Thermal conductivity in A3B intermetallic compounds based on iron and nickel

Intermetallics 4 (1996)

!If

S41-S47

o 1996 Elsevier Science Limited 50966-9795(96)00004-0

Printed in Great Britain. All rightsreserved 0966-979S1961S I5.00

ELSEVIER

Thermal conductivity in A 3B intermetallic compounds based on iron and nickel Shuichi Hanai, Yoshihiro Terada, Kenji Ohkubo, Tetsuo Mohri* & Tomoo Suzuki Division of Materials Science and Engineering, Graduate Schoolof Engineering, Hokkaido University, Kita-ku, Sapporo 060, Japan (Received 17 October 1995; accepted 30 October 1995)

Thermal conductivity of AlB intermetallic compounds, where A denotes iron or nickel and B denotes group IIIb or IVb elements, is investigated by a laser-flash method. Among six kinds of Ll 2 compounds, the largest thermal conductivity observed is 32·8 W m' K-1 of Ni.Ga, In FejGa and Fe3Ge. three polymorphs, i.e. Ll 2, 00 19 and DO). can be achieved by performing a suitable heat treatment. Thermal conductivity of the 00 19 phase is quite close to that of the Ll 2 phase, while the 00 3 phase shows smaller values. In most A)B compounds, the measured thermal conductivities tend to decrease as the position of constituent B becomes horizontally more distant from that of constituent A in the periodic table. Copyright © 1996 Elsevier Science Ltd

Key words: A. miscellaneous intermetallics, B. thermal properties.

1 INTRODUCTION

explore the thermal conductivities of a series of A3B compounds. The aim of the present work is twofold. One is to investigate the thermal conductivities in A 3B intermetallic compounds as a function of composition and to systematize them from the viewpoint of the periodic table. The other is to clarify the correlation between crystal structure and thermal conductivities in A3B intermetallic compounds which have mostly Ll 2 ('Y'), DO I9(f') and/or D03(13' ) structures, being the superlattice of face-centred cubic (fcc), hexagonal close packing (hcp) and body-centred cubic (bee), respectively.

Ordered intermetallic compounds have long been of interest as potential structural materials for use at elevated temperatures.P Despite their brittleness at low temperatures, they provide an ideal basis for further development as high-temperature structural rnaterials"? This is due to the combination of high melting temperature, low density and excellent corrosion resistance at elevated temperatures. For high-temperature structural application of intermetallics, much attention has been paid to mechanical, chemical and thermodynamic properties.6--9 To date, very little attention has been paid to the physical properties of intermetallic compounds. IO•11 It is obvious that high thermal conductivity pushes the operating temperature of structural materials to higher temperatures because of the good cooling ability. However, the thermal conductivities of intermetallic compounds have not been well characterized. Only B2 aluminides and titanides were surveyed in our previous studies. 12•13 In view of the great amount of attention attracted by A 3B compounds with L1 2 structurel 4-21 such as Ni3AI, it is deemed necessary to

2 EXPERIMENTAL

"To Whom correspondence should be addressed.

S4l

The intermetallic compounds employed in this study are listed in Table I. Four kinds of ironbased A3B compounds and six kinds of nickelbased compounds were selected, where A denotes iron or nickel and B denotes AI, Si, Ga or Ge in iron-based compounds and AI, Si, Ga, Ge, In or Sn in nickel-based compounds. Among these six group b elements, AI, Ga and In belong to group Illb in the periodic table, and the others are group IVb elements. In the iron-based compounds, both Fe3Ga and Fe3Ge can form three kinds of crystal structures, L1 2, DO ,9 and D03, while Fe3AI and

S. H ana; et al.

S42

Table 1. AJB Intermetallic compounds used in this study. Crystal structure, homogeneity range of B element and final heat treatment are also shown for each compound, combined with the thermal conductivity data at stoichiometry. Data within parentheses are extrapolated values at stoichiometry A]B

compound Fe]AI Fe]Ga Fe]Ga Fe]Ga Fe]Si FejGe FejGe Fe]Ge Ni]AI Ni]Ga Ni]ln NijSi NijSi Ni]Ge Ni]Sn Ni]Sn

Crystal structure

Symbol

Homogeneity range of B element (at%)

Final heat treatment (K, ks)

Thermal conductivity at stoichiometry (W m' K-1)

DO]

f!

