STRUCTURE AND PHYSICAL PROPERTIES OF SOFT MAGNETIC FeCo BASED ALLOYS
by
Aba Israel Cohen Persiano
July, 1986
A thesis submitted for the degree of Doctor of Philosophy of the University of London
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 PAGE CHAPTER 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...... 7 2.4.1 Order-Disorder and APD Growth...... 8 2.4.2 Precipitation of Second Phase...... 15 2.4.3 Recovery, Recrystallisation and Grain Growth...... 20 2.4.4 Cold-Work Effects and Texture...... 22
2,5 FeCoNb Alloys...... 22
CHAPTER 3 - ELECTRICAL AND MAGNETIC PROPERTIES OF FeCo BASED ALLOYS...... 25
3.1 Electrical Resistivity...... 25 3.1.1 Ordering Effects...... 25 3.1.2 Other Scattering Effects...... 27 3.1.3 Electrical Resistivity of FeCo and FeCo Based Alloys...... 28
3.2 Magnetic Properties of FeCo and FeCo Based Alloys...... 38 3.2.1 Ferromagnetism and FeCo Alloys...... 38 3.2.2 Other Magnetic Properties of FeCo Alloys...... 40
CHAPTER 4 - SOME APPLICATIONS OF MOSSBAUER SPECTROSCOPY APPROPRIATE 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...... 63 5.5.1 Light Microscopy...... 63 5.5.2 Scanning Electron Microscopy (SEM)...... 63 5.5.3 Transmission Electron Microscopy (TEM)...... 63
5.6 X-Ray Diffractometry...... 64 5.6.1 Determination of Degree of Long Range Order...... 64 5.6.2 Determination of Antiphase Domain Size...... 66 5.6.3 Lattice Parameter Measurements...... 67
5.7 Mossbauer Spectroscopy...... 67 5.7.1 Detection of Phases Present...... 68 5.7.2 Magnetic Properties on the atomic Scale...... 68 5.7.3 Site Population...... 68 5.8 Electrical Resistivity...... 69 5.8.1 Dependence with Composition and State of Ordering...... 69 5.8.2 Electrical Resistivity Parameters and Structural Changes...69 5.8.3 A Computer Controlled Resistivity Rig...... 71
5.9 Magnetic Measurements...... 72
CHAPTER 6 - RESULTS...... 76
6.1 Phase Analysis...... 76 6.1.1 DTA Results...... 76 6.1.2 Microstructure...... 78
6.2 Texture...... 89
6.3 Ordering of FeColNb...... ,..,.90 6.3.1 Bragg-Wi 11 iams LRO Parameter (S)...... 90 6.3.2 Lattice Parameter (a0)...... 92 6.3.3 Antiphase Domain Size (D)...... 95
6.4- Electrical Resistivity Results...... 95 6.4.1 Ternary Additions and Ordering Effects...... 95 6.4.2 Effects Due to Microstructural Changes...... 99
6.5 Magnetic Measurements Results...... 101
6.6 Some Parametric Changes with Ordering and Composition.....108 6.6.1 Lattice Parameter...... 108 6.6.2 Temperature Coefficient of the Electrical Resistivity....110 6.6.3 Hyperfine Parameters...... 110
CHAPTER 7 - DISCUSSION...... 116
7.1 A Statistical Analysis of the Site Population of 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 Changes to the Electrical Resistivity of FeCo Based Alloys...... 122
7.4 Microstructure and Electrical Resistivity of FeColNb..... 130 7.4.1 Preliminary Comments...... 130 7.4.2 A New Empirical Function ^>(S,T)...... 131 7.4.3 A New Parameter (S’)...... 132 7.4.4 Application to the Quenched Material (Group 1)...... 134 7.4.5 Application to the Furnace-Cooled Material (Group 2)..... 143
7.5 Microstructure and Magnetic Properties...... 149 7.5.1 Correlation Between Bs and the Hyperfine Field...... 149 7.5.2 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...... 157 7.7.1 LRO Parameter...... 157 7.7.2 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. - 1 - 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.
- 2 - 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 and intermediate compositions the 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. - 3 - Fi gure 2.1 - The FeCo phase diagram, after Nishisawa and Ishida-1984 suetAnce B • = C o Figure 2.2 - The B2 superlattice -4 - 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)] (2.3) which in a B2 superlattice reduces to r = (q - 4)/4 (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, -5 - Figure 2.3 - The variation in the long range order parameter, S, with temperature for FeCo - after Stoloff and Davies-1964. Otf fercnt crystals w APR 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) -6- 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 of technological 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 - 7 - 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 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 - 8 - 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 equiatomic FeCo as function of V content (full lines), after Martin and Geis1er-1952. The broken lines show ri/n+al and n + ai/ocl boundaries under equilibrium conditions for alloys with constant Co (52%); after Koster and Schmid-1955, apud Raynor and Rivlin-1983. -9 - 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 all cases 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. O Clegg (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 O reports a little higher difference (about 0.0030A) between a0 of ordered and disordered nearly equiatomic FeCo with small additions -10- 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 FeCoSi th. Both Si and Al increase 1955 FeCoA1 analysis Tc at about 40°C/at% Stoloff and Davies-1962 FeCo2V x-ray Tc=720°C Clegg and Mag. sat. Buck 1ey-1973 FeCoV x-ray V decreases Tc by li°C/at% Hagiwara FeCoW W increases Tc by 8®C/atX and FeCoCr DTA Cr decreases Tc by 5°C/at* Suzuki-1976 FeCoV V decreases Tc by ll*C/at% Urushi hara Tc increases up to and FeCoW DTA 755°C with 0.2at% W Sato - 1978 and then decreases ======in FeCo:======Si increases Tc by 19°C/wt% W decreases Tc by 6°C/wt% several Cu decreases Tc by li*C/wt% FeCo V decreases Tc by 14"C/wt% Orrock-1985 and DTA Ni decreases Tc by 30°C/wt% FeCoV ======in FeCo2V:======based Si increases Tc by 30°C/wt% a 11oys Mn increases Tc by 18°C/wt% W decreases Tc by 6®C/wt% Cu decreases Tc by llaC/wt% -11- D isordered o F eC o-V • FeC o—Nb ■ FeCo—Cr t i JL FeC o 2 3 4 5 a t 'A Figure 2.7 - The change in lattice parameter of FeCo with var i ous additions of vanadium, chromium and niobium, after Clegg-i97i -12- 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 - 1 3 - (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. -14- 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 -15- Figure 2.9 - Isothermal ordering curves for FeCo (a) and FeCo2.5V (b), after Clegg and Buckley-1973. -16- 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 the cold-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 i Pitt and Rawlings (1981) observed a significant increase in the proportions 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 obtained by Ashby and co-workers for FeCoV under similar conditions. A comparison 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. - 1 7 - 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. -18- 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 to 1.5at%, 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 -2 0 - TABLE 2.2 Precipitation of second phase in FeCo based alloys REFERENCE MATERIAL INFORMATION very small ( 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 but Pitt-1980 no precipitate was observed FeCoVNi after slow cooling from 750°C and if Ni content is 1.8% or less. (V=0.7-1.5%) TTT curve for undeformed alloy has the "nose" at lower Pitt & (Ni=l.8-7.4%) times and higher temperatures Rawlings-1981 when compared to FeCoV. Small grains are due to T2 present. If Co3X compounds are present Severa1 the alloy is ductile. The reason is attributed to LCD ternary zones that, being deficient in Co, do not permit the Kawahara-1983a&b FeCoX formation of B 2 (ordered) volumes. Some Co3 X effective a 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 diameter FeCo2VCu less than 0.5 pm and lattice FeCo2VW parameter 3.6 X; cause grain Orrock-1985 FeCoNi refinement in FeCoVCu, FeCoVW FeCoSi & FeCoNi; no microstructura1 (X=l,3,5 wt%) change was observed in FeCoSi. -21- 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. -2 2 - 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. -2 3 - 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. - 2 4 - 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 the super lattice (Nicholas-1953) . This change is respons ib1e for alterations 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 -2 8 - 1.8 “V 1 | 7 s * \ AI-5.3 o(.