing the A and D iron sites and the resultant Mossbauer spectrum. After Ono et al-1962 (apud Jones -1973)

Figure 4.6- Comparison between experimental (a) and theoretical (b) sixth Mossbauer peak in FeV with different V contents in solid solution. After Wertheim et al-1964.

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6 sites of the second coordination spheres around the Fe atom in a bcc structure. Each vanadium atom in any of these shells was considered responsible for the creation of a Zeeman pattern. The overlap (I) of all these contributions, given in expression 4.1, produces the Mossbauer spectrum shown in figure 4.6.

8 6 8! 6! ci*-n-. (l-c)«*• (4.1). . (8-n)!n! (6-m)!m! l+(E-an-0m)2n*l rtltl

Here n and m represent the number of V atoms in the first and in the second coordination shells respective 11y, c is the vanadium content in solid solution, a and $ are the shifts in the absorption lines due to one V atom respectively in a nearest neighbour site (nn) or in a next nearest neighbour site (nnn) and E is the gamma energy.

Stearns and Wilson (1964) criticized Wertheim’s model in that it was restricted only to nn and nnn impurity sites and extending their calculation to include the 8+6+12+24+8+6 sites up to the 6th coordination sphere of the bcc structure. Nevertheless the general observation shows that the major effect is produced when the impurity is an nn or an nnn atom; eg: for 1 V impurityAH„„ ~-9% and A H nM £-7% of the value of pure iron (330 KOe) with some dependence on the concentration; from the third coordination sphere outwards the resulting AH is either positive or negative and very small - usually less than 1% of H in pure iron (see fig. 4.7). Similar results were found for small additions of Ni, Pd, Rh, Cr, Ru and Mo in Fe in a later study by Stearns (1976). Vincze and Campbell (1973) proposed an intermediate approach by using nn and nnn sites and the average effect of the further neighbour shells. The binomial distribution of impurities in one of the 14 sites of the first + second coordination shells can also be used successfully as reported by Jones (1973) for Mn in Fe rich alloys.

More recently Dubiel and Zinn (1983) calculated the effectiveness of some impurities (Cr,V,Si,A1,Sn) acting as "spin-holes" of the hyperfine field. Their results of such spin-hole effectiveness are: Sn (53%), A1 (60%), Si (76%), Cr (75%) and the highest V (89%).

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N! HZ HZ HA US N6

R <IN UNITS OF LATTICE CONSTANT, c0 )

Su2.

>-occzUlzoo<cctkt►-z

Figure 4.7 - Relative changes in the hyperfine field due to the presence of a foreign atom (Al, Mn or V) in pure iron, as function of its distance to the resonant nucleus, after Stearns and Wi1 son-1964.

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The individual sextets associated with different environments are not always easily distinguishable and the occurrence of a variety of similar atomic configurations can produce a series of non resolved hyperfine fields leading to the broadening of the sextet lines, measured through the half width at the maximum intensities (HWHM) of the peaks (eg Mayo-1981).

As mentioned before, the isomer shift (S ) may also change due to the presence of foreign atoms. For example the isomer shift of the sextet structure, in the specific case of V in Fe, is negative for vanadium in nn and nearly zero for nnn sites (Wertheim et al-1964, Rubinstein et al-1966, Vincze and Carapbe11-1973, Dubiel and Zinn-1983). On the other hand & is positive when Co atoms occupy nn or nnn sites of Fe rich alloys (Vincze and Campbe11-1973).

4.7 Lattice Defects

Lattice defects may be classified into transient Ci.e. in a small volume and for a short time (< 10-8s) e.g. ionic states with short lifetime, fast moving interstitials or dislocations etc.3 and stationary (e.g. vacancies, interstitials, dislocations, impurity atoms, domain and grain boundaries, stacking faults etc.) the latter being the most important in the present case. The lattice distortions due to one or two dimensional defects as impurities, vacancies, dislocations, boundaries, etc cause broadening of the Mossbauer lines by inhomogeneous hyperfine interactions (Gonser-1971). Figure 4.8 (after Sauer-1969) shows clearly these effects in the Mossbauer spectrum of plastically deformed Ta.

4.8 Mossbauer Spectroscopy of FeCo and FeCo Based Alloys

As mentioned before, the major constituent elements of the FeCo based alloys are both in the ferromagnetic condition and thus the differences in the Zeeman pattern due to ordering of these alloys are small. Nevertheless some differences can be noticed in the hyperfine field, isomer shift and HWHM of FeCo alloys between the ordered and disordered conditions.

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Figure 4.8 - Transmission spectra of Ta at room temperature using a 181W source after successive plastic deformation and annealing, after Sauer-1969 (apud Gonser-1971).

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The general observation is that the hyperfine field of FeCo in the disordered (quenched) condition is slightly higher than in the ordered condition (Johnson-1961, Alekseyev et al-1977, Mayo-1981, Eymery and Moine-1978). The increase of H in disordered FeCo is due to the presence of Fe atoms in nn sites (Mayo-1981), and thus to the increase in the contribution of 4s-like conduction-electrons polarization (CEP) to the internal field (Montano and Seehra-1977). The most reliable results give H(ord) = (2.71 ± 0.01) x 107 A/m and H(dis) = (2.78 ± 0.01) x 107 A/m. Fnidiki and Eymery (1985) have reported similar values for FeCo in the ordered and quenched into water conditions but an even higher value (2.845 x 107 A/m) after ion-implantation of argon in an initially quenched sample. This indicates that the labeling "disordered" does not correspond to a fully disordered material since the ion implantation produced further disorder. The latter results were obtained by using Conversion Electrons Mossbauer Spectroscopy (CEMS) in order to detect the surface effects produced by ion implantation.

Mayo (1981) noticed a small change in the isomer shift of equiatomic FeCo on ordering, namely £ (ord) = 0.013 ± 0.003 mm/s and S' (dis) = 0.028 ± 0.003 mm/s. He also reported higher HWHM of the ferromagnetic lines of disordered FeCo, caused by small differences in H due to the presence of Co atoms in both nn or nnn sites in contrast with the ordered condition where the only configuration corresponds to Co and Fe occupying respectively nn and nnn sites relative to the resonant nucleus.

Montano and Seehra (1977) studied the order-disorder and oc, /rt transitions in equiatomic FeCo using in situ Mossbauer spectroscopy. Due to the varying temperatures involved, the changes in the Debye-Waller factor were taken into account. The spectra show symmetrical peaks and the results indicate that the hyperfine magnetic field (H) and the magnetic moment per atom (p) exhibit a similar temperature dependence up to about 430°C, above which an increasing difference between the two quantities was noticed. This difference was associated with the trend of decreasing p and increasing H as the system approaches the order/disorder transition (733°C). At the at/at+Fi transition temperature (962°C) the

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hyperfine magnetic field H dropped abruptly to zero. Above that temperature a single paramagnetic line was observed.

One of the pioneer works on Mossbauer of FeCo based alloys was carried out by Gorodetsky and Shtrikman (1967) in a study of the magnetic hardness of Fe-46%Co-9.8V (Vicalloy). They noticed that annealing a previously quenched (from 950°C) and cold rolled specimen produces a narrowing of the Mossbauer peaks (associated with ordering), the appearance of a paramagnetic phase with 5=-0.47 mm/s (due to percipitation of an fee phase) and the consequent increase of H (see figure 4.9). It is interesting to notice that the material quenched from 950°C (a temperature in the al+n field) and cold-rolled did not show the paramagnetic line.

The results of Gorodetsky and Shtrikman were confirmed by Oron et al (1969) and Yurchikov et al (1973). Oron and co-workers observed that a Vicalloy 'sample quenched from 1050°C was almost completely paramagnetic at room temperature but presented the lines of an irreversible ferromagnetic phase after either immersion in liquid nitrogen (-196°C) or plastically deforming at room temperature. They attributed the disappearance of the paramagnetic line to the transformation of some of the retained paramagnetic T phase into a ferromagnetic a phase. Yurchikov et al (1973) confirmed this observation and also reported that the paramagnetic peak in the Mossbauer spectrum of quenched Vicalloy is still present at temperatures as low as -173°C. These results could be interpreted by considering martensite to be the ferromagnetic phase which is produced by cooling to cryogenic temperatures or cold working. As quenching to -173°C did not produce the ferromagnetic peak, Ms of Vicalloy must lie between -173 and -196°C.

The relative intensity of the sextet structure in the work by Oron et al (1969) was interpreted in terms of the easy magnetization directions. Their findings show that the quenched and cold worked Vicalloy presents a ratio Ii:I2:Is of about 3:0.75:1 which changes to about 3:3.5:1 after annealing the sample for 2h at 600°C; that change was associated with the rotation of the hard axis of magnetization from an orientation almost parallel to one almost

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T Tn— ---1— '— i----•— r T“ '— r(a) VleaUey ,rolied tft#r quiftc>lAfl

frtn ? 5 0 * C

u►-<

( b ) Vie a l loy , elitr x«oi i / i a l m i Mfo/ apilmvm ptrmoAttl MagAit propirllti

_J_♦12VELOCITY [ m m / n e ]

JL...1 f • 12

Figure 4.9 - Mossbauer spectra of Vicalloy at room temperature (a) rolled after being quenched and (b) after being heat treated for optimum permanent magnet properties. After Gorodetsky and Shtrikman - 1967.

Figure 4.10 - Mossbauer spectrum of FeCo2V in the quenched condition The position of the lines corresponding to iron atoms without V atoms nearest or next nearest neighbours is given by (a) while that corresponding to one V atom in those sites is given by (b). After Alekseyev et al-1977.

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normal to the rolling plane. This is in accord with the observations that the recrystallised a grains have the < i11> direction perpendicular to the rolling plane and that the <111> is the hardest axis of magnetization. Another interesting feature reported by Oron et al refers to the good correlation observed between the measured magnetization of Vicalloy and the relative areas of the ferromagnetic Mossbauer lines.

The direct observation of the Mb'ssbauer spectra of FeCoV alloys obtained by the workers mentioned above as well as those presented by Baldokhin et al (1975) in a Mossbauer study of radiofrequency striction of Vicalloy, show an assymmetry of the ferromagnetic peaks although this was not studied or mentioned by the authors. Belozerskiy et al (1977) noticed similar assymmetry in Fe-24Co-14Ni-4V associating it to the presence of V in the alloy.

Alekseyev et al (1977) studied FeCo and FeCoV alloys (up to 2.2 at%V) using electron diffraction and Mossbauer spectroscopy. Their Mossbauer results for FeCo2V show assymmetry of the sextets (fig 4.10) which was associated with effects produced by 1 V atom in one of the 14 sites of the first or second coordination spheres of the bcc structure. The hyperfine fields corresponding to the vanadium free configuration were H(ord) = 2.72 x 107 A/m and H(dis) = 2.75 x 107 A/m) and for 1 V atom in a nn or nnn site were H(ord) = 2.54 x 107 A/m and H(dis) = 2.51 x 107 A/m).

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CHAPTER 5

EXPERIMENTAL PROCEDURE AND TECHNIQUES

5.1 Choice of Experimental Techniques

The experimental techniques chosen in the present work are basically intended to correlate microstructure with the electrical and magnetic properties of nearly equiatomic FeCo based alloys, in particular FeCoNb and FeCoV. The different microstructura1 features were produced by selected thermo-mechanical treatments and their detection was performed by using one or more appropriate techniques.

The temperatures of the main phase transformations (order/disorder and <x,/a, + T,) were obtained using differential thermal analysis (DTA) and the presence of second phase particles was studied by using both microscopy (optical, SEM and TEM) and Mossbauer spectroscopy.

The different degrees of long range order produced were determined by comparing the relative intensities of x-ray superlattice and fundamental peaks. Information on the antiphase domain sizes was obtained by peak broadening measurements carried out on the superlattice peaks. The degree of long range order was also correlated with changes in the lattice parameter, obtained using the same x-ray technique, although special attention was necessary to separate the ordering effect from the precipitation effect on the parameter.

The electrical properties of the alloys were studied through changes in the electrical resistivity and in some associated parameters (e.g. Sp/ST, j>0) and correlated with the major microstructural features. The magnetic properties were studied by means of magnetization curves and compared with Mossbauer parameters such as the hyperfine magnetic field and the magnitude of paramagnetic peaks associated with second phase particles.

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5.2 Material

The FeCoiNb, FeCo2Nb and FeCo3Nb alloys studied in this work were prepared by arc melting the nominally pure base elements under argon atmosphere. The respective contents of 1, 2 and 3 wt% Nb (respectively 0.62, 1.24 and 1.86 at% Nb) were added to equi-weight, ie. approximately equiatomic, iron and cobalt. The FeCo3.6V and FeCo5.4V alloys were prepared by arc melting pure iron, cobalt and 41.0 wt% Fe - 58.2 wt% V alloy in order to obtain equiatomic Fe and Co with either 3.6 or 5.4 wt% V (ie. 4 or 6 at%V respectively). The most significant impurity was 0.5 wt% Si in the FeV base alloy. The alloys were homogenized by hot rolling the ingots at about 900°C to the thickness of 1.0 mm.

The FeCo2V alloy was provided in the form of 0.1125 mm thick and 90% cold-rolled sheet by Telcon Ltd., Crawley, Sussex. The specified composition was 48.0 wt% Fe, 50.0 wt% Co and 2.0 wt% V (ie. 2.2at%V) the major impurity being 0.075 wt% Si. The x-ray energy dispersive raicroana1ysis of the FeCoV and the FeCoNb alloy prepared in the present investigation did not reveal any major impurities.

Other nearly equiatoraic FeCo based alloys used here were kindly supplied by the Department of Metallurgy and Materials Science Imperial College. They are: FeCo 1.5 wt% V 4.5 wt% Ni (C.D. Pitt -1980) and FeCo 5 wt% Ni, FeCo 3 wt% Cu, FeCo 2 wt% V (1, 3 and 5wt% Cu) and FeCo 2 wt% V (1, 3 and 5 wt% W) (C.M.Orrock-1985). These alloys have been employed basically in the comparative study of electrical resistivity as function of composition and ordering. Table 5.1 summarizes the information on the nominal composition of the alloys studied in the present investigation.

5.3 Differential Thermal Analysis (DTA)

The temperature ranges of the main solid state transformations occurring in selected material used in the present study were determined prior to the decision on the heat treatment schedule. This information was obtained from the DTA carried out on the FeCo2V alloy and on samples taken from the hot rolled ingots.

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TABLE 5 .1

Nominal composition of the alloys studied in the present investigation

MATERIAL

STUDIED

NOMINAL COMPOSITION (wt%)

Fe CoTernaryaddition

Quaternaryaddition

FeCoiNb 49.5 49.5 1 Nb -FeCo2Nb 49.0 49.0 2 Nb -FeCo3Nb 48.5 48. 5 3 Nb -

FeCo2V 48.0 50.0 2 V -

FeCo3.6V 46.9 49.5 3.6 V -

FeCo5.4V 46.0 48.6 5.4 V -FeCo3Cu 48.5 48.5 3.0 Cu -FeCo5Ni 47.5 47.5 5.0 Ni -FeCo2VlW 48.5 48.5 2.0 V 1.0 WFeCo2V3W 47.5 47.5 2.0 V 3.0 WFeCo2V5W 46.5 46.5 2.0 V 5.0 WFeCo2VlCu 48.5 48.5 2.0 V 1.0 CuFeCo2V3Cu 47.5 47.5 2.0 V 3.0 CuFeCo2V5Cu 46.5 46.5 2.0 V 5.0 CuFeCol.5V4.5Ni 46.0 48.0 1.5 V 4.5 Ni

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A computer controlled Stanton Redcroft simultaneous thermal analyser (STA 780) has been used to determine the main transition temperatures between room temperature and 1100°C. To minimize the influence of undesired signals, as for instance from recrystallisation or from commencing a run with a non-equilibrium degree of order, the samples were previously sealed under argon atmosphere into quartz capsules and annealed for 2 hours at Q50°C followed by furnace cooling at the rate of 28C/min. This procedure is assumed to have produced a recrystallized and fully ordered structure for the initial condition of the material. A two cycle analysis at heating and cooling rates of 5°C/min was performed for each specimen.

5.4 Thermo Mechanical Treatments

After hot rolling it is necessary to carry out the final fabrication by cold rolling in order to obtain good surface finish anddimensional tolerance. In order to cold roll FeCo alloys it isnecessary to produce the material in the ductile disordered state. This can be achieved by an appropriate quenching from a temperature in the «i field ie. above the order/disorder and below the at/ott+Ti transitions. The DTA results enabled the selection of the heat treatment for the various alloys under investigation; the FeCo5.4V, FeCo3.6V and all the FeCoNb alloys were annealed for 2 hours at respectively 690°C, 740“C and 850°C and quenched into iced brine.

The final thickness was obtained by cold rolling the quenchedspecimens down to 0.25 mm ie. 75% R.A. Such a thickness is adequateto assure a cooling rate of about 8000aC/sec, high enough to keepeven the binary alloy in the disordered state after a quenching from 850°C, as described by Clegg (1971). It is worth mentioning that thealloys containing Nb have shown better rollability than thosecontaining V.

To order the material, the cold rolled FeCo5.4V, FeCo3.6V and all the other alloys were sealed in quartz capsules under argonatmosphere and annealed at respectively 690, 740 and 850°C for 2 hours followed by furnace cooling (FC) at the rate of about 2°C/min.

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The disordered undeformed samples were produced by annealing for 2 hours, under argon flow, the cold rolled FeCo3.6V, FeCo5.4V and all the other alloys at respectively 690, 740 and 850°C followed by quenching into iced brine.

For the magnetization curves, the cold-rolled material received the following heat treatments: anneal in pure dry hydrogen for 2 hours at 850 and 760°C (FeCoNb alloys), at 760 and 740°C <FeCo3.6V) and at 550tfC (FeCo5.4V) followed by furnace cooling. These treatments were chosen because they are similar to those used in industrial practice and those employed by previous workers (e.g. Orrock-1986).

A comparative study involving changes in the LRO parameter, APD sizes, lattice parameter and electrical resistivity was carried out on the FeColNb alloy that had been submitted to the following isochronal heat treatments, finalized by quenching into iced brine :

Group 1 : Disordered and Aged (T,lh) produced by ageing thedisordered undeformed samples for 1 hour at 500, 550, 600, 630, 660, 690, 720, 730, 750 and 780°C.

Group 2 : Furnace Cooled and Aged (T,lh) produced by ageing theordered (i.e. Furnace Cooled) material for 1 hour at 500, 550, 600, 630, 660, 690, 720 and 750°C.

A third group involved the following isothermal heat treatments.

Group 3 : Disordered and aged (550aC,t) produced by ageing thedisordered undeformed FeCoiNb for 0.5, 1, 2, 4, 8 16 and32 hours at 550°C.

All the temperatures were within ± 5°C of the quoted values and restricting the sample lengths to not bigger than 4 cm assured an homogeneous temperature throughout the sample. The times of the heat treatments were within the precision of ± 2 minutes. After heat treatment, the samples had the thin surface oxide layer removed by grinding with fine silicon carbide paper followed by electro- polishing in 20% perchloric acid in ethanol, at - 30°C, and current of about 200 mA. In some cases the grinding stage was omitted.

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5.5 Microscopy

The microstructure of FeCo3.6V and FeCo5.4V, of all the FeCoNb alloys in the furnace cooled and quenched conditions was investigated to enable the correlation between microstructure and physical properties. In addition the raicrostructure of the FeColNb alloy was studied after selected heat treatments.

5.5.1 Light Microscopy

The samples were mounted and polished to ljim, etched in alcoholic ferric chloride to reveal the grains orientation or in 2% nital to reveal the grain boundaries and examined under a light microscope.

5.5.2 Scanning Electron Microscopy (SEM)

A Jeol JSM-35 scanning electron microscope was used to observe the presence of second phase. Due to the reasonable difference between the Nb atomic number and the other constituent elements (Fe and Co), the back scattered electrons image showed good contrast between the niobium rich precipitates and the matrix in the FeCoNb alloys whilst the V rich particles could be revealed only after a quick etching in nital. The employment of the ZAF method to analyse the x-ray dispersive data permitted the quantitative determination of the composition of some of the phases present.

5.5.3 Transmission Electron Microscopy (TEM)

Selected FeCoiNb samples were prepared by the window technique by electropolishing 1 cm2 specimens in 20% perchloric acid in ethanol at about -35°C and with a current of 200 mA. An EMI high-voltage transmission electron microscope (HVEM) was used to study the fine precipitation. The atomic composition of both the matrix and the r2 precipitates were also determined using the micro-analysis system of a Temscan transmission/scanning electron microscope.

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5.6 X-Ray Diffractometry

A Philips PW1710 x-ray diffractometer was used. The facility of automatic computer programmed scanning with integrated peak intensities determination or peak labelling giving direct d-spacing to four decimal places was employed. All the x-ray diffraction samples were given an electro-polish in 20%’ perchloric acid in ethanol, at about -30°C and with a current of 200 mA. The effects of anisotropy were reduced by rotating the samples.

5.6.1 Deternination of Degree of Long Range Order

As may be shown from structure factor calculations, superlattice peaks are always less intense than fundamental peaks. Equation 5.1 shows the dependence of the intensity Cl(hkl)] of a B2 superlattice line (h+k+l=odd) with the degree of long range order S and the atomic scattering factors fA and fB of atoms A and B respective 1y.

I <x SZCf a -f B 32 (5.1)

The intensity also depends on other factors such as multiplicity, temperature, absorption as well as crystal perfection, texture effects etc. Unfortunately, despite the great availability and relative simplicity of using this technique, the x-ray scattering factors for iron and cobalt are nearly equal and the detection of superlattice peaks is very difficult. In contrast, the scattering factors for Fe and Co differ significantly for neutrons and the neutron diffraction technique is the most suitable when accurate absolute determinations are desired (see for example Smith and Rawlings-1976 on the ordering of an FeCol.8%V alloy).

However, the results from the x-ray technique can be improved if a radiation with wavelength close to the K absorption edge of one of the constituent atoms is chosen, with the reduction of the scattering factor of that element. Consequently Co-K<x radiation is often used in studies of FeCo based alloys. However, even with this radiation, calculations show that the superlattice (100) peak is

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about 60 times less intense than the fundamental (200) peak in the equiatomic FeCo alloy (Clegg-1971) and therefore the peaks have to be carefully monitored. In the present work the x-ray technique was chosen to determine the degree of LRO and Co-ka radiation was used to scan the (100) superlattice peaks of all the FeColNb samples of groups 1, 2 and .3 in steps of 0.05° for about 0.5 degree in either side of the peaks. The time for each step was chosen in order to produce an average of 10s counts per step.

The degree of order of the specimens was determined by comparing the intensity of the superlattice (100) peak and the intensity of the fundamental (200) peak. This peak was chosen since any texture effect would affect both the (100) and (200) in a similar manner.

Although the theoretical value of the ratio CI(100)/I(200)] for FeCo using Co-ka radiation is about 1:60, as reported by Clegg (1971), the experimental ratio for FeColNb in the furnace cooled condition was about 1:10.6, a value much higher than the predicted for the binary a 1loy.

It should be noted that the furnace cooled specimens, (termed ’ordered’ in the present work) may have a degree of LRO well below unity. In fact, as reported by Smith and Rawlings (1976), neutron diffraction results show that the so-called ’fully ordered’ condition obtained by heat treating an FeCol.8%V alloy at temperatures in the range 450 to 500°C inclusive for several hours corresponds to an absolute value for S of 0.8. In the same work the results are compared with many other experimental and theoretical S values of the binary FeCo and some different FeCoV alloys. The most reliable results at similar temperatures show small variations around the value S=0.8 for the ’fully ordered’ condition.

Since the presence of vanadium did not significantly alter the maximum value of S, the same independence for niobium additions to the binary FeCo alloy will be assumed. Moreover, considering that the kinetics of ordering below 450°C is usually very slow, it is reasonable to assume the value S=0.8 for the furnace cooled FeColNb studied in the present work.

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The expression used to determine the LRO parameter S is presented inequation 5.2 and takesinto account the observations contained in thelast three paragraphs:

5.6.2 Determination of Antiphase Domain Size

The lack of resolution of the x-rays diffracted from very small particles (about 1000 & or less) produces broadening of theresultant peak (Barrett-1957) and can be used to determine the average size of the particles. Similarly, very small antiphase domains broaden the super lattice lines and the average size of the domains (D) can be estimated by using the Scherrer formula (equation 5.3), which gives D as function of the line broadening (b) the incident wavelength (A) and the Bragg angle (9):

were K is a constant (about unity). The effect of the APD size on the line broadening (b) must be separated from the total line broadening, which is determined by the breadth (B) of the peak at half maximum intensity and which includes other sources of peak enlargement.

The (100) superlattice and the (200) fundamental peaks of FeColNb ingroups 1, 2 and 3 as describedAsection 5.4 were used for the present purpose. In both cases the kai peak was separated from the koc2 by computer analysis based on the Rachinger’s method (Rachinger-1948). The breadth at half height (B’) of the (200) kal line was assumed to include all the sources of peak enlargement other than the APD size component. On the other hand, the breadth (B) at half height of the superlattice (100) kocl line was assumed to include the same sources plus the APD component. The value b was determined by using the following equation:

S= 0.8 x CIO.6 x I(100)/I(200)]1'2 (5-2)

D = K A / b cos 9 (5.3)

b2 = B2 - B ’2 (5.4)

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A discussion on the necessary statistical requiriments and the sources of error on using such a method to determine APD sizes is presented by Clegg(1971). Rogers, Flowers and Rawlings(1975) compared this method with the direct measurement of APD sizes using TEM. They concluded that the major disadvantages of the x-ray method are the poor accuracy on determining large values of D and the lack of information on the APD morphology.

5.6.3 Lattice Parameter Measurements

The d-spacing of (211), (310) and (222) fundamental peaks of the FeCoV and FeCoNb samples in the ordered and disordered states, the 2.5mm thick FeCoNb samples quenched from 800°C and the FeColNb samples of groups 1, 2 and 3 were labelled by scanning at a speed of0.02° per second using Cu-koc radiation. The lattice parameter was taken as the average value obtained from the calculations using the three peaks. The average error was about ± 0.0001 A.

5.7 Mossbauer Spectroscopy

Samples of FeCol.5V4.5Ni and of the complete series of ternary FeCoV and FeCoNb alloys were prepared for Mossbauer spectroscopy. A range of thermo-mechanical treatments was employed in order that a comprehensive study could be made of the correlation between magnetic properties and microstructure. At least three structural conditions were investigated for each alloy, namely: ordered,disordered and aged (at 550°C for 24 hours). In some cases the disordered and deformed condition was also studied.

The samples were ground with silicon carbide paper to a thickness of about 25}im for transmission spectroscopy. The spectra were taken at room temperature in a Mossbauer spectrometer with a 3 7 Co in Rhsource and under triangular velocity control. Before and after each spectrum, a natural iron calibration spectrum was taken in order to improve the accuracy of the results. The resulting data were computer fitted to Lorentzian curves using a least-squares program. The theoretical foundations and some practical aspects of Mossbauer spectroscopy are presented in appendix 1 .

- 6 7 -

5.7.1 Detection of the Phases Present

The ferromagnetic phases (o or 0 4 ’) were easily detected by the presence of a characteristic set of six peaks (sextet) in the Mossbauer spectra. On the other hand, the presence of a pararaagne-tic phase such as Ti or rt , was usually characterized by thepresence of a central peak. Since the iron content of the orr2 phases are estimated to be lower than in the average alloy composition, the relative intensity of these peaks are expected to be reduced. The existence of any isomer shift was taken relative to the iron calibration that was assumed to be zero.

5.7.2 Magnetic Properties on the Atomic Scale

An estimate of the macroscopical magnetic behaviour of the material can be obtained from measurements of the specimens’ magnetic hyperfine field (Hint), since this parameter can be correlated with its saturation magnetization (Johnson et al 1961). The magnetic hyperfine field was determined in the present work by comparing theseparation between lines 1 and 6 of the specimens’ ferromagneticspectrum Cs(specimen)] and that of the iron calibration spectrum Cs(iron)], according to eq. 5.5:

H int = Cs(specimen)/s(iron)3 x 2.63 x 107 A/m (5-5)

The value 2.63 x 107 A/m being the magnetic hyperfine field of natural iron at room temperature.

5.7.3 Site Population

As discussed in section 4.6, the presence of different environments for the 37Fe atom can be deduced from distortions produced in the sextet stucture of the Mossbauer spectrum. This possibility was considered in the present study because of the employment of non- ferromagnetic elements (V and Nb). In the appropriate cases the sextet structure was decomposed into a set of constituent sextets and their relative areas determined by computer analysis of the spectra.

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5. 8 Electrical Resistivity

5.8.1 Dependence With Composition and State of Ordering

The electrical resistivity at 77K of all the studied alloys in the ordered and disordered states was determined by using the four point method. The geometry of the specimens (parallelepiped) dimensions (about 40mm X 1mm X 0.25mm) and the placement of contacts (Ni wires spot welded and separated about 1 0 mm to each other) were chosen in order to minimize the error in using equation 5.6 rather than a more exact but cumbersome expression (Stephens et al 1971).

j> = R A/l (5.6)

This equation correlates the electrical resistance R of a specimen with cross section A and contacts separation 1 to its electrical resistivity p assuming a laminar electric current through the specimen. The experimental error in p (about 1%) was mainly associated with the inaccuracy in the measurement of the dimensions of the sample and the distance between the voltage contacts. The error due to the use of the simple equation 5.6 was estimated to be much less than 0 .1 % and is therefore negligible.

Figure 5.1 shows the electric circuit used to determine the electric resistance of the samples. The inversion in the current flow is a procedure to eliminate the effect presented by possible thermal e.m.f. produced in the electric contacts. The sample holder, which was designed to operate from -196aC to 1008 C, is shown in the same figure. Two different samples could be measured during the same experiment.

5.8.2 Electrical Resistivity Parameters and Structural Changes

The structural features of FeColNb in various microstructural conditions were correlated with the electrical resistivity and some associated parameters as described below. This study involved the measurement of the electrical resistivity and its relative changes with the test temperature in the range between -196aC (77K) and

- 69 -

<\lUj

Ujcl

Figure 5.1 - The main circuit for resistivity measurements, a detail of the sample holder.

show

-7 0 -

about +100°C of samples in groups 1 and 2 referred in section 5.4. The temperature coefficient of the electrical resistivity (Sp/£T)(#) of the samples submitted to different heat treatments was interpreted in terras of the effective number of conduction electrons (N eff) (Coles-1960, Rossiter-1980-a) and associated with alterations in the Brillouin zones due to the ordering process or to changes in the matrix composition due to a precipitation process. As presented in section 3.1.1, the dependence between the two parameters involves the proportionality:

1/N eff a £j>/ST (5.7)

The relaxation time of the free electrons (t ) was also correlated with microstructural changes, such as ordering or the development of small antiphase domains, and was determined from the proportionality presented in expression 5.8 and discussed in section 7.4.4.

t oc C(Sp/ST)/p ] (5.8)

The dimensions of the samples were assumed to be independent of temperature and the relative changes of p with temperature could be obtained from the relative changes of R (i.e Ap/p=AR/R). This procedure permitted an improvement in the accuracy of the relative changes of p to the limit of precision on determining the electrical resistance. In the present case this limit was about 0.1%. The error in the temperature measurements for this specific experiment was about ± 0.1°C.