23-34 26·2-29·2 26·0-29·0 23·2-25·9 10-30 23·7-25·7 23·7-25·7 15·2-21·0 24·0-27·0 22·6-30·0 24·5-25·5 22·8-24·5 24·5-25·5 22·5-25·0 24·0-26·1 23·2-27·2

773. 605 853. 605 913, 432 933, 432 1223, 86·4 873, 605 1173, 86·4 873, 605 1173, 86·4 1173, 86·4 973, 259 1173, 86·4 1373, 3-6 1173. 86·4 1173, 86·4 1323, 86·4

14·0 (22·0) (22·0) 15·2 11 ·2 15·2 15·2 (13·9) 28·2 32·8 16·7 (20·4) J3.1 24·6 47·4 35·3

LI 2

DO l9 DO]

DO]

LI 2

DO l9 DO j

LI, L1;

DO l9

LI 2

DOc

L1 2

DO l9 DO]

y' €

f! f!

y' €

f!

y' y' €

y'

1* y' €

fJ

FejSi are characterized as a unique structure, DO). of thermal conductivity, the density of each comIn the nickel-based compounds, Ni)AI, Ni)Si, pound is required. This was calculated from lattice parameter data. 22- 24 Ni3Ga and NiJGe form only L1 2 structure, whereas DO l9 and D03 are formed by NijSn and DO l9 by Ni3In. A)B intermetallic compounds were produced 3 RESULTS with raw materials of high purity better (>99·9 mass%) by arc-melting on a water-cooled copper 3.1 Thermal conductivity of L1 2-type compounds hearth under an atmosphere of purified argon. Each button was inverted and remelted at least The compositional dependence of the thermal five times in order to ensure homogeneity. The conductivity at room temperature of Llj-type weight loss after melting was confirmed to be <0·1 • gallides and germanides, i.e. Fe3Ga, Fe.Ge, NijGa mass%. All the alloy buttons were further homogand Ni3Ge, is shown in Fig. I. Data for the enized in evacuated Pyrex tubes at 1173 K for Ga-poor side in Fe3Ga and for the Ge-rich side in 86-4 ks and then water-quenched. In some speciNi3Ge cannot be obtained because the y'-singlemens, an annealing treatment was successively I LIz-type carried out to promote ordering at about 50 K ~ below their respective critical temperatures. The I final heat treatments for each A 3B compound s employed in this study are summarized in Table I ~ together with the crystal structure and homogene-e ity range of the B element. ~ A disc specimen with 10 mm diameter and 2 '> '';: mm thickness was electrically discharge-machined ::J "C from the ingot and ground to final size. Care was c:: 0 o taken to remove the surface damage induced by Cd the preceding machining step. Thermal conductivity e v measurements were performed at room tempera...c: E-o ture by a laser-flash method using an ULVAC °20 25 30 TC-7000. Details of the mechanism in the measurement have been described elsewhere. 12 The Ga, Ge concentration, x] at% accuracy of thermal conductivity in this method Fig. 1. Thermal conductivity of NijGa, Ni3Ge, Fe3Ga and was confirmed by using pure metals and some FejGe with L lrtype crystal structure as a function of Ga and Ge concentration at room temperature. conventional alloys, In order to derive the value

_ 50,......------r-----...,

-

(,l

. .