%2n. . s * . \ Xi '.-IO * C 1.6 • 7 7 #K * c>' * : \ P t 10* 1.5 \ (II cm J 14 \ 1.3 12UJ r 0 O ' o ' 10* 10* 10 * It (m in) —► 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 allo ys 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), these publications suffer from a lack of essential microstructural information. Only for FeCoV alloys has the resistivity been adequately 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. The inversion 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 -34- 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 a resistivity 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 (see fig.3.9-B). In both cases the reason for the initial increase in p was attributed to the electronic scattering due to very small ordered nuclei (APD sizes much less than 400 X) in a disordered matrix. Increasing the degree of long-range order and the domain size 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-worked material 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) ordered 1.9 Rossi ter FeCo 1981 disordered 3.1 ordered 1.83 FeCo disordered 2.60 Dinhut et al 1977 ordered 38.9 FeCo2V disordered 32.0 ordered 21 Ashby FeCo2V 1975 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 field theory any ferromagnetic system fulfils two necessary preconditions i) the existence of an atomic magnetic moment (p) - whose natural unit is the Bohr magneton (jiB = eh/47tmc= 9.27 x 10*2 4 Am where e is the electron’s charge, m its mass, h Planck’s constant and c the velocity of light in vacuum) and ii) a special electron exchange interaction of electrostatic origin (measured through the exchange integral J) promoting the parallelism of adjacent spins. The first condition depends on the electronic structure for which the 3d transition elements exhibit specially favourable circumstances; the second involves some geometrical parameters and is favourable when the ratio between the lattice parameter (an) and the 3d shell diameter (d) is higher than 1.5. Figure 3.10 shows the exchange integral as function of the ratio a0/d for transition elements in the iron group. If J>0, the ferromagnetic configuration (parallel spins) is stable since the exchange energy (Utt ) between adjacent spins St and Sj (given by the Heisenberg model ^ ^ Uit = -2J Si.Sj) is negative and thus less than that for non interacting 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 cA 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 moment as function of the electron concentration. After Bozorth-1964. -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. The equiatomic 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 for compositions Co:Fe > 1. He also reports the effects of other additions (Ti, V, Cr, Ni and Cu) to the mean saturation moment of FeCo (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 are little affected by the presence of vanadium, since the reported values for the parameter in equiatomic FeCo are in the ranges 2.9-3.0 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 Y d ( 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). -4 3 - 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. -4 4 - 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 -4 5 - 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,...6 are It sla :1s = UtlatU = 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 isotope produce some interesting effects such as the peculiarities of the spectrum of ordered Fe3Al exemplified below. Since these effects usually involve the close neighbourhood of the resonant nucleus, they are sensitive to ordering. -4 6 - 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. -4 7 - 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 in sites type D, where each Fe atom has 4 Al and 4 Fe nearest neighbours - see figure 4.5. The A sites, having much larger hyperfine field (299 KOe) than the D sites (229 KOe) have a larger split of the peaks. This difference in H shows how the presence of non-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 -4 8 - 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. -4 9 - 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)2 n*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 AHnM £-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%). -5 0 - N! HZ HZ HA US N6 S u 2. >-o cc z Ul z o o < c c tkt ►- z R 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. -5 1 - 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. -5 2 - 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). -5 3 - 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 -5 4 - 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 -5 5 - n— --- 1— '— i----•— r T“ '— r T T (a) VleaUey ,rolied tft#r quiftc>lAfl frtn ?50*C u ►- < (b) Vie alloy , elitr x«oi i/ialmiM fo/ apilmvm ptrmoAttl MagAit propirllti _J_ JL...1 f ♦12 • 12 VELOCITY [ m m / n e ] 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. -5 6 - 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). -5 7 - 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 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. -5 8 - 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 5 wt% 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. -5 9 - TABLE 5.1 Nominal composition of the alloys studied in the present investigation MATERIAL NOMINAL COMPOSITION (wt%) STUDIED Ternary Quaternary Fe Co addition addition 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 W FeCo2V3W 47.5 47.5 2.0 V 3.0 W FeCo2V5W 46.5 46.5 2.0 V 5.0 W FeCo2VlCu 48.5 48.5 2.0 V 1.0 Cu FeCo2V3Cu 47.5 47.5 2.0 V 3.0 Cu FeCo2V5Cu 46.5 46.5 2.0 V 5.0 Cu FeCol.5V4.5Ni 46.0 48.0 1.5 V 4.5 Ni -6 0 - 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 and dimensional tolerance. In order to cold roll FeCo alloys it is necessary 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 quenched specimens down to 0.25 mm ie. 75% R.A. Such a thickness is adequate to assure a cooling rate of about 8000aC/sec, high enough to keep even the binary alloy in the disordered state after a quenching from 850°C, as described by Clegg (1971). It is worth mentioning that the alloys containing Nb have shown better rollability than those containing V. To order the material, the cold rolled FeCo5.4V, FeCo3.6V and all the other alloys were sealed in quartz capsules under argon atmosphere 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. -6 1 - 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 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 the disordered 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 the ordered (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 the disordered undeformed FeCoiNb for 0.5, 1, 2, 4, 8 16 and 32 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. -6 2 - 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. -6 3 - 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 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 -6 4 - 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. -6 5 - The expression used