5.8.3 A Computer Controlled Resistivity Rig

A computerised system was designed and built in order to control the resistivity experiments by measuring automatically the relative changes in the electrical resistivity as function of temperature. Figure 5.2 shows the diagram of the electronic circuit to interface the electrical circuit of figure 5.1 to a micro computer.

NOTE (*): T is the test temperature; not to be mistaken with the quench temperature of the specific heat treatments.

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The circuit of figure 5.2 receives a digital impulse from the output port fixing which operation is to be performed. A selection of five different sub-circuits can be activated, involving current inversion or the choice of four different voltages (from samples 1 or 2 , standard resistor or thermocouple). The selected voltage converted into a digital signal is driven to the input port, read, stored and eventually processed.

5.9 Magnetic Measurements

Magnetic measurements were performed on the FeCo3.6V, FeCo5.4V and all the FeCoNb alloys previously cold-rolled (75% RA) and annealed as described in section 5.4.

Rings of 25 mm outer diameter (OD) and 20 mm inner diameter (ID) were cut out using a spark erosion apparatus. The rings were stacked up to give a thickness of about i mm and the cores were enclosed in toroidal plastic cases of standard sizes so that the primary and the secondary coils would enclose the same areas. A search coil (S) of n=80 turns was wound on the plastic case and over it was wound a magnetising coil (P) of N=100 turns, both windings extending completely around the circumference. Figure 5.3 shows schematically the apparatus used. G-is a ballistic galvanometer and M is a mutual inductance with air core, used for calibration.

Before the tests the material was demagnetised by applying a 50 Hz field of about 1000 A/m and reducing this to zero over a period of about one minute. A current I in the primary circuit creates a magnetic field H in the toroid volume given by:

H = NI/L (5.9)

were L is the mean circumference of the ring CL=ti(0D+ID)/2]. If this field is changed suddenly by changing the current from, for instance +1 to -I, the resulting change in B induces a voltage V in the search coil and the ballistic galvanometer records the voltage integrated over the time that the change occurred. This quantity is

-7 2 -

J I I M T:a1 1 004t04tm

* S U M

F i gure 5.2 - Electronic circuit for computerized control of the main circuit for resistivity measurements

Figure 5.3 - Circuit for the ballistic method of measurement of the magnetic properties of ring specimens.

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5tot in theequal to the total change in the magnetic flux toroid volume:

, V dt = ^ $ t o t (5*10)n

But the total magnetic flux (§tot) has two components given by:

§T 0 T = §« A T + §A I R (5.11)

where §„ A T is the flux in the material under study and §AiR is theflux in the air that fills the rest of the volume of the toroid. Thedetermination of §Air by using a dummy ring (air core) allows the calculation of §*AT and the magnetic induction B by using:

B = $„AT / nA (6.12)

where A is the total cross section area of the rings.

Since this method involves differences, it is important to startfrom a known value of B. This is the reason for the initial demagnetisation of the material (B=0).

Magnetic fields of 4000 A/m were used to saturate the samples before determining the remanence Br - by removing the applied tield- and the coercive force He - by applying an inverted current Ic able to reduce B to zero.

The experimental errors observed in both He and Bs were about ± 5%.

-7 5 -

CHAPTER 6

RESULTS

6.1 Phase Analysis

6.1.1 DTA Results

Figures 6.1 and 6.2 show the results of the two cycles DTA carried out respectively on the FeCoV and FeCoNb alloys. The arrows show the cycle direction. In any cycle, the peak at temperatures near 700°C corresponds to the order/disorder transition while the other peak at higher temperatures corresponds to the a,/a,+rt transformation. The discrepancy observed in the positions of two correspondent peaks of any particular transformation, between the heating and thecooling cycles, is due to the non equilibrium condition of the tests. This thermal hysteresis effect was minor for the order/ disorder transformation whereas the a, /«, +rt transformation on heating was at a considerably higher temperatures than that on coo 1 ing.

The value of a specific transition temperature is better expressed by averaging the temperatures of the respective peaks in the two cycles. Although the maximum point of any DTA peak corresponds to the maximum rate of transformation, this position was used in order to produce the average temperature mentioned above. This procedure does not lead to major errors on averaging the temperatures and is the easiest way on finding a representative point for any specific transformation. The dotted lines in figures 6.1 and 6.2 show how the average transition temperature changes with composition; these values are also shown in table 6.1. The large peak observed in the cooling curve of FeCo5.4V suggests the overlap of the ot, /«t +r, and order/disorder transformations. The temperature hysteresis in this particular case is large.

The results show that the FeCoV alloys exhibit decreasing transition temperatures for both the order/disorder and the <xt /a, +T, transformations; as well as larger cc, /«, +f, temperature hysteresis,

- 7 6 -

DTV

(ar

bit

rary

uni

ts)

DTV

(ar

bit

rary

uni

ts)

Figure 6 .1 - DTA plot of FeCoV alloys.

Figure 6.2 - DTA plot of FeCoNb alloys

- 7 7 -

with increasing vanadium content. The transition temperatures for FeCoV alloys are in good agreement with those reported by other wokers, particularly those presented by Ellis and Greiner (1941). The fit is specially good when the heating and cooling peaks are close to each other. The addition of up to 3 wt% Nb does not greatly affect these transition temperatures.

TABLE 6.1

Order/disorder and at/«i+r\ transition temperatures (in °C) in FeCoV and FeCoNb alloys

^'^^TRANSFORMATI ONALLOY ORDER/DISORDER at / <Xi + r\

FeCo2V 713 934

FeCo3.6V 705 869

FeCo5.4V 680 803

FeColNb 734 971

FeCo2Nb 730 967

FeCo3Nb 729 963

6.1.2 Microstructure

The size and morphology of the grains in the FeCoV and FeCoNb alloys investigated in the present work are shown in the light micrographs of figures 6.3 and 6.4 respectively. The light, scanning and transmission electron micrographs (figures 6.5 and 6 .6 ) reveal some of the details of the r2 precipitation. It is interesting to note that the precipitates present in the FeCoNb alloys are approximately spherical and that they tend to form in colonies (fig. 6 .6 -a).

-7 8 -

QUENCHED FURNACE COOLED

(e) (f)» ....■»50 finFigure 6.3 - Light micrographs showing the grains norphology in FeCoV alloys quenched (a, c and e) and furnace cooled (bf d and f).

79-

QUENCHED FURNACE COOLED

(e) (f)I------ 1

100 yin

Figure 6.4 - Light micrographs showing the grains morphology in FeCoNb alloys quenched (a, c and e) and furnace cooled (b, d and f).

80-

(e) <f)

i---------- 1lOOua

Figure 6.5 - Micrographs showing T2 precipitates in FeCoNb alio/s quenched (a, b, d, e, g and h) and furnace cooled (c, f and i). Figures a, d and g are light micrographs, the others are scanning electron micrographs obtained by using the backscattered electrons image technique.

-8 1 -

(c)

Figure 6 . 6 - Micrographs exhibiting some details of r 2 precipitation in FeCoNb alloys: (a) backscattered electrons image showing a colony of precipitate particles in ordered FeCo3Nb; (b and c) transmission electron micrographs showing approximately spherical r 2 particles in FeColNb quenched and aged for ih at 630°C.

-82-

The average grain size of the at matrix, as determined by the mean linear intercept method, and the volume fractions of second phase present in both furnace cooled and quenched conditions of FeCoV alloys are presented in table 6.2. The experimental error in the grain size was about 2 0 % while the error in the volume fraction of second phase was estimated to be about 50%; in other words, the quoted volume fractions are only an indicative of the amount of second phase present in the alloys. The same microstructural features for the FeCoNb alloys are shown in table 6.3. From tables6.2 and 6.3 the following deductions can be made: (i) in both FeCoV and FeCoNb alloys the grain size decreases and the second phase volume fraction increases with increasing ternary content; (ii) the volume fraction of second phase is larger in the furnace cooled than in the quenched condition.

The energy dispersive analysis of the FeCoNb alloys, using the Terascan electron microscope, showed an average composition of the globular precipitate particles of about 49 at%Co, 35at%Fe and 15at%Nb; the Nb content of the matrix could not be accurately determined since its value was low and within the experimental error. As reported in the last chapter, etching was necessary to reveal the presence of gamma precipitates in the FeCoV alloys when using the SEM. Due to the irregularities produced in the samples surface, this procedure spoils the results from the energy dispersive analysis. However, a semi-quantitative analysis could be performed and showed that the V content of the matrix (a,) is constant at a value of about 8 to 1 0 times less than that of the precipitate particles. Assuming that the V-rich precipitates have about the same composition as the Nb-rich particles, one can estimate that the V content in the matrix of those alloys is between about 1.5 and 2 at% independent of the nominal composition of the alloys (2.2, 4.0 and 6.0 at% V). This technique also indicates that the V content of the matrix of the FeCoVNi alloy aged for 24 hours at 650°C is well below the nominal composition. In all the cases analysed, the presence of iron in the precipitate particles was detected through a strong signal. Thus the particles contain some Fe and are not simply Co3Nb or Co3 V as suggested by Kawahara(1983-a&b).

-8 3 -

TABLE 6.2

Average grain diameter (in pm) and volume fraction of second phase (in X) in FeCoV alloys in furnace cooled and quenched conditions

condition furnace coo 1 ed Quenchedgr. size 2 nd phase gr. size 2 nd phase

V content ^x. (pm) (X) (pm) (X)

2.0 wtX 1 2 0 19 0

3.6 wtX 1 0 2 1 15 16

5.4 wtX * > 30 # > 40

* Difficult to determine due to high proportions of 2nd phase present

TABLE 6.3

Average grain diameter (in pm) and volume fraction of second phase (in X) in FeCoNb alloys in furnace cooled and quenched conditions

^x. condition furnace coo 1 ed Quenchedgr. size 2 nd phase gr. size 2 nd phase

Nb content ^x. (pm) (X) (pm)

1 wtX 41 7 33 6

2 wtX 2 0 1 1 18 1 0

3 wtX 15 14 15 1 1

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The Mossbauer spectra showed clearly the presence of two magnetically different phases in almost all the alloys studied. The ferromagnetic phase was distinguished by the characteristic set of six peaks (sextet) while the paramagnetic phase was detected through the presence of a central pair of singlets or a doublet. Typical spectra for cold worked FeCoNb and FeCoV alloys are shown in fig 6.7

As can be seen in the spectrum B of fig. 6.7, the sextet peaks of the FeCoV alloy are not symmetrical. This characteristic was common to all the FeCoV alloys and the only exception was the FeCoVNi alloy aged at 650*C for 24 hours. This assymmetry was analysed assuming the presence of 2 or 3 constituent sextets. All these spectra gave a satisfactory fit using 2 sextets, but in the case of FeCo3.6V and FeCo5.4V three sextets also gave an acceptable fit even though the intensity of the third sextet was only few percent of the total intensity. The arrows in the spectrum B (fig. 6.7) indicate the positions of the sixth peaks of the two constituent sextets in the FeCoV sample. None of the FeCoNb spectra presented this sort of assymmetry. The arrow in the spectrum A (fig.6 .7) shows the paramagnetic peak in the FeCo2Nb alloy.

The relative areas of the peaks present in the Mossbauer spectrum of FeCoV alloys as function of the vanadium content are given in fig. 6 .8 . The full symbols represent the quenched or quenched and cold worked material (disordered condition) and the open symbols represent the ordered condition, namely furnace cooled (circles) or aged material (squares); figure 6 . 8 also contains information from the two (circles) and three (triangles) sextet analysis; the results from FeCoVNi quenched or aged are represented by full or open diamonds respectively.

Figure 6.9 shows the relative areas of the paramagnetic peaks in the Mossbauer spectra of FeCoV and FeCoNb in different microstructura1 conditions, as function of the ternary addition. The full circles represent the quenched or quenched and cold worked material. The open circles and open squares represent the furnace cooled and aged material respectively.

-8 5 -

Rel

ativ

e co

unts

*

velocity (mm/s)

Figure 6.7 - Typical MSssbauer spectra of (A) FeCoNb and (B) FeCoV alloys. The arrow in spectrum A shows the paramagnetic component systematically observed in the FeCoNb alloys; the arrows in spectrum B show the positions of the sixth line of the two constituent sextets observed in some of the FeCoV alloys. In some spectra of FeCoV alloys the computer analysis of the assymmetry of the ferromagnetic lines indicated the presence of a third set of sextets, in such cases the difference between the magnetic split of two adjacent sextets was constant.

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£4002 20co

CO©a0 10>•HjO0 0

o1 2 3 4 5 6

vanadium content (at%)

Figure 6 . 8 - Relative areas of the peaks of the ferromagnetic phase (sextets A, B and C) and of the paramagnetic phase (central peak) in the Mossbauer spectra of FeCoV and FeCoVNi alloys as function of the V content. The full symbols represent the material in the disordered condition (i.e. quenched or quenched + cold-worked); the open symbols correspond to the material in the ordered condition, namely furnace cooled= O or aged at 550°C for 24 hours= □ . The results from FeCoVNi quenched or aged at 650°C for 24 hours are represented by full and open diamonds respectively. The triangles correspond to the three sextet analyses; all the other symbols represent data obtained from two sextet analyses.

-8 7 -

ternary addition (at%)

Figure 6.9 - Relative areas of the paramagnetic peaks in the Mossbauer spectra of FeCoV and FeCoNb alloys as function of the content of the ternary addition. The symbols represent the the material in the conditions: • = quenched; O = furnace cooled and □ = aged at 550°C for 24 hours.

-88-

It is interesting to note in figure 6.9 that, for a given composition, the peak area increases with the time of heat treatment i.e. in the sequence: quenched, furnace cooled, aged. The areas also increase with the ternary addition. For a given ternary content the relative area of the paramagnetic peak is greater in the material containing niobium. The extrapolation of the curves in figure 6.9 indicates the absence of paramagnetic phase for vanadium contents less than about l.SatX and niobium contents less than about 0.3at%.

It is worth noticing the differences between the relative areas of the paramagnetic peaks (fig.6 .9) and the volume fractions of second phase in the same specimens (tables 6.2 and 6.3). The extreme example of this difference is given by the FeCo5.4V alloy, which in the quenched condition exhibits a relative area for the paramagnetic peak of only 4% and a volume fraction greater than 40%.

The computer analysis of the Mossbauer paramagnetic peaks, treated as a pair of singlets, gave isomer shifts relative to natural iron of +0.05 ± 0.03 and -0.26 ± 0.03 mm/s for the FeCoV alloys and +0.01 ± 0.04 and -0.38 ± 0.06 mm/s for the FeCoNb alloys independent of the ternary content. The experimental error in analysing very weak peaks (relative areas<i%) did not permit reliable values for g .

6.2 Texture

Texture can affect the relative intensity of the Mo'ssbauer peaks as presented in section 4.4. The relative intensities of the lines in the Zeeman hyperfine pattern were quantified using the parameter P given by equation 6 .1 :

P = 2 I, / (I, + I3) (6 .1 )

where I is the intensity and the subscripts refer to lines 1 , 2 and3. For the cold worked samples, the P values were almost constant for all the FeCoNb alloys (about 0.50) and increased with the vanadium content in the order 0.52, 0.77 and 1.1 respectively for FeCo2, 3.6 and 5.4V, while for all the other conditions of the alloys (quenched, furnace cooled or aged) the P values were nearly constant (1 . 1 ± 0 .1 ) independent of the ternary element or its

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content. These results show partial agreement with the findings of Oron et al (1969) who report a similar ratio for cold-worked Vicalloy of P ~ 0.40 but a somewhat higher ratio for the annealed material of P s 1.8.

6.3 Ordering of FeColNb

The characteristics of ordering in the FeColNb alloy were studied through the determination of the Bragg-Wi11iams LRO parameter (S), the lattice parameter (an), and the antiphase domain size (D) of the material heat treated as specified in section 5.4 (groups 1, 2and 3). The heat treatments employed in groups 1 and 3 were chosen in order to study the kinetics of ordering in an initially disordered structure under isochronal and isothermal conditions respectively. On the other hand the samples of group 2, initially ordered (FC) and isochonally heat treated for 1 hour were intended to produce the equilibrium states of order in the range of temperature studied.

6.3.1 Bragg-Vi11iaas LRO Parameter (S)

Isochronal ordering : Figure 6.10 shows the x-ray results for the LRO parameter (S), after the 1 hour heat treatment, as function of the ageing temperature of the FeCoiNb initially ordered i.e furnace cooled (curve A) or initially disordered (curve B).

Curve A in fig. 6.10 exhibits a continuous decrease of S with increasing ageing temperature of the material previously ordered and a final sharp drop near Tc (about 730"C). Assuming that 1 hour is enough for the FC material to achieve the LRO equilibrium at the specified ageing temperatures, curve A in figure 6.10 can be taken as the FeColNb S vs T equilibrium curve. This curve has the same general shape as the plots of S vs T presented in the review by Stoloffand Davies (1964) for equiatomic FeCo (see fig. 2.3), with the only disagreement being that the values are generally lower in the present case except near Tc where the values are a little hi gher.

- 9 0 -

Figure 6 .10 - Long range order parameter (S) of FeCoiNb initially ordered (curve A) and initially disordered (curve B) as function of the ageing temperature (ageing time = 1 hour).

Figure 6.11 - Long range order parameter (S) of FeCoiNb initially disordered, as function of the ageing time at 550°C. The broken line indicates the "equi1ibrium" value of S at 550°C, i.e. that for the material initially ordered and aged for i hour at 550*0.

-9 1 -

On the other hand, curve B in fig. 6.10 shows that the previously disordered material has an initial rise of the LRO parameter towards the equilibrium values of curve A, as the ageing temperature increases up to 690°C. Between 690*C and Tc the two curves coincide, indicating that the equilibrium S is achieved within 1 hour for the previously disordered material at these temperatures.

Isothermal ordering : The LRO parameter of FeColNb initially disordered and then aged at 550°C increased with the ageing time as shown in figure 6.11. The increase of S presents an asymptotic convergence to the equilibrium value at 550°C (S=0.71 indicated by the discontinuous line). It is interesting to note that this equilibrium value was not achieved within the maximum time used in the investigation of 32 hours.

6.3.2 Lattice Parameter (aG)

Isochronal heat treatments : Figures 6.12 and 6.13 show the lattice parameter as function of ageing temperature of FeColNb initially disordered and initially ordered respectively (groups 1 and 2 ).

In figure 6.12 the increase of a0 up to 550°C follows the same tendency expected for an increasingly ordered FeCo based alloy (Clegg-1971, Orrock-1985). The subsequent inversion in this trend is discussed in the next chapter.

The specimens initially furnace cooled show a continuous drop in aD with increasing ageing temperature (figure 6.13). This tendency can be associated with the decreasing degree of LRO of the material in the same range of temperature as presented in the last section. The slight inversion of concavity, observed between 550 and 660°C, is discussed in the next chapter.

Isothermal heat treatment : The changes in the lattice parameter as function of ageing time of the FeColNb disordered and aged isothermally at 550°C is shown in figure 6.14. The continuous increase of a0 is consistent with the increasing order observed for the same specimens (compare figures 6.11 and 6.14).

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latt

ice

par

amet

er

(A)

F i gure 6.12 - Lattice parameter (a0) of FeColNb initially disordered as function of the ageing temperature (ageing time = i hour). The broken line indicates the calculated a0 for S=i (see page 132).

F i gure 6.13 - Lattice parameter (a0) of FeColNb initially ordered as function of the ageing temperature (ageing time = 1 hour).

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latti

ce p

aram

eter

(A

)

Figure 6.14 - Lattice parameter (a0) of FeColNb initially disordered, as function of the ageing time at 550°C.

-9 4 -

6 .3 .3 Antiphase Donain S ize (D)

Isochronal heat treatments : The APD sizes, as determined fromx-ray line broadening, of the FeColNb previously disordered, as function of the ageing temperature are presented in figure 6.15-3.- The micrograph in figure 6.15-b is a dark field image of the APD for the material aged at 630°C for the same time (1 hour), taken by using one of the superlattice reflections shown in figure 6.15-c. A comparison between figures 6.15-A and B shows that the results for the APD sizes obtained by using the x-ray technique are close to the observed through the TEM. It is interesting to observe the increase of the APD size with increasing ageing temperature, followed by an apparent saturation and then a final drop near Tc. The initially ordered (FC) material had a starting APD size of about 1000 A and larger values after ageing the material for one hour at different temperatures. Unfortunately the inaccuracy of the Scherrer method for determining sizes above 1000 X did not permit accurate determination of the APD size for this specific group.

Isothermal heat treatment : The APD size as function of the root square of the ageing time of FeColNb in the isothermal heat treatment employed in group 3 is presented in figure 6.16 which clearly demonstrates a tw2 dependence. Such a dependence is the same as that observed in FeCoV (English-1966, Clegg and Buckley-1973, Ashby-1975) or in the binary alloy (Brown-1978).

6.4 Electrical Resistivity Results

6.4.1 Ternary Additions and Ordering Effects

The electrical resistivity of FeCo(2,3.6 and 5.4 wt%)V, FeCo2V(l,3 and 5 wt%)Cu, FeCo3Cu, FeCo2V(l,3 and 5 wt%)W, FeCo(l,3 and 5 wt%)Nb and FeCo5Ni in both the furnace cooled and quenched conditions were measured in liquid nitrogen (77 K = -196#C) and the results are displayed in table 6.4. Also presented in the same table are the electrical resistivity of FeCol.5V4.5Ni in both aged (for 24h at 650°C) and quenched conditions and, for comparison, the values obtained by Rossiter (1981) for the binary alloy under similar experimental conditions.

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(a)

i-------- 11000 A (b)

Figure 6.15 - (a) APD sizes as function of the ageing temperature in FeColNb initially disordered (group 1) -ageing time = 1 hour- (b) dark field image of the antiphase domains in the material disordered and aged at 630°C for 1 hour, taken by using one of the superlattice reflections shown in figure (c).

-96-

F i gure 6.16 - APD sizes of FeCoiNb initially disordered, as function of the root square of the ageing time at 550°C.

-9 7 -

TABLE 6 .4

Electrical resistivity (in jiflcm) of FeCo based alloys at -196 C in the furnace cooled (FC) and quenched (Q) conditions

CONDITION P F C CONDITION p F C hALLOY (pQcm) ( iQcm) ALLOY (jiQcm) (pQcm)

FeCo * 1.95 3.09 FeCo2VlW 36.3 30.9

FeCo2V 48.0 42.3 FeCo2V3W 38.4 35.7

FeCo3.6V 48.2 47.5 FeCo2V5W 37.4 36.3

FeCo5.4V 48.4 60.7 FeCol.5V4.5Ni #13.0 23.3

FeCo2VlCu 45. 1 39.9 FeCo5Ni 3.65 3.96

FeCo2V3Cu 43.7 37.4 FeColNb 3.12 5.07

FeCo2V5Cu 40.2 33.7 FeCo2Nb 3.06 5.27

FeCo3Cu 2.09 3.54 FeCo3Nb 3. 16 5.50

* Results for the binary alloy are from Rossiter (1981).# Sample aged for 24 h at 650*C.

-9 8 -

The f o l l o w i n g g e n e r a l t r e n d s can be drawn f rom t a b l e 6 . 4 : ( i ) t h e

a d d i t i o n of V t o FeCo i n c r e a s e s t h e e l e c t r i c a l r e s i s t i v i t y by a

f a c t o r of a b o u t 20 ( a s p r e v i o u l y e s t a b l i s h e d by many o t h e r w o r k e r s )

w h i l e a l l t h e o t h e r t e r n a r y a d d i t i o n s a r e f a r l e s s e f f e c t i v e ; ( i i )

t h e a d d i t i o n of q u a t e r n a r y e l e m e n t s t o FeCoV a l l o y s shows a d i l u t i o n

e f f e c t on t h e i n c r e a s e i n p ; ( i i i ) w i t h e x c e p t i o n of FeCo5.4V and

Fe Col . 5V4 . 5Ni a l l t h e t e r n a r y o r q u a t e r n a r y a l l o y s c o n t a i n i n g

vanadium e x h i b i t an i n c r e a s e i n t h e r e s i s t i v i t y w i t h o r d e r i n g ( i n

a g r e e me n t w i t h D i nh u t e t a l - 1 9 7 7 ) w h e r e a s a l l t h e o t h e r a l l o y s show

t h e o p p o s i t e b e h a v i o u r . The h i g h e s t change i n p due t o h e a t

t r e a t m e n t was o b s e r v e d in Fe Co l . 5V4 . 5Ni where t h e p a r a m e t e r was

r e d u c e d by a b o u t 44% a f t e r b e i n g aged f o r 24h a t 650*C. I t i s

i m p o r t a n t t o m e n t i o n t h a t no s i g n i f i c a n t change i n p was o b s e r v e d on

c o l d - r o l l i n g que nc hed s p e c i m e n s , a l t h o u g h t h e ef fec t of c o l d r o l l i n g

was o n l y i n v e s t i g a t e d f o r t h e FeCo2V, FeColNb and Fe Col . 5V4 . 5Ni

a l 1oys .

6.4.2 Effects due to Microstructural Changes

A s p e c i f i c s t u d y r e l a t i n g e l e c t r i c a l r e s i s t i v i t y and m i c r o s t r u c t u r e

has been d e v e l o p e d f o r t h e FeColNb a l l o y . T h i s i n v o l v e d t h e

meas ur emen t of t h e r e d u c e d e l e c t r i c a l r e s i s t i v i t y ( p ( T ) / p ( 2 98 ) ) of

g r o u p s 1 and 2, a s d e s c r i b e d i n c h a p t e r 5, a s f u n c t i o n of t h e

m e a s u r i n g t e m p e r a t u r e f rom 77K ( - 1 9 6 * 0 t o a b o u t 373K ( 1 0 0 * 0 The

d e p e n d e n c e of p ( T ) / p ( 2 9 8 ) w i t h t e m p e r a t u r e was compu t e r a n a l y s e d and

t h e b e s t f u n c t i o n o b t a i n e d u s i n g t h e l e a s t - s q u a r e s method was t h e

s e c o n d - o r d e r p o l y n o mi a l r e p r e s e n t e d by:

p ( T ) / p ( 2 9 8 ) = A0 + At T + A2T2 ( 6 - 2 )

where A ( 0 ) , A ( 1 ) and A(2) a r e c o n s t a n t s and T t h e a b s o l u t e t e s t

t e m p e r a t u r e .

F i g u r e 6 . 1 7 shows t y p i c a l e xa mp l es of such a d e p e n d e n c e ; t h e f u l l

symbol s r e p r e s e n t t h e e x p e r i m e n t a l r e s u l t s f o r FeColNb quenched f rom

850*C ( i . e . i n t h e d i s o r d e r e d c o n d i t i o n ) and t h e open symbol s

c o r r e s p o n d t o t h e same a l l o y f u r n a c e c o o l e d f rom 850*C ( i . e i n t h e

o r d e r e d c o n d i t i o n ) . The c o n t i n u o u s l i n e s a r e t h e b e s t s e cond o r d e r

- 9 9 -

p(T

)/p

(29

8)

temperature (K)

F i gure 6 . 1 7 - R e l a t i v e e l e c t r i c a l r e s i s t i v i t y of o r d e r e d and d i s o r d e r e d FeColNb as f u n c t i o n of t e m p e r a t u r e . The c o n t i n u o u s l i n e s c o r r e s p o n d t o t h e b e s t f i t s u s i n g second o r d e r p o l y n o m i a l s .

-1 0 0 -

p o l y n o mi a l f i t t o t h e d a t a . The a v e r a g e r e l a t i v e d e v i a t i o n be t we en

t h e v a l u e s f o r p ( T ) / p ( 2 9 8 ) d e t e r m i n e d from e q u a t i o n 6 . 2 and t h e

e x p e r i m e n t a l d a t a was 0.3% i . e . a b o u t t h e same o r d e r a s t h e

e x p e r i m e n t a l d a t a e r r o r . The same o r d e r of e r r o r was o b s e r v e d f o r

t h e r e p r o d u c i b i l i t y of t h e c o n s t a n t s A0 , At and A2 f rom

d i s t i n c t s p e c i me n s g i v e n i d e n t i c a l h e a t t r e a t m e n t s . For t h i s r e a s o n

v a l u e s f o r t h e r e s i s t i v i t y p ( T) o r i t s s l o p e r e l a t i v e t o t h e t e s t

t e m p e r a t u r e (Sp/ST) can be c a l c u l a t e d a n a l y t i c a l l y f rom e q u a t i o n

6 . 2 w i t h o u t f u r t h e r i n c r e a s i n g t h e e x p e r i m e n t a l e r r o r .

D e s p i t e t h e l a c k of knowl edge on t h e b e h a v i o u r of t h e e l e c t r i c a l

r e s i s t i v i t y of t h i s s p e c i f i c a l l o y n e a r OK, i t w i l l be assumed t h a t

e q u a t i o n 6 . 2 i s v a l i d t o t h a t l i m i t . T h i s seems t o be r e a s o n a b l e ,

c o n s i d e r i n g t h a t t h e b i n a r y a l l o y e x h i b i t s t h e same p a r a b o l i c

b e h a v i o u r i n t h e t e m p e r a t u r e r an g e 4 . 2 - 250K • ( R o s s i t e r - 1 9 8 1 f o r

e q u i a t o m i c FeCo) as o b s e r v e d i n t h e p r e s e n t i n v e s t i g a t i o n f o r t h e

t e m p e r a t u r e r a n g e 77-373K

The v a l u e s of A0 , Ai and A2 a r e p r e s e n t e d i n t a b l e s 6 . 5 and 6 . 6

f o r FeColNb r e s p e c t i v e l y que nc hed and aged ( g r o u p i ) and f u r n a c e

c o o l e d and aged ( g roup 2 ) ; t h e t a b l e s a l s o show t h e a b s o l u t e

r e s i s t i v i t i e s a t 298K tp (298 > ] .

6.5 Hagnetic Measurements Results

The D.C. normal i n d u c t i o n c u r v e s f o r FeCo 3 . 6 and 5 . 4 V and f o r FeCo

1, 2 and 3 Nb submit ted t o d i f f e r e n t h e a t t r e a t m e n t s a r e p r e s e n t e d in

f i g u r e s 6 . 1 8 t o 6 . 2 0 . The normal i n d u c t i o n c u r v e f o r t h e T e l c o n

PMD-49 i s a l s o g i v e n i n t h e same f i g u r e s as a c o m p a r a t i v e r e f e r e n c e .