-

S43

Thermalconductivity in AJB intermetallic compoundsbasedon Fe and Ni

phase field is limited to one side of stoichiometry for each alloy system." In order to estimate the thermal conductivity at stoichiometry, extrapolations were attempted by straight lines from both sides of stoichiometry on a linear scale of ordinate as shown in Fig. 1. It can be seen that the thermal conductivity takes a maximum value at stoichiometry and decreases with the deviation from it. The thermal conductivity at stoichiometry in Ni3Ga extrapolated from the Ga-rich side is in good agreement with that extrapolated from the Ga-poor side. For Fe3Ge having lower thermal conductivity, these characteristics cannot be clearly observed, which may be due to the fact that the l' single-phase field is rather confined in the vicinity of stoichiometry. In Fe3Ga, the ')I'-single-phase cannot be achieved at stoichiometry but the thermal conductivity at stoichiometry is obtainable by the extrapolation of data from off-stoichiometry. The magnitudes of the thermal conductivity Aestimated for stoichiometry are in the following order: A[Ni 3Ga]y' > A[Ni 3Ge]y' > A[ Fe3Ga]y' > A[ Fe3Ge]y ' (I) It is realized that the thermal conductivity of the gallide is larger than that of the germanide for a given element A in A3B compounds; and that the thermal conductivities of the nickel compounds are larger than those of the iron compounds. The values of thermal conductivity are summarized in Table I. Figure 2 shows the variation in thermal conductivity with composition for the Ll -type aluminide _

50

I

A[Ni 3Ga]y' > A[NilAI]y' > A[NilGe]y' > A[NilSi]y'

3.2 Thermal conductivity and crystal structure Figure 3 shows the thermal conductivities at room temperature of FejGa with DO l9 and 001 structures. For both structures, the extrapolation is

!

I

Fe3Ga

solid:Williams I-

-

I-

-

I-

o :D 0 19 6 :D0 3

I

I-

/~

~'Si

~~ of.o/J A"6

I-

I

-

I

!

30

25

AI,

Si concentration,

x] at%

Fig. 2. Thermal conductivity of Ni3AI and Ni3Si with Llj-type crystal structure as a function of AI and Si concentration at room temperature. along with the results for Ni 3AI obtained by Williams et 01. 26 The result for NilSi with distorted DOc structure is also shown.

-

-

Lr~

0

~NbSi(DOc)

-

I

I

l-

(2)

It is noted that gallium and aluminium belong to group IIIb in the periodic table, while silicon and germanium belong to group IVb. The thermal conductivities of NilAI and Ni-Si at stoichiometry are also listed in Table 1.

50

Liz-type

~

and silicide, NilAI and NijSi. In NilAI, the thermal conductivity reaches a maximum at stoichiometry and decreases with the deviation from stoichiometry, showing the general trend demonstrated in Fig. I. The values of thermal conductivity for NilAI found in the present study are similar to those reported by Williams et al.,26 denoted by solid circles at 24 and 25 at% aluminium. In the Ni-Si alloy system, the l' single-phase field is limited only to the Si-poor side" in which the behaviour is quite similar to that of NiJAl. The thermal conductivity at stoichiometry for Ni1Si having a distorted DOc structure, which is metastable below 1263 K,27.28 has been measured at room temperature and is shown also in Fig. 2. The obtained value is 13·1 W m:' K-1, which is smaller than 20·4 W m' K-1 of the L1 2 structure. For the four kinds of nickel-based L1 2 compounds, the thermal conductivity A at stoichiometry is in the following order:

~ ...,0;

.

+.~ I

0

I

25 Ga concentration,

q1

_

30

xl at%

Fig. 3. Thermal conductivity of Fe)Ga with Ll2"' 00 19 " and D03"type crystal structures as a function of Ga concentration at room temperature. The thermal conductivity of the cornpound with L12 structure is shown by a thick line, which is presented in Fig. I.