to determine the LRO parameter S is presented in equation 5.2 and takesinto account the observations contained in the last three paragraphs: S= 0.8 x CIO.6 x I(100)/I(200)]1'2 (5-2) 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 the resultant 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): D = K A / b cos 9 (5.3) 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 in groups 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: b2 = B2 - B ’2 (5.4) -66- 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 of 0.02° 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 Rh source 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 r t , was usually characterized by the presence of a central peak. Since the iron content of the or r2 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 the separation between lines 1 and 6 of the specimens’ ferromagnetic spectrum 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. - 68 - 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 - <\l Uj Uj c l Figure 5.1 - The main circuit for resistivity measurements, show a detail of the sample holder. -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. -7 1 - 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 1:a 1 0 0 4 t04tm * 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. -7 4 - equal to the total change in the magnetic flux 5tot in the 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 the flux in the air that fills the rest of the volume of the toroid. The determination 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 start from 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 the cooling 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 -7 6 - DTV (arbitrary units) DTV (arbitrary units) Figure F i g u r e 6 . 2- D T Ap l o t o fF e C o N b a l l o y s 6 .1- DTA plot ofFeCoV alloys. 77- 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 ON ALLOY ORDER/DISORDER at / 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 fin Figure 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) i------1 lOOua 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. -81- (c) Figure 6 . 6 - Micrographs exhibiting some details of r2precipitation 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 tables 6.2 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 Quenched gr. 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 Quenched gr. 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 -8 4 - 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 - F i g u r e 6 . 7 -T y p i c a lM S s s b a u e rs p e c t r a o f( A )F e C o N(B bFe a n C d ) o V FeCoV alloys the computer analysis the assymmetry of the of Bshow the positions alloys. sixth the constituent line two theof of The arrow in spectrum shows theparamagnetic A component ferromagnetic lines indicated thepresence third of set a of sextets observed ins y s t some e m a t of i c a the l l y o FeCoV b s e r v alloys. e di some In spectra nt h of e F e C o N b a l l o y s ;t h e a r r o w si ns p e c t r u m t w o a d j as c e e n x t ts e e t x s tin , e t s sw u a c s hc c o a n s s e t s at n h t e . d i f f e r e n c eb e t w e e nt h e m a g n e t i c s pof l i t Relative counts eoiy (mm/s) velocity -86- * £40 0 2 20 co CO © a 0 10 > •H jO 0 0 o 1 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 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 and 3. 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 -8 9 - 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, 2 and 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). -9 2 - F i g u r e 6 . 1 3 -L a t t i c ep a r a m e t e( r a 0)Feo C fin o l i N t b i aor l l d y e r e d a sf u n c t i o n o ft h e a g e i n gt e m p e r a t u r e( a g e i n gt i m e= F i g u r e 6 . 1 2 - L a t t i c e p a r a m e t e( r a 0)o fF e C o l N bi n i t i a l l y d i s o r d e r e d b r o k e nl i n ei n d i c a t e st h ec a l c u l a t e d a lattice parameter (A) as function of the ageing temperature (ageing time hour). i The = 93- 3 -9 0 fo rS = i( s e ep a g e1 3 2 ) . 1 hour). F i g u r e 6 . 1 4 -L a t t i c e p a r a m e t e( r a 0)o fF e C o l N bi n i t i a l l y d i s o r d e r e d , a sf u n c t i o n o ft h e a g e i n gt i m e a t 5 5 0 ° C . lattice parameter (A) 94- 4 -9 6.3.3 Antiphase Donain Size (D) Isochronal heat treatments : The APD sizes, as determined from x-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. -9 5 - (a) i------1 1000 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 h ALLOY (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 following general trends can be drawn from table 6.4: (i) the addition of V to FeCo increases the electrical resistivity by a factor of about 20 (as previouly established by many other workers) while all the other ternary additions are far less effective; (ii) the addition of quaternary elements to FeCoV alloys shows a dilution effect on the increase in p; (iii) with exception of FeCo5.4V and FeCol.5V4.5Ni all the ternary or quaternary alloys containing vanadium exhibit an increase in the resistivity with ordering (in agreement with Dinhut et al-1977) whereas all the other alloys show the opposite behaviour. The highest change in p due to heat treatment was observed in FeCol.5V4.5Ni where the parameter was reduced by about 44% after being aged for 24h at 650*C. It is important to mention that no significant change in p was observed on cold-rolling quenched specimens, although the effect of cold rolling was only investigated for the FeCo2V, FeColNb and FeCol.5V4.5Ni a l 1oys. 6.4.2 Effects due to Microstructural Changes A specific study relating electrical resistivity and microstructure has been developed for the FeColNb alloy. This involved the measurement of the reduced electrical resistivity (p(T)/p(298)) of groups 1 and 2, as described in chapter 5, as function of the measuring temperature from 77K (-196*0 to about 373K (100*0 The dependence of p(T)/p(298) with temperature was computer analysed and the best function obtained using the least-squares method was the second-order polynomial represented by: p(T)/p(298) = A0 + At T + A2T2 (6-2) where A(0),A(1) and A(2) are constants and T the absolute test temperature. Figure 6.17 shows typical examples of such a dependence; the full symbols represent the experimental results for FeColNb quenched from 850*C (i.e. in the disordered condition) and the open symbols correspond to the same alloy furnace cooled from 850*C (i.e in the ordered condition). The continuous lines are the best second order -99- ue .7 Rltv eetia rssiiy f ree and ordered of resistivity electrical Relative - 6.17 F i gure orsod o h bs ft uig eod re polynomials. order second using fits best the to correspond disordered FeColNb as function of temperature. The continuous lines lines continuous The temperature. of function FeColNb as disordered p(T)/p(298) eprtr (K) temperature -100- polynomial f it to the data. The average relative deviation between the values for p(T)/p(298) determined from equation 6.2 and the experimental data was 0.3% i.e. about the same order as the experimental data error. The same order of error was observed for the reproducibility of the constants A0 , At and A2 from distinct specimens given identical heat treatments. For this reason values for the resistivity p(T) or its slope relative to the test temperature (Sp/ST) can be calculated analytically from equation 6.2 without further increasing the experimental error. Despite the lack of knowledge on the behaviour of the electrical resistivity of this specific alloy near OK, it will be assumed that equation 6.2 is valid to that limit. This seems to be reasonable, considering that the binary alloy exhibits the same parabolic behaviour in the temperature range 4.2-250K • (Rossiter-1981 for equiatomic FeCo) as observed in the present investigation for the temperature range 77-373K The values of A0, Ai and A2 are presented in tables 6.5 and 6.6 for FeColNb respectively quenched and aged (group i) and furnace cooled and aged (group 2); the tables also show the absolute resistivities at 298K tp (298 > ]. 