The v a l u e s f o r c o e r c i v e f o r c e and s a t u r a t i o n i n d u c t i o n of t h e a l l o y s

a r e p r e s e n t e d i n t a b l e 6 . 7 .

The r e s u l t s show i n c r e a s i n g improvement i n t h e s o f t m a g n e t i c

p r o p e r t i e s ( i . e . h i g h e r Bs and lower He) w i t h d e c r e a s i n g t e r n a r y

a d d i t i o n . A n n e a l i n g t e m p e r a t u r e has l i t t l e e f f e c t on Bs b u t He

d e c r e a s e s w i t h i n c r e a s i n g t e m p e r a t u r e . These t r e n d s a r e s i m i l a r t o

t h o s e o b s e r v e d by Or r ock (1986) f o r smal l a d d i t i o n s of Cu and W t o

FeCo2V and aged a s i n t h e p r e s e n t work. N e v e r t h e l e s s t h e same a u t h o r

-1 0 1 -

TABLE 6 .5

C o e f f ic ie n ts A0 , At and A2 fo r equation 6 .2 and e le c t r i c a l

r e s i s t i v i t y a t 298K CJX298)] fo r FeColNb quenched from 850°C and

aged fo r 1 hour a t temperature T (group 1)

AGEING

TEMPERATURE

( *C)

Ao

xl O1

Ai

xlO4 ( K- ‘ )

a2

xlO4 (K-2 )

p (298)

( jiftcm)

Q * 4 . 8 8 9 . 3 0 2 . 6 4 8 . 81

500 4 . 9 5 9 . 8 7 2 . 3 7 7 . 9 0

550 4 . 9 0 9 . 4 7 2 . 5 5 7 . 2 9

600 4 . 9 8 8 . 8 9 2 . 6 6 7 . 8 2

630 4 . 9 9 9 . 1 0 2 . 5 8 8 . 21

660 4 . 81 9 . 4 2 2 . 6 6 8 . 3 9

690 4 . 91 9 . 3 1 2 . 5 9 8 . 6 9

720 4 . 6 3 9 . 4 2 2 . 8 7 8 . 4 2

730 4 . 3 6 10 . 02 2 . 9 9 8 . 8 3

750 4 . 3 5 10 . 38 2 . 7 8 8 . 4 7

780 4 . 3 8 9 . 6 9 3 . 0 6 9. 10

* Q corresponds to the material in the initial condition.i.e. quenched from 850°C.

-1 0 2 -

TABLE 6 .6

Coefficients A0, Ai and A2 for equation 6.2 and electrical resistivity at 298K [p(298)J for FeColNb furnace cooled and aged

at temperature T for 1 hour (group 2)

A G E IN G

TEM PER ATU R E

(°C)Ao

xi O1

A t

xlO4 ( K- 1 )

a2x l O*( K- 2 )

p (298)

( jiQcm)

FC * 3 . 8 2 12 . 07 2 . 9 0 6 . 3 5

500 3 . 9 3 11 .46 2 . 9 8 6 . 8 8

550 4 . 0 9 10 .29 3 . 1 9 7 . 0 9

575 4 . 1 4 11 . 53 2 . 7 3 7 . 2 7

600 4. 15 11.25 2 . 8 0 7 . 5 5

630 4 . 2 4 11 . 18 2 . 7 2 7 . 5 7

660 4 . 3 5 11. 10 2 . 6 4 7 . 8 9

690 4 . 3 6 11 .59 2 . 4 6 8 . 2 6

720 4 . 3 1 11. 15 2 . 6 5 8 . 5 3

750 4. 13 11 . 30 2 . 8 1 9 . 2 2

# FC corresponds to the material in the initial conditioni.e. furnace cooled

-1 0 3 -

Figure 6.18 - Magnetization curves of FeCoV alloys annealed for 2 hours at different temperatures (indicated between brackets) followed by furnace cooling. The magnetization curve for the Telcon PMD-49 is presented as a comparative reference.

-1 0 4 -

Figure 6.19 - Magnetization curves hours at 850°C followed by furnace for the Telcon PHD-49 is presented

of FeCoNb alloys annealed cooling. The magnetization as a comparative reference

for 2 curve

-1 0 5 -

H ( A / m )

F i gure 6.2 0 - Magnetization curves of FeCoNb alloys annealed for 2 hours at 760°C followed by furnace cooling. The magnetization curve for the Telcon PMD-49 is presented as a comparative reference.

-1 0 6 -

TABLE 6 .7

C o e r c i v e f o r c e (He) and s a t u r a t i o n m a g n e t i z a t i o n (Bs)

of FeCo b a s ed a l l o y s

PARAMETER

ALLOY

He

(A/m)

Bs

(T)

He

(A/m)

Bs

(T)

ANNEALED AT 7 6 0 #C ANNEALED AT 850°C

FeCo2V 95 2 . 3 2 90 2 . 35

FeColNb 355 2 . 3 4 300 2 . 32

FeCo2Nb 470 2 . 2 9 425 2 . 24

FeCo3Nb 665 2 . 2 0 610 2 . 1 2

ANNEALED AT 740°C ANNEALED AT 760°C

FeCo3.6V 1360 2. 18 990 2.01

ANNEALED AT 550°C -- -

FeCo5.4V 3930 1.66 - - -

-1 0 7 -

o b s e r v e d b e t t e r s o f t m a g n e t i c p r o p e r t i e s i n t h e FeCo5Ni aged a t

760*C t h a n t h e aged a t 850*C i n c o n t r a s t w i t h t h e p r e v i o u s

o b s e r v a t i o n s .

6.6 Some Paraaeteric Changes with Ordering and Composition

6.6.1 Lattice Parameter

The l a t t i c e p a r a m e t e r s of t h e FeCoV and t h e FeCoNb a l l o y s have been

d e t e r m i n e d f o r t h e m a t e r i a l i n t h e o r d e r e d and in t h e d i s o r d e r e d

s t a t e . T h a t p a r a m e t e r was a l s o d e t e r m i n e d f o r 2 . 5 mm t h i c k FeCoNb

s p e c i me n s k e p t f o r 1 hour a t 800°C and t h e n que nc hed i n t o i c e d

b r i n e . F i g u r e 6 . 2 1 shows t h e s e l a t t i c e p a r a m e t e r s a s f u n c t i o n of t h e

t e r n a r y a d d i t i o n c o n t e n t . The FeCoNb a l l o y s a r e r e p r e s e n t e d by

c i r c l e s and t h e FeCoV by s q u a r e s ; t h e f u r n a c e c o o l e d and t h e

quenched s a mp l e s a r e r e p r e s e n t e d by open and f u l l symbol s

r e s p e c t i v e l y . The c r o s s e s r e p r e s e n t t h e 2 . 5 mm t h i c k s a mpl e s

quenched f rom 800*0. The FeCo5.4V (6a t *V) p r o d u c e d b r oa d e n e d

d i f f r a c t i o n p e a k s , t h e r e b y i n c r e a s i n g t h e e r r o r i n t h e l a t t i c e

p a r a m e t e r by a b o u t one o r d e r of m a g n i t u d e , compared w i t h t h e o t h e r

r e s u l t s . The r e s u l t s f o r a„ i n quenched and i n f u r n a c e c o o l e d

FeCoV and FeCoNb as o b t a i n e d by Cl egg (1971) a r e a l s o shown i n t h e

same f i g u r e . In a l l c a s e s t h e o r d e r e d s t r u c t u r e s gave l a t t i c eO

p a r a m e t e r s of a b o u t 0 . 0 0 2 0 A l a r g e r t h a n t h e c o r r e s p o n d i n g

d i s o r d e r e d a l l o y s . The e f f e c t of c o m p o s i t i o n shows i n c r e a s i n g

l a t t i c e p a r a m e t e r s w i t h t h e vanadium c o n t e n t whe r e as v a r y i n g t h e

n i ob i um c o n t e n t be t ween 1 and 3 wt* i n c l u s i v e ( 0 . 6 2 t o 1 . 86 a t * )

does n o t s i g n i f i c a n t l y i n f l u e n c e t h e l a t t i c e p a r a m e t e r . The r e i s a

good a g r e e m e n t be t ween t h e p r e s e n t d a t a and t h o s e o b t a i n e d by Clegg

(1971) r e g a r d i n g FeCoV a l l o y s and on t h e FeCo0.37*wt a l l o y .

The 2 . 5 mm t h i c k s p e c i me n s c o n t a i n i n g Nb p r oduc e d an i n t e r m e d i a t e

l a t t i c e p a r a m e t e r a t a b o u t 25* of t h e way be t ween t h e v a l u e s f o r t h e

d i s o r d e r e d and t h e o r d e r e d s a m p l e s ; i . e . c l o s e r t o t h e v a l u e s of t h e

t h i n d i s o r d e r e d s a mp l e s . A c c o r d i n g t o t h e method d e v e l o p e d by Or rock

(1986) t h i s c o r r e s p o n d s t o a d e g r e e of long r a nge o r d e r of a b o u t 20*

and c e r t a i n l y s uc h a low d e g r e e of o r d e r would a c c o u n t f o r t h e good

r e l i a b i l i t y of t h e s e a l l o y s .

-1 0 8 -

Figure 6.21 - Lattice parameter of FeCoV (squares) and FeCoNb alloys (circles) as function of the ternary addition content. The data obtained by Clegg (1971) for FeCoV (diamonds) and FeCoNb (triangles) are also plotted. The quenched and the furnace cooled material are represented by full and open symbols respectively. The 2.5mm thick FeCoNb samples quenched from 800°C are represented by crosses.

-1 0 9 -

6.6.2 Temperature Coefficient of the Electrical Resistivity

F i g u r e 6 . 2 2 shows t h e e f f e c t of t h e n i ob i um c o n t e n t and t h e s t a t e of

o r d e r on t h e p a r a m e t e r [ (£j>/ST)/j> (298) ] of FeCoNb a l l o y s . A l t hough

no s e n s i t i v e d e p e n d e n c e on t h e Nb c o n t e n t i s o b s e r v e d , i t i s c l e a r

t h a t t h e r e i s a marked d i f f e r e n c e i n t h e p a r a m e t e r f o r s a mp l e s i n

t h e o r d e r e d and t h e d i s o r d e r e d c o n d i t i o n s , t h e f o r me r h a v i n g a lower

C ( £ j > / £ T) / p (298) 1 t h a n t h e l a t t e r . The same b e h a v i o u r was o b s e r v e d

by R o s s i t e r (1981) f o r e q u i a t o m i c FeCo.

6.6.3 Hyperfine Parameters

*i ) M a g n e t i c H y p e r f i n e F i e l d

F i g u r e 6 . 2 3 shows t h e m a g n e t i c h y p e r f i n e f i e l d f o r s e x t e t A (HA)

o b t a i n e d f rom Mossbauer s p e c t r o s c o p y f o r t h e FeCoNb, FeCoV and

FeCoVNi a l l o y s a s f u n c t i o n of t h e n i ob i um or vanadium c o n t e n t s . The

h y p e r f i n e f i e l d f o r s e x t e t B (H# ) o b t a i n e d from t h e two s e x t e t

a n a l y s i s of t h e FeCoV and FeCoVNi a l l o y s t h a t e x h i b i t e d some

a s s ymme t r y i n t h e Zeeman h y p e r f i n e p a t t e r n s i s a l s o shown. The

FeCoNb, FeCoV and FeCoVNi a l l o y s a r e r e p r e s e n t e d by c i r c l e s , s q u a r e s

and di amonds r e s p e c t i v e l y ; t h e open symbol s r e p r e s e n t t h e f u r n a c e

c o o l e d a n d / o r t h e aged m a t e r i a l s ( i . e . t h e o r d e r e d c o n d i t i o n ) w h i l e

t h e f u l l symbol s r e p r e s e n t t h e quenched a n d / o r t h e quenched and

de fo r med s a mp l e s ( i . e . t h e d i s o r d e r e d c o n d i t i o n ) . The t y p i c a l e r r o r

was a b o u t 0.4% f o r s e x t e t A and 1% f o r s e x t e t B.

The r e s u l t s show t h a t , w i t h i n t h e e x p e r i m e n t a l e r r o r , t h e h y p e r f i n e

f i e l d i n b o t h t h e s i n g l e and t h e two s e x t e t s s t r u c t u r e s a r e

i n d e p e n d e n t of t h e t e r n a r y e l e m e n t s a s we l l a s t h e i r c o n t e n t . In a l l

c a s e s t h e d i s o r d e r e d s t r u c t u r e s had c o m p a r a t i v e l y h i g h e r H* and

lower Hb t h a n t h o s e f o r t h e o r d e r e d c o n d i t i o n . The a v e r a g e v a l u e s

of H, p r e s e n t e d i n t a b l e 6 . 8 , a r e shown i n f i g u r e 6 . 2 3 by t h e

d i s c o n t i n u o u s l i n e s . The v a l u e s o b s e r v e d h e r e a r e i n r e a s o n a b l e

a g r e e me n t w i t h t h o s e f ound by o t h e r a u t h o r s ( s e e t a b l e 6 . 8 ) .

-1 1 0 -

(6p

/6T

)/p

(29

8)

x 10

3 . 0 0

2 . 5 0

o0 ordered 0

disordered---------------------------

1.0 2.0niobium con ten t (at%)

F i g u r e 6.22 - C(Sp/ST)/ p 2 9 e 3 d e t e r m i n e d a t 298K f o r FeCoNb a l l o y s o r d e r e d (open s ymbol s ) and d i s o r d e r e d ( f u l l symbol s ) a s f u n c t i o n of t h e n i ob i um c o n t e n t .

-Ill-

E2 .8

~------------ 1-------

• •

-------T

•

1

s e x t e t Al -----------1------

d i s o r d e r e d

tK Oe

♦ ■ ■

2 .7

Joii' o

___1___

- Ocr□ o r d e r e d

□ _ 3 4 0

3 3 02 .6

O s e x t e t B□ -

o r d e r e d

1 □ - 3 2 0♦ d i s o r d e r e d

2 .5 — ■ ■

________ 1 ____L _____l___ _L_ r ____ r1 2 3 4 5 6

te rnary addition (a t%)F i g u r e 6 . 2 3 - H y p e r f i n e f i e l d i n FeCoNb ( c i r c l e s ) , FeCoV ( s q u a r e s ) and FeCoVNi a l l o y s (d i amonds ) f o r s e x t e t s A and B a s f u n c t i o n of t h e t e r n a r y c o n t e n t (Nb or V). The o r d e r e d and t h e d i s o r d e r e d s p e c i me n s a r e r e p r e s e n t e d by open and f u l l symbol s r e s p e c t i v e l y .

0 . 0 4

w^ 0 . 0 3 E

i 0.02w<DE.£ 0.01

F i g u r e 6 . 2 4 - I somer s h i f t of s e x t e t A i n FeCoNb ( c i r c l e s ) , FeCoV ( s q u a r e s ) and FeCoVNi a l l o y s ( d i amonds ) as f u n c t i o n of t h e t e r n a r y c o n t e n t (Nb or V). The o r d e r e d and t h e d i s o r d e r e d s p e c i me n s a r e r e p r e s e n t e d by open and f u l l symbol s r e s p e c t i v e l y .

1----------------r• •

• ♦ *

disord ered

O □ ordered □O- - - - -

o o

J____________ I

2 3 4 5te rnary addit ion (at%)

-1 1 2 -

TABLE 6.8

Magnetic hyperfine field (H) and isomer shift <£) of FeCo and based alloys - the subscripts A and B represent sextets A and B

PARAMETER

SOURCE/CON&Tv*^^

H*

( X 107 A/m)

H.

( X 107 A/m) (mm/sec)

PRESENT

WORK

FeCo(Nb/V)

QUENCHED 2 . 7 6 ± 0 . 0 1 2 . 5 1 ± 0 . 0 3 0 . 0 3 3 ± 0 . 0 4

ANNEALED 2 . 7 1 + 0 . 0 1 2 . 5 7 + 0 . 0 3 0 . 0 2 0 + 0 . 0 3

FINDIKY AND

EYMERY-1985

FeCo

Q + RAD 2 . 8 4 5 - -

QUENCHED 2 . 7 8 9 - -

ANNEALED 2 . 7 1 6 - -

MAYO-1981

FeCo

QUENCHED 2 . 7 8 - 0 . 0 2 8

ANNEALED 2. 71 - 0 . 0 1 3

ALEKSEYEV-77

FeCo2V

QUENCHED 2 . 7 8 2 . 5 0 -

ANNEALED 2 . 7 3 2 . 5 3 -

ALEKSEYEV-77

FeCo

QUENCHED 2 . 7 8 - -

ANNEALED 2 . 7 4 - -

MONTANO AND

SEEHRA-1977

FeCo

ANNEALED 2. 71 - -

JOHNSON-1961

FeCo

DISORD? 2 . 8 2 - -

ORD? 2 . 7 6 - -

-1 1 3 -

i i ) HWHM

For b o t h s e x t e t A (FeCoNb, FeCoV and FeCoVNi) and s e x t e t B (FeCoV

and FeCoVNi) t h e h a l f w i d t h a t h a l f i n t e n s i t y of t h e Mbssbauer l i n e s

(HWHM) d i d n o t show s i g n i f i c a n t de pe nde nc e w i t h t h e a d d i t i o n a l

e l e m e n t or i t s c o n t e n t , a l t h o u g h some d i f f e r e n c e s wer e n o t i c e d f o r

d i f f e r e n t t h e r m o - m e c h a n i c a l t r e a t m e n t s or s e x t e t c o n s i d e r e d . The

a v e r a g e v a l u e s of t h e p a r a m e t e r a r e d i s p l a y e d i n t a b l e 6 . 9 and t h e

g e n e r a l f e a t u r e s a r e :

SEXTET A: L i t t l e d i f f e r e n c e be t we e n t h e v a l u e s of HWHM of s a mp l e s

f u r n a c e c o o l e d (FC) que nc hed (Q) and aged (A) w i t h t h e s e t h r e e

c o n d i t i o n s h a v i n g a v a l u e of a p p r o x i m a t e l y 0 . 1 3 0 mm/s. However t h e

a v e r a g e v a l u e of t h e p a r a m e t e r f o r t h e m a t e r i a l i n t h e c o l d - w o r k e d

c o n d i t i o n i s s i g n i f i c a n t l y h i g h e r ( 0 . 1 5 6 mm/s) t h a n f o r t h e o t h e r

c o n d i t i o n s .

SEXTET B: Al l t h e v a l u e s of HWHM a r e g r e a t e r t h a n t h e o b s e r v e d i n

s e x t e t A. The d i f f e r e n c e s be t we e n t h e f o u r c o n d i t i o n s a r e g r e a t e r

t h a n i n s e x t e t A a l t h o u g h w i t h h i g h e r s t a n d a r d d e v i a t i o n s . The

p a r a m e t e r i n c r e a s e s i n t h e o r d e r : CHWHM(A) < HWHM (FC) < HWHM (Q) <

HWHM (CW)], b u t t h e d i f f e r e n c e b e t we en HWHM of t h e two o r d e r e d

c o n d i t i o n s (FC and A) was w i t h i n t h e e x p e r i m e n t a l e r r o r and . could be

c o n s i d e r e d t o have t h e same v a l u e of a b o u t 0 . 2 4 0 mm/s.

i i i ) I somer S h i f t (S)

F i g u r e 6 . 2 4 shows t h e i somer s h i f t f o r s e x t e t A ( SA ) of t h e FeCoNb,

FeCoV and FeCoVNi a l l o y s a s f u n c t i o n of t h e n i ob i um o r vanadium

c o n t e n t s . The s ymbol s a r e t h e same a s t h o s e f o r f i g u r e 6 . 2 0 . The

v a l u e s of S f o r s e x t e t B were i n s i g n i f i c a n t . The o b s e r v e d e r r o r was

15% f o r t h e o r d e r e d and 12 % f o r t h e d i s o r d e r e d c o n d i t i o n . The

r e s u l t s show t h a t t h e o r d e r e d s t r u c t u r e has a lower t h a n t h e

d i s o r d e r e d s t r u c t u r e . T h i s o b s e r v a t i o n i s i n a g r e e m e n t w i t h Mayo

(1981) f o r FeCo a l t h o u g h t h e a b s o l u t e v a l u e s d i f f e r a s shown i n

t a b l e 6 . 8 . In b o t h t h e o r d e r e d and t h e d i s o r d e r e d c o n d i t i o n s t h e

v a l u e s of S, w i t h i n t h e e x p e r i m e n t a l e r r o r , a r e i n d e p e n d e n t of t h e

i e r n l r y c o n t e n t . The a v e r a g e v a l u e s of S* , p r e s e n t e d i n t a b l e 6 . 8

a r e r e p r e s e n t e d i n f i g u r e 6 . 2 4 by t h e d i s c o n t i n u o u s l i n e s .

-1 1 4 -

TABLE 6.9

Aver age HWHM ( i n mra/s) a s f u n c t i o n of t h e r m o - m e c h a n i c a l t r e a t m e n t

s e x t e t A c o r r e s p o n d s t o FeCo( V/ VNi /Nb) s e x t e t B c o r r e s p o n d s t o

FeCo( V/VNi )

SEXTET

CONDIT I 0 l 3 \ ^ ^

A

(mm/s )

B

(mm/s)

COLD WORKED (CW) . 156 ± .011 . 356 ± . 017

DISORDERED (D) . 132 ± .005 .301 ± . 030

ORDERED (FC) .126 ± .005 . 253 ± .031

AGED (A) . 1 3 4 ± .006 .226 ± . 035

-1 1 5 -

CHAPTER 7

DISCUSSION

7.1 A Statistical Analysis of the Site Population of Low Vanadium in Eguiatoaic FeCo Alloys

Mossbauer s p e c t r o s c o p y of b i n a r y i r o n a l l o y s c o n t a i n i n g a few

p e r c e n t a g e of t h e a l l o y i n g a d d i t i o n has shown t h a t vanadium p r o d u c e s

a d d i t i o n a l s e x t e t s , w i t h s m a l l e r h y p e r f i n e f i e l d s t h a n t h a t f o r

i r o n , wh e r e as c o b a l t and n i c k e l o n l y l e a d t o some l i n e b r o a d e n i n g

(Wer the i m e t a l 1964, Vi nc z e and Campbel l 1973) , o r p e r h a p s a minor

s h i f t ( a b o u t + 2%) i n t h e h y p e r f i n e f i e l d ( R u b i n s t e i n e t a l - 1 9 6 6 ) .

Fur thermore, o n l y a we l l d e f i n e d s i n g l e s e x t e t has been r e p o r t e d f o r

e q u i a t o m i c FeCo (Mayo 1981, A l e k s e y e v e t a l 1977, Montano and S e e h r a

1977) and t h e r e f o r e , i t i s c o n c l u d e d t h a t t h e t w o / t h r e e s e x t e t s

o b s e r v e d i n t h e FeCoV and FeCoVNi a l l o y s s t u d i e d i n t h e p r e s e n t work

a r e a t t r i b u t a b l e t o t h e p r e s e n c e of vanadium. T h i s has been

p r e v i o u s l y s u g g e s t e d i n t h e l i t e r a t u r e ( e . g B e l o z e r s k i y e t a l - 1 9 7 7 ,

A l e k s e y e v e t a l - 1 9 7 7 ) t o e x p l a i n t h e assymrae t ry o b s e r v e d i n t h e

Mossbaue r s p e c t r u m of some FeCo b a s e d a l l o y s w i t h s ma l l a d d i t i o n s of

vanadium.

The o u t e r s e x t e t of t h e s p e c t r a f rom FeCoV and FeCoVNi a l l o y s i n t h e

d i s o r d e r e d s t a t e , i e quenched o r quenched and c o l d worked

c o n d i t i o n s , has h i g h e r v a l u e s of t h e h y p e r f i n e f i e l d (HA) and

i s ome r s h i f t (SA) t h a n i n t h e o r d e r e d s t a t e , i e f u r n a c e c o o l e d or

age d c o n d i t i o n s . However HA and SA a r e t h e same, w i t h i n

e x p e r i m e n t a l e r r o r , f o r a l l t h e a l l o y s f o r a g i v e n s t r u c t u r a l

c o n d i t i o n and a l s o a b o u t t h e same a s t h e s e p a r a m e t e r s f o r t h e s i n g l e

s e x t e t i n t h e b i n a r y FeCo as o b s e r v e d by o t h e r a u t h o r s ( s e e t a b l e

6 . 8 ) . T h i s s u g g e s t s t h a t t h e o u t e r s e x t e t i s a s s o c i a t e d w i t h t h e Fe

a toms w i t h a vanadium f r e e l o c a l e n v i r o n m e n t . T h i s i s c o n f i r m e d by

t h e b i n o m i a l s t a t i s t i c a l a n a l y s i s f o r t h e random d i s t r i b u t i o n of t h e

V a toms i n n e a r e s t n e i g h b o u r or n e x t n e a r e s t n e i g h b o u r s i t e s t o t h e

i r o n atom i n a bcc l a t t i c e a s f o l l o w s :

-1 1 6 -

E q u a t i o n 7 . 1 g i v e s t h e p r o b a b i l i t y P(n ,m) of f i n d i n g n and m

vanadium atoms r e s p e c t i v e l y i n t h e f i r s t and s ec o n d c o o r d i n a t i o n

s p h e r e s of a g i v e n bc c s o l i d s o l u t i o n c o n t a i n i n g a t o m i c f r a c t i o n s C

of vanadium a t oms .

P ( n , m ) = C(8! 6 1 ) ( 1 - 0 ‘ 4 * " - • C"** } / C ( 8 - n > ! ( 6 - m ) !n !m!] ( 7 . 1 )

In f a c t , even f o r t h e h i g h e s t nomina l vanadium c o n t e n t u s e d h e r e

(6at%) t h e p r o b a b i l i t y of a vanadium f r e e e n v i r o n m e n t i n t h e s e two

c o o r d i n a t i o n s p h e r e s (14 a t oms ) i s b i g g e r t h a n any o t h e r

c o n f i g u r a t i o n i n v o l v i n g t h e p r e s e n c e of vanadium, i e P ( 0 , 0 ) > P(n ,m)

f o r any n+m d i f f e r e n t f rom z e r o , and hence t h e o b s e r v e d i n t e n s e

o u t e r s e x t e t w i t h i d e n t i c a l Mossbauer p a r a m e t e r s t o t h o s e of FeCo i s

t o be e x p e c t e d f rom FeCoV and FeCoVNi a l l o y s .

F i g u r e 7 . 1 shows how t h e p r o b a b i l i t y of vanadium a toms o c c u p y i n g t h e

f i r s t a n d / o r t h e s ec o n d c o o r d i n a t i o n s p h e r e s a r o u n d t h e Fe atom i n a

bc c l a t t i c e c ha n g e s w i t h t h e vanadium c o n t e n t i n s o l i d s o l u t i o n .

Cur ve s PO, PI and P2 r e p r e s e n t r e s p e c t i v e l y t h e composed p r o b a b i l i t y

of z e r o , one o r two vanadium a toms i n any s i t e of t h e f i r s t o r

s e cond c o o r d i n a t i o n s p h e r e s i e PO = P ( 0 , 0 ) , PI = P ( 1 , 0 ) + P ( 0 , 1 ) ,

P2 = P ( 2 , 0) + P ( l , 1) + P ( 0 , 2 ) .

From a c o m p a r i s o n of t h e r e l a t i v e a r e a s of t h e i n n e r s e x t e t s w i t h

t h e vanadium oc c u p a n c y p r o b a b i l i t i e s , i t f o l l o w s t h a t s e x t e t B i s a

c o n s e q u e n c e of a vanadium atom i n a n e a r e s t (nn) or n e x t n e a r e s t

(nnn) n e i g h b o u r s i t e , and s e x t e t C i s a s s o c i a t e d w i t h two vanadium

a toms i n t h e s e s i t e s . The s m a l l e r h y p e r f i n e f i e l d and t h e movement

of t h e i somer s h i f t t o w a r d s n e g a t i v e v a l u e s f o r t h e i n n e r s e x t e t a r e

c o n s i s t e n t w i t h t h e e f f e c t t h a t vanadium has i n b i n a r y FeV a l l o y s

(Wer the im e t a l 1964, Vi ncze and Campbel l 1973) . Moreover s e x t e t B

has l a r g e r HWHM t h a n s e x t e t A, i n d i c a t i n g a g r e a t e r number of

d i f f e r e n t a t o m i c c o n f i g u r a t i o n s f o r s e x t e t B compared w i t h s e x t e t A.

T h i s c o n f i r m s t h e p r o p o s e d model s i n c e s e x t e t A i n v o l v e s o n l y Fe and

Co a toms w h i l e s e x t e t B i n v o l v e s a l s o one vanadium a toms i n two

p o s s i b l e c o n f i g u r a t i o n s (nn or n nn ) .

-1 1 7 -

(%) Aimqeqojd

CD

in

CD

04

O

OCO

c• M M

E3• MM

"a03c03>

F i gu r e 7 . 1 - P r o b a b i l i t y of a vanadium f r e e (PO), one vanadium and two vanadium a toms t.P2) c o n f i g u r a t i o n s in t h e f i r s t and c o o r d i n a t i o n s p h e r e s a r o u n d t h e Fe s i t e in a bcc s t r u c t u r e FeCoV a l l o y w i t h e q u i a t o m i c Fe-Co c o m p o s i t i o n , as r u n c t i o n o vanadium c o n t e n t i n t h e m a t r i x .

( P i ) s econd

of a f t h e

-1 1 8 -

C l e a r l y i f t h e p a r a m a g n e t i c p h a s e (T2 ) i s vanadium r i c h , t h e n t h e

f e r r o m a g n e t i c p h a s e (ocjor a ! ) of t h e m a t r i x mus t c o n t a i n l e s s

vanadium t h a n t h e g i v e n by t h e c o m p o s i t i o n of t h e a l l o y , a s o b s e r v e d

i n t h e r e s u l t s f rom e n e r g y d i s p e r s i v e a n a l y s i s ( s e c t i o n 6 . 1 . 2 ) .

T h e r e f o r e , a s t h e volume f r a c t i o n of any of t h e p a r a m a g n e t i c p h a s e s

i n c r e a s e s i n a g i v e n a l l o y , t h e r e s h o u l d be a c o n c o m i t a n t i n c r e a s e

i n t h e a r e a of s e x t e t A and a d e c r e a s e i n t h e a r e a s of t h e i n n e r

s e x t e t s which a r e a s s o c i a t e d w i t h t h e vanadium a toms i n t h e l o c a l

e n v i r o n m e n t of i r o n . T h i s i s i n d e e d t h e c a s e , a s shown i n f i g u r e

6 . 8 . In a l l c a s e s t h e l o n g e r i s t h e h e a t t r e a t m e n t ( i n t h e s e q u e n c e :

d i s o r d e r e d , o r d e r e d and aged c o n d i t i o n s ) t h e h i g h e r i s t h e a r e a

c o r r e s p o n d i n g t o t h e p a r a m a g n e t i c p h a s e and s e x t e t A and t h e lower

t h e a r e a s of s e x t e t s B and C.

