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Amorphization of intermetallic compounds by hydrogen absorption
Materials Science and Engineering, A 133 ( 1991 ) 316- 320
316
Amorphizationof intermetalliccompoundsby hydrogenabsorption K. Aoki, X.-G. Li, T. Aihara and T. Masumoto Institute for Materials Research, Tohoku University, Sendai 980 (Japan)
Abstract The crystallographic structures of AxBI_ x (A= a hydride-forming metal, B = non-hydride-forming metal) intermetallic compounds before and after hydrogen absorption have been identified using X-ray diffraction, to know the types of amorphizing intermetallic compounds. Amorphous alloys are formed by hydrogenation of the intermetallic compounds with the C 15, C23, B82, D019 and L 12 structures and having relatively low thermal stabilities. The compositions of these compounds are expressed as AB 2, A2B and A3B.
1. Introduction In recent years, the solid state amorphization reactions (SSAR), such as hydrogen-induced amorphization (HIA), mechanical alloying and so on, have attracted much attention as novel preparation methods of amorphous alloys [1]. HIA, i.e. the transformation from a crystalline to an amorphous alloy induced by hydrogen, was first demonstrated by Yeh et al. in the metastable Zr3Rh with the Lle structure [2]. Subsequently, the present authors have shown that hydrogenation of C15 Laves compounds RM 2 (R = a rare earth metal, M = Fe, Co, Ni) gives rise to amorphization near room temperature [3-8]. However, it is still uncertain what kinds of intermetallic compounds amorphize by hydrogen absorption. Furthermore, the process and the mechanism of HIA are still obscure. To understand the nature of the HIA phenomenon, it is useful to know the types of amorphizing intermetallic compounds. In the present work, the structures of hydrogenated intermetallic compounds with various crystal structures and melting points are examined to know the types of amorphizing intermetallic compounds. 2. Experimental details
A~BI_x intermetallic compounds (A= a hydride-forming metal, B = non-hydride-forming metal) were prepared by arc melting in an argon atmosphere. The ingots were homogenized in an 0921-5093/91/$3.50
evacuated quartz tube to obtain single phases. The hydrogenation treatment was carried out under constant conditions, i.e. pulverized samples (under 100 mesh) were reacted with 5.0 MPa hydrogen (7N) between 293 K and 773 K for 86.4 ks. The structures of the samples before and after hydrogen absorption were examined by powder X-ray diffraction (XRD) using the monochromated Cu Ka-radiation. Some samples were further examined by transmission electron microscopy and differential scanning calorimetry. 3. Results and discussion
Crystallographic structures of the hydrogenated AxBl-x compounds (A=a rare earth metal, Ti, Zr, Hf, Ca, Mg, B = A1, Ga, In, Mn, Fe, Co, Ni, Cu, Ag, Sn, Pb) were examined in the present work. In this paper we highlight the experimental results obtained in GdFe2 and Ce3AI compounds. Figure 1 shows XRD patterns of GdFe 2 hydrogenated at various temperatures. The XRD pattern of the homogenized sample indicates that this consists of the C 15 structure. GdFe 2 absorbs hydrogen in the crystalline state at 300 K without any change in the crystal structure, although Bragg peaks shift to the lower angle side, indicating volume expansion of the unit cell. In the XRD pattern of the sample hydrogenated at 423 K, the Bragg peaks disappear and are replaced by a broad maximum. An electron micrograph of the sample showing such a maxi© Elsevier Sequoia/Printed in The Netherlands
317 I
I
I
I
Hydrogenated at 5.0 MPa H2
o GdH2
z
,,
o
i
I
g o
i
l
~--Fe
[
i
0o0on o.... ° : > ' A
"2
a-Ce~AIHx
" IX
a
~
o
It
i
~
L
iE
Z o ~ ~
~
~673K
~,
.,a
E
~
523 K
:'-'-Tx
V HydrogenDesorpbon × rr'
•=' e-,
423 K 300
I
~
40(1
500
i
7(i)0
600
i
8(/(I
900
Temperature ,K
Fig. 3. The DSC curves of the hydrogenated GdF% and CecAl alloys. ¢o
Original GdFe2 '
x25
~ ~
° Cell2 . CeAI 2
/ - -
¢'4 O
20
i
I
I
30
40
1
50 60 20 /(~/180) rad
¢'4
[
70
m O
O
80
Fig. 1. The powder XRD patterns of GdF% hydrogenated at various temperatures.