6.5 Hagnetic Measurements Results The D.C. normal induction curves for FeCo 3.6 and 5.4 V and for FeCo 1, 2 and 3 Nb submitted to different heat treatments are presented in figures 6.18 to 6.20. The normal induction curve for the Telcon PMD-49 is also given in the same figures as a comparative reference. The values for coercive force and saturation induction of the alloys are presented in table 6.7. The results show increasing improvement in the soft magnetic properties (i.e. higher Bs and lower He) with decreasing ternary addition. Annealing temperature has little effect on Bs but He decreases with increasing temperature. These trends are similar to those observed by Orrock (1986) for small additions of Cu and W to FeCo2V and aged as in the present work. Nevertheless the same author -101- TABLE 6 .5 Coefficients A0, At and A2 for equation 6.2 and electrical r e s is tiv it y at 298K CJX298)] for FeColNb quenched from 850°C and aged for 1 hour at temperature T (group 1) AGEING TEMPERATURE Ao Ai a2 p (298) ( *C) xlO1 xlO4(K-‘ ) xlO4(K-2) (jiftcm) Q * 4.88 9.30 2.64 8.81 500 4.95 9.87 2.37 7.90 550 4.90 9.47 2.55 7.29 600 4.98 8.89 2.66 7.82 630 4.99 9.10 2.58 8.21 660 4.81 9.42 2.66 8.39 690 4.91 9.31 2.59 8.69 720 4.63 9.42 2.87 8.42 730 4.36 10.02 2.99 8.83 750 4.35 10.38 2.78 8.47 780 4.38 9.69 3.06 9. 10 * Q corresponds to the material in the initial condition. i.e. quenched from 850°C. -102- 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) AGEING TEMPERATURE Ao At a2 p (298) (°C) xiO1 xlO4(K-1) xlO*(K-2) (jiQcm) FC * 3.82 12.07 2.90 6.35 500 3.93 11.46 2.98 6.88 550 4.09 10.29 3.19 7.09 575 4.14 11.53 2.73 7.27 600 4. 15 11.25 2.80 7.55 630 4.24 11.18 2.72 7.57 660 4.35 11. 10 2.64 7.89 690 4.36 11.59 2.46 8.26 720 4.31 11. 15 2.65 8.53 750 4. 13 11.30 2.81 9.22 # FC corresponds to the material in the initial condition i.e. furnace cooled -103- 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 of FeCoNb alloys annealed for 2 hours at 850°C followed by furnace cooling. The magnetization curve for the Telcon PHD-49 is presented as a comparative reference -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 Coercive force (He) and saturation magnetization (Bs) of FeCo based alloys PARAMETER He Bs He Bs ALLOY (A/m) (T) (A/m) (T) ANNEALED AT 760#C ANNEALED AT 850°C FeCo2V 95 2.32 90 2.35 FeColNb 355 2.34 300 2.32 FeCo2Nb 470 2.29 425 2.24 FeCo3Nb 665 2.20 610 2.12 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 -- - -107- observed better soft magnetic properties in the FeCo5Ni aged at 760*C than the aged at 850*C in contrast with the previous observations. 6.6 Some Paraaeteric Changes with Ordering and Composition 6.6.1 Lattice Parameter The lattice parameters of the FeCoV and the FeCoNb alloys have been determined for the material in the ordered and in the disordered state. That parameter was also determined for 2.5 mm thick FeCoNb specimens kept for 1 hour at 800°C and then quenched into iced brine. Figure 6.21 shows theselattice parameters as function of the ternary addition content. The FeCoNb alloys are represented by circles and the FeCoV by squares; the furnace cooled and the quenched samples are represented by open and full symbols respectively. The crosses represent the 2.5 mm thick samples quenched from 800*0. The FeCo5.4V (6at*V) produced broadened diffraction peaks, thereby increasing the error in the lattice parameter by about one order of magnitude, compared with the other results. The results for a„ in quenched and in furnace cooled FeCoV and FeCoNb as obtained by Clegg (1971) are also shown in the same figure. In all cases the ordered structures gave lattice O parameters of about 0.0020 A larger than the corresponding disordered alloys. The effect of composition shows increasing lattice parameters with the vanadium content whereas varying the niobium content between 1 and 3 wt* inclusive (0.62 to 1.86 at*) does not significantly influence the lattice parameter. There is a good agreement between the present data and those obtained by Clegg (1971) regarding FeCoV alloys and on the FeCo0.37*wt alloy. The 2.5 mm thick specimens containing Nb produced an intermediate lattice parameter at about 25* of the way between the values for the disordered and the ordered samples; i.e. closer to the values of the thin disordered samples. According to the method developed by Orrock (1986) this corresponds to a degree of long range order of about 20* and certainly such a low degree of order would account for the good reliability of these alloys. -108- 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 Figure 6.22 shows the effect of the niobium content and the state of order on the parameter [ (£j>/ST)/j> (298) ] of FeCoNb alloys. Although no sensitive dependence on the Nb content is observed, it is clear that there is a marked difference in the parameter for samples in the ordered and the disordered conditions, the former having a lower C (£j>/£T)/p(298) 1 than the latter. The same behaviour was observed by Rossiter (1981) for equiatomic FeCo. 6.6.3 Hyperfine Parameters * i ) Magnetic Hyperfine Field Figure 6.23 shows the magnetic hyperfine field for sextet A (HA) obtained from Mossbauer spectroscopy for the FeCoNb, FeCoV and FeCoVNi alloys as function of the niobium or vanadium contents. The hyperfine field for sextet B (H#) obtained from the two sextet analysis of the FeCoV and FeCoVNi alloys that exhibited some assymmetry in the Zeeman hyperfine patterns is also shown. The FeCoNb, FeCoV and FeCoVNi alloys are represented by circles, squares and diamonds respectively; the open symbols represent the furnace cooled and/or the aged materials (i.e. the ordered condition) while the full symbols represent the quenched and/or the quenched and deformed samples (i.e. the disordered condition).The typical error was about 0.4% for sextet A and 1% for sextet B. The results show that, within the experimental error, the hyperfine field in both the single and the two sextets structures are independent of the ternary elements as well as their content. In all cases the disordered structures had comparatively higher H* and lower Hb than those for the ordered condition. The average values of H, presented in table 6.8, are shown in figure 6.23 by the discontinuous lines. The values observed here are in reasonable agreement with those found by other authors (see table 6.8). -110- Figure Figure ree (pn ybl) n dsree (ul ybl) s ucin of function as symbols) (full disordered and symbols) (open ordered h noim content. niobium the (6p/6T)/p(298) x 10 3.00 2.50 6.22- C (Sp/ST) /p2 9 e 3 determined at at determined 3e o -Ill- ibu cnet (at%) content niobium 1.0 ordered 0 298K ------disordered for FeCoNb alloys alloys FeCoNb for 0 2.0 ~------1------T 1 l ------1------t 2.8 KOe • sextet A E • • disordered ♦ ___ ■ ■ □ ordered ' i i Jo □ _ o 1 - Ocr 340 2.7 ___ 330 2.6 O sextet B ordered □ - □ - 320 1 ♦ disordered 2.5 — ■ ■ ______1 ____L _____l___ _L_ r ____r 1 2 3 4 5 6 ternary addition (at%) Figure 6.23 - Hyperfine field in FeCoNb (circles), FeCoV (squares) and FeCoVNi alloys (diamonds) for sextets A and B as function of the ternary content (Nb or V). The ordered and the disordered specimens are represented by open and full symbols respectively. 