S i m i l a r r e a s o n i n g may be u s e d t o e x p l a i n t h e vanadium de p e n d e n c e of

t h e s e x t e t a r e a s . Wi th i n c r e a s i n g vanadium up t o and i n c l u d i n g

3.6wt% ( i e 4at%) t h e vanadium c o n t e n t of t h e m a t r i x and t h e

p r o p o r t i o n of p a r a m a g n e t i c s e cond p h a s e b o t h i n c r e a s e , hence t h e

a r e a s of s e x t e t A d e c r e a s e whe r e as a l l o t h e r a r e a s i n c r e a s e ( s e e

f i g . 6 . 8 ) . The p a r t i c u l a r h e a t t r e a t m e n t g i v e n t o t h e FeCo5.4V a l l o y

gave a s i g n i f i c a n t volume f r a c t i o n of vanadium r i c h s e cond p ha s e

(T2 and m a r t e n s i t e ) so r emovi ng much of t h e vanadium from t h e

m a t r i x and i n c r e a s i n g t h e a r e a of s e x t e t A.

Thus , i t has be e n shown t h a t t h e p r e s e n c e of a p a r a m a g n e t i c pha s e

may be d e t e c t e d f rom t h e c h a n g e s i n t h e f e r r o m a g n e t i c s e x t e t s

a s s o c i a t e d w i t h t h e r e d u c t i o n s i n t h e vanadium c o n t e n t of t h e m a t r i x

a s we l l a s f rom t h e o c c u r r e n c e of c e n t r a l p e a k s . I ndeed i t i s

p o s s i b l e t o d e t e r m i n e t h e vanadium c o n t e n t of t h e m a t r i x f rom t h e

d a t a of f i g u r e s 6 . 8 and 7 . 1 . i f i t i s assumed t h a t t h e r e l a t i v e

a r e a s of t h e s e x t e t s a r e i n t h e same p r o p o r t i o n s a s t h e vanadium

oc c upa nc y p r o b a b i l i t i e s . The r e s u l t s of such an a n a l y s i s a r e

p r e s e n t e d i n t a b l e 7 . 1 ; The t y p i c a l e r r o r f o r a g i v e n vanadium

c o n t e n t d e t e r m i n a t i o n was ± 0 . 3 at% and ± 0 . 6 a tX f o r t h e 2 and 3

s e x t e t a n a l y s i s r e s p e c t i v e l y . The r e s u l t s f o r t h e vanadium c o n t e n t

of t h e m a t r i x f rom t h e 2 and 3 s e x t e t s a n a l y s e s a r e i n good

a g r e e m e n t w i t h e a c h o t h e r a s we l l a s w i t h t h e semi q u a n t i t a t i v e

m i c r o a n a l y s e s . For t h e quenched (Q), quenched and c o l d worked (CW)

-1 1 9 -

TABLE 7.1

Vanadium c o n t e n t i n s o l u t i o n i n FeCoV a l l o y s ( i n a tX) a s deduced

f rom t h e c o m p a r i s o n of f i g u r e s 6 . 8 and 7 . 1 . The a b b r e v i a t i o n s a r e :

ift = que nc hed , CW = c o l d - w o r k e d , A = aged a t 550°C f o r 24h and

FC = f u r n a c e c o o l e d .

a l l o y c o n d i t i o n 2 s e x t e t s

(at%)

3 s e x t e t s

(at%)

FeCo l . 5V4 . 5Ni

Q. or Q + CW 1 . 3 —

A 0 . 0 —

FeCo2V

ft or Q + CW 1 . 8 —

FC 1. 8 —

A 0 . 8 —

FeCo3.6V

ft o r ft + CW 2 . 2 2. 1

FC 2 . 3 2 . 2

A 1. 5 —

FeCo5.4V

ft or ft + CW 1. 9 1 . 9

FC 1 . 8 1 . 8

A 0 . 9 —

-1 2 0 -

and f u r n a c e c o o l e d c o n d i t i o n s (FC) t h e m a t r i x c o m p o s i t i o n i s a b o u t 2

at% V f o r a l l t h e FeCoV a l l o y s s t u d i e d , b u t o n l y a b o u t h a l f t h e

v a l u e f o r t h e aged s t a t e (A) . Much lower vanadium c o n t e n t s were

o b s e r v e d i n t h e FeCoVNi a l l o y . S i m i l a r t r e n d s can be o b t a i n e d f rom

t h e e x t r a p o l a t i o n of t h e c u r v e s c o r r e s p o n d i n g t o FeCoV a l l o y s i n

f i g . 6 . 9 , a s commented i n t h e l a s t c h a p t e r ( s e c t i o n 6 . 1 . 2 ) .

7.2 The Preferential Site for Vanadium in FeCo Alloys

As d i s c u s s e d i n c h a p t e r 4, t h e s h i f t i n t h e h y p e r f i n e f i e l d

of t h e 57Fe n u c l e u s (AH) p r o d u c e d by smal l amount s of vanadium added

t o p u r e i r o n ha s shown an o s c i l l a t o r y b e h a v i o u r d e p e n d i n g on t h e

d i s t a n c e be t we e n t h e vanadium a tom, t r e a t e d a s an i m p u r i t y , and t h e

r e s o n a n t n u c l e u s i n a bcc s t r u c t u r e ( s e e f i g* 4 . 7 a f t e r

S t e a r n s - 1 9 6 4 ) . The maj or e f f e c t i s p r od u c e d when t h e s o l u t e a tom

o c c u p i e s a s i t e i n t h e f i r s t o r i n t h e s econd c o o r d i n a t i o n s p h e r e

( r e s p e c t i v e l y AH~-8 t o -9% and AH~-6 to-7% of H i n p u r e Fe ) .

The e x p e r i m e n t a l c o n d i t i o n s and t h e comput e r a n a l y s i s c a r r i e d o u t on

t h e Mossbauer s p e c t r a of t h e p r e s e n t work d i d n o t r e s o l v e s e t s of

p e a ks w i t h v e r y s ma l l s h i f t s r e l a t i v e t o ea ch o t h e r . For t h i s r e a s o n

t h e e f f e c t of one vanadium atom i n t h e f i r s t or s ec o n d c o o r d i n a t i o n

s p h e r e s of t h e 5 7 Fe atom in a FeCo m a t r i x was t a k e n a s i d e n t i c a l and

t h e a v e r a g e e f f e c t of b o t h c o n f i g u r a t i o n s c o u l d be drawn from t h e

r e s u 1t s .

S i n c e i n t h e d i s o r d e r e d s t a t e b o t h Fe and Co have t h e same

p r o b a b i l i t y of o c c u p y i n g any s i t e , i t can be assumed t h a t t h e

vanadium atom a l s o can occupy a ny s i t e . From t h i s a s s u m p t i o n , i t can

be c o n c l u d e d t h a t s e x t e t B i n t h e d i s o r d e r e d a l l o y s was p r o d u c e d by

a m i x t u r e of t h e two d i f f e r e n t c o n f i g u r a t i o n s : i ) Cn=l , m=03 and

i i ) tn=0 , m=l ] . The a v e r a g e e f f e c t of b o t h c o n f i g u r a t i o n s

c o r r e s p o n d s t o A H = Hfl - HB = - 2 . 5 xlO4 A/m or a r e l a t i v e r e d u c t i o n

of 9 % f o r t h e d i s o r d e r e d s t a t e ( s e e f i g . 6 . 2 3 ) .

On t h e o t h e r hand t h e d i f f e r e n c e be t ween t h e i n t e r n a l f i e l d of

s e x t e t s A and B i n t h e o r d e r e d s t a t e i s AH = - 1 . 4 x 104 A/m which

c o r r e s p o n d s t o a r e l a t i v e r e d u c t i o n of o n l y 5.3%. I f t h e vanadium

-1 2 1 -

atom d i d n o t have any p r e f e r e n t i a l s i t e i n t h e o r d e r e d c o n d i t i o n ,

t h e r e d u c t i o n AH = H* Hg i n t h e h y p e r f i n e f i e l d of t h e

o r d e r e d c o n d i t i o n p r o d u c e d by 1 V atom s h o u l d be t h e same a s t h a t

f o r t h e d i s o r d e r e d s t a t e , whe r e a s t h e o b s e r v e d r e d u c t i o n f o r t h e

o r d e r e d s t a t e i s s i g n i f i c a n t l y s m a l l e r . Assuming t h e e x t e n s i o n of

t h e S t e a r n s * o b s e r v a t i o n s t o t h e a l l o y s s t u d i e d h e r e , t h e r e i s a

s t r o n g i n d i c a t i o n t h a t t h e vanadium atom in t h e o r d e r e d s t a t e

o c c u p i e s a s i t e i n t h e s ec o n d c o o r d i n a t i o n s p h e r e of t h e r e s o n a n t Fe

n u c l e u s . In t h e B2 s t r u c t u r e ( o r d e r e d s t a t e ) t h i s c o o r d i n a t i o n

s p h e r e i s o c c u p i e d by Fe a toms and so i t can be c o n c l u d e d t h a t t h e

vanadium atom o c c u p i e s p r e f e r e n t i a l l y an Fe s i t e . T h i s c o n c l u s i o n i s

i n a g r e e m e n t w i t h t h e s i t e p r e f e r e n c e f o r vanadium i n FeCoV a l l o y s ,

s u g g e s t e d by Mal ’ t s e v e t a l (1975) from m a g n e t i c moment and

t r a n s i t i o n t e m p e r a t u r e d a t a of v a r i o u s b i n a r y s y s t e m s .

7.3 Effects of Ternary Additions and Microstrugtural Changes to the Electrical Resistivity of FeCo based Alloys

The s o l i d l i n e s i n f i g u r e s 7 . 2 t o 7 . 5 show t h e e l e c t r i c a l

r e s i s t i v i t y of r e s p e c t i v e l y FeCo-xV, FeCo2V-yW, FeCo2V-yCu and

FeCo-xNb i n t h e f u r n a c e c o o l e d and quenched c o n d i t i o n s a s f u n c t i o n

of t h e t e r n a r y (x) or q u a t e r n a r y (y) c o n t e n t .

FeCoV Alloys:The v a l u e of t h e e l e c t r i c a l r e s i s t i v i t y a t 77 K of quenched ( f rom

850°C) FeCo2V was c o mp a r a b l e t o t h a t o b t a i n e d a t t h e same

t e m p e r a t u r e by Ashby (1975) i n s i m i l a r l y quenched and c o l d - r o l l e d

(25% RA) FeCo2V and was a b o u t 25% above t h a t r e p o r t e d by Chen (1962)

f o r t h e r e s i s t i v i t y a t 4 . 2 K of FeCoV w i t h t h e same nomi na l

c o m p o s i t i o n and quenched from 800*C. Th i s d i s c r e p a n c y c o u l d be

e x p l a i n e d n o t o n l y b e c a u s e of t h e d i f f e r e n c e i n t h e m e a s u r i n g

t e m p e r a t u r e s b u t a l s o c o n s i d e r i n g t h a t t h e q u e n c h i n g f rom 850°C k e p t

more vanadium a toms i n s o l u t i o n , p r o d u c i n g h i g h e r r e s i s t i v i t y t h a n

t h e q u e n c h i n g f rom 800*C. As r e p o r t e d in t h e l a s t c h a p t e r , t h e

e f f e c t of c o l d - r o l l i n g does n o t a f f e c t s i g n i f i c a n t l y t h e e l e c t r i c a l

r e s i s t i v i t y of t h i s a l l o y . The r e i s a s i g n i f i c a n t d i s c r e p a n c y

be tween t h e r e s i s t i v i t y v a l u e s of FeCo2V f u r n a c e c o o l e d i n t h e

p r e s e n t i n v e s t i g a t i o n and t h a t o b t a i n e d by Ashby ( 1 9 7 5 ) . She r e p o r t s

-1 2 2 -

a v a l u e a b o u t 50% lower t h a n t h a t meas u r ed h e r e f o r t h e same a l l o y

u n d e r s i m i l a r e x p e r i m e n t a l c o n d i t i o n s . N e v e r t h e l e s s t h e r e s u l t s f o r

t h e e l e c t r i c a l r e s i s t i v i t y of a l l t h e d i f f e r e n t FeCo b a s e d a l l o y s

s t u d i e d i n t h e p r e s e n t i n v e s t i g a t i o n i n b o t h que nc hed and f u r n a c e

c o o l e d c o n d i t i o n s a r e c o n s i s t e n t a s shown i n f i g u r e s 7 . 2 t o 7 . 5 . In

a d d i t i o n t h e f a c t t h a t p ( o r d e r e d ) > p ( d i s o r d e r d ) o b s e r v e d h e r e f o r

a l m o s t a l l t h e FeCoV a l l o y s i s i n a g r e e me n t w i t h D i n h u t e t a l

( 1 9 7 7 ) ; t h e same was n o t o b s e r v e d by Ashby.

The n e a r l y s t a b i l i z e d c u r v e s i n f i g u r e 7 . 2 ( e x c e p t t h e p o i n t

c o r r e s p o n d i n g t o 5 . 6 wt% (6 at%) V) can be i n t e r p r e t e d a s a

c o n s eq u e n c e of t h e a c h i e v e m e n t of t h e s o l u b i l i t y l i m i t of vanadium

i n FeCo ( a r o u n d 2 at% i n s a mp l e s quenched from 850°C) . T h i s c o n f i r m s

t h e r e s u l t s d i s c u s s e d i n t h e p r e v i o u s s e c t i o n of t h e p r e s e n t work.

The marked d r o p i n t h e e l e c t r i c a l r e s i s t i v i t y of c o l d - w o r k e d

FeCo l . 5V4 . 5Ni a f t e r a g e i n g f o r 24h a t 650°C ( s e e t a b l e 6 . 4 ) i s a l s o

c o n s i s t e n t w i t h t h e r e s u l t s i n t h e p r e v i o u s s e c t i o n , s i n c e t h e

w i t h d r a wa l of vanadium f rom t h e m a t r i x s o l i d s o l u t i o n on a g e i n g

r e d u c e s t h e r e s i s t i v i t y t o w a r d s t h e v a l u e o b s e r v e d f o r e q u i a t o m i c

FeCo. Th i s a l s o e x p l a i n s why t h a t p a r t i c u l a r FeCoV b a s e d a l l o y has

p ( o r d e r e d ) < p ( d i s o r d e r e d ) i . e . aged ( o r d e r e d ) Fe Col . 5V4 . 5Ni has

lower p n o t b e c a u s e o f c h a n g e s i n t h e d e g r e e of o r d e r b u t

p r i n c i p a l l y b e c a u s e i t c o n t a i n s l e s s vanadium a toms i n s o l u t i o n t h a n

t h e r e s p e c t i v e quenched m a t e r i a l . The o t h e r e x c e p t i o n t o t h e u s u a l

t r e n d (p ( o r d e r e d ) > p ( d i s o r d e r e d ) , f o r FeCoV b a s e d a l l o y s was t h e

FeCo5.4V a l l o y . T h i s e x c e p t i o n can be a t t r i b u t e d most p r o b a b l y t o

t h e p r e s e n c e of a dua l m i c r o s t r u c t u r e a s d i s c u s s e d b e f o r e .

FeCoVW alloys:The a d d i t i o n of a b o u t 0 . 3 at% W t o FeCo2V p r o d u c e s a d r o p of a b o u t

20% i n t h e e l e c t r i c a l r e s i s t i v i t y of b o t h que nc hed and f u r n a c e

c o o l e d m a t e r i a l s . Above t h a t W c o n t e n t t h e r e s i s t i v i t y t e n d s to s t a b i l i z e or even i n c r e a s e s l i g h t l y ( s e e t h e s o l i d l i n e s i n f i g u r e

7 . 3 ) . Th i s b e h a v i o u r can be u n d e r s t o o d by p r o p o s i n g a s i m p l e

d i l u t i o n model , p r e s e n t e d in e q u a t i o n 7 . 2 , t h a t g i v e s t h e e l e c t r i c a l

r e s i s t i v i t y of a q u a t e r n a r y FeCoxAyB a l l o y , w i t h low a t o m i c c o n t e n t s

x and y of t h e e l e m e n t s A and B, a s t h e combined e f f e c t t h a t e a c h

e l e m e n t (A or B) has on a l t e r i n g t h e e l e c t r o n i c s t r u c t u r e of FeCo a s

-1 2 3 -

vanadium content (at%)

F i g u r e 7 . 2 - The e l e c t r i c a l r e s i s t i v i t y a t 77K of o r d e r e d ( open symbol s ) and d i s o r d e r e d ( f u l l s ymbol s ) FeCoxV a l l o y s a s f u n c t i o n of t h e vanadium c o n t e n t . The v a l u e s f o r FeCo a r e t h o s e r e p o r t e d by R o s s i t e r (1981) f o r t h e b i n a r y a l l o y i n s i m i l a r e x p e r i m e n t a l c o n d i t i o n s . The r e s i s t i v i t y v a l u e s a t 77K f o r t h e Fe Col . 5V4 . 5Ni a l l o y d i s o r d e r e d ( i . e . quenched -Q-) and o r d e r e d ( i . e . aged a t 650°C f o r 24 h o u r s -A- ) a r e a l s o p l o t t e d .

-1 2 4 -

tungs ten con ten t (at%)

F i g u r e 7 . 3 - The e l e c t r i c a l r e s i s t i v i t y a t 77K of FeCo2VyW a l l o y s i n t h e o r d e r e d (open symbol s ) and i n t h e d i s o r d e r e d ( f u l l s ymbol s ) c o n d i t i o n s , a s f u n c t i o n of t h e W c o n t e n t . The b r o k e n l i n e s c o r r e s p o n d t o t h e o r e t i c a l v a l u e s c a l c u l a t e d by u s i n g e q u a t i o n 7 . 2 . The c u r v e f o r FeCoyW i s t h a t r e p o r t e d by Bo z o r t h (196a-) - s e e f i g . 3 . 5 - n o r m a l i z e d f o r t h e t e m p e r a t u r e employed in t h e p r e s e n t c a s e .

-1 2 5 -

a donor , a c c e p t o r or n e u t r a l a tom. Such a model does n o t c o n s i d e r

t h e mutua l i n t e r a c t i o n s be t we e n t h e minor e l e m e n t s and i s g i v e n by

t h e w e i g h t e d a v e r a g e of t h e c o n t r i b u t i o n s of t h e s e e l e m e n t s t o t h e

r e s i s t i v i t y of t h e b i n a r y a l l o y a s f o l l o w s :

^(FeCoxAyB) = CxjXFeCoxA) + yp(FeCoyB) ] / ( x+y)

or

p(FeCoxAyB)=p(FeCo) + ( x 2 C SjXFeCoxA) /£x] + y2 [ £p ( FeCoyB) / £y 3} / ( x+y)

(eq. 7.2)

where J>(FeCo) , £j>(FeCoxA)/dx and £J> (FeCoyB) / £y a r e r e s p e c t i v e l y

t h e e l e c t r i c a l r e s i s t i v i t y of t h e b i n a r y a l l o y and i t s d i f f e r e n t i a l

i n c r e m e n t s due t o sma l l a d d i t i o n s of t h e e l e m e n t s A and B. The

d o t t e d l i n e s i n f i g u r e 7 . 3 show t h e r e s u l t of t h e a p p l i c a t i o n of

t h i s model t o o r d e r e d and d i s o r d e r e d FeCoxVyW, u s i n g x = c o n s t a n t =

2 . 2 a t % V and y = v a r i a b l e up t o 0 . 3 at% W, above which i t was k e p t

c o n s t a n t due t o t h e a c h i e v e m e n t of t h e maximum s o l u b i l i t y of W i n

t h e m a t r i x of t h e a l l o y , a s p r o p o s e d by Or r ock ( 1 9 8 6 ) . I t can be

s e e n t h a t t h e model c o r r e c t l y shows t h e f a l l i n r e s i s t i v i t y w i t h t h e

a d d i t i o n of up t o 0 . 3 at% W and a l s o p r e d i c t s t h a t t h e p a r a m e t e r

s h o u l d r e ma i n c o n s t a n t whe r e a s a s l i g h t i n c r e a s e i s e x p e r i m e n t a l l y

o b s e r v e d . The s ma l l i n c r e m e n t i n p(FeCoxVyW) f o r y > 0 . 3 at% W as

we l l a s t h e d r o p i n p(FeCoyW) i n t h e same c o m p o s i t i o n r a n g e ( s e e

f i g u r e 3 . 5 a f t e r B o z o r t h - 1 9 6 4 ) c o u l d be due t o a common c a u s e . One

p o s s i b i l i t y i s a s l i g h t d r o p i n t h e W c o n t e n t i n s o l i d s o l u t i o n f o r

nomina l c o m p o s i t i o n s g r e a t e r t h a n t h e l i m i t of 0 . 3 a t X . Al so t h e

model does n o t t a k e i n t o a c c o u n t t h e e f f e c t of s e cond pha s e

p a r t i c l e s p e r s e .

FeCoVCu alloys:The i n c r e a s i n g a d d i t i o n of Cu t o FeCo2V p r o d u c e s a s t e a d y d r op in

t h e e l e c t r i c a l r e s i s t i v i t y of b o t h o r d e r e d and d i s o r d e r e d a l l o y s

( s e e t h e s o l i d l i n e i n f i g u r e 7 . 4 ) . T h i s can be u n d e r s t o o d

c o n s i d e r i n g t h e d i l u t i o n model p r o p o s e d a bove , t o g e t h e r w i t h t h e

f a c t t h a t c op p e r has a c o m p l e t e l l y f u l l d - s h e l l and so doe s n o t

c hange s i g n i f i c a n t l y t h e e l e c t r i c a l r e s i s t i v i t y of FeCo a s c o n f i r m e d

-1 2 6 -

i n t h e p r e s e n t work f o r FeCo3Cu. The d o t t e d l i n e s i n f i g u r e 7 . 4 a r e

t h e r e s u l t of t h e a p p l i c a t i o n of e q u a t i o n 7 . 2 t o t h i s a l l o y s y s t e m,

c o n s i d e r i n g x = c o n s t a n t = 2 . 2 at% V and t h e t o t a l s o l u b i l i t y of Cu i n

FeCo2V up t o 4 . 5 a t * ( i . e . y = v a r i a b l e be t we en 0 and 4 . 5 a tX Cu) .

The c l e a r d i f f e r e n c e b e t w e e n e x p e r i m e n t a l and t h e o r e t i c a l c u r v e s i n

f i g . 7 . 4 can be e x p l a i n e d i f one a s sume s t h a t Cu ha s a l i m i t e d

s o l u b i l i t y i n FeCo2V whi ch i n c r e a s e s s l i g h t l y w i t h i n c r e a s i n g

a d d i t i o n of t h e e l e m e n t t o t h e s y s t e m . Th i s i s i n good a g r e e m e n t

w i t h Or r ock (198B) who o b s e r v e d t h e p r e s e n c e of C u - r i c h p r e c i p i t a t e s

i n s p e c i me n s w i t h q u a t e r n a r y c o n t e n t s a s low as 0 . 9 a t * a s we l l a s

an e x p a n d i n g l a t t i c e p a r a m e t e r , a s s o c i a t e d w i t h i n c r e a s i n g

s o l u b i l i t y of Cu i n t h e m a t r i x , w i t h f u r t h e r a d d i t i o n of t h e e l e m e n t

t o FeCo2V. Ac c o r d i ng t o t h e p r o p o s e d r e s i s t i v i t y model t h e c o n t e n t

of c o p p e r i n s o l i d s o l u t i o n i n f u r n a c e - c o o l e d FeCo2.2VyCu mi gh t be

a b o u t 0 . 1 5 , 0 . 2 3 and 0 . 4 5 a tX f o r nomina l c o m p o s i t i o n s of

r e s p e c t i v e l y 0 . 9 , 2 . 7 and 4 . 5 at% Cu and t h e p r e d i c t e d q u a t e r n a r y

c o n t e n t i n t h e r e s p e c t i v e m a t r i x e s of quenched s p e c i me n s mi gh t be a

l i t t l e h i g h e r ( a b o u t 0 . 1 5 , 0 . 3 2 and 0 . 6 3 a t % Cu r e s p e c t i v e l y ) .

FeCoNb alloys:The n e a r l y s t a b l e c u r v e s of t h e e l e c t r i c a l r e s i s t i v i t y of FeCoNb

a l l o y s a t 77K a s f u n c t i o n of t h e t e r n a r y c o n t e n t ( f i g . 7 . 5 ) i s a

c o n s e q u e n c e of t h e s a t u r a t i o n of n i ob i um i n s o l i d s o l u t i o n due t o a

s o l u b i l i t y l i m i t of t h e e l e m e n t i n FeCo be low 0 . 6 at% Nb (1 w t * ) .

T h i s f a c t i s a l s o c o n f i r m e d by t h e p r e s e n c e of n i o b i u m - r i c h

p r e c i p i t a t e s i n FeColwtXNb ( s e e f i g . 6 . 5 ) a s we l l a s by t h e

s t a b i l i z a t i o n of t h e l a t t i c e p a r a m e t e r of FeCoNb a l l o y s i n t h e same

r a n g e of c o m p o s i t i o n ( s e e f i g . 6 . 2 1 ) . F i g u r e 6 . 9 o b t a i n e d f rom t h e

Mossbauer s p e c t r a of t h i s m a t e r i a l i n d i c a t e s a s o l u b i l i t y l i m i t of

a b o u t 0 . 3 at% Nb. Us i ng t h i s l i m i t and that r e s i s t i v i t y d a t a , i t i s

p o s s i b l e t o e s t i m a t e an i n c r e m e n t of a b o u t 7 pQcm/at% i n t h e

r e s i s t i v i t y of FeCoNb. Such an i n c r e m e n t , l i k e t h e r e p o r t e d by Chen

(1962) f o r T i , V, and Cr , i s be t ween one and two o r d e r s of ma g n i t u d e

g r e a t e r t h a n t h e i n c r e m e n t s p r o d u c e d by t h e a d d i t i o n of Cu, Ni and

Mn t o FeCo.

-1 2 7 -

F i g u r e 7 . 4 - The e l e c t r i c a l r e s i s t i v i t y a t 77K of FeCo2VyCu a l l o y s i n t h e o r d e r e d (open s ymbol s ) and i n t h e d i s o r d e r e d ( f u l l s ymbol s ) c o n d i t i o n s , a s f u n c t i o n of t h e Cu c o n t e n t . The b r o k e n l i n e s c o r r e s p o n d t o t h e o r e t i c a l v a l u e s c a l c u l a t e d by u s i n g e q u a t i o n 7 . 2 and a s sumi ng t h e t o t a l s o l u b i l i t y of c oppe r i n FeCo up t o a b o u t 4 . 5 at% Cu. The c u r v e s f o r FeCoyCu were based i n t h e d a t a f rom FeCo3wt%Cu a t 77K measur ed i n t h e p r e s e n t work and t h a t r e p o r t e d by R o s s i t e r (1981) f o r FeCo a t t h e same t e m p e r a t u r e .

-1 2 8 -

niobium con ten t (at%)

F i g u r e 7 . 5 - The e l e c t r i c a l r e s i s t i v i t y a t 77K in o r d e r e d ( open s ymbol s ) and d i s o r d e r e d ( f u l l s ymbol s ) FeCoxNb a l l o y s as f u n c t i o n of t h e t e r n a r y c o n t e n t . The v a l u e s f o r FeCo a r e t h o s e r e p o r t e d by R o s s i t e r (1981) f o r t h e a l l o y i n s i m i l a r e x p e r i m e n t a l c o n d i t i o n s .

-1 2 9 -

7 .4 M ic ro s tru c tu re and the E le c t r i c a l R e s is t i v i t y of FeColNb

7.A.1 Preliainary Comments

S i n c e t h e e l e c t r i c a l r e s i s t i v i t y of a m a t e r i a l de pe nds on t h e d e g r e e

of o r d e r (S) and t h e t e m p e r a t u r e ( T ) , t h e . p a r a b o l i c de p e n d e n c e of

t h e r e s i s t i v i t y of FeCoiNb a s f u n c t i o n of t e m p e r a t u r e o b s e r v e d in

t h e p r e s e n t work i n t h e r a n g e 77-373K, and a l s o i n e q u i a t o m i c FeCo

( e . g . R o s s i t e r - 1 9 8 1 ; S e e h r a and Si 1 i n s k y - 1 9 7 6 ) , c o u l d be i n t e r p r e t e d

by c o n s i d e r i n g S a s a v a r i a b l e d e p e n d e n t on t h e t e s t t e m p e r a t u r e . In

t h e p r e s e n t c a s e , however , t h e r a n g e of t e m p e r a t u r e f o r t h e

r e s i s t i v i t y mea s u r eme n t s was low enough t o keep t h e a t o m i c o r d e r

unchanged and t h u s S i s t a k e n a s a s p e c i m e n ’ s c o n s t a n t , i n d e p e n d e n t

of t h e t e m p e r a t u r e of t h e r e s i s t i v i t y t e s t s . In t h e s e c i r c u m s t a n c e s ,

t h e d e p e n d e n c e of p on T2 i n e q u a t i o n 6 . 2 i s n o t r e l a t e d t o

c ha nge s i n S, b u t most p r o b a b l y , t o t h e t y p i c a l t e m p e r a t u r e

de p e n d e n c e of t h e e l e c t r i c a l r e s i s t i v i t y e x h i b i t e d i n f e r r o m a g n e t i c

t r a n s i t i o n m e t a l s ( s u c h a s Fe and Co) t h a t can be a s s o c i a t e d w i t h

i n t e r a c t i o n s be t we e n t h e c o n d u c t i o n s - e l e c t r o n s and l o c a l i z e d

d - e i e c t r o n s w i t h v a r y i n g d e g r e e of s p i n o r d e r . In f a c t , i n o t h e r

t y p i c a l s i t u a t i o n s of s - d i n t e r a c t i o n s , s uc h a s t h a t o b s e r v e d by

P o t t e r (1937) f o r t h e e l e c t r i c a l r e s i s t i v i t y of p u r e Ni t h e d a t a f i t

v e r y we l l t h e s e c ond o r d e r p o l i n o m i a l p r e s e n t e d i n e q u a t i o n 6 . 2

( c h i - s q u a r e = 9 x 1 0 ' 4 ).