544

S. Hanaiet al.

indicated by a thin line. The data for the Ll 2 structure ('Y') shown in Fig. 1 is also reproduced as a thick line. Note that the E and 'Y' single-phase fields are restricted only to the Ga-rich side. All the thermal conductivity data for the DO l9 structure fall well on the thick line. This implies that the thermal conductivities of the DO l9 structure and the L12 structure are intrinsically quite similar. On the contrary, the thermal conductivity of the DO) phase at stoichiometry extrapolated from off-stoichiometry is smaller than those of Ll 2 and DO l9 structures. Thus, the magnitudes of the thermal conductivities at stoichiometry in Fe.Ga are summarized by the following relations: (3)

and

A[A)B]y . > A[A)B]w

(4)

Figure 4 shows the compositional dependence of the thermal conductivity of FejGe with DO J9 and DO] structures. Data relating to the Ll 2 structure are indicated by the thick line. The thermal conductivities for the DO l 9 structure, indicated by open circles, fall well on the thick line. Therefore, it is again suggested that the thermal conductivities of the DO l9 and Ll 2 structures are quite close to each other. The thermal conductivity at stoichiometry for the DO) structure (/3') cannot be strictly estimated by extrapolation. The open triangle within parentheses in Fig. 4 indicates the average value of four data in the compositional ....

50

I

Fe3Ge o :D019

I

....~

I

6 :D03

I

I

S

I

~

I

I

-W,'* I

I-

b.) l-

,

I

25 Ge concentration, x] at%

-

range between 16 and 21 at% Ge, where 11 single phase is stabilized. No increasing or decreasing trend with deviation from stoichiometry was detected. The inequality (4) can be also observed in Fe.Ge, Figure 5 shows the thermal conductivities of NijSn with DO J9 and D03 structures and that of Ni 3In with D019 structure. In Ni 3Sn, the slope is greater at the Sn-poor side of stoichiometry than at the Sn-rich side for both structures. The inequality (4) is more clearly obeyed for Ni.Sn. Values of the thermal conductivity at stoichiometry of Fe3Ga and FejGe with L12, DO l9 and D03 crystal structures, Ni 3Sn with DO l 9 and D03 and Ni 3In with DO l9 are summarized in Table 1. We attempt to visualize all the measured thermal conductivities in the periodic table as shown in Fig. 6. The bars drawn by thick lines indicate the thermal conductivity with Ll 2 and DO l9 crystal structures, whereas those drawn by a thin line show the bee derivative (D03) . In the next section, the magnitude of thermal conductivities in A 3B compounds is discussed in connection with the position of constituent elements A and B in the periodic table. Also, the effect of crystal structure on thermal conductivity is discussed.

4 DISCUSSION 4.1 Thermal conductivity and periodic table 4.1.1 Position ofconstituent A The L 12 crystal structure can be achieved in gallides (A]Ga) and germanides (A3Ge), when the .. I

l

r---------r------,

....~ I S

~

-e

-

50

~ 'S:

.~

o

:::I -0

c::

-

( i <,

-

6·1

0 u

«!

S ..

-= E-<

/

l-

Q)

30

Fig. 4. Thermal conductivity of FejGe with L12- , 0° 19 - and DOl-type crystal structures as a function of Ge concentration at room temperature. ~) is the average value of four data with DO) structure in the compositional range between 16 and 21 at% Ge. The thermal conductivity of the compound with L12 structure is shown by a thick line, which is presented in Fig. 1.

00"

0 20

I

I

-

NbIn(D0 19 )

-

!.

25

30

In, Sn concentration, x] at% Fig. 5. Thermal conductivity of Ni)Sn with DOI9 - and 00)type crystal structures as a function of Sn concentration at room temperature. Data for Nijln at stoichiometry with 00 19 structure are also shown.

Thermal conductivity in AlB intermetallic compounds basedon Fe and Ni

I

~I

'"

Fig. 6. Part of the periodic table to show the thermal conductivity in Fe3B and NiJB intermetallic compounds. The th ick line shows the thermal conductivity with L12 and DDI9 crystal structures. and the thin line shows the data for the bee deri vati ve (DO»).

constituent A is iron and nickel. In the case of gallides (A 3Ga), the thermal conductivity of the iron compound is smaller than that of the nickelbased one, i.e. A[Fe3Ga)". < A[Ni 3Ga)"-, This trend also holds true in the case of germanides. Therefore, in A3B compounds, the thermal conductivity of nickel compounds (Ni]B) is larger than that of iron -based ones (Fe 3B) for a fixed constituent B of gallium or germanium. In a previous paper, thermal conductivity data of B2 aluminides, gallides and titanides were presented." The magnitude of the measured thermal conductivities are in the following order: A[FeAI]A[CoTi]>A[NiTi]. The thermal conductivity of the iron compound is the largest of the three at a host constituent of Ti, which belongs to group IVa.