1------r 0.04 • • disord ered w ^ 0.03 • ♦ * E O □ □ i 0.02 O- -- -- ordered w o o J______I 2 3 4 5 ternary addition (at%) Figure 6.24 - Isomer shift of sextet A in FeCoNb (circles), FeCoV (squares) and FeCoVNi alloys (diamonds) as function of the ternary content (Nb or V). The ordered and the disordered specimens are represented by open and full symbols respectively. -112- 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 H* H. SOURCE/CON&Tv*^^ ( X 107 A/m) ( X 107 A/m) (mm/sec) PRESENT QUENCHED 2.76 ± 0.01 2.51 ± 0.03 0.033 ± 0.04 WORK FeCo(Nb/V) ANNEALED 2.71 + 0.01 2.57 + 0.03 0.020 + 0.03 Q + RAD 2.845 - - FINDIKY AND EYMERY-1985 QUENCHED 2.789 - - FeCo ANNEALED 2.716 - - QUENCHED 2.78 - 0.028 MAYO-1981 FeCo ANNEALED 2.71 - 0.013 QUENCHED 2.78 2.50 - ALEKSEYEV-77 FeCo2V ANNEALED 2.73 2.53 - QUENCHED 2.78 -- ALEKSEYEV-77 FeCo ANNEALED 2.74 - - MONTANO AND SEEHRA-1977 ANNEALED 2.71 - - FeCo DISORD? 2.82 - - JOHNSON-1961 FeCo ORD? 2.76 - - -113- i i ) HWHM For both sextet A (FeCoNb, FeCoV and FeCoVNi) and sextet B (FeCoV and FeCoVNi) the half width at half intensity of the Mbssbauer lines (HWHM) did not show significant dependence with the additional element or its content, although some differences were noticed for different thermo-mechanical treatments or sextet considered. The average values of the parameter are displayed in table 6.9 and the general features are: SEXTET A: Little difference between the values of HWHM of samples furnace cooled (FC) quenched (Q) and aged (A) with these three conditions having a value of approximately 0.130 mm/s. However the average value of the parameter for the material in the cold-worked condition is significantly higher (0.156 mm/s) than for the other conditions. SEXTET B: All the values of HWHM are greater than the observed in sextet A. The differences between the four conditions are greater than in sextet A although with higher standard deviations. The parameter increases in the order: CHWHM(A) < HWHM (FC) < HWHM (Q) < HWHM (CW)], but the difference between HWHM of the two ordered conditions (FC and A) was within the experimental error and .could be considered to have the same value of about 0.240 mm/s. i i i ) Isomer Shift (S) Figure 6.24 shows the isomer shift for sextet A (SA) of the FeCoNb, FeCoV and FeCoVNi alloys as function of the niobium or vanadium contents. The symbols are the same as those for figure 6.20. The values of S for sextet B were insignificant. The observed error was 15% for the ordered and 12 % for the disordered condition. The results show that the ordered structure has a lower than the disordered structure. This observation is in agreement with Mayo (1981) for FeCo although the absolute values differ as shown in table 6.8. In both the ordered and the disordered conditions the values of S, within the experimental error, are independent of the iern lry content. The average values of S*, presented in table 6.8 are represented in figure 6.24 by the discontinuous lines. -114- TABLE 6.9 Average HWHM (in mra/s) as function of thermo-mechanical treatment sextet A corresponds to FeCo(V/VNi/Nb) sextet B corresponds to FeCo(V/VNi) SEXTET A B CONDIT I0l3\^^ (mm/s) (mm/s) COLD WORKED (CW) .156 ± .011 .356 ± .017 DISORDERED (D) .132 ± .005 .301 ± .030 ORDERED (FC) .126 ± .005 .253 ± .031 AGED (A) .134 ± .006 .226 ± .035 -115- CHAPTER 7 DISCUSSION 7.1 A Statistical Analysis of the Site Population of Low Vanadium in Eguiatoaic FeCo Alloys Mossbauer spectroscopy of binary iron alloys containing a few percentage of the alloying addition has shown that vanadium produces additional sextets, with smaller hyperfine fields than that for iron, whereas cobalt and nickel only lead to some line broadening (Wertheim et al 1964, Vincze and Campbell 1973), or perhaps a minor shift (about + 2%) in the hyperfine field (Rubinstein et al-1966). Furthermore, only a well defined single sextet has been reported for equiatomic FeCo (Mayo 1981, Alekseyev et al 1977, Montano and Seehra 1977) and therefore, it is concluded that the two/three sextets observed in the FeCoV and FeCoVNi alloys studied in the present work are attributable to the presence of vanadium. This has been previously suggested in the literature (e.g Belozerskiy et al-1977, Alekseyev et al-1977) to explain the assymraetry observed in the Mossbauer spectrum of some FeCo based alloys with small additions of vanadium. The outer sextet of the spectra from FeCoV and FeCoVNi alloys in the disordered state, ie quenched or quenched and cold worked conditions, has higher values of the hyperfine field (HA) and isomer shift (SA) than in the ordered state, ie furnace cooled or aged conditions. However HA and SA are the same, within experimental error, for all the alloys for a given structural condition and also about the same as these parameters for the single sextet in the binary FeCo as observed by other authors (see table 6.8). This suggests that the outer sextet is associated with the Fe atoms with a vanadium free local environment. This is confirmed by the binomial statistical analysis for the random distribution of the V atoms in nearest neighbour or next nearest neighbour sites to the iron atom in a bcc lattice as follows: -116- Equation 7.1 gives the probability P(n,m) of finding n and m vanadium atoms respectively in the first and second coordination spheres of a given bcc solid solution containing atomic fractions C of vanadium atoms. P(n,m)= C(8! 6 1 ) ( 1 - 0 ‘4 *"-• C"** } / C(8-n>!(6-m)!n !m!] (7.1) In fact, even for the highest nominal vanadium content used here (6at%) the probability of a vanadium free environment in these two coordination spheres (14 atoms) is bigger than any other configuration involving the presence of vanadium, ie P(0,0) > P(n,m) for any n+m different from zero, and hence the observed intense outer sextet with identical Mossbauer parameters to those of FeCo is to be expected from FeCoV and FeCoVNi alloys. Figure 7.1 shows how the probability of vanadium atoms occupying the first and/or the second coordination spheres around the Fe atom in a bcc lattice changes with the vanadium content in solid solution. Curves PO, PI and P2 represent respectively the composed probability of zero, one or two vanadium atoms in any site of the first or second coordination spheres ie PO = P(0,0), PI = P(1,0) + P(0,1), P2 = P(2,0) + P(l, 1) + P(0,2). From a comparison of the relative areas of the inner sextets with the vanadium occupancy probabilities, it follows that sextet B is a consequence of a vanadium atom in a nearest (nn) or next nearest (nnn) neighbour site, and sextet C is associated with two vanadium atoms in these sites. The smaller hyperfine field and the movement of the isomer shift towards negative values for the inner sextet are consistent with the effect that vanadium has in binary FeV alloys (Wertheim et al 1964, Vincze and Campbell 1973). Moreover sextet B has larger HWHM than sextet A, indicating a greater number of different atomic configurations for sextet B compared with sextet A. This confirms the proposed model since sextet A involves only Fe and Co atoms while sextet B involves also one vanadium atoms in two possible configurations (nn or nnn). -117- CD in CD O CO c • M M 04 E 3 • MM " a 03 c 03 > O (%) Aimqeqojd F i gure 7.1 - Probability of a vanadium free (PO), one vanadium (Pi ) and two vanadium atoms t.P2) configurations in the firs t and second coordination spheres around the Fe site in a bcc structure of a FeCoV alloy with equiatomic Fe-Co composition, as runction o