On t h e o t h e r hand , e q u a t i o n 3 . 1 p r o p o s e d by R o s s i t e r , g i v e s t h e

r e s i s t i v i t y p ( S , T ) f o r a normal met a l be low t h e Debye t e m p e r a t u r e ,

where a l i n e a r de pe nde nc e w i t h t e m p e r a t u r e i s e x p e c t e d , and

c o n s e q u e n t l y , e q u a t i o n 3 . 1 does n o t c o m p l e t e l y e x p r e s s t h e

r e l a t i o n s h i p b e t we en t h e two v a r i a b l e s S and T i.e. , i n t h e p r e s e n t

c a s e e q u a t i o n 3 . 1 must be r e p l a c e d by an e x p r e s s i o n , c o n t a i n i n g t h e

T2 component i f i t i s t o s a t i s f y t h e e x p e r i m e n t a l r e s u l t s s uc h a s

t h a t shown i n f i g u r e 6 . 1 7 .

A s i m p l e e x p r e s s i o n t h a t s a t i s f i e s our e x p e r i m e n t a l d a t a may be

o b t a i n e d by t h e a d d i t i o n of a T2 component t o e q u a t i o n 3 . 1 . I t

f o l l o w s f rom t a b l e s 6 . 5 and 6 . 6 t h a t t h e d e r i v a t i v e £2f>/ST2 =

2 D(298) Aa ( s e e e q u a t i o n 6 . 2 ) i s n o t c o n s t a n t e . g . a t low

-1 3 0 -

t e m p e r a t u r e s i t d e c r e a s e s w i t h i n c r e a s i n g S; a s i m i l a r t r e n d i s

shown a t h i g h t e m p e r a t u r e s ( 6 9 0 - 7 3 0 ° C ) . P r o v i d e d i n t h e s e r e g i o n s

o r d e r i n g , r a t h e r t h a n o t h e r m i c r o s t r u c t u r a l c h a n g e s i s d o m i n a n t , i t

i s r e a s o n a b l e t o assume t h a t t h e c ompl e me n t a r y q u a d r a t i c t e r m f o r

e q u a t i o n 3 . 1 i s S d e p e n d e n t and d e c r e a s e s w i t h i n c r e a s i n g o r d e r .

Ano t he r i m p o r t a n t f e a t u r e t o be c o n s i d e r e d i s t h e f a c t t h a t £j>/£T i s

p r o p o r t i o n a l t o t h e i n v e r s e of t h e e f f e c t i v e number of c o n d u c t i o n

e l e c t r o n s ( Ne f f ) a s m e n t i o n e d i n s e c t i o n 3 . 1 . 1 . T h i s p a r a m e t e r i s

b a n d - s t r u c t u r e d e p e n d e n t and can be changed by a t o m i c o r d e r i n g or by

o t h e r phenomena s uch a s c h a n g e s i n t h e s o l u t e c o n t e n t of t h e m a t r i x

a s a c o n s e q u e n c e of a p r e c i p i t a t i o n p r o c e s s . S i n c e i n t h e low end of

a g e i n g t e m p e r a t u r e p r e c i p i t a t i o n e f f e c t s s h o u l d be i n s i g n i f i c a n t ,

t h e o n l y r e a s o n f o r t h e c h a n g i n g of Nef f i s a s s o c i a t e d w i t h t h e

o r d e r i n g ; hence a r e a s o n a b l e c o i n c i d e n c e be t we en t h e e x p e r i m e n t a l

£j»/£T and t h e t h e o r e t i c a l £ ^ ( S , T ) / £ T f rom t h e e x p r e s s i o n t h a t

r e p l a c e s e q u a t i o n 3 . 1 i s e x p e c t e d f o r s p e c i me n s aged a t low

t e m p e r a t u r e s .

The p r ob l e m i n d e t e r m i n i n g a g e n e r a l e q u a t i o n f o r p a s a f u n c t i o n of

S and T d e pe nds n o t o n l y on c o n s i d e r a t i o n s such a s those p r e v i o u s l y

m e n t i o n e d , b u t a l s o on t h e a c c u r a c y of t h e e x p e r i m e n t a l d a t a . In

t h i s c o n t e x t , t h e e x p e r i m e n t a l e r r o r s i n p and S a r e t h e main s o u r c e

of i n a c c u r a c y f o r t h e i n t e n d e d f u n c t i o n , n o t o n l y w i t h r e s p e c t t o

t h e n u m e r i c a l v a l u e s of i t s c o n s t a n t s b u t a l s o t o i t s a n a l y t i c a l

e x p r e s s i o n . A f t e r t h e e q u a t i o n i s d e t e r m i n e d and i t s c o n s t a n t s

c a l c u l a t e d , i t i s i m p o r t a n t t o remember t h a t t h e c o n s t a n t s a r e

f u n c t i o n of a s p e c i f i c s t a t e of t h e m a t e r i a l and any c hange ( o t h e r

t h a n i n S and T) can be r e s p o n s i b l e f o r a l t e r a t i o n s i n t h e i r v a l u e s .

Thus , t h e t e r m i n o l o g y " r e f e r e n c e sample or m a t e r i a l " employed i n t h e

p r e s e n t work i s a p p l i e d t o t h e s p e c i f i c c o n d i t i o n of t h e m a t e r i a l

f o r which t h e r e f e r r e d c o n s t a n t s have been c a l c u l a t e d .

7.4.2 A New Empirical Function p(S,T)

C o n s i d e r i n g t h e f e a t u r e s d e s c r i b e d in t h e l a s t s e c t i o n , i t was

p o s s i b l e t o f i n d a number of f u n c t i o n s t h a t c o u l d a p p r o x i m a t e l y

s a t i s f y t h e s u g g e s t e d c o n d i t i o n s . However , t h e b e s t f i t c o r r e s p o n d e d

-1 3 1 -

t o t h e f o l l o w i n g e q u a t i o n :

p ( S , T ) = Cpo < 0 ) ( 1 - S2 ) + <B/n0 )T + C ( 1 - S 2 )T2 3 / (1-AS2 ) ( 7 . 3 )

The new c o n s t a n t C a s we l l a s t h e f o r me r one s f rom e q u a t i o n 3 . 1 were

d e t e r m i n e d i n e a c h s p e c i f i c c o n d i t i o n of t h e m a t e r i a l and , as

m e n t i o n e d b e f o r e , may a l t e r i f t h e m a t e r i a l u n d e r g o e s an a d d i t i o n a l

t r a n s f o r m a t i o n ( e . g . p r e c i p i t a t i o n ) . For t h i s r e a s o n , t h e

r e l a t i o n s h i p be t we en r e s i s t i v i t y and m i c r o s t r u c t u r e of FeColNb in

g r oups 1 and 2 w i l l be d i s c u s s e d s e p a r a t e l y .

7.4.3 A new Parameter S*

The long r a n g e o r d e r p a r a m e t e r S can be s u c c e s s f u l l y o b t a i n e d f rom

c h a n g e s i n t h e l a t t i c e p a r a m e t e r ( e . g . Cl egg - 1971; Or r ock - 198B)

by u s i n g e x p r e s s i o n 7 . 4 :

S = Ca0 - a 0 ( DI S) ] / Ca0 (ORD) - a 0 ( DIS) ] ( 7 . 4 )

The v a l u e s a 0 , a 0 (DIS) and a 0 (ORD) a r e t h e l a t t i c e p a r a m e t e r s of t h e

m a t e r i a l i n t h e s t a t e s a g e d , d i s o r d e r e d and o r d e r e d r e s p e c t i v e l y .

N e v e r t h e l e s s , i f a p r e c i p i t a t i o n p r o c e s s t a k e s p l a c e d u r i n g t h e

o r d e r i n g , t h e c h a n g e s i n l a t t i c e p a r a m e t e r w i l l i n c l u d e e f f e c t s due

t o b o t h t r a n s f o r m a t i o n s and i n t h e s e c i r c u m s t a n c e s e q u a t i o n 7 . 4 w i l l

n o t y i e l d t h e LRO parameter . Th i s i s e x e m p l i f i e d by t h e l a t t i c e

p a r a m e t e r of FeColNb i n gr oup 1 ( i e . quenched + a ge d) which

i n c r e a s e s a t low t e m p e r a t u r e s and d e c r e a s e s a f t e r 550*C ( s e e f i g . 6.

12) . The i n i t i a l i n c r e a s e can be i n t e r p r e t e d t o be due t o o r d e r i n g

and t h e LRO p a r a m e t e r S c a l c u l a t e d u s i n g eq . 7 . 4 i s c o n s i s t e n t w i t h

t h e v a l u e s o b t a i n e d f rom s u p e r l a t t i c e me a s u r eme n t s up t o 550*C

i n c l u s i v e ( compare f i g s . 6 . 1 2 and 6 . 1 0 - c u r v e B) . The c a l c u l a t e d

l a t t i c e p a r a m e t e r t h a t t h e m a t e r i a l s h o u l d have i f i t was p o s s i b l e

t o p r o d u c e a f u l l y o r d e r e d spe c i men ( S=l ) w i t h no p r e c i p i t a t i o n i s

a 0 =2.8601 % ( s e e t h e d i s c o n t i n u o u s l i n e i n f i g . 6 . 1 2 ) . The change

i n a 0 a bove 550°C i s r e l a t e d t o b o t h o r d e r i n g , t h a t t e n d s t o

i n c r e a s e a 0 , and t h e o u t w e i g h i n g p r e c i p i t a t i o n e f f e c t , t h a t t e n d s

t o d e c r e a s e a 0 , a s d i s c u s s e d be low:

-1 3 2 -

A c c o r d i n g t o V e g a r d ’ s law, t h e l a t t i c e p a r a m e t e r ( a 0 ) of a p r i m a r y

s o l i d s o l u t i o n v a r i e s n e a r l y l i n e a r l y w i t h t h e a t o m i c c o n c e n t r a t i o n

( c ) of a s u b s t i t u t i o n a l s o l u t e e l e m e n t :

a<> (c) = a 0 (0) + kc ( 7 . 5 )

where a<> (0) i s t h e s o l u t e - f r e e l a t t i c e p a r a m e t e r of t h e s o l v e n t and

k i s a p o s i t i v e c o n s t a n t f o r s o l u t e a toms b i g g e r t h a n t h e s o l v e n t .

D i f f e r e n t i a t i n g 7 . 5 g i v e s :

A a 0 (c) : k A c ( 7 . 6 )

Assuming t h e v a l i d i t y of V e g a r d ’ s law f o r t h e m a t r i x a s c h a n g e s of

c o m p o s i t i o n o c c u r due t o t h e p r e c i p i t a t i o n p r o c e s s , one can r e l a t e

t h e l a t t i c e p a r a m e t e r Ca0 ( a ) ] a f t e r t h e p r e c i p i t a t i o n p r o c e s s has

t a k e n p l a c e t o i t s v a l u e b e f o r e t h e p r o c e s s Ca0 ( b ) ] u s i n g :

a 0 ( a ) = a 0 (b) + k A c ( 7 . 7 )

where A c i s t h e c ha nge i n t h e s o l u t e c o n c e n t r a t i o n of t h e m a t r i x

due t o p r e c i p i t a t i o n . In t h e p r e s e n t c a s e t h e a t o m i c r a d i i of Fe, Co

and Nb a r e r e s p e c t i v e l y 1 . 2 4 , 1 . 26 and 1 . 4 2 %. t h a t makes k > 0. Th i s

means t h a t t h e w i t h d r a wa l of Nb o u t of s o l u t i o n , due t o

p r e c i p i t a t i o n , r e d u c e s a 0 a s o b s e r v e d i n f i g u r e 6 . 1 2 .

The m i s u s e of e q u a t i o n 7 . 4 by e mpl oy i ng t h e l a t t i c e p a r a m e t e r a 0 (a)

a f t e r a p r e c i p i t a t i o n p r o c e s s p r o d u c e s t h e p a r a m e t e r S ’ :

S ’ = La0 (a) - a 0 ( D I S ) ] / C(a0 (ORD) - a 0 (DI S) ] ( 7 . 8 )

Us i ng t h e e x p r e s s i o n ( 7 . 7 ) i n t o ( 7 . 8 ) g i v e s :

S ’ = tCa0 (b) + kAc] - a 0 (DIS)} / Ca«(ORD) - a 0 (DIS) ( 7 . 9 )

b u t Ca0 (b) - a 0 (DIS)3 / ( a 0 (ORD) - a 0 (DIS) = S and e q u a t i o n 8 . 9 can

be r e w r i t t e n :

S ’ = S + K, A c ( 7 . 1 0 )

where Ki = k / t a 0 (ORD) - a 0 ( D! S ) ] . Thus , t h e p a r a m e t e r S ’ c o n t a i n s

i n f o r m a t i o n on t h e o r d e r i n g a s wel l a s on t h e d e v i a t i o n of t h e

m a t r i x c o m p o s i t i o n due t o p r e c i p i t a t i o n .

-1 3 3 -

S u b s t i t u t i n g S f rom e q u a t i o n 7 . 1 0 CS=S’ - Kt A c J i n t o e q u a t i o n 7 . 3

l e a d s t o an e x p r e s s i o n f o r p a s a f u n c t i o n of S’ ,T and Ac t h a t c o u l d

be s e p a r a t e d i n two component s Q( S’ ,T) and § ( A c , T ) . Assuming t h e

s i m i l a r i t y be t we en f u n c t i o n s Q and (> l e a d s t o :

The d i f f e r e n c e be t we en p ( S , T ) and p ( S ’ ,T) b e i n g t h e e f f e c t of

p r e c i p i t a t i o n on t h e e l e c t r i c a l r e s i s t i v i t y .

7.4.4 Application to the Quenched Material (group 1)

To d e t e r m i n e t h e f o u r c o n s t a n t s of e q u a t i o n 7 . 3 , a s s o c i a t e d w i t h t h e

m a t e r i a l i n t h e s t a r t i n g c o n d i t i o n i e . a f t e r b e i n g quenched f rom

SSO^C, i t was assumed t h a t no c hange i n Nef f ( o t h e r t h a n t h e

e x p e c t e d f o r t h e c h a n g i n g S) has o c c u r r e d i n t h e m a t e r i a l a f t e r

b e i n g aged f o r 1 hour a t 500°C. The f o u r c o n s t a n t s d e t e r m i n e d a r e :

p 0 ( 0)= 4 . 3 0 jiflcm; B/ n0 = 8 . 1 9 x 10" 3 pQcmK"1 ; 0 2 . 3 3 x 10"3 pflcmK"2

and A = - 6 . 00 x 1 0 " 1 .

I) CSp/ST3 and alterations of Neff

F i g u r e 7 . 6 shows t h e e x p e r i m e n t a l ( f u l l c i r c l e s ) and t h e t h e o r e t i c a l

r e s u l t s f rom t h e a p p l i c a t i o n of t h e S v a l u e s , o b t a i n e d f rom

s u p e r l a t t i c e m e a s u r e me n t s , i n t o e q u a t i o n 7 . 3 (open c i r c l e s ) of t h e

d e r i v a t i v e Sp/ST d e t e r m i n e d a t 298K, a s f u n c t i o n of t h e a g e i n g

t e m p e r a t u r e of FeColNb i n gr oup 1. The same f i g u r e shows t h e

t h e o r e t i c a l r e s u l t s f rom t h e a p p l i c a t i o n of t h e S ’ v a l u e s , o b t a i n e d

f rom l a t t i c e p a r a m e t e r m e a s u r e m e n t s , i n t o e q u a t i o n 7 . 3 ( t r i a n g l e s ) .

A r e a s o n a b l y good f i t b e t we e n t h e t h e o r e t i c a l and e x p e r i m e n t a l

v a l u e s up t o 550°C can be o b s e r v e d i n f i g u r e 7 . 6 . In t h i s i n t e r v a l ,

t h e d e c r e a s e of *p/ST c o r r e s p o n d s t o t h e i n c r e a s e of Nef f c a u s e d by

t h e o n s e t of o r d e r i n g and i s i n a g r e e me n t w i t h R o s s i t e r (1981) f o r

t h e o r d e r i n g of FeCo. For t e m p e r a t u r e s above 550°C b o t h e x p e r i m e n t a l

Sp/ST and c a l c u l a t e d Sp ( S ’ , T ) / £ T ( f i g u r e 7 . 6 - c u r v e A) show a

p (S, T) = p ( S ’ , T ) ‘ + §<A c , T)

or ( 7 . 1 1 )

-1 3 4 -

F i g u r e 7 . 6 - E x p e r i m e n t a l S^/ST ( # ) and t h e o r e t i c a l £ p ( S , T ) / S T ( 0 > and Sj>(S’ , T ) / £ T ( V ) d e t e r m i n e d a t 298K i n FeColNb i n i t i a l l y d i s o r d e r e d ( g r o u p 1) , a s f u n c t i o n of t h e a g e i n g t e m p e r a t u r e ( a g e i n g t i me = i h )

50 0 6 0 0 70 0 800ageing temperature <°C)

F i g u r e 7 . 7 - E x p e r i m e n t a l (£p/ST)/J>0 ( • ) and t h e o r e t i c a lCSp(S, T)/ST]/J> (S,0) ( O ) and C SJ> (S\T ) / ST ] //> (S ’ , 0) ( A )d e t e r m i n e d a t 298K in FeCoiNb i n i t i a l l y d i s o r d e r e d ( g r o u p 1) , a s f u n c t i o n of t h e a g e i n g t e m p e r a t u r e ( a g e i n g t i me = lh>

-1 3 5 -

p o s i t i v e a g e i n g t e m p e r a t u r e de p e n d e n c e i n c o n t r a s t t o t h e c a l c u l a t e d

Sp ( S , T ) / ST ( f i g 7 . 6 - c u r v e B). The l a t t e r p r e d i c t s a smooth minimum,

a s a c o n s e q u e n c e of S i n i t i a l l y i n c r e a s i n g up t o 690*C, and t h e n

f a l l i n g a s t h e a g e i n g t e m p e r a t u r e a p p r o a c h e s Tc ( s e e f i g 6 . 1 0 ) .

The d i f f e r e n c e b e t we en c u r v e s A and B i n f i g u r e 7 . 6 must be due t o

t h e d e v e l o p m e n t of a s e c ond p r o c e s s ( o t h e r t h a n t h e o r d e r i n g )

a f f e c t i n g N e f f . T h i s s e cond p r o c e s s i s d e t e c t e d by t h e r e s i s t i v i t y

and l a t t i c e p a r a m e t e r m e a s u r em e n t s , b u t does n o t i n f l u e n c e t h e

s u p e r l a t t i c e d i f f r a c t i o n r e s u l t s i . e . t h e i n t e n s i t y of t h e

s u p e r l a t t i c e l i n e s g i v e s t h e t r u e d e g r e e of long r a n g e o r d e r .

Such a phenomenon i n v o l v i n g Nef f i s r e l a t e d t o a l t e r a t i o n s i n t h e

m a t e r i a l ’ s e l e c t r o n band s t r u c t u r e and c o u l d be c a u s e d by c h a n g e s i n

t h e m a t r i x c o m p o s i t i o n by, f o r exampl e , a p r e c i p i t a t i o n p r o c e s s .

Th i s h y p o t h e s i s of a p r e c i p i t a t i o n p r o c e s s i s c o n s i s t e n t w i t h t h e

r e d u c t i o n o b s e r v e d i n t h e l a t t i c e p a r a m e t e r on a g e i n g t h e

d i s o r d e r e d m a t e r i a l a t t e m p e r a t u r e s above 550°C ( s e e f i g u r e 6 . 1 2 ) .

F u r t h e r e x p e r i m e n t a l e v i d e n c e f o r p r e c i p i t a t i o n i n t h i s s y s t e m i s

r e p o r t e d i n s e c . 6 . 1 . 2 , name l y t h e i n c r e a s e i n t h e volume f r a c t i o n

of s e c ond p h a s e , a f t e r a g e i n g t h e a l l o y f o r 24h a t t e m p e r a t u r e s as

low a s 550*C, a s o b s e r v e d by SEM as we l l a s d e t e c t e d by Mossbauer

s p e c t r o s c o p y .

Between a b o u t 720 and 730°C a s h a r p i n c r e a s e of £p/£T i s o b s e r v e d

( f i g u r e 7 . 6 - c u r v e A) and a l s o p r e d i c t e d by £ p ( S , T ) / £ T ( c u r v e B) .

T h i s b e h a v i o u r i s p r o b a b l y a s s o c i a t e d w i t h t h e s h a r p d r o p of

o r d e r i n g n e a r Tc ( a b o u t 7 30° C) , which g i v e s a r a p i d f a l l i n Nef f and

i s t h u s d e t e c t e d by t h e e l e c t r i c a l r e s i s t i v i t y p a r a m e t e r . The

e x p e r i m e n t a l r e s u l t s i n d i c a t e a s u b s e q u e n t d r op i n t h e p a r a m e t e r f o r

a g e i n g t e m p e r a t u r e s above Tc. S i n c e t h e S v a l u e s a r e c o n s t a n t in

t h i s r e g i o n (S=0) s uch a d r o p must be a c o n s e q u e n c e of c h a n g e s i n

t h e m a t r i x c o m p o s i t i o n . T h i s t e n d e n c y i s c o n s i s t e n t w i t h t h e t r e n d

of i n c r e a s i n g e q u i l i b r i u m s o l u b i l i t y w i t h a g e i n g t e m p e r a t u r e s a t

t h e s e e l e v a t e d t e m p e r a t u r e s ; t h e r e f o r e t h e o b s e r v e d d r o p i n t h e

p a r a m e t e r can be a s s o c i a t e d w i t h an i n c r e a s i n g p r e s e n c e of Nb a toms

in s o l i d s o l u t i o n w i t h i n c r e a s i n g a g e i n g t e m p e r a t u r e s , a l t h o u g h i t

i s wor t h of n o t e t h a t t h e l a t t i c e p a r a m e t e r me a s u r e me n t s d i d n o t

show s i g n i f i c a n t c ha nge s above Tc.

-1 3 6 -

The g e n e r a l i n c r e a s e of £p / £T ( i . e . d e c r e a s e of N e f f ) o b s e r v e d

d u r i n g t h e p r e c i p i t a t i o n p r o c e s s a s we l l a s i t s d r o p ( i . e . i n c r e a s e

of Ne f f ) w i t h i n c r e a s i n g s o l u b i l i t y of Nb i n t h e m a t r i x s u g g e s t s

t h a t t h e component e l e m e n t s of t h e Nb r i c h p r e c i p i t a t e , a s a who l e ,

a f f e c t t h e m a t e r i a l ’ s band s t r u c t u r e a s an e l e c t r o n do n o r .

11) C (£p/ST)/f>o 1 and alterations of t

In t h e r e l a x a t i o n t i me a p p r o x i m a t i o n (Mot t and W i l l s - 1 9 3 6 ) t h e

e l e c t r i c a l r e s i s t i v i t y i s g i v e n by:

p = m* / ( N e f f e 2 t ) ( 7 . 12 )

where m* i s t h e e l e c t r o n ’ s e f f e c t i v e mass , e i t s c h a r g e , t i t s

r e l a x a t i o n t i m e and , a s b e f o r e , Nef f i s t h e e f f e c t i v e number of

c o n d u c t i o n e l e c t r o n s . The e f f e c t i v e mass m* can be t r e a t e d a s a

c o n s t a n t i f i t i s as sumed t h a t t h e band s t r u c t u r e e f f e c t s a r e

m a n i f e s t e d o n l y i n Nef f ( R o s s i t e r 1 9 8 0 - a ) .

S i n c e Nef f a 1 / (Sp/ST) ( C o l e s - 1 9 6 0 ) , i t f o l l o w s f rom e q u a t i o n

7 . 1 2 t h a t :

t <x C ( S p / S T ) / p 3 (7. 13)

T h i s p a r a m e t e r i s e x p e c t e d t o be s e n s i t i v e t o c h a n g e s i n S ( e . g

R o s s i t e r - 1 9 8 1 ) a s wel l a s t o o t h e r t r a n s f o r m a t i o n s a l t e r i n g t such

a s t h e f o r m a t i o n of p r e c i p i t a t e s or t h e d e v e l o p me n t of APD.

F i g u r e 7 . 7 shows t h e p a r a m e t e r C ( Sp/ST)/p<> 3, de termined a t 298K, of

FeColNb i n g r oup 1 a s f u n c t i o n of t h e a g e i n g t e m p e r a t u r e . As in

f i g u r e 7 . 6 t h e f u l l c i r c l e s , open c i r c l e s and t r i a n g l e s r e p r e s e n t

r e s p e c t i v e l y t h e e x p e r i m e n t a l C ( £ p / S T ) / p 0 ] and t h e c a l c u l a t e d

( C S p ( S , T ) / S T ] / p 0 } and ( CSp( S ’ , T ) / S T ] / p 0 ) .

S i n c e t h e o r d e r e d s t r u c t u r e p r e s e n t s l e s s e f f e c t i v e s c a t t e r i n g c r o s s

s e c t i o n , an i n c r e a s e in t i s e x p e c t e d w i t h i n c r e a s i n g S. Th i s

f e a t u r e can be s e e n in f i g u r e 7 . 7 - c u r v e A; t h e r e i s an i n c r e a s e of

t h e c a l c u l a t e d S component of t h e p a r a m e t e r up t o 690*C, where t h e

m a t e r i a l r e a c h e s i t s maximum o r d e r , and g i v e s a maximum i n t h e

-1 3 7 -

p r e d i c t e d t , which i s t h e n f o l l o w e d by a d r o p as c o n s e q u e n c e of t h e

d e c r e a s e of S n e a r t h e t r a n s i t i o n t e m p e r a t u r e .

Curve B i n f i g . 7 . 7 shows t h e p r e d i c t e d { L£j> ( S ’ , T ) / S T] /p0 ) . As

e x p e c t e d , t h e c o i n c i d e n c e b e t we en c u r v e s B and A i s k e p t w h i l e S and

S ’ have t h e same v a l u e i . e . up t o 550°C. Above t h i s a g e i n g

t e m p e r a t u r e , t h e p r e d i c t e d v a l u e b a s e d on S ’ d r i f t s downwards . Such

a d e v i a t i o n i s a c o n s eq u e n c e of a r e d u c t i o n of t and i s a s s o c i a t e d

w i t h i n c r e a s i n g s c a t t e r i n g of t h e c o n d u c t i o n e l e c t r o n s . T h i s i s

a t t r i b u t e d a g a i n , t o t h e p r e c i p i t a t i o n p r o c e s s t h a t t a k e s p l a c e

above 550°C. Al t h o u g h p r e c i p i t a t i o n can l ea d t o an. i n c r e a s e i n t ,

( b e c a u s e of t h e c l e a n e r m a t r i x i t p r o d u c e s ) , i n i t s e a r l y s t a g e s t h e

t e n d e n c y i s i n c r e a s e t h e Bragg s c a t t e r i n g due t o t h e p r e s e n c e of

c l u s t e r s of a toms or G.P. z one s ( R o s s i t e r and We l l s - 1 9 7 1 a and b;

J o n e s e t a l 1971, H i l l e l e t ' a l . 1975) . The same mechanism was

s u g g e s t e d by Ashby e t a l (1978) t o e x p l a i n t h e i n c r e a s e i n t h e

e l e c t r i c a l r e s i s t i v i t y o b s e r v e d on a g e i n g undefor raed FeCo2V.

The e x p e r i m e n t a l p a r a m e t e r C ( Sj>/£T) /p<> ] ( c u r v e C in f i g . 7 . 7 )

p r e s e n t s a p e r f e c t c o i n c i d e n c e t o t h e t h e o r e t i c a l v a l u e s o n l y i n t h e

v e r y f i r s t p o i n t i . e . a f t e r b e i n g quenched from 850°C, ( t h e

c o n d i t i o n u s e d t o c a l c u l a t e t h e c o n s t a n t s us ed in e q u a t i o n 7 . 3 ,

hence t h e c o i n c i d e n c e ) . Ageing t h e m a t e r i a l f o r 1 hour a t 500*C

r e d u c e s t h e p a r a m e t e r , d e s p i t e t h e o r d e r i n g , p r o d u c i n g a d r o p of

a b o u t 10% be low t h e l e v e l p r e d i c t e d f rom S and S ’ . T h i s r e d u c t i o n of

t h e p a r a m e t e r c o r r e s p o n d s t o t h e d e v e l o p me n t of a p r o c e s s r e d u c i n g t

t h a t c o u l d n o t be d e t e c t e d t h r o u g h S or S ’ ♦

The u n d e r s t a n d i n g of s uc h a r e d u c t i o n becomes c l e a r e r on c ompa r i ng

f i g u r e 7 . 7 t o f i g u r e 6 . 1 5 . The l a t t e r shows t h a t t h e APD s i z e i s an

i n c r e a s i n g f u n c t i o n of t h e a g e i n g t e m p e r a t u r e and a t lowo

t e m p e r a t u r e s i t s v a l u e , of 100-400 A, i s of t h e same o r d e r of

m a g n i t u d e a s t h e mean f r e e p a t h (MFP) of t h e c o n d u c t i o n e l e c t r o n s

( J o n e s and S y k e s - 1 9 3 8 ) . In t h i s c a s e , t h e a n t i p h a s e b o u n d a r i e s a c t

a s s c a t t e r i n g b a r r i e r s and t h e r e s u l t i n g r e d u c t i o n i n t o u t w e i g h t s

t h e i n c r e a s e p r od u c e d by t h e sma l l n o n - e q u i l i b r i u m d e g r e e of long

r a n g e o r d e r ( 0 . 2 9 ) mea s u r ed a t t h i s t e m p e r a t u r e . A l t h o u g h t h e

l a t t i c e p a r a m e t e r (and so S ’ ) i s s e n s i t i v e t o t h e o r d e r i n g and t h e

-1 3 8 -

p r e c i p i t a t i o n p r o c e s s , i t c a n n o t d e t e c t APD e f f e c t s . Thus , t h e

d i f f e r e n c e be t we e n t h e e x p e r i m e n t a l p a r a m e t e r ( f i g u r e 7 . 7 - c u r v e C)

and t h e c a l c u l a t e d p a r a m e t e r b a s ed on S ’ ( c u r v e B i n f i g 7 . 7 ) ,

r e p r e s e n t s t h e APD s i z e c o n t r i b u t i o n t o t t h a t S ’ c o u l d n o t d e t e c t .

F i g u r e 7 . 8 shows t h e d i f f e r e n c e be t we e n c u r v e s B and C of f i g u r e 7 . 7

a s f u n c t i o n of t h e a g e i n g t e m p e r a t u r e . From t h i s f i g u r e , t h e APD

s i z e e f f e c t on t r e a c h e s i t s maximum a t a g e i n g t e m p e r a t u r e s of a b o u t

550- 575°C and d e c r e a s e s w i t h i n c r e a s i n g a g e i n g t e m p e r a t u r e i . e . w i t h

i n c r e a s i n g APD s i z e . A c c o r d i n g t o t h e R o s s i t e r - W e l 1s t h e o r y t h e

e l e c t r o n s ’ mean f r e e p a t h (MFP) i s e x p e c t e d t o be a b o u t t h e same a s

t h e APD s i z e v a l u e a t i t s maximum t i n t e r f e r e n c e . I t means t h a t i n

t h e p r e s e n t a l l o y t h e e l e c t r o n s ’ MFP i s a b o u t 3 x 102 X.