4.1.2 Position ofconstituent B in horizontal direction As mentioned previously, an iron compound (Fe 3B) can form L1 2 structure when the constituent B is Ga and Ge. DO] structure is also achieved when B is AI, Si, Ga and Ge. For the Fe 3B compounds with Ll 2 structure, the thermal conductivity of Fe3Ga is larger than that of Fe3Ge as indicated in cqn (I), i.e. A[Fe 3Ga)y.>A[Fe]Ge].y..

545

This trend is also true for DO] structure: A[Fe3Ga],B.>A[Fe3Ge],B., although the difference is less significant. For the third period elements AI and Si, the thermal conductivity of Fe3AI with DO] structure presents a larger value than Fe.Si. This tendency becomes more prominent when the iron is replaced with nickel, as is demonstrated in Fig. 6. By summarizing these results together with those in the previous section, an empirical rule can be established in A 3B intermetallic compounds that the thermal conductivity decreases as the position of constituent B becomes horizontally more distant from that of constituent A in the periodic table. It is recalled that this rule also holds for B2 aluminides, gallides and titanides." The thermal conductivity of Ni 3B shows rather exceptional behaviour when the constituent B belongs to the fifth period in the periodic table. For DO ,9 structure, the thermal conductivity of Ni 3In is smaller than that of Ni.Sn: A[Ni 3In](.A[Ni](AI,Ge))Y .. We report more details of the effect of ternary addition on thermal conductivity in Ni 3AI in a future publication." 4.}.3 Position ofconstituentB in vertical direction In order to clarify the dependence of the thermal conductivity on the position of constituent B in a fixed group of the periodic table, it is desirable to maintain the same crystal structure. However, the dependence of the thermal conductivity on the structural difference between DOl9 and Ll 2 structures is expected to be negligible, as will be discussed in the next section. Therefore, it may be reasonable for nickel-based compounds to compare the thermal conductivities of Ni 3In and Ni.Sn having D0 19 structure with those of Ni 3Al, Ni]Si, Ni 3Ga and Ni]Ge having L1 2 structure. The thermal conductivity increases when the position of constituent B goes down the periodic table in a fixed group (column). For example, for group IVb: A[Ni]Si)".
546

S. H ana; et al.

compounds, the comparisons are made for four compounds soley with 00 19 structure. It is confirmed that the thermal conductivity increases as the position of constituent B goes down in a fixed group in the periodic table: A[Fe3Al]p.
4.2 Effect of crystal structure Among the three kinds of crystal structure mentioned in this study, L1 2 and 00 19 structures are geometrically close-packed phases (GCP) with a coordination number of twelve." The 003 phase, which is not a GCP phase, has the lowest density among the three. It is recalled that, for both Fe3Ga and Fe3Ge, there exists no significant difference in thermal conductivities between 00 19 structure and L12 structure, whereas the 003 structures show smaller values, as indicated in eqns (3) and (4). The implication of these results is briefly discussed as follows. Electrical resistivity data have been reported for Ni3Al,26.31.32 Ni3Fe,33,34 Ni3Mn35.36 and CU3Au37--45 with L1 2 structure and for Fe3Al,46--48 Fe3Ga49 and Fe3Si5o.5t with 003 structure. By combining these data with thermal conductivity data obtained in the present study, it is recognised that the Wiedemann-Franz law holds in the A 3B compounds at room temperature as well as in pure metal elements and B2 compounds." This indicates that the dominant carrier of thermal conduction is electrons rather than phonons in the A3B intermetallic compounds. Thermal conductivity Aet carried by electrons is written as: (5)

where n is the electron concentration, k Boltzmann's constant, T absolute temperature, rn the mass of the electron and T}. is a relaxation time of electron collision. 52-54 The parameters nand TA vary from one crystal structure to another and the present results imply that the products of nand TA are nearly equal for L1 2 and 0019 structures, and that the transition to 003 decreases the magnitude. More detailed mechanisms of the change of these values induced by the transformation still remain to be clarified.