f the vanadium content in the matrix. -118- Clearly if the paramagnetic phase (T2) is vanadium rich, then the ferromagnetic phase (ocjor a!) of the matrix must contain less vanadium than the given by the composition of the alloy, as observed in the results from energy dispersive analysis (section 6.1.2). Therefore, as the volume fraction of any of the paramagnetic phases increases in a given alloy, there should be a concomitant increase in the area of sextet A and a decrease in the areas of the inner sextets which are associated with the vanadium atoms in the local environment of iron. This is indeed the case, as shown in figure 6.8. In all cases the longer is the heat treatment (in the sequence: disordered, ordered and aged conditions) the higher is the area corresponding to the paramagnetic phase and sextet A and the lower the areas of sextets B and C. Similar reasoning may be used to explain the vanadium dependence of the sextet areas. With increasing vanadium up to and including 3.6wt% (ie 4at%) the vanadium content of the matrix and the proportion of paramagnetic second phase both increase, hence the areas of sextet A decrease whereas all other areas increase (see fig.6.8). The particular heat treatment given to the FeCo5.4V alloy gave a significant volume fraction of vanadium rich second phase (T2 and martensite) so removing much of the vanadium from the matrix and increasing the area of sextet A. Thus, it has been shown that the presence of a paramagnetic phase may be detected from the changes in the ferromagnetic sextets associated with the reductions in the vanadium content of the matrix as well as from the occurrence of central peaks. Indeed it is possible to determine the vanadium content of the matrix from the data of figures 6.8 and 7.1. if it is assumed that the relative areas of the sextets are in the same proportions as the vanadium occupancy probabilities. The results of such an analysis are presented in table 7.1; The typical error for a given vanadium content determination was ± 0.3 at% and ± 0.6 atX for the 2 and 3 sextet analysis respectively. The results for the vanadium content of the matrix from the 2 and 3 sextets analyses are in good agreement with each other as well as with the semi quantitative micro analyses. For the quenched (Q), quenched and cold worked (CW) -119- TABLE 7.1 Vanadium content in solution in FeCoV alloys (in atX) as deduced from the comparison of figures 6.8 and 7.1. The abbreviations are: ift = quenched, CW = cold-worked, A = aged at 550°C for 24h and FC = furnace cooled. alloy condition 2 sextets 3 sextets (at%) (at%) Q. or Q + CW 1.3 — FeCol.5V4.5Ni A 0.0 — ft or Q + CW 1.8 — FeCo2V FC 1.8 — A 0.8 — ft or ft + CW 2.2 2. 1 FeCo3.6V FC 2.3 2.2 A 1.5 — ft or ft + CW 1.9 1.9 FeCo5.4V FC 1.8 1.8 A 0.9 — -120- and furnace cooled conditions (FC) the matrix composition is about 2 at% V for all the FeCoV alloys studied, but only about half the value for the aged state (A). Much lower vanadium contents were observed in the FeCoVNi alloy. Similar trends can be obtained from the extrapolation of the curves corresponding to FeCoV alloys in fig.6.9, as commented in the last chapter (section 6.1.2). 7.2 The Preferential Site for Vanadium in FeCo Alloys As discussed in chapter 4, the shift in the hyperfine field of the 57Fe nucleus (AH) produced by small amounts of vanadium added to pure iron has shown an oscillatory behaviour depending on the distance between the vanadium atom, treated as an impurity, and the resonant nucleus in a bcc structure (see fig* 4.7 after Stearns-1964). The major effect is produced when the solute atom occupies a site in the first or in the second coordination sphere (respectively AH~-8 to -9% and AH~-6 to-7% of H in pure Fe). The experimental conditions and the computer analysis carried out on the Mossbauer spectra of the present work did not resolve sets of peaks with very small shifts relative to each other. For this reason the effect of one vanadium atom in the first or second coordination spheres of the 57Fe atom in a FeCo matrix was taken as identical and the average effect of both configurations could be drawn from the resu1ts. Since in the disordered state both Fe and Co have the same probability of occupying any site, it can be assumed that the vanadium atom also can occupy any site. From this assumption, it can be concluded that sextet B in the disordered alloys was produced by a mixture of the two different configurations: i) Cn=l , m=03 and ii) tn=0 , m=l]. The average effect of both configurations corresponds to A H = Hfl - HB = -2.5 xlO4 A/m or a relative reduction of 9 % for the disordered state (see fig. 6.23). On the other hand the difference between the internal field of sextets A and B in the ordered state is AH =-1.4 x 104 A/m which corresponds to a relative reduction of only 5.3%. If the vanadium -121- atom did not have any preferential site in the ordered condition, the reduction AH = H* Hg in the hyperfine field of the ordered condition produced by 1 V atom should be the same as that for the disordered state, whereas the observed reduction for the ordered state is significantly smaller. Assuming the extension of the Stearns* observations to the alloys studied here, there is a strong indication that the vanadium atom in the ordered state occupies a site in the second coordination sphere of the resonant Fe nucleus. In the B2 structure (ordered state) this coordination sphere is occupied by Fe atoms and so it can be concluded that the vanadium atom occupies preferentially an Fe site. This conclusion is in agreement with the site preference for vanadium in FeCoV alloys, suggested by Mal’tsev et al (1975) from magnetic moment and transition temperature data of various binary systems. 7.3 Effects of Ternary Additions and Microstrugtural Changes to the Electrical Resistivity of FeCo based Alloys The solid lines in figures 7.2 to 7.5 show the electrical resistivity of respectively FeCo-xV, FeCo2V-yW, FeCo2V-yCu and FeCo-xNb in the furnace cooled and quenched conditions as function of the ternary (x) or quaternary (y) content. FeCoV Alloys: The value of the electrical resistivity at 77 K of quenched (from 850°C) FeCo2V was comparable to that obtained at the same temperature by Ashby (1975) in similarly quenched and cold-rolled (25% RA) FeCo2V and was about 25% above that reported by Chen (1962) for the resistivity at 4.2 K of FeCoV with the same nominal composition and quenched from 800*C. This discrepancy could be explained not only because of the difference in the measuring temperatures but also considering that the quenching from 850°C kept more vanadium atoms in solution, producing higher resistivity than the quenching from 800*C. As reported in the last chapter, the effect of cold-rolling does not affect significantly the electrical resistivity of this alloy. There is a significant discrepancy between the resistivity values of FeCo2V furnace cooled in the present investigation and that obtained by Ashby (1975). She reports -122- a value about 50% lower than that measured here for the same alloy under similar experimental conditions. Nevertheless the results for the electrical resistivity of all the different FeCo based alloys studied in the present investigation in both quenched and furnace cooled conditions are consistent as shown in figures 7.2 to 7.5. In addition the fact that p (ordered) > p (disorderd) observed here for almost all the FeCoV alloys is in agreement with Dinhut et al (1977); the same was not observed by Ashby. The nearly stabilized curves in figure 7.2 (except the point corresponding to 5.6 wt% (6 at%) V) can be