-~
20
473
30
40
50
60
70
Fig. 2. A transmission electron micrograph (a) and a diffraction pattern (b) of the GdFe2 hydrogenated at 423 K.
2O/0t/180) rad Fig. 4. The XRD patterns of C%AI with the D0t~~ structure hydrogenated at various temperatures.
mum is featureless (Fig. 2(a)) and the corresponding diffraction pattern shows a broad halo, characteristic of an amorphous phase (Fig. 2(b)). Furthermore, the DSC curve of the sample shows two exothermic peaks along with the endothermic peak resulting from partial desorption of hydrogen, as seen in Fig. 3. These observations indicate that an amorphous phase was obtained by hydro-
genation of GdFe 2 at 423 K. At still higher temperatures new Bragg peaks appear, indexed by GdH 2 and a-Fe. Figure 4 shows XRD patterns of CegA1 with the D019 structure hydrogenated at various temperatures. In the XRD patterns of the sample hydrogenated at both 298 K and 373 K, the Bragg peaks disappear and are replaced by a
318
broad maximum. TEM of the sample showing such a maximum supports the amorphous nature of the sample. The DSC curve of the same sample shows an exothermic crystallization peak, as seen in Fig. 3. An endothermic peak is seen in this alloy above the crystallization peak in contrast to GdFe2Hx, which suggests that no hydrogen desorption occurs from the amorphous phase. XRD, TEM and DSC results indicate that an amorphous phase was obtained by hydrogenation below 373 K. At a still higher temperature (573 K), new Bragg peaks appear, indexed by Cell 2 and CeA12 (the C15 phase), In this compotmd a hydrogenated crystalline c-Ce3A1Hx phase is not formed.
Tables 1, 2 and 3 show the structures of the compounds hydrogenated around 300 K, 400 K and 600 K. In these tables the crystal structures, the nature of the phase transformation, and the decomposition temperatures (or the melting points) of the typical alloys are also listed. As seen in the tables, more than 60 intermetallic compounds have amorphized by hydrogen absorption. Amorphizing compounds, are expressed as AB2, A2B and A3B. No amorphization has been observed in the other compounds such as AB, AB 3 and ABs. In the AB 2 compounds, only the C15 Laves compounds amorphize by hydrogen absorption, as seen in Table 1. The RFe: and RCo2 cornAxB1-x
TABLE 1 The structures of the AB2 compound hydrogenated around 300 K, 400 K and 600 K, the crystal structures, the nature of the phase transformation, and the decomposition temperatures (or the melting points) of the typical alloys C 15 structure Compounds
Nature of the phase transformation
300 K
400 K
600 K
RFe2 (R = Y, Sm, Gd, Tb, Dy, Ho, Er)
Peritectic GdFe2 ( 1353 K)
c-RFe2Hx
Am a
RH 2 + a-Fe
CeFe 2
Peritectic (1046 K)
Am
Am
CeFe2 + a-Fe
RCo 2 (R = Ce, Pr, Nd, Tb, Dy, Ho)
Peritectic GdCo2 ( 1373 K)
c-RCo2Hx
Am
RH 2 + fl-Co
RNi2 (R=Y, Ce, Pr, Sm, Gd, Tb, Dy, Ho, Er)
Peritectic GdNi 2 (1343 K)
Am
Am
RH 2 + RNi 5
LaNi 2
Metastable
Am
Am
LaH2 + LaNi5
RA12 (R =Y, La, Ce, Pr, Nd, Sin, Gd, Ho, Er)
Congruent GdA12 (1803 K)
--
--
--
aAm=amorphous.
TABLE 2 The structures of the A2B compound hydrogenated around 300 K, 400 K and 600 K, the crystal structures, the nature of the phase transformation, and the decomposition temperatures (or the melting points) of the typical alloys (a) C23 structure Compounds
Nature of the phase transformation
300 K
400 K
600 K
R~AI (R = Y, Pr, Nd, Sm, Gd, Tb, Dy, Ho)
Peritectic GdAI 2 ( 1223 K)
Am a
Am
RH 2 + RAI2 (C15)
R2In (R = La, Ce, Nd, Sin, Gd, Tb, Dy, Ho, Er)
Congruent Gdln2 (1463 K)
Am
Am
RH 2 +
Zr2AI
Peritectoid (1523 K)
(b) B8e structure
dAm = amorphous.