5 CONCLUSIONS Thermal conductivity of A 3B intermetallic compounds based on iron and nickel, having L1 r , 00)9" and 003-type crystal structures, was investigated at room temperature using a laser-flash method. The results are summarized as follows. (1) Thermal conductivity takes a maximum at stoi-

chiometry and decreases with the deviation from stoichiometry, irrespective of the crystal structure. At stoichiometry, Ni3Ga has the highest thermal conductivity of 32·8 W m' K-1 among six kinds of Ll--type compounds and Ni3Sn has the highest thermal conductivity of 47·4 and 35·3 W m' K-1 among four kinds of 00 19 compounds and five kinds of 003 compounds, respectively. (2) Thermal conductivity of A 3B compounds decreases as the position of constituent B becomes horizontally more distant from that of constituent A in the periodic table. This is the rule observed also in B2-type aluminides, galtides and titanides. The exception, however, is found for Ni3In and Ni3Sn with 00 19 structure. (3) Thermal conductivity of A3B compounds becomes higher as the position of constituent B goes down the periodic table at a fixed constituent A. Again, an exception is found for Ni3In with 00 19 structure. (4) Based on the thermal conductivity data in Fe3Ga, FeJGe and Ni3Sn, the following relations are concluded. Thermal conductivities with 00 19 structure are quite close to those with L1 2 structure: A[A 3B]t.=A[A 3B]Y., while a 003 compound has a smaller thermal conductivity than an L1 2 compound: A[A 3B]p'
Thermalconductivity in AJB intermetallic compounds basedon Fe and Ni 3. Kumar. K. S.• Mannan, S. K. & Wiswanadham, R. K..

Acta Metall. Mater., 40 (1992) 1201. 4. Barinov, S. M. & Evdokimov, V. Y.• Acta Metall. Mater.• 4J (1993) 801. 5. Stoloff, N. S., Metall. Trans. A. 24A (1993) 561. 6. Desai. P. D., J. Phys. Chern. Ref Data, J6 (1987) 109. 7. Darolia, R., J. Metals. 43 (1991) 44. 8. Xu, Y. & Schulson, E. M., Acta Metall. Mater .• 43 (1995) 2121. 9. Ito. O . & Tamaki, H., Acta Metall. Mater ., 43 (1995) 2731. 10. Rossiter. P. L. & Bykovec, B., Phil. Mag. B. 38 (1978) 555. II. Shirai. Y., Masaki. K .• Inoue , T .• Nishitani, S. R. & Yamaguchi, M., Intermetallics, 3 (1995) 381. 12. Terada, Y., Ohkubo, K., Nakagawa. K.• Mohri, T. & Suzuki, T., Intermetallics, 3 (1995) 347. 13. Terada, Y., Mohri, T. & Suzuki. T., in High Temperature Ordered Intermetallic Alloys 6, Mater. Res. Soc. Symp. Proc., 364 (1995) 201. 14. Guard, R. W. & Westbrook, 1. H., Trans. TMS-AIME, 2J5. (1959) 807. 15. Aoki, K. & Izumi, 0., J. Jpn Inst. Met .•39 (1975) 1282. 16. Rawlings , R. D. & Staton-Bevan. A. E.• 1. Mater. Sci ., 10 (1975) 505. 17. Suzuki, T.. Oya, Y. & Ochiai, S., Metall. Trans. A, 15A (1984) 173. 18. Matuszyk , W., Camus, G .• Duquette. D. J. & Stoloff, N. S., Metall. Trans. A. 21A (\990) 2967. 19. Hemker, K. 1.. Mills. M. J. & Nix. W. D .. Acta Metall. Mater., 39 (1991) 1901. 20. Suzuki, T.. Mishima, Y. & Miura, S.• Mater. Sci. Eng. A. A146 (1991) 245. 21. Rong, T. S., Jones. I. P. & Smallman. R. E.• Acta Metall. Mater., 43 (\995) 3085. 22. Pearson, W. B.• ed., A Handbook of Lattice Spacing and Structures of Metals and Alloys. Pergamon Press. London. 1958. 23. Pearson. W. B., ed.• A Handbook of Lattice Spacing and Structures of Metals and Alloys Vol. 2. Pergamon Press, London, 1967. 24. Villars, P. & Calvert, L. D.. Pearson's Handbook of Crystallographic Data for Intermetallic Phases Vols 1-3. ASM. Metals Park, OH, 1985. 25. Massalski, T. B.• ed .• Binary Alloy Phase Diagrams 2nd edn, ASM International, Materials Park . OH. 1990.

547

26. Williams, R. K.• Graves, R. S.• Weaver. F. 1. & McElroy. D. L., in High Temperature Ordered Intermetallic Alloys. Mater. Res. Soc. Symp. Proc .. 39 (1985) 505. 27. Oya, Y. & Suzuki. T.• Z. Metallkde 74 (1983) 21. 28. Suzuki. T.• Materia Japan. 34 (1995) 568. 29. Terada, Y.• Ohkubo, K.• Mohri, T. & Suzuki, T., to be published. 30. Beattie Jr. H. J., in Intermetallic Compound. ed. J. H. Westbrook. John Wiley & Sons, New York, 1967. p. 144. 31. Williams, R. 0 .• Trans. Metall. Soc A/ME. 215 (\959) 1026. 32. Silcock, J. M.• Met . Sci. 1.,5 (1971) 182. 33. Kaya, S., I . Faculty Sci. llokkaido Imp. Univ., 2 (1938) 29. 34. Wakelin , R. J. & Yates, E. L., Proc. Phys. Soc .• B66 (1953) 221. 35. Kaya, S. & Nakayama, N., Proc. Phys. Math. Soc. Japan, 22 (1940) 126. 36. Thompson, N.• Proc. Phys. Soc. London. 52 (1940) 217. 37. Seemann. H. J.• Z. Physik, 62 (1930) 824. 38. Johanson, C H. & Linde, 1. 0 .• Ann. Phys.• 25 (1936) I. 39. Sykes. C & Evans. H.• I . Inst . Metals. 58 (1936) 255. 40. Jones. F. W. & Sykes. C, Proc. Roy . Soc. (A). 166 (1938) 376. 41. Siegel. S.• Phys . Rev., 57 (1940) 537. 42. Komer, A. & Sidorov, S., I. Phys. USSR, 4 (1941) 552. 43. Coles, B. R., Physico, 26 (1960) 143. 44. Anquetil, M. C , J. Phys. Rad.• 23 (1962) 113. 45. Jacobsson, P. & Sundqvist, B.• J. Phys. Chern. Solids, 49 (1988) 441. 46. Sykes. C & Evans . H.• Proc. Roy. Soc. London, J45 (1934) 529. 47. Masumoto, H. & Saito. H.• Sci. Repts Research Insts , Tohoku Univ., A4 (1952) 338. 48. Bennett , W. D., J. Iron Steel lnst .• 171 (1952) 372. 49. Kawamiya, N., Phys. Rev., B44 (\991) 12406. 50. Budnick , 1. D.• Muir. W. B., Niculescu, V. & Raj, K .• in Transition Metals. Institute of Physics. London. 1978, p. 196. 51. Nishino, Y.• Inoue. S. & Asano, S.• Phys. Rev., B48 (1993) 13607. 52. Kittel. C, Introduction to Solid State Physics. John Wiley and Sons. New York. 1953. 53. Blatt. F . J.• Physics of Electronic in Solids, McGraw-Hill. New York, 1968. 54. Ibach, H. & Luth, H.• Festkorperphyslk, Springer-Verlag, Berlin, 1981.