interpreted as a consequence of the achievement of the solubility limit of vanadium in FeCo (around 2 at% in samples quenched from 850°C). This confirms the results discussed in the previous section of the present work. The marked drop in the electrical resistivity of cold-worked FeCol.5V4.5Ni after ageing for 24h at 650°C (see table 6.4) is also consistent with the results in the previous section, since the withdrawal of vanadium from the matrix solid solution on ageing reduces the resistivity towards the value observed for equiatomic FeCo. This also explains why that particular FeCoV based alloy has p (ordered) < p (disordered) i.e. aged (ordered) FeCol.5V4.5Ni has lower p not because of changes in the degree of order but principally because it contains less vanadium atoms in solution than the respective quenched material. The other exception to the usual trend (p (ordered) > p (disordered), for FeCoV based alloys was the FeCo5.4V alloy. This exception can be attributed most probably to the presence of a dual microstructure as discussed before. FeCoVW alloys: The addition of about 0.3 at% W to FeCo2V produces a drop of about 20% in the electrical resistivity of both quenched and furnace cooled materials. Above that W content the resistivity tends to stabilize or even increase slightly (see the solid lines in figure 7.3). This behaviour can be understood by proposing a simple dilution model, presented in equation 7.2, that gives the electrical resistivity of a quaternary FeCoxAyB alloy, with low atomic contents x and y of the elements A and B, as the combined effect that each element (A or B) has on altering the electronic structure of FeCo as -123- vanadium content (at%) Figure 7.2 - The electrical resistivity at 77K of ordered (open symbols) and disordered (full symbols) FeCoxV alloys as function of the vanadium content. The values for FeCo are those reported by Rossiter (1981) for the binary alloy in similar experimental conditions. The resistivity values at 77K for the FeCol.5V4.5Ni alloy disordered (i.e. quenched -Q -) and ordered (i.e. aged at 650°C for 24 hours -A-) are also plotted. -124- tungsten content (at%) Figure 7.3 - The electrical resistivity at 77K of FeCo2VyW alloys in the ordered (open symbols) and in the disordered (full symbols) conditions, as function of the W content. The broken lines correspond to theoretical values calculated by using equation 7.2. The curve for FeCoyW is that reported by Bozorth (196a-) -see fig. 3.5- normalized for the temperature employed in the present case. -125- a donor , acceptor or neutral atom. Such a model does not consider the mutual interactions between the minor elements and is given by the weighted average of the contributions of these elements to the resistivity of the binary alloy as follows: ^(FeCoxAyB) = CxjXFeCoxA) + yp(FeCoyB) ]/( x+y) or p(FeCoxAyB)=p(FeCo) + (x2 C SjXFeCoxA)/£x] + y2 [ £p (FeCoyB)/£y 3} / (x+y) (eq. 7.2) where J>(FeCo), £j>(FeCoxA)/dx and £J> (FeCoyB)/£y are respectively the electrical resistivity of the binary alloy and its differential increments due to small additions of the elements A and B. The dotted lines in figure 7.3 show the result of the application of this model to ordered and disordered FeCoxVyW, using x = constant = 2.2 at % V and y = variable up to 0.3 at% W, above which it was kept constant due to the achievement of the maximum solubility of W in the matrix of the alloy, as proposed by Orrock (1986). It can be seen that the model correctly shows the fall in resistivity with the addition of up to 0.3 at% W and also predicts that the parameter should remain constant whereas a slight increase is experimentally observed. The small increment in p(FeCoxVyW) for y > 0.3 at% W as well as the drop in p(FeCoyW) in the same composition range (see figure 3.5 after Bozorth-1964) could be due to a common cause. One possibility is a slight drop in the W content in solid solution for nominal compositions greater than the limit of 0.3 atX. Also the model does not take into account the effect of second phase particles per se. FeCoVCu alloys: The increasing addition of Cu to FeCo2V produces a steady drop in the electrical resistivity of both ordered and disordered alloys (see the solid line in figure 7.4). This can be understood considering the dilution model proposed above, together with the fact that copper has a completelly full d-shell and so does not change significantly the electrical resistivity of FeCo as confirmed -126- in the present work for FeCo3Cu. The dotted lines in figure 7.4 are the result of the application of equation 7.2 to this alloy system, considering x=constant=2.2 at% V and the total solubility of Cu in FeCo2V up to 4.5 at* (i.e. y = variable between 0 and 4.5 atX Cu). The clear difference between experimental and theoretical curves in fig.7.4 can be explained if one assumes that Cu has a limited solubility in FeCo2V which increases slightly with increasing addition of the element to the system. This is in good agreement with Orrock (198B) who observed the presence of Cu-rich precipitates in specimens with quaternary contents as low as 0.9 at* as well as an expanding lattice parameter, associated with increasing solubility of Cu in the matrix, with further addition of the element to FeCo2V. According to the proposed resistivity model the content of copper in solid solution in furnace-cooled FeCo2.2VyCu might be about 0.15, 0.23 and 0.45 atX for nominal compositions of respectively 0.9, 2.7 and 4.5 at% Cu and the predicted quaternary content in the respective matrixes of quenched specimens might be a little higher (about 0.15, 0.32 and 0.63 at % Cu respectively). FeCoNb alloys: The nearly stable curves of the electrical resistivity of FeCoNb alloys at 77K as function of the ternary content (fig.7.5) is a consequence of the saturation of niobium in solid solution due to a solubility limit of the element in FeCo below 0.6 at% Nb (1 wt*). This fact is also confirmed by the presence of niobium-rich precipitates in FeColwtXNb (see fig. 6.5) as well as by the stabilization of the lattice parameter of FeCoNb alloys in the same range of composition (see fig. 6.21). Figure 6.9 obtained from the Mossbauer spectra of this material indicates a solubility limit of about 0.3 at% Nb. Using this limit and that resistivity data, it is possible to estimate an increment of about 7 pQcm/at% in the resistivity of FeCoNb. Such an increment, like the reported by Chen (1962) for Ti, V, and Cr, is between one and two orders of magnitude greater than the increments produced by the addition of Cu, Ni and Mn to FeCo. -127- Figure 7.4 - The electrical resistivity at 77K of FeCo2VyCu alloys in the ordered (open symbols) and in the disordered (full symbols) conditions, as function of the Cu content. The broken lines correspond to theoretical values calculated by using equation 7.2 and assuming the total solubility of copper in FeCo up to about 4.5 at% Cu. The curves for FeCoyCu were based in the data from FeCo3wt%Cu at 77K measured in the present work and that reported by Rossiter (1981) for FeCo at the same temperature. -128- niobium content (at%) Figure 7.5 - The electrical resistivity at 77K in ordered (open symbols) and disordered (full symbols) FeCoxNb alloys as function of the ternary content. The values for FeCo are those reported by Rossiter (1981) for the alloy in similar experimental conditions. -129- 7.4 Microstructure and the Electrical Resistivity of FeColNb 7.A.1 Preliainary Comments Since the electrical resistivity of a material depends on the degree of order (S) and the temperature (T), the. parabolic dependence of the