Am
RIn 3
319 TABLE 3 The structures of the A3B compound hydrogenated around 300 K, 400 K and 600 K, the crystal structures, the nature of the phase transformation, and the decomposition temperatures (or the melting points) of the typical alloys (a) D(/l~ structure Compounds
Nature of the phase transformation
300 K
400 K
600 K
R3Ga (R = Nd, Sm)
Peritectic Nd~Ga (1059 K)
Am a
Am
R3GaH x (f.c.c.)
R3AI (R = La, Ce, Nd, Nd, Pr)
Peritectic Nd~A1 (948 K)
Am
Am
RH 2 + RAI 2 (C 15 )
c-Ti~AIHx
c-Ti3AIH x
c-Ti3AIH x
--
Am
Zr3InH ~(f.c.c.)
Ti3AI (b) L12(f.c.c.) structure Zr31 n Zr3AI
Peritectoid (1248 K)
--
Am
Zr,Rh
Metastable (rapidly quenched)
--
Am
R3In (R = Ce, Pr, Sin, Nd)
Peritectoid Pr3In (1040 K)
Am
Am
RH 2 + Rln 3
~'Am = amorphous.
pounds absorb hydrogen in the crystalline state at room temperature, amorphize around 400 K and decompose into RH 2 and pure metal (iron or cobalt) around 600 K. On the other hand, the GdNi 2 compounds amorphize at room temperature and around 400 K, and decompose into RH 2 and other intermetaUic compounds RNi 5 around 600 K. In these alloys, c-RNi2H x are not formed in contrast to GdFe2 and GdC02. Even if compounds have the C15 structure some, such as RAI2, do not amorphize by hydrogen absorption. The melting points of the RA12 compounds are considerably higher than those of RM 2. The present results indicate that the intermetallic compounds having high thermal stabilities are difficult to amorphize by hydrogen absorption. In the A2B type compounds, the C23 compounds such as R2A1 and the B82 compounds such as R2In and Zr2A1 amorphize, as seen in Table 2. These compounds amorphize around 300 K and 400 K, but decompose into RH2 and the other compounds around 600 K. In the A3B type compounds, the D019 compounds such as R3Ga and R3A1 and the L12 compounds such as Zr3M (M=In, AI, Rh) and R3In amorphize below 400 K. It is interesting to note that the D0~9 type compounds R3Ga transform to the f.c.c, compounds c-R3GaHx and the L12 corn-
pound Zr3In becomes the f.c.c, alloy c-Zr3InHx at elevated temperatures. Ti3A1 with the D 0 t 9 structure and a high melting point does not amorphize. The present work indicates that HIA is confined to the intermetallic compounds with the specific crystal structures in contrast to the other SSARs. This fact suggests that HIA occurs when hydrogen atoms occupy special environments. In spite of these crystal structures, some compounds having high melting points have not become amorphous. We propose, based on the present experimental results, that the intermetallic compounds, which become amorphous by hydrogen absorption, are as follows: (i) they contain a hydride-forming metal; (ii) they have specific crystal structures as mentioned above; and (iii) they are thermally unstable, i.e. they have relatively low melting points or decompose into intermetallic compounds.
References 1 W. L. Johnson, Prog. Mater. Sci., 30(1986) 81. 2 X. L. Yeh, K. Samwer and W. L. Johnson, AppI. Phys. Lett., 42 (1983) 242. 3 K. Aoki, K. Shirakawa and T. Masumoto, Sci. Rep. Res. Inst. Tohoku Univer., A-32(1985) 239.
320 4 K. Aoki, T. Yamamoto and T. Masumoto, Scr. Metall., 21 (1987) 27. 5 K. Chattopadyhay, K. Aoki and T. Masumoto, Scr. Metall., 21 (1987)365. 6 K. Aoki, T. Yamamoto, Y. Satoh, K. Fukamichi and T.
Masumoto, Acta Metall., 35 (1987) 2465. 7 K. Aoki, A. Yanagitani, X-G. Li and T. Masumoto, Mater. Sci. Eng., 97(1988) 35. 8 K. Aoki, X.-G. Li, A. Yanagitani and T. Masumoto, Trans. Jpn. Inst. Met., 29(1988) 101.
316
Amorphizationof intermetalliccompoundsby hydrogenabsorption K. Aoki, X.-G. Li, T. Aihara and T. Masumoto Institute for Materials Research, Tohoku University, Sendai 980 (Japan)
Abstract The crystallographic structures of AxBI_ x (A= a hydride-forming metal, B = non-hydride-forming metal) intermetallic compounds before and after hydrogen absorption have been identified using X-ray diffraction, to know the types of amorphizing intermetallic compounds. Amorphous alloys are formed by hydrogenation of the intermetallic compounds with the C 15, C23, B82, D019 and L 12 structures and having relatively low thermal stabilities. The compositions of these compounds are expressed as AB 2, A2B and A3B.
1. Introduction In recent years, the solid state amorphization reactions (SSAR), such as hydrogen-induced amorphization (HIA), mechanical alloying and so on, have attracted much attention as novel preparation methods of amorphous alloys [1]. HIA, i.e. the transformation from a crystalline to an amorphous alloy induced by hydrogen, was first demonstrated by Yeh et al. in the metastable Zr3Rh with the Lle structure [2]. Subsequently, the present authors have shown that hydrogenation of C15 Laves compounds RM 2 (R = a rare earth metal, M = Fe, Co, Ni) gives rise to amorphization near room temperature [3-8]. However, it is still uncertain what kinds of intermetallic compounds amorphize by hydrogen absorption. Furthermore, the process and the mechanism of HIA are still obscure. To understand the nature of the HIA phenomenon, it is useful to know the types of amorphizing intermetallic compounds. In the present work, the structures of hydrogenated intermetallic compounds with various crystal structures and melting points are examined to know the types of amorphizing intermetallic compounds. 2. Experimental details
A~BI_x intermetallic compounds (A= a hydride-forming metal, B = non-hydride-forming metal) were prepared by arc melting in an argon atmosphere. The ingots were homogenized in an 0921-5093/91/$3.50
evacuated quartz tube to obtain single phases. The hydrogenation treatment was carried out under constant conditions, i.e. pulverized samples (under 100 mesh) were reacted with 5.0 MPa hydrogen (7N) between 293 K and 773 K for 86.4 ks. The structures of the samples before and after hydrogen absorption were examined by powder X-ray diffraction (XRD) using the monochromated Cu Ka-radiation. Some samples were further examined by transmission electron microscopy and differential scanning calorimetry. 3. Results and discussion
Crystallographic structures of the hydrogenated AxBl-x compounds (A=a rare earth metal, Ti, Zr, Hf, Ca, Mg, B = A1, Ga, In, Mn, Fe, Co, Ni, Cu, Ag, Sn, Pb) were examined in the present work. In this paper we highlight the experimental results obtained in GdFe2 and Ce3AI compounds. Figure 1 shows XRD patterns of GdFe 2 hydrogenated at various temperatures. The XRD pattern of the homogenized sample indicates that this consists of the C 15 structure. GdFe 2 absorbs hydrogen in the crystalline state at 300 K without any change in the crystal structure, although Bragg peaks shift to the lower angle side, indicating volume expansion of the unit cell. In the XRD pattern of the sample hydrogenated at 423 K, the Bragg peaks disappear and are replaced by a broad maximum. An electron micrograph of the sample showing such a maxi© Elsevier Sequoia/Printed in The Netherlands
317 I
I
I
I
Hydrogenated at 5.0 MPa H2
o GdH2
z
,,
o
i
I
g o
i
l
~--Fe
[
i
0o0on o.... ° : > ' A
"2
a-Ce~AIHx
" IX
a
~
o
It
i
~
L
iE
Z o ~ ~
~
~673K
~,
.,a
E
~
523 K
:'-'-Tx
V HydrogenDesorpbon × rr'
•=' e-,
423 K 300
I
~
40(1
500
i
7(i)0
600
i
8(/(I
900
Temperature ,K
Fig. 3. The DSC curves of the hydrogenated GdF% and CecAl alloys. ¢o
Original GdFe2 '
x25
~ ~
° Cell2 . CeAI 2
/ - -
¢'4 O
20
i
I
I
30
40
1
50 60 20 /(~/180) rad
¢'4
[
70
m O
O
80
Fig. 1. The powder XRD patterns of GdF% hydrogenated at various temperatures.
-~
20
473
30
40
50
60
70
Fig. 2. A transmission electron micrograph (a) and a diffraction pattern (b) of the GdFe2 hydrogenated at 423 K.
2O/0t/180) rad Fig. 4. The XRD patterns of C%AI with the D0t~~ structure hydrogenated at various temperatures.
mum is featureless (Fig. 2(a)) and the corresponding diffraction pattern shows a broad halo, characteristic of an amorphous phase (Fig. 2(b)). Furthermore, the DSC curve of the sample shows two exothermic peaks along with the endothermic peak resulting from partial desorption of hydrogen, as seen in Fig. 3. These observations indicate that an amorphous phase was obtained by hydro-
genation of GdFe 2 at 423 K. At still higher temperatures new Bragg peaks appear, indexed by GdH 2 and a-Fe. Figure 4 shows XRD patterns of CegA1 with the D019 structure hydrogenated at various temperatures. In the XRD patterns of the sample hydrogenated at both 298 K and 373 K, the Bragg peaks disappear and are replaced by a
318
broad maximum. TEM of the sample showing such a maximum supports the amorphous nature of the sample. The DSC curve of the same sample shows an exothermic crystallization peak, as seen in Fig. 3. An endothermic peak is seen in this alloy above the crystallization peak in contrast to GdFe2Hx, which suggests that no hydrogen desorption occurs from the amorphous phase. XRD, TEM and DSC results indicate that an amorphous phase was obtained by hydrogenation below 373 K. At a still higher temperature (573 K), new Bragg peaks appear, indexed by Cell 2 and CeA12 (the C15 phase), In this compotmd a hydrogenated crystalline c-Ce3A1Hx phase is not formed.
Tables 1, 2 and 3 show the structures of the compounds hydrogenated around 300 K, 400 K and 600 K. In these tables the crystal structures, the nature of the phase transformation, and the decomposition temperatures (or the melting points) of the typical alloys are also listed. As seen in the tables, more than 60 intermetallic compounds have amorphized by hydrogen absorption. Amorphizing compounds, are expressed as AB2, A2B and A3B. No amorphization has been observed in the other compounds such as AB, AB 3 and ABs. In the AB 2 compounds, only the C15 Laves compounds amorphize by hydrogen absorption, as seen in Table 1. The RFe: and RCo2 cornAxB1-x
TABLE 1 The structures of the AB2 compound hydrogenated around 300 K, 400 K and 600 K, the crystal structures, the nature of the phase transformation, and the decomposition temperatures (or the melting points) of the typical alloys C 15 structure Compounds
Nature of the phase transformation
300 K
400 K
600 K
RFe2 (R = Y, Sm, Gd, Tb, Dy, Ho, Er)
Peritectic GdFe2 ( 1353 K)
c-RFe2Hx
Am a
RH 2 + a-Fe
CeFe 2
Peritectic (1046 K)
Am
Am
CeFe2 + a-Fe
RCo 2 (R = Ce, Pr, Nd, Tb, Dy, Ho)
Peritectic GdCo2 ( 1373 K)
c-RCo2Hx
Am
RH 2 + fl-Co
RNi2 (R=Y, Ce, Pr, Sm, Gd, Tb, Dy, Ho, Er)
Peritectic GdNi 2 (1343 K)
Am
Am
RH 2 + RNi 5
LaNi 2
Metastable
Am
Am
LaH2 + LaNi5
RA12 (R =Y, La, Ce, Pr, Nd, Sin, Gd, Ho, Er)
Congruent GdA12 (1803 K)
--
--
--
aAm=amorphous.
TABLE 2 The structures of the A2B compound hydrogenated around 300 K, 400 K and 600 K, the crystal structures, the nature of the phase transformation, and the decomposition temperatures (or the melting points) of the typical alloys (a) C23 structure Compounds
Nature of the phase transformation
300 K
400 K
600 K
R~AI (R = Y, Pr, Nd, Sm, Gd, Tb, Dy, Ho)
Peritectic GdAI 2 ( 1223 K)
Am a
Am
RH 2 + RAI2 (C15)
R2In (R = La, Ce, Nd, Sin, Gd, Tb, Dy, Ho, Er)
Congruent Gdln2 (1463 K)
Am
Am
RH 2 +
Zr2AI
Peritectoid (1523 K)
(b) B8e structure
dAm = amorphous.
Am
RIn 3
319 TABLE 3 The structures of the A3B compound hydrogenated around 300 K, 400 K and 600 K, the crystal structures, the nature of the phase transformation, and the decomposition temperatures (or the melting points) of the typical alloys (a) D(/l~ structure Compounds
Nature of the phase transformation
300 K
400 K
600 K
R3Ga (R = Nd, Sm)
Peritectic Nd~Ga (1059 K)
Am a
Am
R3GaH x (f.c.c.)
R3AI (R = La, Ce, Nd, Nd, Pr)
Peritectic Nd~A1 (948 K)
Am
Am
RH 2 + RAI 2 (C 15 )
c-Ti~AIHx
c-Ti3AIH x
c-Ti3AIH x
--
Am
Zr3InH ~(f.c.c.)
Ti3AI (b) L12(f.c.c.) structure Zr31 n Zr3AI
Peritectoid (1248 K)
--
Am
Zr,Rh
Metastable (rapidly quenched)
--
Am
R3In (R = Ce, Pr, Sin, Nd)
Peritectoid Pr3In (1040 K)
Am
Am
RH 2 + Rln 3
~'Am = amorphous.
pounds absorb hydrogen in the crystalline state at room temperature, amorphize around 400 K and decompose into RH 2 and pure metal (iron or cobalt) around 600 K. On the other hand, the GdNi 2 compounds amorphize at room temperature and around 400 K, and decompose into RH 2 and other intermetaUic compounds RNi 5 around 600 K. In these alloys, c-RNi2H x are not formed in contrast to GdFe2 and GdC02. Even if compounds have the C15 structure some, such as RAI2, do not amorphize by hydrogen absorption. The melting points of the RA12 compounds are considerably higher than those of RM 2. The present results indicate that the intermetallic compounds having high thermal stabilities are difficult to amorphize by hydrogen absorption. In the A2B type compounds, the C23 compounds such as R2A1 and the B82 compounds such as R2In and Zr2A1 amorphize, as seen in Table 2. These compounds amorphize around 300 K and 400 K, but decompose into RH2 and the other compounds around 600 K. In the A3B type compounds, the D019 compounds such as R3Ga and R3A1 and the L12 compounds such as Zr3M (M=In, AI, Rh) and R3In amorphize below 400 K. It is interesting to note that the D0~9 type compounds R3Ga transform to the f.c.c, compounds c-R3GaHx and the L12 corn-
pound Zr3In becomes the f.c.c, alloy c-Zr3InHx at elevated temperatures. Ti3A1 with the D 0 t 9 structure and a high melting point does not amorphize. The present work indicates that HIA is confined to the intermetallic compounds with the specific crystal structures in contrast to the other SSARs. This fact suggests that HIA occurs when hydrogen atoms occupy special environments. In spite of these crystal structures, some compounds having high melting points have not become amorphous. We propose, based on the present experimental results, that the intermetallic compounds, which become amorphous by hydrogen absorption, are as follows: (i) they contain a hydride-forming metal; (ii) they have specific crystal structures as mentioned above; and (iii) they are thermally unstable, i.e. they have relatively low melting points or decompose into intermetallic compounds.
References 1 W. L. Johnson, Prog. Mater. Sci., 30(1986) 81. 2 X. L. Yeh, K. Samwer and W. L. Johnson, AppI. Phys. Lett., 42 (1983) 242. 3 K. Aoki, K. Shirakawa and T. Masumoto, Sci. Rep. Res. Inst. Tohoku Univer., A-32(1985) 239.
320 4 K. Aoki, T. Yamamoto and T. Masumoto, Scr. Metall., 21 (1987) 27. 5 K. Chattopadyhay, K. Aoki and T. Masumoto, Scr. Metall., 21 (1987)365. 6 K. Aoki, T. Yamamoto, Y. Satoh, K. Fukamichi and T.
Masumoto, Acta Metall., 35 (1987) 2465. 7 K. Aoki, A. Yanagitani, X-G. Li and T. Masumoto, Mater. Sci. Eng., 97(1988) 35. 8 K. Aoki, X.-G. Li, A. Yanagitani and T. Masumoto, Trans. Jpn. Inst. Met., 29(1988) 101.