D e s p i t e t h e v a r y i n g d i f f e r e n c e be t we e n c u r v e s B and C i n f i g u r e 7 . 7 ,

i t i s p o s s i b l e t o o b s e r v e i n c u r v e C, w i t h i n t h e e x p e r i m e n t a l e r r o r ,

t h e i n i t i a l o r d e r i n g e f f e c t , be t we e n 500 and 5 5 0 “C, a s we l l a s t h e

o n s e t of t h e p r e c i p i t a t i o n p r o c e s s . Between 660 and 690*C no

s i g n i f i c a n t d i f f e r e n c e be t we en c u r v e s B and C i s o b s e r v e d and t h e

APD e f f e c t on t i s n e g l i g i b l e above t h a t l i m i t .

Above 660°C t h e b e h a v i o u r of t h e a l l o y becomes more u n d e r s t a n d a b l e

by t h e a n a l y s i s of f i g u r e 7 . 9 where t h e d i f f e r e n c e b e t w e e n c u r v e s - A

and C of f i g u r e 7 . 7 i s p l o t t e d a g a i n s t t h e a g e i n g t e m p e r a t u r e ; t h e

i n n e r d o t t e d l i n e r e p r e s e n t s t h e d i f f e r e n c e be t we e n t h e c u r v e s A and

B. The s e p a r a t i o n of t h e e f f e c t of APD s i z e and p r e c i p i t a t i o n , a s

d e t e c t e d by t h e i r i n f l u e n c e s on t , i s r e p r e s e n t e d by t h e s e c t o r s

marked APD and PPT ( p r e c i p i t a t i o n ) .

The s e c t o r PPT shows t h e t y p i c a l p r o f i l e o b s e r v e d f o r p vs a g e i n g

t e m p e r a t u r e ( Smuger esky e t a l - 1 9 6 9 ) or p vs t i me ( H i l l e l e t a l - 1 9 7 5 )

d u r i n g GP z one s f o r m a t i o n by c l u s t e r i n g of s o l u t e a t o ms . The peak a t

690°C c o r r e l a t e s t o t h e a c h i e v e m e n t of a c r i t i c a l p r e - p r e c i p i t a t e

c l u s t e r s i z e . A c c o r d i n g t o H i l l e l e t a l . t h e c r i t i c a l s i z e i s

d e p e n d e n t on t h e c l u s t e r ’ s morphol ogy o r , a c c o r d i n g t o R o s s i t e r i t

i s r o u g h l y of t h e same o r d e r of m a g n i t u d e a s t h e e l e c t r o n s MFP which

f o r t h e s t u d i e d a l l o y i s a b o u t 3 x 102 X as d e duc ed in t h i s

s e c t i o n . The l a c k of i n f o r m a t i o n on t h e p r e - p r e c i p i t a t e morphol ogy

-1 3 9 -

F i g u r e 7 . 8 - D i f f e r e n c e be t we en c u r v e s B and C In f i g u r e 7 . 7 .

F i g u r e 7 . 9 - D i f f e r e n c e be t ween c u r v e s A and C ( ® ) and be t ween c u r v e s A and B ( © ) i n f i g u r e 7 . 7 . The s e c t o r s marked APD and PPT c o r r e s p o n d , r e s p e c t i v e l y , t o t h e a n t i p h a s e domains and p r e c i p i t a t e c o n t r i b u t i o n s t o t h e i n c r e a s e of t .

-1 4 0 -

does n o t p e r m i t any b e t t e r c o n c l u s i o n on t h i s s u b j e c t . For a g e i n g

t e m p e r a t u r e s above t h e peak , t h e c l u s t e r e f f e c t on t d r o p s s h a r p l y

and t h e c l e a n e r m a t r i x , a s e x p e c t e d , p l a y s t h e mos t i m p o r t a n t r o l e

i n p r o d u c i n g t h e l a r g e t . T h i s e f f e c t o u t we i g h s t h e t e n d e n c y of

r e d u c i n g t by t h e r a p i d d i s o r d e r i n g t h a t o c c u r s s i m u l t a n e o u s l y o v e r

t h i s t e m p e r a t u r e r a n g e .

In f i g u r e 7 . 7 t h e d e s c e n d e n t e x p e r i m e n t a l c u r v e a t t e m p e r a t u r e s

above Tc, showing r e d u c i n g t w i t h i n c r e a s i n g a g e i n g t e m p e r a t u r e i s

c o n s i s t e n t w i t h t h e p r e d i c t e d i n c r e a s i n g e q u i l i b r i u m s o l u b i l i t y of

Nb w i t h t e m p e r a t u r e i . e . t h e h i g h e r t h e t e m p e r a t u r e ( above Tc) t h e

g r e a t e r i s t h e amount of Nb i n s o l u t i o n ( a c t i n g a s s c a t t e r i n g

c e n t r e s ) and t h e lower i s t .

Ill) Residual Electrical Resistivity (p0)

The r e s i d u a l r e s i s t i v i t y has a l r e a d y been used i n t h e p r e v i o u s

d i s c u s s i o n on C( S p / S T ) / p 0 3 , which e n a b l e d t h e c h a n g e s i n t w i t h

h e a t t r e a t m e n t t o be d e t e r m i n e d . F u r t h e m o r e , c h a n g e s i n Nef f have

been s t u d i e d by means of ( £ p / S T ) . N e v e r t h e l e s s i t i s of i n t e r e s t t o

u s e t h e s e p r e v i o u s d a t a t o examine how t h e more commonly e n c o u n t e r e d

p a r a m e t e r (p0 ) i s a f f e c t e d by m i c r o s t r u c t u r a l m o d i f i c a t i o n s , a s

p 0 i s a f u n c t i o n of b o t h t and Nef f ( s e e e q u a t i o n 7 . 1 2 ) .

F i g u r e 7 . 1 0 shows t h e r e s i d u a l r e s i s t i v i t y p 0 of FeColNb i n i t i a l l y

que nc hed from 850°C ( g r oup 1) a s f u n c t i o n of t h e a g e i n g t e m p e r a t u r e .

The symbol s us ed a r e t h e same a s i n f i g u r e s 7 . 6 and 7 . 7 , i . e . f u l l

c i r c l e s , open c i r c l e s and t r i a n g l e s r e p r e s e n t i n g r e s p e c t i v e l y t h e

e x p e r i m e n t a l p 0 and t h e t h e o r e t i c a l v a l u e s of p ( S , 0 ) and p ( S ’ , 0 )

c a l c u l a t e d by u s i n g t h e e m p i r i c a l v a l u e s of S and S ’ i n t o eq. 7 . 3 .

The i n i t i a l d r o p i n t h e e x p e r i m e n t a l j>0 ( c u r v e A i n f i g u r e 7 . 1 0 )

i s c a u s e d by t h e r i s e i n b o t h Nef f and t due t o t h e o n s e t of

o r d e r i n g . The s u b s e q u e n t i n c r e a s e of p 0 i s m a i n l y c a u s e d by t h e

r e d u c t i o n of Nef f (due t o t h e p r e - p r e c i p i t a t i o n p r o c e s s ) s i n c e t h e

e x p e r i m e n t a l t i s n e a r l y c o n s t a n t b e t we en 500 and a b o u t 660*C, a s

p r e v i o u s l y de duced from C( S p / S T ) / p 0 3.

-1 4 1 -

(uiouri)

F i s u r e 7 . 1 0 - E x p e r i m e n t a l p 0 ( • ) and t h e o r e t i c a l j>(S,0) ( O > a n d j > ( S ’ , 0 ) ( A ) of FeCoiNb i n i t i a l l y d i s o r d e r e d ( g r oup i ) a s f u n c t i o n of t h e a g e i n g t e m p e r a t u r e ( a g e i n g t ime = l h ) .

-1 4 2 -

The r e d u c t i o n of t h e p a r a m e t e r b e t we en 690 and 730*C c o u l d be c a u s e d

by t h e combined e f f e c t of d e c r e a s i n g Nef f a s a r e s u l t of t h e s h a r p

f a l l i n o r d e r n e a r Tc, which t e n d s t o i n c r e a s e p<> and t h e more

s i g n i f i c a n t i n c r e a s e i n t due t o a c l e a n e r m a t r i x c o n t a i n i n g

p r e c i p i t a t e s g r e a t e r t h a n t h e c r i t i c a l s i z e , which t e n d s t o d e c r e a s e

P-

The f i n a l i n c r e a s e of , above Tc, a l s o can be e x p l a i n e d i n

t e r ms of two c o n c u r r e n t p a r a m e t e r s ; t h e i n c r e a s e of N e f f , t e n d i n g t o

d e c r e a s e j>0 , and t h e d o m i n a t i n g e f f e c t of r e d u c i n g t and hence

i n c r e a s e p 0 . Both c ha nge s a r e c a u s e d by t h e i n c r e a s e of t h e

e q u i l i b r i u m s o l u b i l i t y of Nb i n s o l i d s o l u t i o n w i t h t h e a g e i n g

t e m p e r a t u r e . I t f o l l o w s t h a t Nb i n s o l i d s o l u t i o n works more

e f f e c t i v e l y a s a s c a t t e r i n g c e n t r e t h a n as a donor of e l e c t r o n s .

The d i f f e r e n c e b e t we en c u r v e s A and B i n f i g u r e 7 . 1 0 r e p r e s e n t t h e

APD c o n t r i b u t i o n t o p 0 and t h e d i f f e r e n c e be t we e n c u r v e s B and C

i n t h e same f i g u r e r e p r e s e n t t h e c o n t r i b u t i o n of t h e p r e c i p i t a t i o n

p r o c e s s t h r o u g h i t s combined e f f e c t on t and Ne f f .

7.4.5 Application to the Furnace-Cooled Material (Group 2)

The h e a t t r e a t m e n t employed t o g e n e r a t e t h e o r d e r e d s t a r t i n g

m a t e r i a l of g r oup 2 p r o d u c e d a t t h e same t i me some a d d i t i o n a l

p r e c i p i t a t i o n , compared w i t h t h e s t a r t i n g c o n d i t i o n of g roup 1. T h i s

a d d i t i o n a l p r e c i p i t a t i o n was o b s e r v e d i n t h e SEM m i c r o g r a p h s ( s e e

f i g u r e 6 . 5 ) and d e t e c t e d t h r o u g h t h e i n c r e a s e of t h e p a r a m a g n e t i c

peak i n t h e Mossbauer s p e c t r a ( s e e f i g u r e 6 . 9 ) . The change i n t h e

m a t r i x c o m p o s i t i o n due t o t h e a d d i t i o n a l p r e c i p i t a t i o n r e p r e s e n t s a

new c o n d i t i o n f o r t h e m a t e r i a l a nd , a s d i c u s s e d b e f o r e , a new s e t of

c o n s t a n t s f o r e q u a t i o n 7 . 3 must be d e t e r m i n e d .

Two d i f f e r e n t s p e c i me n s w i t h t h e same m a t r i x c o m p o s i t i o n a r e

r e q u i r e d t o c a l c u l a t e t h e r e f e r r e d c o n s t a n t s . In t h e c a s e of group 1

t h e quenched s pe c i men and t h e s p e c i me n h e a t t r e a t e d a t 500*0 were

c o n s i d e r e d t o s a t i s f y t h i s c o n d i t i o n . However , i n g r oup 2 i t i s n o t

so o b v i o u s which s pe c i me ns s h o u l d be t a k e n f o r t h e d e t e r m i n a t i o n of

t h e c o n s t a n t s , a l t h o u g h i t i s c l e a r t h a t any c o m p o s i t i o n a l c h a n g e s

-1 4 3 -

i n t h e m a t r i x a r e r e l a t i v e l y s ma l l t h e r e f o r e t h e c o n s t a n t s were

c a l c u l a t e d by t a k i n g an a v e r a g e o v e r t h e t e m p e r a t u r e r a n g e of t h e

i n v e s t i g a t i o n , t h e a v e r a g e v a l u e s c o r r e s p o n d e d t o : p<> (0) = 5 . 0 0 pQcm

E / n 0 ? . 8 . 3 2 x- IQ3 pQcmK"1 ; C=2.93 x. IQ" 5 jiQcmK"2 . a nd A=3.3Q x 1 0 " 1 . .

I t i s i n t e r e s t i n g t o n o t e t h a t t h e v a l u e s of c o n s t a n t s B / n 0 and C

a r e a b o u t t h e same a s t h e o b s e r v e d f o r t h e quenched m a t e r i a l ,

w h i l e j>o(0) and A show m a r k e d l y d i f f e r e n t v a l u e s , s p e c i a l l y A which

was n e g a t i v e f o r g roup 1 and p o s i t i v e f o r g r oup 2.

A c c o r d i n g t o R o s s i t e r , t h e s i g n of A i s s i g n i f i c a n t a s f a r a s t h e

de pe nde nc e of Nef f on t h e d e g r e e of l o n g - r a n g e o r d e r i s c o n c e r n e d .

T h i s can be de duc ed f rom e q u a t i o n 3 . 1 : A > 0 l e a d s t o d e c r e a s i n g

Nef f w i t h i n c r e a s i n g S w h i l e A < 0 l e a d s t o i n c r e a s i n g Nef f w i t h

i n c r e a s i n g S. N e v e r t h e l e s s , i n t h e p r e s e n t c a s e , e q u a t i o n 7 . 3

i n d i c a t e s i n c r e a s i n g Nef f w i t h i n c r e a s i n g S f o r b o t h A > 0 or A < 0,

t h e o n l y d i f f e r e n c e b e i n g t h e s m a l l e r c ha nge s of £p/ST ( and t h u s

of Ne f f ) w i t h S f o r A > 0, when compared w i t h A < 0.

A pr ob l em s i m i l a r t o t h e d e t e r m i n a t i o n of t h e c o n s t a n t s f o r g r oup 2

i n e q u a t i o n 7 . 3 a r o s e i n t h e d e t e r m i n a t i o n of t h e p a r a m e t e r S ’ f rom

t h e l a t t i c e p a r a m e t e r m e a s u r em e n t s . The FC s t a r t i n g c o n d i t i o n had a

l a t t i c e p a r a m e t e r t h a t c o r r e s p o n d e d t o a low s o l u t e c o n c e n t r a t i o n i n

t h e m a t r i x due t o t h e p r e c i p i t a t i o n t h a t had o c c u r r e d . U n f o r t u n a t e l y

a h e a t t r e a t m e n t c o u l d n o t be d e v i s e d t o g i v e t h e d i s o r d e r e d

c o n d i t i o n w i t h t h e same m a t r i x c o m p o s i t i o n , hence t h e a p p r o p r i a t e

a 0 (DIS) c o u l d n o t be mea s u r ed or even a c c u r a t e l y d e duc e d . Some

q u a l i t a t i v e c o m p a r i s o n s , however , can be made a s d i s c u s s e d be low.

I ) [gp/ST3 vs Agei ng T e i p e r a t u r e

F i g u r e 7 . 11 shows t h e e x p e r i m e n t a l £p/ST a t 298K ( f u l l c i r c l e s ) and

t h e c a l c u l a t e d p a r a m e t e r u s i n g S i n e q u a t i o n 8 . 3 (open c i r c l e s ) a s

f u n c t i o n of t h e q u e n c h i n g t e m p e r a t u r e of FeColNb in g r oup 2. I t i s

i n t e r e s t i n g t o n o t e t h e good f i t b e t ween t h e t h e o r e t i c a l and

e x p e r i m e n t a l v a l u e s on t h e whole e x t e n s i o n of t h e h i g h t e m p e r a t u r e

end (600 - 7 2 0 * 0 . Ta k i ng i n t o a c c o u n t t h e r e l a t i o n s h i p be t we e n

£p/ST and N e f f , i t i s p r o p o s e d t h a t i n t h i s r an g e of t e m p e r a t u r e ,

-1 4 4 -

Fi gure 7 . 1 1 - E x p e r i m e n t a l £j>/£T ( • ) and t h e o r e t i c a l £ p ( S , T ) / £ T ( O ) d e t e r m i n e d a t 298K i n FeColNb i n i t i a l l y o r d e r e d ( g r o u p 2) a s f u n c t i o n of t h e a g e i n g t e m p e r a t u r e ( a g e i n g t i me = l h ) .

F i g u r e 7 . 1 2 - E x p e r i m e n t a l ( £ p / £ T ) / p 0 ( • ) and t h e o r e t i c a lC £J> (S, T) / £T 3 /p ( S, 0) ( O ) d e t e r m i n e d a t 298K in FeCoiNb i n i t i a l l y o r d e r e d ( g r oup 2) a s f u n c t i o n of t h e a g e i n g t e m p e r a t u r e ( a g e i n g t i me = 1 hour )

-1 4 5 -

t h e c h a n g e s i n Nef f a r e c a u s e d e s s e n t i a l l y by t h e a l t e r a t i o n s i n t h e

LRO of t h e m a t e r i a l ( s e e f i g u r e 6 . 1 0 - c u r v e A).

The r e l a t i v e l y s ma l l s c a t t e r of t h e e x p e r i m e n t a l - d a t a , r e l a t i v e t o

t h e c a l c u l a t e d p a r a m e t e r a t low a g e i n g t e m p e r a t u r e s doe s n o t p e r m i t

any c o n c l u s i o n on t h e phenomenon p r o d u c i n g such a c ha nge . Most

p r o b a b l y i t c o r r e s p o n d s t o f u r t h e r s ma l l p r e c i p i t a t i o n i n t h e

o r d e r e d m a t r i x , a s s u g g e s t e d by t h e p e c u l i a r c h a n g e s i n t h e l a t t i c e

p a r a m e t e r be t we e n 550 and a b o u t 630°C ( s e e f i g u r e 6 . 1 3 ) . I t i s wor t h

e m p h a s i z i n g t h a t t h e m i c r o s t r u c t u r a 1 c ha nge s due t o t h e h e a t

t r e a t m e n t s p e r f o r me d i n t h e s a mp l e s of gr oup 2 were minor and i t i s

d i f f i c u l t t o draw c l e a r c o n c l u s i o n s a b o u t t h e i r n a t u r e . T h i s p r ob l em

e x t e n d s t o t h e n e x t two p a r a m e t e r s a n a l y s e d .

11) C(Sp/ST)/pa] vs Ageing Temperature

The e x p e r i m e n t a l d a t a and t h e c a l c u l a t e d v a l u e s ( u s i n g S) of

C ( S p / S T ) / p 0 ] ( f u l l and open c i r c l e s r e s p e c t i v e l y ) d e t e r m i n e d a t

298K f o r FeColNb i n g roup 2 a r e p r e s e n t e d i n f i g u r e 7 . 1 2 a s f u n c t i o n

of a g e i n g t e m p e r a t u r e . The r e s u l t s can be s e p a r a t e d i n two s e c t o r s .

The f i r s t s e c t o r i n v o l v e s t h e s a mp l e s aged a t t e m p e r a t u r e s up t o

a b o u t 550°C, and i s c h a r a c t e r i z e d by a r e a s o n a b l e c o n c o r d a n c e ( i . e .

s ma l l s c a t t e r ) be t we e n t h e e x p e r i m e n t a l and t h e c a l c u l a t e d p o i n t s ,

i n d i c a t i n g t h a t , w i t h i n t h e e x p e r i m e n t a l e r r o r , no maj o r d e v i a t i o n

of t i s p r e s e n t o t h e r t h a n t h e e x p e c t e d f rom t h e c h a n g e s of S.

The s ec o n d s e c t o r , above a b o u t 6 0 0 8C, p r e s e n t s an i n i t i a l downwards

d r i f t of t h e e x p e r i m e n t a l d a t a p o i n t s r e l a t i v e t o t h e e x p e c t e d

p o i n t s ( be t we e n a b o u t 600 and 690°C) which i n d i c a t e s a r e d u c t i o n of

[ ( S p / S T ) / p 0 3 ( and t h u s of t ) r e l a t i v e t o t h e e x p e c t e d v a l u e f o r t h e

r e f e r e n c e m a t e r i a l w i t h same S. T h i s i s f o l l o w e d by an i n v e r s i o n in

t h e d r i f t so t h a t , f rom 6 9 0 8C upwar ds , a r e l a x a t i o n t i me h i g h e r t h a n

t h e e x p e c t e d f o r a g i v e n v a l u e of S i s o b t a i n e d .

F i g u r e 7 . 1 3 shows t h e d i f f e r e n c e b e t we en t h e t h e o r e t i c a l and t h e

e x p e r i m e n t a l d a t a p o i n t s of f i g u r e 7 . 1 2 a s f u n c t i o n of t h e a g e i n g

t e m p e r a t u r e . A c omp a r i s o n be t we e n f i g u r e 7 . 1 3 and t h e s e c t o r PPT of

-1 4 6 -

F i g u r e 7 . 1 3 - D i f f e r e n c e b e t we en t h e t h e o r e t i c a l and e x p e r i m e n t a l c u r v e s i n f i g u r e 7 . 1 2 .

ageing temperature (°C)

F i gur e 7 . 14 - E x p e r i m e n t a l p0 ( • ) and t h e o r e t i c a l p ( S , 0 ) ( O ) of FeColNb i n i t i a l l y o r d e r e d ( g r oup 2) a s f u n c t i o n of t h e a g e i n g t e m p e r a t u r e ( a g e i n g t i me = l h ) .

-1 4 7 -

f i g u r e 7 . 9 shows e v i d e n t s i m i l a r i t i e s which r e i n f o r c e t h e s u g g e s t i o n

t h a t t h i s b e h a v i o u r i s a s s o c i a t e d w i t h t h e p o s s i b l e d e v e l o p m e n t of

c l u s t e r s of s o l u t e a toms i n t h e a l l o y i n t h a t r an g e of t e m p e r a t u r e

a s d i s c u s s e d b e f o r e . *

An i n t e r e s t i n g f e a t u r e r e l a t i v e t o the- r e l a x a t i o n t i me ( t ) of some

s a mp l e s i n g r oups 1 and 2 C i . e FeColNb r e s p e c t i v e l y ( quenc he d +

a ge d) and ( f u r n a c e c o o l e d + a g e d ) ] i s p r e s e n t e d i n f i g u r e 7 . 1 2 :

l e v e l A r e f e r s t o t h e v a l u e of C ( Sp/ST)/ j>0 3 of t h e i n i t i a l FC

s a mpl e , whi ch a f t e r b e i n g aged a t 750*C f o r 1 hour i s r e d u c e d t o B;

l e v e l C r e f e r s t o t h e a s quenched ( f r om 8 5 0 * 0 m a t e r i a l , which

c hanged t o D a f t e r b e i n g aged f o r 1 hour a t 7 5 0 “C. A and C a r e

o p p o s i t e e x t r e m e s of d e g r e e of o r d e r a s we l l a s of Nb c o n t e n t i n

s o l i d s o l u t i o n and , c o n s e q u e n t l y exa mpl es of h i g h and low t

r e s p e c t i v e l y . T h e i r aged c o u n t e r p a r t s B and D, g i v e n s u f f i c i e n t t i me

a t 750*C t o a t t a i n e q u i l i b r i u m , would be i n i d e n t i c a l s t r u c t u r a l

s t a t e s . The C ( Sf>/ST)/p0 ] v a l u e s of B and D a r e s i m i l a r b u t n o t

i d e n t i c a l and i t i s c l e a r t h a t 1 hour a t t h i s t e m p e r a t u r e i s n o t

l ong enough f o r c o m p l e t e e q u a l i z a t i o n of s t r u c t u r e and he nc e t .

Ill) Residual Electrical Resistivity vs Ageing Temperature

The e x p e r i m e n t a l j>0 and t h e t h e o r e t i c a l J>(S,0) of t h e FeColNb in

g r oup 2 a r e shown i n f i g u r e 7 . 1 4 ( r e s p e c t i v e l y f u l l and open

s ymbol s ) a s f u n c t i o n of t h e a g e i n g t e m p e r a t u r e . The good f i t be t we en

e x p e r i m e n t a l and t h e o r e t i c a l p o i n t s a t a g e i n g t e m p e r a t u r e s be t ween

500 and a b o u t 550*C was e x p e c t e d s i n c e o n l y minor c h a n g e s , o t h e r

t h a n o r d e r i n g , o c c u r r e d in t h i s r a n g e of t e m p e r a t u r e . From a b o u t

600*C t h e d i f f e r e n c e s be t we e n t h e e x p e r i m e n t a l and c a l c u l a t e d

r e s i s t i v i t y a r e a s s o c i a t e d o n l y w i t h t h e t component . The

r e s i s t i v i t y v a l u e s a r e i n i t i a l l y h i g h e r (due t o lower t ) and f i n a l l y

lower (due t o h i g h e r t ) t h a n t h e e x p e c t e d v a l u e s f o r t h e same S.

Here a g a i n t h e smal l d i f f e r e n c e s be t we e n e x p e r i m e n t a l and

t h e o r e t i c a l c u r v e s i n d i c a t e minor c h a n g e s i n t h e m i c r o s t r u c t u r e of

t h e m a t e r i a l i n g roup 2.

-1 4 8 -

7.5 Mlcroatructure and Magnetic Properties

7.5.1 Correlation Between Bs and the Hyperfine Field.'

S i n c e t h e a l l o y s i n t h e p r e s e n t work g e n e r a l l y c o n t a i n s e c ond p h a s e

p a r t i c l e s a nd , i n some c a s e s a number of h y p e r f i n e f i e l d s

c o r r e s p o n d i n g t o t h e d i v e r s e l o c a l e n v i r o n m e n t s , t h e s p e c i f i c a t i o n

of an u n i q u e v a l u e of H f o r a g i v e n a l l o y i s d i f f i c u l t .

N e v e r t h e l e s s , t h e e x p r e s s i o n p r o p o s e d i n e q u a t i o n 7 . 1 4 a l l o w s one t o

d e t e r m i n e an a v e r a g e v a l u e <H> of t h e h y p e r f i n e f i e l d of o r d e r e d

a l l o y s :

<H> = Z ai H{ ( 7 . 1 4 )l

where t h e i ndex ( i ) r e p r e s e n t s t h e f i r s t o r s e cond s e x t e t ( i . e . Hi

= 2 . 7 1 x 107 A/m and H2 = 2 . 5 7 x 107 A/m a s o b t a i n e d f o r t h e

f i r s t and s e cond s e x t e t s of t h e o r d e r e d m a t e r i a l s , i n d e p e n d e n t of

t h e c o m p o s i t i o n o r t e r n a r y e l e m e n t ) ; a, i s a c o e f f i c i e n t t h a t

i n d i c a t e s t h e c o n t r i b u t i o n of e a ch a t o m i c c o n f i g u r a t i o n (1 or 2) and

i s g i v e n by:

a t = A j / (At + A2 + nAp A n * ) ( 7 . 1 5 )

were At , A2 , and APAra a r e t h e r e l a t i v e a r e a s of r e s p e c t i v e l y

s e x t e t s 1, 2 and t h e p a r a m a g n e t i c p h a s e p e a ks i n t h e Mossbauer

s p e c t r a ; n i s a c o r r e c t i o n f a c t o r f o r t h e r e l a t i v e a r e a of t h e

p a r a m a g n e t i c p h a s e t h a t must t a k e i n t o a c c o u n t t h e f o l l o w i n g p o i n t s :

i ) U s u a l l y , t h e r a t i o be t we e n t h e a r e a c o r r e s p o n d i n g t o t h e

f e r r o m a g n e t i c s e x t e t and t h a t of t h e p a r a m a g n e t i c peak i s g r e a t e r

t h a n t h e r e s p e c t i v e volume f r a c t i o n s and a f a c t o r n> 1 . 9 s h o u l d be

c o n s i d e r e d , a s d e s c r i b e d i n s e c t i o n 4 . 2 and i i ) t h e i r o n c o n t e n t of

t h e p a r a m a g n e t i c p ha s e i s lower t h a n t h e m a t r i x c o m p o s i t i o n ( a s

shown by t h e m i c r o - a n a l y s i s ) and c o n s e q u e n t l y t h e r e l a t i v e a r e a of

t h e p a r a m a g n e t i c p h a s e i n t h e Mossbauer s p e c t r u m i s r e d u c e d .

Us i ng n=3 . 5 y i e l d s an a l m o s t p e r f e c t p r o p o r t i o n a l i t y ( c o r r e l a t i o n

c o e f f i c i e n t = 0 . 9 9 6 ) t h r o u g h t h e o r i g i n be t we en t h e mea s u r ed Bs and

t h e c a l c u l a t e d <H> ( s e e c u r v e A i n f i g u r e 7 . 1 5 ) . N e v e r t h e l e s s , a

-1 4 9 -

< H > ( x 1 0 7 A/m)

F i g u r e 7 . 1 5 - S a t u r a t i o n m a g n e t i z a t i o n of f u r n a c e c o o l e d FeCoV ( t r i a n g l e s ) and FeCoNb a l l o y s ( c i r c l e s ) as f u n c t i o n of t h e r e s p e c t i v e a v e r a g e h y p e r f i n e f i e l d s <H> c a l c u l a t e d by u s i n g n=3 . 5 ( whi ch g i v e s a s t r a i g h t l i n e t h r o u g h t h e o r i g i n ) and n = 5 . 0 in e q u a t i o n 7 . 1 4 .

-1 5 0 -

f a c t o r of a b o u t n=5 i s more r e a l i s t i c i f one compares t h e c o r r e c t e d

r e l a t i v e a r e a s of t h e p a r a m a g n e t i c p e a k s ( i . e . n x Ap a r a ) w i t h t h e

o b s e r v e d s e cond p h a s e volume f r a c t i o n s ( s e e t a b l e 7 . 2 and c u r v e B in

f i g u r e 7 . 1 5 ) . A' good l i n e a r r e l a t i o n s h i p , b u t n o t t h r o u g h t h e

o r i g i n , be t ween Bs and <H> i s o b t a i n e d f o r n = 5 . 0 .

T a b l e 7 . 2 compar es t h e o b s e r v e d volume f r a c t i o n s i n f u r n a c e c o o l e d

FeCoNb and FeCoV a l l o y s w i t h t h e c o r r e c t e d r e l a t i v e a r e a s of t h e

p a r a m a g n e t i c p e a ks i n t h e c o r r e s p o n d i n g Mossbauer s p e c t r a ( u s i n g

n = 5 . 0 ) a s we l l a s w i t h t h e maximum volume f r a c t i o n s of s e c ond pha s e

e x p e c t e d i n t h e o r d e r e d a l l o y s . These r e s u l t s c o n s i d e r e d t h e

c o m p o s i t i o n of t h e s o l u t e r i c h p a r t i c l e s (35 a t * Fe , 49 a t * Co and

15 a t * X - a s o b t a i n e d f rom t h e m i c r o - a n a l y s i s of t h e FeCoNb a l l o y s )

and t h e s p e c i f i c mass of t h e two p h a s e s d e t e r m i n e d by u s i n g t h e

r e s p e c t i v e a t o m i c s t r u c t u r e s (B2 f o r t h e m a t r i x and L l 2 f o r t h e

p r e c i p i t a t e s ) and t h e r e s p e c t i v e l a t t i c e p a r a m e t e r s .

C o n s i d e r i n g t h e e x p e r i m e n t a l e r r o r i n t h e q u a n t i t i e s e x p r e s s e d i n

t a b l e 7 . 2 t h e f o l l o w i n g o b s e r v a t i o n s can be made: i ) Al most a l l t h e

Nb i s p r e c i p i t a t e d o u t of s o l i d s o u t i o n w h i l e a reasonable amount of V

(« 2*) r e m a i n s d i s s o l v e d i n t h e m a t r i x , c o n f i r m i n g t h e Mossbauer and

a n a l y s i s d a t a , i i ) The good a g r e e m e n t be t we e n t h e c o r r e c t e d APara

and t h e volume f r a c t i o n of s e cond p h a s e o b s e r v e d i n a l l t h e FeCoNb

and i n FeCo2V ( 2 . 2 a t * ) a l l o y s i n d i c a t e s t h a t a l l t h e s e c ond p h a s e

p r e s e n t i n t h e s e a l l o y s i s p a r a m a g n e t i c (T2 p a r t i c l e s ) , whe r e as

p a r t of t h e s e cond p h a s e i n FeCo3.6V ( i . e 4 a t * V) and FeCo5.4V

( i . e . 6 a t * V) i s f e r r o m a g n e t i c , most p r o b a b l y m a r t e n s i t e , a s

can be i n f e r r e d f rom some r e s u l t s r e p o r t e d by p r e v i o u s w o r k e r s ( e . g .

G o r o d e t s k y and S h t r i k m a n - 1 9 6 7 ; Oron e t a l - 1 9 6 9 ) and d i s c u s s e d i n

s e c t i o n 4 . 8 .

A s i m i l a r c o n c l u s i o n can be o b t a i n e d f rom t h e quenched s p e c i me n s . In

f a c t , t h e r a t i o b e t w e e n t h e o b s e r v e d volume f r a c t i o n of s e cond p h a s e

i n quenched FeCo3.6V and FeCo5.4V and t h e r e s p e c t i v e Arara i s

a b o u t n=10, a v a l u e we l l above t h e n o r m a l l y o b s e r v e d f o r t h e o t h e r

a l l o y s s t u d i e d . T h i s a l s o s u g g e s t s t h e p r e s e n c e of t h e two

m a g n e t i c a l l y d i f f e r e n t s e cond p h a s e s (T2 and m a r t e n s i t e ) i n t h e s e

a l 1oys .

-1 5 1 -

TABLE 7.2

E x p e r i m e n t a l and c a l c u l a t e d s e cond p h a s e volume f r a c t i o n s

i n FeCoNb and FeCoV a l l o y s f u r n a c e c o o l e d f rom 850*C

T e r n a r y

nomi na l comp.

(X)

E x p e r i m e n t a l

volume f r a c .

(X)

Ap A R A x 5

(X)

Maximum #

volume f r a c .

(X)

0 . 6 2 a tX Nb 7 3 4

1 . 2 4 a tX Nb 11 8 8

1 . 8 6 a tX Nb 14 14 12

2 . 2 a tX V 0 * 0 14

4 . 0 a tX V 21 10 59

6 . 0 a t * V >30 24 72

* Not d e t e c t e d in t h e p r e s e n t SEM s t u d i e s b u t p r e c i p i t a t e s were

s e e n by P i t t and Ra w l i n g s (1981) u s i n g TEM.

# C a l c u l a t e d a s sumi ng a l l Nb or V i n t h e p r e c i p i t a t e .

-1 5 2 -

The p a r a m e t e r s t h a t d e f i n e a good s o f t m a g n e t i c m a t e r i a l ( h i g h

s a t u r a t i o n i n d u c t i o n , low c o e r c i v e f o r c e and a h i g h maximum

p e r m e a b i l i t y a t low f i e l d s t r e n g t h ) , a r e i n t e n d e d t o p r o d u c e a

m a t e r i a l w i t h e a s y s a t u r a t i o n / d e m a g n e t i z a t i o n u nde r s ma l l a p p l i e d

f i e l d s . The p r e s e n c e of l a r g e g r a i n s and low l e v e l of i m p u r i t y or

s e cond p h a s e p a r t i c l e s a r e f u n d a m e n t a l f o r t h e a c h i e v e m e n t of t h o s e

c h a r a c t e r i s t i c s ( O r r o c k - 1 9 8 6 ) .

The c h a n g e s i n t h e c o e r c i v e f o r c e and in t h e s a t u r a t i o n

m a g n e t i z a t i o n p r o d u c e d by t h e p r e s e n c e of p a r a m a g n e t i c s ec o n d p h a s e

p a r t i c l e s i n t h e FeCoNb and FeCoV a l l o y s of t h e p r e s e n t s t u d y can be

s e e n i n f i g u r e s 7 . 1 6 and 7 . 1 7 r e s p e c t i v e l y . In t h e s e f i g u r e s t h e

mea s u r ed He and Bs of t h e FeCoNb a l l o y s f u r n a c e c o o l e d f rom 8 5 0 #C

( c i r c l e s ) and of t h e FeCo 2, 3 . 6 and 5 . 4 V a l l o y s r e s p e c t i v e l y

f u r n a c e c o o l e d f rom 850, 740 and 550°C ( t r i a n g l e s ) a r e p l o t t e d a s

f u n c t i o n of t h e volume f r a c t i o n of t h e p a r a m a g n e t i c p h a s e o b t a i n e d

a s d i s c u s s e d i n t h e l a s t s e c t i o n . Thes e f i g u r e s c l e a r l y d e m o n s t r a t e

t h e d i l u t i o n e f f e c t p r o d u c e d by t h e p a r a m a g n e t i c p a r t i c l e s , and t h u s

t h e c o r r e l a t i o n be t we en t h e i n c r e a s i n g amount of p a r a m a g n e t i c s econd

p h a s e p a r t i c l e s and t h e d e c r e a s i n g Bs or i n c r e a s i n g He. The

d e c r e a s i n g g r a i n s i z e w i t h i n c r e a s i n g s o l u t e c o n t e n t w i l l a l s o

c o n t r i b u t e t o t h e i n c r e m e n t i n He. In f a c t , b o t h FeCoNb and FeCo2V

a l l o y s were f u r n a c e c o o l e d f rom 850°C, an opt imum t e m p e r a t u r e which

p r o d u c e s maximum g r a i n s i z e s f o r o t h e r FeCo b a s e d a l l o y s ( e . g .

FeCoV, FeCoNi , FeCoVCu and FeCoVW - Or r ock 1985) . A c o mp a r i s o n

b e t w e e n f i g u r e s 7 . 1 6 and 7 . 1 7 shows t h a t Bs i s l e s s a f f e c t e d by t h e

h e a t t r e a t m e n t employed t h a n i s He. T h i s i s i n a g r e e m e n t w i t h Or r ock

(1985) who o b s e r v e d t h a t He was more s e n s i t i v e t o m i c r o s t r u c t u r a l

c h a n g e s , namel y g r a i n s i z e and t e x t u r e t h a n was Bs. For a g i v e n

volume f r a c t i o n of p a r a m a g n e t i c p h a s e t h e FeCoNb a l l o y s show b e t t e r

m a g n e t i c p r o p e r t i e s most p r o b a b l y b e c a u s e of t h e l a r g e r g r a i n sUe*

7.6 Texture and the Hyperfine Field

As p r e s e n t e d i n c h a p t e r 4, t h e r e l a t i v e p r o b a b i l i t i e s f o r t h e

t r a n s i t i o n s f o r pe a ks 1, 2 and 3 of t h e f e r r o m a g n e t i c Mossbauer

s p e c t r u m a r e r e s p e c t i v e l y 3 ( 1 + c o s 2 9 ) / 4 , s i n 29 and ( l + c o s 2 9 ) / 4

where 9 i s t h e a n g l e be t we e n t h e i ncoming gamma r a d i a t i o n and t h e

7 .S .2 The E ffe c t o f Second Phase P a r t ic le s on Bs and He

-1 5 3 -

(A/m

)

F i g u r e 7 . 1 6 - C o e r c i v e f o r c e He of f u r n a c e c o o l e d FeCoV ( t r i a n g l e s ) and FeCoNb ( c i r c l e s ) a s f u n c t i o n of t h e r e s p e c t i v e volume f r a c t i o n s of t h e p a r a m a g n e t i c p h a s e as d e t e r m i n e d i n s e c t i o n 7 . 5 . 1

F i g u r e 7 . 1 7 - S a t u r a t i o n m a g n e t i z a t i o n Bs of f u r n a c e c o o l e d FeCoV ( t r i a n g l e s ) and FeCoNb ( c i r c l e s ) a s f u n c t i o n of t h e r e s p e c t i v e volume f r a c t i o n s of t h e p a r a m a g n e t i c p h a s e a s d e t e r m i n e d i n s e c t i o n 7 . 5 . 1

-1 5 4 -

h y p e r f i n e m a g n e t i c f i e l d (Cohen 1976) . S i n c e t h e peak i n t e n s i t i e s

a r e p r o p o r t i o n a l t o t h e s e p r o b a b i l i t i e s , t h e p a r a m e t e r P d e f i n e d i n

s e c t i o n 6 . 2 ( e q u a t i o n 6 . 1 ) can be r e w r i t t e n a s :

P = (2 s i n 2 9 ) / ( 2 - s i n 2 9) ( 7 . 1 6 )

From e q u a t i o n 7 . 1 6 a p o l y c r y s t a l l i n e m a t e r i a l w i t h a p r e f e r r e d

o r i e n t a t i o n w i l l have a v a l u e of P t h a t de pe nds on t h e a n g l e 9. So a

t e x t u r e t h a t g i v e s 9=0, I t : I 2 : I 3 = 3 : 0 : 1 would r e s u l t i n P=0.

On t h e o t h e r hand , a r andoml y o r i e n t a t e d m a g n e t i c m a t e r i a l demands a

more complex c a l c u l a t i o n , w i t h t h e i n t e g r a t i o n b e t w e e n 0 and 2^ of

t h e e x p r e s s i o n s f o r t h e r e l a t i v e t r a n s i t i o n p r o b a b i l i t i e s e x p r e s s e d

i n t h e l a s t p a r a g r a p h o r of eq. 7 . 1 6 , g i v i n g I t : I 2 : I 3 = 3 : 2 : 1 o r P=1

Ac c o r d i n g t o Or r ock ( 1 9 8 6 ) , t h e t e x t u r e of h e a v i l y c o l d r o l l e d

n e a r l y e q u i a t o m i c FeCo b a s ed a l l o y s w i t h sma l l a d d i t i o n s of V, Ni ,

VCu and VW e x h i b i t a ( OOl )Cl lO] t e x t u r e ( t h e i n d i c e s ( x y z ) t h k l ]

r e p r e s e n t t h e p l a n e (xyz) t h a t l i e s p a r a l l e l t o t h e r o l l i n g p l a n e

and t h e Chkl ] d i r e c t i o n t h a t i s p a r a l l e l t o t h e r o l l i n g d i r e c t i o n ) .

A f t e r a n n e a l i n g , t h i s t e x t u r e c ha n g e s t o ( 1 1 D C 2 1 1 ] . I t i s as sumed

h e r e t h a t t h e a l l o y s u s e d i n t h e p r e s e n t work e x h i b i t t h e same

d e f o r m a t i o n and r e c r y s t a l l i s a t i o n t e x t u r e s a s d e t e r m i n e d by Or r o c k .

As r e p o r t e d i n s e c t i o n 6 . 2 , t h e P v a l u e s o b t a i n e d f rom t h e r e l a t i v e

i n t e n s i t i e s of t h e Mossbauer s p e c t r a of t h e c o l d worked m a t e r i a l

were be t we en a b o u t 0 . 5 and 1 c o r r e s p o n d i n g t o a v e r a g e < s i n 29>

be t ween 0 . 4 and 0 . 6 7 or <9> b e t we en 40 and 55 d e g r e e s . One way of

s e a r c h i n g f o r a p r e f e r e n t i a l d i r e c t i o n of t h e h y p e r f i n e m a g n e t i c

f i e l d f o r t h i s s i t u a t i o n i s j u s t t o l ook f o r a d i r e c t i o n t h a t

p r e s e n t s i n t e r m e d i a t e a n g l e (40<9<55°) i n r e s p e c t t o t h e p o l e of

(100) ( i . e . t h e d i r e c t i o n C100] of t h e i n c i d e n t gamma r a d i a t i o n ) or

a f a m i l y of d i r e c t i o n s t h a t p r e s e n t s b o t h low and h i g h a n g l e s so

t h a t t h e a v e r a g e i n t e r a c t i o n c o u l d g i v e t h e d e s i r e d P.

Among t h e low i ndex d i r e c t i o n s some f a m i l i e s have one or more

d i r e c t i o n s s a t i s f y i n g such c o n d i t i o n s eg <100> w i t h 9=0 and 9 0 ° ;

<120> w i t h 9= 2 6 . 5 7 , 6 3 . 4 3 and 90*; <112> w i t h 9=35 . 27 and 6 5 . 9 ° ;

<110> w i t h 9=45 and 9 0 ° ; <22i> w i t h 9=48 . 18 and 7 2 . 5 3 ° and , n e a r t h e

u ppe r l i m i t , <111> wi t h 9 = 5 4 . 7 3 ° .

-1 5 5 -

A c o m p a r i s o n be t we e n t h e s e p o s s i b l e p r e f e r e n t i a l d i r e c t i o n s f o r H

and t h e d i r e c t i o n s of m a g n e t i z a t i o n of o t h e r f e r r o m a g n e t i c a l l o y s

c o u l d c l a r i f y t h i s q u e s t i o n . Or r ock (1986) deduc ed t h a t t h e

d i r e c t i o n of e a s y m a g n e t i z a t i o n i n FeCo b a s e d a l l o y s i s <111> w h i l e

<100> i s t h e h a r d d i r e c t i o n , i n c o n t r a s t w i t h t h e u s u a l b e h a v i o u r of

f e r r o m a g n e t i c i r o n - b a s e d a l l o y s where t h e o p p o s i t e i s o b s e r v e d ; i . e .

<100> b e i n g t h e e a s y and < 111 > t h e h a r d d i r e c t i o n of m a g n e t i z a t i o n .

C o n s i d e r i n g t h e f a c t s p r e s e n t e d i n t h e l a s t t h r e e p a r a g r a p h s , t h e

d i r e c t i o n <111> a s o b s e r v e d f o r e a s y m a g n e t i z a t i o n of FeCo b a s e d

a l l o y s c o u l d be t h e most p r o b a b l e d i r e c t i o n of t h e h y p e r f i n e

m a g n e t i c f i e l d . N e v e r t h e l e s s , t h e l owe s t ( and o n l y ) a n g l e be t we en

t h a t s e t of d i r e c t i o n s and C100] ( t h e d i r e c t i o n of t h e gamma

r a d i a t i o n ) i s 8 = 5 4 . 7 3 ° t h a t g i v e s P = l , a v a l u e t o o h i g h , o n l y

o b s e r v e d f o r FeCo5.4V. Examin i ng t h e o t h e r p o s s i b l e d i r e c t i o n s and

t a k i n g t h e a v e r a g e g i v e s an even h i g h e r v a l u e ( P ~ 1 . 3 ) . On t h e o t h e r

hand i f t h e a v e r a g e i s w e i g h t e d t o w a r d s low a n g l e s t h e n P c o u l d

a p p r o a c h t h e o b s e r v e d v a l u e s .

The p r e s e n t a n a l y s i s d e m o n s t r a t e s t h a t t h e d e f o r m a t i o n t e x t u r e i s

i n d e p e n d e n t of t h e n i ob i um c o n t e n t , s i n c e P i s a l m o s t c o n s t a n t f o r

t h o s e a l l o y s , and t h a t t h e d e f o r m a t i o n t e x t u r e i s l e s s d e v e l o p e d t h e

s m a l l e r i s t h e amount of c o l d - w o r k a n d / o r t h e h i g h e r t h e vanadium

c o n t e n t .

The P v a l u e s f o r t h e a n n e a l e d m a t e r i a l ( f u r n a c e c o o l e d or a ge d) were

a b o u t u n i t y . T h i s o b s e r v a t i o n shows some a g r e e m e n t w i t h Or r ock

(1986) who found a domi na n t ( l l i ) C 2 1 i 3 t e x t u r e - w i t h some ( 1 1 2 ) C l l 0 ]

and ( OOl ) t i l O D - f o r t h e a n n e a l e d c o n d i t i o n , and t h e d o mi na n t t e x t u r e

g i v e s P~1 . 2 i f t h e e a s y d i r e c t i o n of m a g n e t i z a t i o n i s <111>.

Ano t he r a s p e c t t h a t r e f l e c t s t h e s t a t e of d e f o r m a t i o n of t h e

s p e c i me n s i s t h e l a r g e HWHM o b s e r v e d in t h e c o l d - w o r k e d s a mp l e s a s a

c o n s eq u e n c e of a wide v a r i e t y of e n v i r o n m e n t s of t h e r e s o n a n t

n u c l e u s , due t o t h e d e f e c t s g e n e r a t e d by c o l d - r o l l i n g t h e s p e c i me n s .

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7 .7 O rdering of FeCoNb A llo ys

7.7.1 Long Range Order Parameter

F i g u r e 7 . 1 8 shows t h e LRO p a r a m e t e r of t h e FeCoNb a l l o y s aged f o r 4

h ou r s a t 550*C as f u n c t i o n of t h e t e r n a r y c o n t e n t . The same f i g u r e

p r e s e n t s t h e e q u i l i b r i u m LRO p a r a m e t e r of FeCoV and FeCo0.37Nb

a l l o y s o b t a i n e d by Cl egg (1971) a t t h e same t e m p e r a t u r e . The f a c t o r

0 . 8 has been u s e d t o n o r m a l i z e t h e d a t a f rom Cl egg b a s e d on t h e

o b s e r v a t i o n s of Smi t h and Ra wl i ngs ( 1 9 7 6 ) , a s had be e n done t o a l l

t h e d a t a f rom t h e p r e s e n t i n v e s t i g a t i o n ( s e e s e c t i o n 5 . 6 . 1 ) .

The c u r v e s i n f i g u r e 7 . 1 8 show d e c r e a s i n g S w i t h i n c r e a s i n g t e r n a r y

c o n t e n t . The c u r v e f o r t h e n i ob i um a l l o y s shows good c o n s i s t e n c y

be t we e n t h e d a t a f rom t h e p r e s e n t work and t h o s e f rom Cl egg ( 1 9 7 1 ) .

The r e l a t i v e p o s i t i o n i n g of t h e c u r v e s shows t h a t n i ob i u m i s more

e f f e c t i v e i n r e d u c i n g S t h a n vanadium.

F i g u r e 7 . 1 9 c ompar es t h e i s o t h e r m a l o r d e r i n g a t 550°C of FeColNb

f rom t h e p r e s e n t work w i t h FeCo and some FeCo b a s ed a l l o y s

d e t e r m i n e d by Cl egg ( 1 9 7 1 ) . As i n f i g . 7 . 1 8 , C l e g g ’ s d a t a have been

n o r m a l i z e d by u s i n g t h e f a c t o r 0 . 8 . The d e l a y i n g e f f e c t t h a t n i ob i um

has on t h e d e v e l o p m e n t of o r d e r i s c l e a r l y d e m o n s t r a t e d .

S i n c e t h e o r d e r i n g mechani sm must i n v o l v e d i f f u s i o n ( B e e l e r - 1 9 6 5 ;

Eymery e t a l - 1 9 7 4 ) , t h e r e t a r d i n g e f f e c t of n i ob i um i n FeCo a l l o y s

may be a c o n s e q u e n c e of i t s i n f l u e n c e on t h e v a c anc y mo t i o n p r o b a b l y

due t o i t s l a r g e a t o m i c s i z e which may r e s u l t in an i n c r e a s e i n t h e

v a c c a n c y - s o 1u t e i n t e r a c t i o n e n e r g y . Ot he r r e a s o n s , r e l a t e d t o t h e

e l e c t r o n i c s t r u c t u r e of n i ob i um, c o u l d a l s o be i n f l u e n c i n g t h e

o r d e r i n g mechanism of FeCo a l l o y s a s s u g g e s t e d by o t h e r a u t h o r s such

a s Cl egg and Buc k l e y ( 19 7 3 ) .

7.7.2 APD Growth

F i g u r e s 7 . 2 0 and 7 . 2 1 compare r e s p e c t i v e l y i s o t h e r m a l and

i s o c h r o n a l APD gr owt h of FeColNb w i t h FeCo and FeCoV a l l o y s s t u d i e d

by o t h e r w o r k e r s . Both f i g u r e s show t h e s t r o n g e f f e c t c a u s e d by t h e

-1 5 7 -

F i gu r e 7 . 1 8 - LRO p a r a m e t e r a s f u n c t i o n of t h e t e r n a r y a d d i t i o n i n i n i t i a l l y d i s o r d e r e d FeCo ba s e d a l l o y s aged a t 550°C. The c i r c l e s r e p r e s e n t t h e FeCoNb a l l o y s aged f o r 4h in t h e p r e s e n t work,* t h e t r i a n g l e s r e p r e s e n t t h e ^ e q u i 1i b r i u m * v a 1ue s ( a f t e r 1 hour or l e s s ) f o r FeCo, FeCoV and FeCo0.37Nb a l l o y s a s r e p o r t e d by C l e g g - 1 9 7 1 .

F i g u r e 7 . 1 9 - LRO p a r a m e t e r as f u n c t i o n of t h e a g e i n g t ime of i n i t i a l l y d i s o r d e r e d FeCo, FeCoV and FeCoNb a l l o y s age d a t 550°C.

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F i g u r e 7 . 2 0 - APD s i z e s a s f u n c t i o n of t h e a g e i n g t i me of i n i t i a l l y d i s o r d e r e d FeCo, FeCoV and FeCoNb a l l o y s aged a t 550°C.

ageing temperature • (°C)

F i g u r e 7 . 2 1 - APD s i z e s a s f u n c t i o n of t h e a g e i n g t e m p e r a t u r e ( a g e i n g t i me = 1 hou r ) i n FeCo, FeCoV and FeCoNb a l l o y s i n i t i a l l y d i s o r d e r e d . The key f o r t h e symbol s i s d i s p l a y e d in f i g u r e 7 . 2 0 .

-1 5 9 -

p r e s e n c e of n i ob i um on d e l a y i n g t h e gr owt h of a n t i - p h a s e domai ns i n

FeCo b a s e d a l 1oys .

The a c t i v a t i o n e n e r g y f o r APD grcrwth c a n * be o b t a i n e d by a s s umi ng

t h a t t h e APD growt h k i n e t i c s i s a n a l o g o u s t o normal g r a i n gr owt h

k i n e t i c s a s p r o p o s e d by H i l l e r t (1961) and a p p l i e d s u c c e s s f u l l y

i n FeCo b a s e d a l l o y s * by o t h e r w o r k e r s ( e . g . Ashby- 1975 ,

E n g l i s h - 1 9 6 6 , C l e g g - 1 9 7 1 ; t h e two l a t t e r w i t h t h e c o r r e c t i o n s

d i s c u s s e d i n t h e work of R o g e r s , F l ower and Raw 1i n g s - 1975) i n t h e

s t u d y of APD growth i n FeCo2V. A s i m i l a r k i n e t i c s a p p r o a c h was

employed i n t h e p r e s e n t work by c ompa r i ng t h e APD s i z e s o b t a i n e d

f rom i s o c h r o n a l and i s o t h e r m a l a g e i n g s a s f o l l o w s :

aAssuming t h e t i me d e p e n d e n c e of i s o t h e r m a l growt h t o be D oc t 1/2

a s o b s e r v e d i n t h e p r e s e n t and by s e v e r a l o t h e r w o r k e r s ( e . g .

E n g l i s h - 1966, C l e g g - 1 9 7 1 , Ashby-1975) - where D i s t h e APD s i z e and

t t h e a g e i n g t i me of an i n i t i a l l y d i s o r d e r e d s pe c i me n - one can

e s t a b l i s h t h e f o l l o w i n g r e l a t i o n s h i p :

D2 - Do2 = K t exp ( -Q/RT) ( 7 . 1 7 )

were D0 i s t h e v a l u e of D f o r t =0 , K i s a c o n s t a n t , Q t h e

a c t i v a t i o n e n e r g y of APD gr owt h , R t h e u n i v e r s a l gas c o n s t a n t ( 8 . 3 1 4

J m o l ' 1 K"1 ) and T t h e a b s o l u t e t e m p e r a t u r e . Us ing t h e same

v a l u e of D from two d i f f e r e n t h e a t t r e a t m e n t s ( an i s o t h e r m a l a t

t e m p e r a t u r e T, f o r t h e t ime t i and t h e o t h e r i s o c h j r o n a l f o r

t i me t 2 a t t e m p e r a t u r e T2 ) and a s sumi ng t h a t D0 i s t h e same in

b o t h c a s e s , i t i s p o s s i b l e t o d e t e r m i n e t h e a c t i v a t i o n e n e r g y of t h e

growt h p r o c e s s by u s i n g :

t , e x p ( -Q/RTi ) = t 2 exp ( -Q/RT2 ) ( 7 . 1 8 )

The a p p l i c a t i o n of e q u a t i o n 7 . 1 8 t o t h e FeColNb s t u d i e d h e r e gave a

c o n s t a n t a c t i v a t i o n e n e r g y of a b o u t 232 KJ/mol i n t h e r an g e

550- 660°C, a v a l u e c o m p a r a b l e w i t h t h e f i n d i n g s of Ashby (1975) i . e .

255 KJ/mol f o r FeCo2V in t h e r a n g e 473-650®C or 294 KJ/mol o b t a i n e d

by E n g l i s h (1966) or 284 KJ/mol o b t a i n e d by Clegg and Buc k l e y (1973)

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f o r FeCoV a l l o y s . The two l a t t e r v a l u e s were r e c a l c u l a t e d by Ro g e r s ,

F l ower and Ra wl i n g s (1975) g i v i n g 377 and 213 KJ/mol r e s p e c t i v e l y .

A l t hough t h e a c t i v a t i o n e n e r g i e s a r e s i m i l a r f o r FeCoNb and FeCoV

a l l o y s , c o r r e s p o n d i n g t o t h e f o r m a t i o n p l u s m i g r a t i o n e n e r g i e s f o r

v a c a n c i e s i n t h e d i s o r d e r e d FeCo s ys t e m ( Smi t h and R a w l i n g s - 1 9 7 6 ) ,

t h e r a t e of t h e p r o c e s s e s b e i n g b a s i c a l l y d i f f e r e n t a s shown in

f i g u r e s 7 . 2 0 and 7 . 2 1 , mus t l e a d t o d i f f e r e n t c o n s t a n t s K in

e q u a t i o n 7 . 1 7 f o r e a ch a l l o y .

S i n c e n i ob i um p r o d u c e s an u n p r e c e d e n t e d r e d u c t i o n i n b o t h t h e

o r d e r i n g and APD k i n e t i c s i n FeCo a l l o y s , t h e r e i s a g r e a t p o t e n t i a l

f o r t h e e l e m e n t a s an a l l o y i n g a d d i t i o n t h a t w i l l e n a b l e t h e

m a t e r i a l t o be p r o d u c e d more e a s i l y i n t h e d i s o r d e r e d c o n d i t i o n .

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CHAPTER 8

CONCLUSIONS AND SUGGESTIONS FOR FURTHER WORK

8 . 1 C o n c l u s i o n s

( i ) The a d d i t i o n of V t o FeCo r e d u c e s s i g n i f i c a n t l y b o t h t h e

o r d e r / d i s o r d e r and a l / oc i + n t r a n s i t i o n t e m p e r a t u r e s of t h e

m a t e r i a l ; t h e same was n o t o b s e r v e d on a d d i n g Nb t o FeCo.

( i i ) The p r e s e n c e of nn Fe a toms i n d i s o r d e r e d b i n a r y FeCo and

FeCo b a s e d t e r n a r y and q u a t e r n a r y a l l o y s a l t e r s t h e exc hange

i n t e g r a l , d e t e c t e d t h r o u g h t h e i n c r e a s e of t h e h y p e r f i n e

f i e l d , by a b o u t 2% r e l a t i v e t o t h a t v a l u e i n t h e o r d e r e d

c o n d i t i o n .

( i i i ) A c o m p a r i s o n be t we en t h e random b i n o m i a l d i s t r i b u t i o n of V

a toms i n t h e f i r s t and s e cond c o o r d i n a t i o n s p h e r e s of t h e bcc

s t r u c t u r e and t h e Mossbauer s p e c t r a of FeCoV a l l o y s shows

t h a t t h e p r e s e n c e of a V atom i n an nn or nnn s i t e r e l a t i v e

t o t h e Fe atom i n d i s o r d e r e d FeCo r e d u c e s t h e m a g n e t i c

h y p e r f i n e f i e l d by a b o u t 9%; when t h e V atom o c c u p i e s an nnn

s i t e , i n t h e o r d e r e d m a t e r i a l , t h e r e d u c t i o n i s of a b o u t 5%.

T h i s b e h a v i o u r i n d i c a t e s t h a t t h e vanadium atom i n s o l i d

s o l u t i o n in FeCo t e n d s t o occupy t h e Fe s i t e s .

( i v ) The vanadium c o n t e n t i n s o l i d s o l u t i o n i n FeCo que nc hed from

t e m p e r a t u r e s i n t h e r a n g e 690-850°C i s l i m i t e d t o a maximum

of a b o u t 2 at% and t e n d s t o be lower ( a b o u t 1 - 1 . 5 at%) a f t e r

a g e i n g t h e c o l d - w o r k e d m a t e r i a l a t 550°C f o r long t i m e s .

Vanadium p r e c i p i t a t e s a s V - r i c h p a r a m a g n e t i c p a r t i c l e s

(T2 ) ; t h e a d d i t i o n of Ni t o FeCoV e n h a n c e s t h e

p r e c i p i t a t i o n p r o c e s s and an even lower V c o n t e n t i s o b s e r v e d

i n t h e m a t r i x of t h e aged m a t e r i a l .

(v) The s o l u b i l i t y l i m i t of Nb i n FeCo quenched f rom 850°C i s

a b o u t 0 . 3 at% and t e n d s t o be r e d u c e d a f t e r a g e i n g t h e

m a t e r i a l a t lower t e m p e r a t u r e s . The Nb p r e c i p i t a t e s i n t h e

-1 6 2 -

form of s p h e r o i d a l p a r a m a g n e t i c p a r t i c l e s which have a

c o m p o s i t i o n of a b o u t 49 at% Co, 35 at% Fe and 15 at% Nb.

(vi>> The a d d i t i o n of, Cu o r Ni t o FeCo i n c r e a s e s t h e e l e c t r i c a l

r e s i s t i v i t y of t h e a l l o y by a b o u t 0 . i and 0 . 2 5 pQcm/at%

r e s p e c t i v e l y , w h e r e a s t h e i n c r e a s e i n t h e r e s i s t i v i t y due t o

t h e a d d i t i o n of Nb and 1/ t o t h e s y s t e m i s a b o u t two o r d e r s of

m a g n i t u d e g r e a t e r ( r e s p e c t i v e l y 7 pQcm/at%, up t o a b o u t 0 . 3

a t * Nb, and 20 pOcm/atX, up t o a b o u t 2 at% V) most p r o b a b l y

due t o s i m i l a r i n f l u e n c e s of t h e Nb and V atom upon t h e

e l e c t r o n i c s t r u c t u r e of t h e b a s e a l l o y (FeCo) . Thus , t h e

g r e a t e r r e s i s t i v i t y of t h e V - c o n t a i n i n g a l l o y s i s t h e

c o n s e q u e n c e of - the h i g h e r s o l u b i l i t y of V in FeCo,

( v i i ) The e l e c t r i c a l r e s i s t i v i t y of a l o w - s o l u t e q u a t e r n a r y

FeCoxAyB a l l o y c a n be a p p r o x i m a t e l y d e t e r m i n e d by c o n s i d e r i n g

t h e d i l u t i o n of t h e e f f e c t s t h a t e a c h e l e m e n t , A or B in

s o l i d s o l u t i o n i n FeCo, p r e s e n t s s e p a r a t e l y t o t h e e l e c t r o n i c

s t r u c t u r e of t h e b i n a r y a l l o y . The a p p l i c a t i o n of t h e model

t o FeCoVW and FeCoVCu y i e l d s r e s u l t s c o n s i s t e n t w i t h t h e

m i c r o s t r u c t u r a l f e a t u r e s of t h e a l l o y s .

( v i i i ) The p a r a b o l i c t e m p e r a t u r e de p e n d e n c e of t h e e l e c t r i c a l

r e s i s t i v i t y of FeColNb i s t y p i c a l of f e r r o m a g n e t i c t r a n s i t i o n

m e t a l s and t h e s e c ond d e r i v a t i v e of t h e e l e c t r i c a l

r e s i s t i v i t y r e l a t i v e t o t h e t e m p e r a t u r e ( S2f> (S, T ) / £ T 2 )

i s S d e p e n d e n t and d e c r e a s e s w i t h i n c r e a s i n g S, i n d i c a t i n g

g r e a t e r s u s c e p t i b i l i t y of t h e s p i n o r d e r t o t h e c h a n g e s i n

t e m p e r a t u r e of s y s t e m s w i t h lower d e g r e e s of a t o m i c o r d e r .

( i x ) The t e m p e r a t u r e c o e f f i c i e n t of t h e e l e c t r i c a l r e s i s t i v i t y

(£J>/ST) d e c r e a s e s w i t h i n c r e a s i n g e f f e c t i v e number of

c o n d u c t i o n e l e c t r o n s ( Ne f f ) ( i . e . i n c r e a s i n g o r d e r a n d / o r

p r e s e n c e of Nb a toms i n s o l i d s o l u t i o n ) , whe r e as t h e

a s s o c i a t e d p a r a m e t e r C ( £j>/ST) / p 0 3 i n c r e a s e s w i t h i n c r e a s i n g

r e l a x a t i o n t i me of t h e c o n d u c t i o n e l e c t r o n s ( t ) ( i . e .

i n c r e a s i n g o r d e r , c l e a n e r m a t r i x a n d / o r l a r g e r APD and GP

z one s compared w i t h t h e mean f r e e p a t h of t h e c o n d u c t i o n

-1 6 3 -

e l e c t r o n s ) . Such d e p e n d e n c i e s i n d i c a t e t h a t some

p r e c i p i t a t i o n o c c u r s i n quenched FeColNb when aged a t

t e m p e r a t u r e s be t we e n 550 and 690°C; t h e p r e c i p i t a t i o n i s a l s o

d e t e c t e d . t h r o u g h t h e c h a n g e s i n . t he l a t t i c e p a r a m e t e r and t h e

a s s o c i a t e d p a r a m e t e r ( S ’ ) . The gr owt h of APD and t h e p o s s i b l e

d e v e l o p m e n t of a p r e - p r e c i p i t a t i o n p r o c e s s s u g g e s t t h a t t h e

mean f r e e p a t h of t h e c o n d u c t i o n e l e c t r o n s i s a b o u t 3 x

102 ^. The combined e f f e c t of Nef f and t shows t h a t t h e

p r e s e n c e of Nb i n s o l i d s o l u t i o n a f f e c t s t h e e l e c t r i c a l

r e s i s t i v i t y of FeCoNb a l l o y s more a s a s c a t t e r i n g c e n t r e t h a n

a s a f a c t o r which i n c r e a s e s N e f f .

(x) For b o t h t h e FeCoV and t h e FeCoNb s y s t e m s , t h e c o e r c i v e f o r c e

(He) i s more s e n s i t i v e t o m i c r o s t r u c t u r a l c h a n g e s ( e . g . g r a i n

s i z e o r t h e p r e s e n c e of s e cond p h a s e p a r t i c l e s ) p r o d u c e d by

t h e h e a t t r e a t m e n t s employed t h a n i s t h e s a t u r a t i o n

m a g n e t i z a t i o n (.Bs),

( x i ) A c o m p a r i s o n be t we en t h e s a t u r a t i o n m a g n e t i s a t i o n and t h e

a v e r a g e m a g n e t i c h y p e r f i n e f i e l d i n o r d e r e d FeCoV, d e f i n e d in

t e r ms of t h e p r o p o r t i o n a l c o n t r i b u t i o n of two o b s e r v e d

c o n f i g u r a t i o n s ( z e r o and one vanadium atom in an nn or nnn

s i t e ) , and i n o r d e r e d FeCoNb shows a l i n e a r de p e n d e n c e

( c o r r e l a t i o n c o e f f i c i e n t = 0 . 9 9 9 ) be t we e n t h e two q u a n t i t i e s

when a c o r r e c t i o n f a c t o r n=5 ( t o c o n v e r t t h e r e l a t i v e a r e a s

of t h e p a r a m a g n e t i c l i n e s i n t h e Mossbauer s p e c t r a i n t o t h e

c o r r e s p o n d e n t volume f r a c t i o n of p a r a m a g n e t i c p a r t i c l e s ) i s

u s e d . A r e a s o n a b l y good f i t b e t ween t h e c o r r e c t e d r e l a t i v e

a r e a s of t h e p a r a m a g n e t i c l i n e s i n t h e Mossbauer s p e c t r a

( u s i n g n=5) and t h e volume f r a c t i o n of s e cond p h a s e p a r t i c l e s

i n a l l t h e FeCoNb and in FeCo2V a l l o y s i n d i c a t e s t h a t p a r t of

t h e V - r i c h s e cond p h a s e p r e s e n t i n FeCo3.6V and FeCo5.4V

(mos t p r o b a b l y m a r t e n s i t e ) i s f e r r o m a g n e t i c .

( x i i ) The a d d i t i o n of Nb t o FeCo p r o d u c e s an u n p r e c e d e n t e d

r e d u c t i o n i n t h e k i n e t i c s of o r d e r i n g and APD growt h i n FeCo

a l l o y s . The t i me de pe nde nc e f o r t h e APD gr owt h i n FeColNb

shows a D ot t WJ k i n e t i c s w i t h a c t i v a t i o n e n e r g y of a b o u t 232

KJ/mol ( i n t h e r a n g e 550- 660°C) c o mp a r a b l e t o t h e e n e r g y

f o r d i f f u s i o n in d i s o r d e r e d FeCo.

-1 6 4 -

8 .2 Suggestions fo r F u rth e r Work

( i ) U n l i k e t h e g e n e r a l t r e n d p r e s e n t e d by o t h e r s y s t e m s , t h e

4 e l e c t r i c a l r e s i s t i v i t y of FeCo2V and FeCo2V b a s e d a l l o y s i s

g r e a t e r i n t h e o r d e r e d t h a n i n t h e d i s o r d e r e d c o n d i t i o n .

D i nh u t e t a l (1977) u s e d F r i e d e l ’ s model t o s u g g e s t t h e

f i l l i n g of v i r t u a l bound s t a t e s of a more t h a n h a l f empty VBS

which e x p l a i n s t h e i n c r e a s e of t h e r e s i s t i v i t y of o r d e r e d

FeCoV a l l o y s . N e v e r t h e l e s s t h e y d i d n o t c o n s i d e r any

m i c r o s t r u c t u r a l f e a t u r e t o i n t e r p r e t s uc h a b e h a v i o u r . In t h e

p r e s e n t work t h e same t r e n d was o b s e r v e d , b u t n o t e x p l a i n e d

s i n c e t h e maj or a t t e n t i o n c o r r e l a t i n g r e s i s t i v i t y and

m i c r o s t r u c t u r e was f o c u s e d on t h e FeCoNb s ys t e m .

N e v e r t h e l e s s , t h e method d e v e l o p e d in t h e p r e s e n t work can be

u s e d t o d e t e r m i n e t h e r o l e p l a y e d by t h e m i c r o s t r u c t u r a l

c h a n g e s ( s u c h a s t h e d e v e l o p m e n t of GP zones and APD gr owt h)

t o t h e a t y p i c a l c ompor t ment of t h e e l e c t r i c a l r e s i s t i v i t y of

o r d e r e d FeCoV a l l o y s .

( i i ) The e x c e p t i o n a l p e r f o r m a n c e e x h i b i t e d by n i o b i u m i n l o we r i ng

t h e o r d e r i n g k i n e t i c s of FeCo may be a b l e t o be u s e d i n

c o n j u n c t i o n w i t h o t h e r opt imum p r o p e r t i e s a s s o c i a t e d w i t h

o t h e r a d d i t i o n s . For exampl e t h e c o m b i n a t i o n of a b o u t 0 . 3 at%

Nb w i t h up t o 2 at% vanadium migh t p r o d u c e an a l l o y w i t h

e l e c t r i c a l r e s i s t i v i t y p r o b a b l y g r e a t e r t h a n t ha t o b s e r v e d in

o t h e r q u a t e r n a r y s y s t e ms ( su c h a s FeCoVNi), l i t t l e o r no

p a r a m a g n e t i c p r e c i p i t a t i o n and low o r d e r i n g k i n e t i c s ,

f u l f i l l i n g a l m o s t a l l t h e i d e a l c o n d i t i o n s of a commerc i a l

s o f t m a g n e t i c m a t e r i a l . Some of t h e m i c r o s t r u c t u r a l f e a t u r e s

can be a l s o c o n t r o l l e d i n o r d e r t o p r o d u c e a m a t e r i a l w i t h

h i g h e r e l e c t r i c a l r e s i s t i v i t y a s s u g g e s t e d i n t h e p r e s e n t

work.

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APPENDIX

THE HQSSBAUER EFFECT AND HOSSBAUER SPECTROSCOPY

i - The H o s s b a u e r E f f e c t

The Mo’s s b a u e r E f f e c t , d i s c o v e r e d by R. L. Hos s ba ue r i n 1957, c o n s i s t s

of a n u c l e a r e m i s s i o n or a b s o r p t i o n of gamma r a d i a t i o n w i t h o u t t h e

n u c l e u s r e c o i l e f f e c t . Such a r e c o i l of a f r e e n u c l e u s i s due t o t h e

c o n s e r v a t i o n of momentum d u r i n g any e m i s s i o n or a b s o r p t i o n of gamma

r a d i a t i o n . Due t o t h e r e c o i l e f f e c t , t h e r a d i a t e d e n e r g y g i v e n by

t h e d i f f e r e n c e be t we en a n u c l e a r e x c i t e d s t a t e e n e r g y (E*) and a

gr ound s t a t e e n e r g y (Eo) i s r e d u c e d by an amount Er ( r e c o i l

e n e r g y ) . On t h e o t h e r hand , t h e t a r g e t n u c l e u s p e r f o r m i n g t h e

i n v e r s e t r a n s i t i o n ( f rom Eo t o E*) w i l l r e q u i r e an e x t r a amount Er

i n o r d e r t o p r omot e t h e t r a n s i t i o n and c o n s e r v e t h e t o t a l momentum.

The e m i t t e d Ee and t h e a b s o r b e d e n e r g y E* a r e g i v e n by e q u a t i o n s

A . 1 and A . 2 r e s p e c t i v e l y .

E6 = < E* - Eo ) - A E r A. 1

E* = ( E* - Eo ) + A E r A. 2

The d i f f e r e n c e be t we en Ee and Ea i s r e s p o n s i b l e f o r t h e l a c k of

r e s o n a n c e , by gamma e m i s s i o n / a b s o r p t i o n , be t we en an e m i t t e r n u c l e u s

d e c a y i n g f rom t h e e x c i t e d s t a t e and a t a r g e t n u c l e u s i n t h e g round

s t a t e . The n u c l e a r t he r ma l mo t i on g e n e r a t e s a Dopp l e r component t o

t h e r e c o i l e n e r g y , r e s p o n s i b l e f o r i t s G a u s s i a n d i s t r i b u t i o n a r o u n d

Ee and Ea. A l t hough t h i s t h e r ma l b r o a d e n i n g f a v o u r s t h e r e s o n a n c e ,

i t does n o t p r o d u c e enough o v e r l a p p i n g be t we en Ee and Ea in o r d e r t o

c a u s e a c o n s i d e r a b l e r e s o n a n t e f f e c t ( F i g u r e A l ) .

N e v e r t h e l e s s , i n t h e s o l i d s t a t e t h e a toms a r e bound t o t h e c r y s t a l

l a t t i c e and t h e r e c o i l e f f e c t i s r e d u c e d , b e c a u s e of t h e f a c t t h a t

i t i n v o l v e s t h e movement of t h e whole s t r u c t u r e i n s t e a d of a s i n g l e

atom. In t h i s c a s e t h e r e c o i l e n e r g y i s r e l e a s e d on c r e a t i n g phonons

i n t h e c r y s t a l l a t t i c e . The s i m p l e s t a p p r o a c h f o r s uch an

i n t e r a c t i o n i n v o l v e s t h e E i n s t e i n model of s o l i d s , i n which t h e

-1 6 6 -

F i g u r e A . 1 - D i s t r i b u t i o n of e n e r g y of t h e gamma r a d i a t i o n e m i t t e d or a b s o r b e d by a f r e e n u c l e u s .

F i gur e A. 2 - A s c h e m a t i c a r r a n g e m e n t f o r a Mossbauer s p e c t r o m e t e r .

-1 6 7 -

t r a n s f e r of e n e r g y t o t h e l a t t i c e t a k e s p l a c e i n i n t e g r a l m u l t i p l e s

of hQ/2«, where h i s P l a n c k ’ s c o n s t a n t and Q t h e common v i b r a t i o n a l

f r e q u e n c y . I f t h e r e c o i l e n e r g y i s l e s s t h a n hft/27t, t h e n e i t h e r z e r o

o r one u n i t o f • v i b r a t i o n a 1 e n e r g y may be t r a n s f e r r e d t o t h e l a t t i c e .

I t has been shown t h a t , when many e m i s s i o n / a b s o r p t i o n t a k e p l a c e ,

t h e a v e r a g e e n e r g y t r a n s f e r r e d i s e qua l t o t h e r e c o i l e n e r g y Er .

T h i s means t h a t i f a f r a c t i o n ( f ) of z e r o - p h o n o n t r a n s f e r t a k e s

p l a c e , t h e r e w i l l be a f r a c t i o n ( 1 - f ) of one - phonon t r a n s f e r such

t h a t

( i - f ) h Q/ 2T t =AEr A . 3

In t h e z e r o - p h o n o n t r a n s f e r , t h e whole c r y s t a l r a t h e r t h a n a s i n g l e

n u c l e u s r e c o i l s . In s uc h c a s e t h e e m i s s i o n o r a b s o r p t i o n i s

r e c o i l l e s s , f o r a l l t h e p r a c t i c a l p u r p o s e s , and an a l m o s t p e r f e c t

r e s o n a n c e t a k e s p l a c e .

In a more d e t a i l e d a n a l y s i s ( T . C . G i b b - 1 9 7 6 ) i n v o l v i n g t h e Debye

model f o r s o l i d s t h e r e c o i l l e s s f r a c t i o n f i s g i v e n by

f = exp { - A E r / K e D [ ( 3 / 2 ) + ( « T / 9 0 ) 2 ]} A . 4

where K i s B o l t z m a n ’ s c o n s t a n t and 60 i s Debye’ s t e m p e r a t u r e .

E q u a t i o n A. 4 shows t h a t f i n c r e a s e s w i t h d e c r e a s i n g t e m p e r a t u r e

( r e l a t i v e t o 9 „ ) a s we l l a s w h i t h d e c r e a s i n g Er , which means

d e c r e a s i n g gamma e n e r g y . D e s p i t e of t h e f a c t t h a t e q u a t i o n A . 4 i s

s t r i c t l y v a l i d f o r t h e a c o u s t i c v i b r a t i o n a l mode ( i . e . a l a t t i c e of

i d e n t i c a l a t oms) i t i n d i c a t e s t h e p a r a m e t e r s which a r e i m p o r t a n t i n

d e t e r m i n i n g t h e f r a c t i o n of r e c o i l f r e e t r a n s i t i o n s i n o t h e r s y s t e ms

2 - The Mossbauer Spe c t r um

A s i m p l e e x p e r i m e n t can be d e v i s e d t o d e m o n s t r a t e t h e Mossbauer

e f f e c t : A s o l i d m a t r i x c o n t a i n i n g t h e e x c i t e d n u c l e i of a s u i t a b l e

i s o t o p e i s u s e d a s t h e s o u r c e of gamma r a y s . A s e cond m a t r i x

c o n t a i n i n g t h e same e l e m e n t i n t h e gr ound s t a t e ( c a l l e d t a r g e t ) i s

p l a c e d a l o n g s i d e i n o r d e r t o a b s o r b t h e r a d i a t i o n . A d e t e c t o r i s

p l a c e d in l i n e b e h i n d t h e t a r g e t f o r m e a s u r i n g t h e r a d i a t i o n

t r a n s m i t e d . If t h e i d e a l c o n d i t i o n s f o r r e s o n a n c e a r e p r e s e n t ( e . g .

-1 6 8 -

T ^ 0 j j ) t h e t a r g e t w i l l a b s o r b t h e r a d i a t i o n r e - e m i t t i n g i t

i n a l l d i r e c t i o n s and t h e d e t e c t o r w i l l r e c e i v e a low s i g n a l .

I f t h e s o u r c e moves f o r w a r d s a nd b a c k wa r d s , i t p r o d u c e s r e s p e c t i v e l y

an i n c r e a s e and a d e c r e a s e i n t h e gamma r a d i a t i o n e n e r g y , b e c a u s e of

t h e Dopp l e r s h i f t . Th i s d r i f t o u t of t h e r e s o n a n c e c o n d i t i o n

i n c r e a s e s t h e t r a n s mi t t e d r a d i a t i o n . A p l o t of t h e t r a n s m i s s i o n a s

f u n c t i o n of t h e s o u r c e v e l o c i t y w i l l show a s t r o n g e r s i g n a l f o r

v e l o c i t i e s d i f f e r e n t frum z e r o ; when V=0 t h e r e s o n a n c e t a k e s p l a c e and

a low t r a n s m i s s i o n , or more a p p r o p r i a t e l y , a s t r o n g a b s o r p t i o n i s

o b s e r v e d .

A c t u a l l y some r e s o n a n t a b s o r p t i o n i s a l s o o b s e r v e d f o r v e l o c i t i e s

s l i g h t l y o u t of t h e r e s o n a n c e p o i n t . The i i n e s h a p e of t h e a b s o r p t i o n

i s d e r i v e d f rom t h e H e i s e n b e r g u n c e r t a i n t y i n t h e gamma e n e r g y ( D .

The r e a s o n f o r s uch an u n c e r t a i n t y l i e s on t h e s h o r t t ime ( t ) t h e

n u c l e u s i s k e p t i n t h e e x c i t e d s t a t e . For t h i n a b s o r b e r s t h e

e xp e r i me n t a l l y observed l i n e s h a p e i s a L o r e n t z i a n and i s r e p r e s e n t e d

by t h e t o t a l c r o s s s e c t i o n

o-(E) = CTo { ( T / 2 ) 2 / C (E-E, ) 2 + O V 2 ) 2 3 } A . 5

where E i s t h e t a r g e t t r a n s i t i o n e n e r g y , Eg i s t h e gamma e n e r g y ,

or0 i s t h e maximum c r o s s s e c t i o n f o r a b s o r p t i o n (a c o n s t a n t t h a t

de pe nds on t h e n u c l e a r s p i n s i n t h e ground and i n t h e e x c i t e d s t a t e s

Ig and Ie r e s p e c t i v e l y ) and I" i s t h e n a t u r a l h a l f - w i d t h ( i . e . t h e

f u l l l i n e w i d t h a t t h e h a l f maximum a b s o r p t i o n i n t e n s i t y ) .

U n f o r t u n a t e l y o n l y few e l e m e n t s f u l f i l l t h e n e c e s s a r y c o n d i t i o n s t o

p r o d u c e a r e a s o n a b l y s t r o n g Mossbauer e f f e c t . The most commonly us ed

i s o t o p e i s 37Fe, i n which t h e t r a n s i t i o n be t ween I e = 3 / 2 and Ig = 1 / 2

p r o d u c e s a 1 4 . 4 Kev gamma r a d i a t i o n . D e s p i t e i t s low a bunda nc e i n

n a t u r a l i r o n ( 2 . 17%) , t h i s i s o t o p e p r o d u c e s enough a b s o r p t i o n t o be

n o t i c e d even i n a l l o y s l i k e e q u i a t o m i c FeCo where i t r e p r e s e n t s o n l y

a b o u t 1% of t h e t o t a l number of a t oms . N e v e r t h e l e s s , when t h e i r o n

c o n t e n t i s low, i t i s p o s s i b l e t o e n r i c h t h e m a t e r i a l w i t h 5 7 - i r o n

( e . g . J o n e s and De nn e r - 1 9 7 4 , N i c h o l l s and R a w l i n g s - 1 9 7 7 ) .

-1 6 9 -

3 - The Mos sbaue r S p e c t r o m e t e r

The e x t r e m e l y na r r ow w i d t h of t h e r e c o i l l e s s l i n e ( e . g . T=5 x 10" 9 eV

f o r t h e 57Fe) i n c o n j u n c t i o n w i t h t h e p o s s i b i l i t y of- modu l a t i ng ,

t h e i r r a d i a t e d gamma e n e r g y by moving t h e s o u r c e r e l a t i v e t o t h e

a b s o r b e r i s t h e most i m p o r t a n t f e a t u r e of t h e Mossbauer

s p e c t r o s c o p y . T h i s t e c h n i q u e i s p a r t i c u l a r l y i m p o r t a n t i n s t u d y i n g

t h e sma l l c h a n g e s i n t h e e n e r g y of t h e n u c l e a r s t a t e d e s c r i b e d by

t h e so c a l l e d h y p e r f i n e i n t e r a c t i o n s d i s c u s s e d i n t h e n e x t s e c t i o n .

F i g u r e A2 shows s c h e m a t i c a l l y t h e main f e a t u r e s of a Mossbauer

s p e c t r o m e t e r d e s i g n e d t o s t u d y s uc h i n t e r a c t i o n s .

4 - H y p e r f i n e I n t e r a c t i o n s

The i n t e r a c t i o n s be t we en a n u c l e a r p r o p e r t y ( e . g i n t e r n a l m a g n e t i c

f i e l d ) and an e l e c t r o n i c or o t h e r a t o m i c p r o p e r t y ( e . g . t h e

d e n s i t y of s - e l e c t r o n s i n t h e n u c l e u s s i t e ) a r e u s u a l l y c a l l e d

h y p e r f i n e i n t e r a c t i o n s . The r e a r e t h r e e main k i n d s of h y p e r f i n e

i n t e r a c t i o n s name l y :

i ) I s o a e r S h i f t (S) - A cha nge i n t h e e l e c t r o n i c d e n s i t y a t t h e

n u c l e u s s i t e p r o d u c e s a s h i f t (£) i n t h e n u c l e u s e n e r g y and a

c o n s e q u e n t s h i f t of t h e Mossbauer a b s o r p t i o n l i n e t o t h e r i g h t o r t o

t h e l e f t of t h e z e r o v e l o c i t y . Such a s h i f t i s g i v e n by:

S = KtC Y T (0) - V 8 (0) 3) A . 5

where K i s a n u c l e a r d e p e n d e n t p a r a m e t e r , V t ( 0) and V A(0) a r e t h e

p r o b a b i l i t y d e n s i t y f o r t h e s - e l e c t r o n s a t t h e n u c l e u s volume i n t h e

t a r g e t and i n t h e s o u r c e r e s p e c t i v e l y .

i i ) N u c l e a r Ze e a a n E f f e c t - R e f l e c t s t h e e x i s t e n c e of a m a g n e t i c

f i e l d i n t h e n u c l e a r s i t e . The i n t e r a c t i o n be t we e n t h e n u c l e a r

d i p o l e moment ji and an i n t e r n a l or e x t e r n a l m a g n e t i c f i e l d H a t t h a t

s i t e s p l i t s t h e n u c l e a r s t a t e w i t h s p i n I i n t o 2 l + i e n e r g y

s u b - l e v e l s g i v e n by:

Ei = - gjin H rat A . 6

-1 7 0 -

F i g u r e A . 3 - The e n e r g y l e v e l r e p r e s e n t a t i o n and r e s u l t a n t s p e c t r u m f o r m a g n e t i c h y p e r f i n e s p l i t t i n g of an I g =1/2 t o I . =3 / 2 t r a n s i t i o n . The i n t e n s i t i e s of t h e l i n e s has a r a t i o 3 : 2 : 1 : 1 : 2 : 3 , a p p r o p r i a t e t o a p o l y c r y s t a 11i n e a b s o r b e r w i t h o u t any p r e f e r e n t i a l o r i e n t a t i o n f o r t h e h y p e r f i n e f i e l d .

-1 7 1 -

where p„=5 . 05 x 10’ 31 J / G i s t h e n u c l e a r magne t on , g = p / I p „ i s

t h e n u c l e a r g - f a c t o r and mt i s t h e m a g n e t i c quantum number which

c a n t a k e t h e 2 I + i v a l u e s be t we en I and - I . In a Mossbauer e x p e r i m e n t

t h e r e may be a t r a n s i t i o n f rom t h e g r ound s t a t e w i t h a - n u c l e a r s p i n

quantum number Ig and m a g n e t i c moment pg t o t h e e x c i t e d s t a t e w i t h

n u c l e a r s p i n l e and m a g n e t i c moment pe. The m a g n e t i c f i e l d w i l l

s p l i t b o t h e n e r g y l e v e l s i n t o 21g+l and 2 I e + l s u b l e v e l s

r e s p e c t i v e l y . N e v e r t h e l e s s , n o t a l l t h e t r a n s i t i o n s w i l l t a k e p l a c e ,

b u t o n l y t h e ones o b e y i n g t h e s e l e c t i o n r u l e A m= 0 , ± 1 . F i g u r e A3

shows t h e s i x a l l o w e d t r a n s i t i o n s ( s u c h a s i n Fe) b e t w e e n s t a t e s

I g = i / 2 and I e = 3 / 2 . A c o n s e q u e n c e of t h e s i x a l l o w e d t r a n s i t i o n s i s

t h a t t h e Mossbauer s p e c t r u m f o r t h i s p a r t i c u l a r c a s e i s e x p e c t e d t o

show s i x a b s o r p t i o n p e a k s .

i i i ) Q u a d r u p o l e S p l i t t i n g - D e v i a t i o n s f rom t h e s p h e r i c a l symmetry

of t h e n u c l e a r c h a r g e and i t s i n t e r a c t i o n w i t h t h e l o c a l e l e c t r i c a l

f i e l d g r a d i e n t i s r e s p o n s i b l e f o r t h e s p l i t of t h e n u c l e a r e n e r g y

s t a t e i n t o d i f f e r e n t l e v e l s . As a c o n s e q u e n c e , a mul t ip l e l i n e

s p e c t r u m i s o b s e r v e d .

-1 7 2 -

AKNQULEDGEMENTS

I would l i k e t o g i v e my t h a n k s t o Dr. R.D. Ra w l i n g s

f o r h i s c o m p e t e n t and f r i e n d l y s u p e r v i s i o n d u r i n g t h e

c o u r s e of t h i s p r o j e c t and t o my w i f e , T i l a , f o r t h e

e n c o u r a g e m e n t t h r o u g h o u t t h i s work. I am a l s o

i n d e b t e d t o Dr. C.M. Or r ock and t o Dr . S. C a r t e r f o r

u s e f u l d i s c u s s i o n s and a s s i s t a n c e and t o Mr. K.

H o r t i n , Mr. I . Hu t t o n and Mr. R. Sweeney f o r

t e c h n i c a l s u p p o r t .

I would l i k e t o e x p r e s s my g r a t i t u d e t o p r o f e s s o r

D.W. P a s h l e y f o r t h e p r o v i s i o n of l a b o r a t o r y

f a c i l i t i e s ; t o t h e B r a z i l i a n P o s t - G r a d u a t e E d u c a t i o n

F e d e r a l Agency (CAPES), t o t h e Commi t t ee of

V i c e - C h a n c e l l o r s and P r i n c i p a l s of t h e U n i v e r s i t i e s

of t h e U n i t e d Kingdom (CVCP) and t o t h e F e d e r a l

U n i v e r s i t y of Minas G e r a i s (UFMG) f o r t h e i r f i n a n c i a l

s u p p o r t ; t o t h e C h e m i s t r y De p a r t me n t - I m p e r i a l

C o l l e g e and t o t h e P h y s i c s De p a r t m e n t - UFMG f o r t h e

s u p p o r t on Mossbauer s p e c t r o s c o p y and t o T e l c o n

M e t a l s Lt d f o r t h e p r o v i s i o n of m a t e r i a l and t h e u s e

of e qu i p m e n t .

-173

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