resistivity of FeCoiNb as function of temperature observed in the present work in the range 77-373K, and also in equiatomic FeCo (e.g. Rossiter-1981; Seehra and Si 1 insky-1976), could be interpreted by considering S as a variable dependent on the test temperature. In the present case, however, the range of temperature for the resistivity measurements was low enough to keep the atomic order unchanged and thus S is taken as a specimen’s constant, independent of the temperature of the resistivity tests. In these circumstances, the dependence of p on T2 in equation 6.2 is not related to changes in S, but most probably, to the typical temperature dependence of the electrical resistivity exhibited in ferromagnetic transition metals (such as Fe and Co) that can be associated with interactions between the conduction s-electrons and localized d-eiectrons with varying degree of spin order. In fact, in other typical situations of s-d interactions, such as that observed by Potter (1937) for the electrical resistivity of pure Ni the data fit very well the second order polinomial presented in equation 6.2 (chi-square = 9 x 10'4). On the other hand, equation 3.1 proposed by Rossiter, gives the resistivity p(S,T) for a normal metal below the Debye temperature, where a linear dependence with temperature is expected, and consequently, equation 3.1 does not completely express the relationship between the two variables S and T i.e. , in the present case equation 3.1 must be replaced by an expression, containing the T2 component if it is to satisfy the experimental results such as that shown in figure 6.17. A simple expression that satisfies our experimental data may be obtained by the addition of a T2 component to equation 3.1. It follows from tables 6.5 and 6.6 that the derivative £2f>/ST2 = 2 D(298) Aa (see equation 6.2) is not constant e.g. at low -130- temperatures it decreases with increasing S; a similar trend is shown at high temperatures (690-730°C). Provided in these regions ordering, rather than other microstructural changes is dominant, it is reasonable to assume that the complementary quadratic term for equation 3.1 is S dependent and decreases with increasing order. Another important feature to be considered is the fact that £j>/£T is proportional to the inverse of the effective number of conduction electrons (Neff) as mentioned in section 3.1.1. This parameter is band-structure dependent and can be changed by atomic ordering or by other phenomena such as changes in the solute content of the matrix as a consequence of a precipitation process. Since in the low end of ageing temperature precipitation effects should be insignificant, the only reason for the changing of Neff is associated with the ordering; hence a reasonable coincidence between the experimental £j»/£T and the theoretical £^(S,T)/£T from the expression that replaces equation 3.1 is expected for specimens aged at low temperatures. The problem in determining a general equation for p as a function of S and T depends not only on considerations such as those previously mentioned, but also on the accuracy of the experimental data. In this context, the experimental errors in p and S are the main source of inaccuracy for the intended function, not only with respect to the numerical values of its constants but also to its analytical expression. After the equation is determined and its constants calculated, it is important to remember that the constants are function of a specific state of the material and any change (other than in S and T) can be responsible for alterations in their values. Thus, the terminology "reference sample or material" employed in the present work is applied to the specific condition of the material for which the referred constants have been calculated. 7.4.2 A New Empirical Function p(S,T) Considering the features described in the last section, it was possible to find a number of functions that could approximately satisfy the suggested conditions. However, the best f it corresponded -131- to the following equation: p(S,T) = Cpo <0)(1-S2) + The new constant C as well as the former ones from equation 3.1 were determined in each specific condition of the material and, as mentioned before, may alter if the material undergoes an additional transformation (e.g. precipitation). For this reason, the relationship between resistivity and microstructure of FeColNb in groups 1 and 2 will be discussed separately. 7.4.3 A new Parameter S* The long range order parameter S can be successfully obtained from changes in the lattice parameter (e.g. Clegg - 1971; Orrock - 198B) by using expression 7.4: S = Ca0 - a0 (DIS)] / Ca0(ORD) - a0(DIS)] (7.4) The values a0 ,a0(DIS) and a0(ORD) are the lattice parameters of the material in the states aged, disordered and ordered respectively. Nevertheless, if a precipitation process takes place during the ordering, the changes in lattice parameter will include effects due to both transformations and in these circumstances equation 7.4 will not yield the LRO parameter. This is exemplified by the lattice parameter of FeColNb in group 1 (ie. quenched + aged) which increases at low temperatures and decreases after 550*C (see fig. 6. 12). The initial increase can be interpreted to be due to ordering and the LRO parameter S calculated using eq. 7.4 is consistent with the values obtained from superlattice measurements up to 550*C inclusive (compare figs. 6.12 and 6.10-curve B). The calculated lattice parameter that the material should have if it was possible to produce a fully ordered specimen (S=l) with no precipitation is a0=2.8601 % (see the discontinuous line in fig. 6.12). The change in a0 above 550°C is related to both ordering, that tends to increase a0 , and the outweighing precipitation effect, that tends to decrease a0, as discussed below: -1 3 2 - According to Vegard’s law, the lattice parameter (a0) of a primary solid solution varies nearly linearly with the atomic concentration (c) of a substitutional solute element: a<> (c) = a0 (0) + kc (7.5) where a<> (0) is the solute-free lattice parameter of the solvent and k is a positive constant for solute atoms bigger than the solvent. Differentiating 7.5 gives: Aa0(c) : kAc (7.6) Assuming the validity of Vegard’s law for the matrix as changes of composition occur due to the precipitation process, one can relate the lattice parameter Ca0(a)] after the precipitation process has taken place to its value before the process Ca0(b)] using: a0 (a) = a0 (b) + kAc (7.7) where A c is the change in the solute concentration of the matrix due to precipitation. In the present case the atomic radii of Fe, Co and Nb are respectively 1.24, 1.26 and 1.42 %. that makes k > 0. This means that the withdrawal of Nb out of solution, due to precipitation, reduces a0 as observed in figure 6.12. The misuse of equation 7.4 by employing the lattice parameter a0 (a) after a precipitation process produces the parameter S’ : S’ = La0(a) - a0(DIS)] / C(a0(ORD) - a0(DIS)] (7.8) Using the expression (7.7) into (7.8) gives: S’ = tCa0(b) + kAc] - a0(DIS)} / Ca«(ORD) - a0(DIS) (7.9) but Ca0(b) - a0(DIS)3 / (a0(ORD) - a0(DIS) = S and equation 8.9 can be rewritten: S’ = S + K, Ac (7.10) where Ki = k /ta 0(ORD) - a0(D!S)]. Thus, the parameter S’ contains information on the ordering as well as on the deviation of the matrix composition due to precipitation. -1 3 3 - Substituting S from equation 7.10 CS=S’- Kt Ac J into equation 7.3 leads to an expression for p as a function of S’ ,T and Ac that could be separated in two components Q(S’ ,T) and §(Ac,T). Assuming the similarity between functions Q and (> leads to: