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Electronic structure and transport properties of sp-electron quasicrystals in comparison with the Frank-Kasper crystals and amorphous alloys
Materials Science and Engineering, A 133 ( 1991 ) 111-114
111
Electronic structure and transport properties of sp-electron quasicrystals in comparison with the Frank-Kasper crystals and amorphous alloys Uichiro Mizutani and A. Kamiya Department of Crystalline Materials Science, Nagoya University, Faro-cho, Chikusa-ku, Nagoya 464-01 (Japan)
T. Matsuda Department of Physics, Aichi University of Education, Kariya-shi, 448 (Japan)
S. Takeuchi Institute for Solid State Physics, The University of Tokyo, Roppongi, Minato-ku, Tokyo 106 (Japan)
Abstract The electron transport properties and the density of states at E v have been studied on various spelectron quasicrystals (QC) and Frank-Kasper (FK) crystals. A comparison was made with the data for sp-electron amorphous alloys. A similarity with amorphous alloys is found in the magnitude of p, the interrelation between ), and p and the p - T dependence. This is attributed to the breakdown of the Bloch condition. On the other hand, a similarity with the FK crystals is found in the 7 versus e/a relation. A Fermi sufface-Brillouin zone interaction similar to that in FK crystals is suggested. It is concluded that QCs exhibit features characteristic of an amorphous alloy or of a crystal, depending on the electronic properties studied.
1. Introduction Experimental data on the electron transport properties of quasicrystals (abbreviated as QC) have been extensively accumulated in the last few years. This is because, among QCs fabricated after the discovery of the AI-Mn spin glass, a group of those possessing sp-electrons at the Fermi level has been recognized to be appropriate to extract information about the scattering mechanism of conduction electrons interacting with the quasiperiodic lattice. Indeed, the same guiding principle has been emphasized in the amorphous alloys [1]. In the present work, we discuss the electron transport properties in spelectron QCs with reference to the data available for the sp-electron amorphous alloys [2] and the Frank-Kasper (abbreviated as FK) crystals. 2. Experimental procedure and results The QCs studied in this work include triacontahedron-type Mg-Zn-AI, Mg-A1-Ag, Mg-A10921-5093/91/$3.50
Cu, M g - G a - Z n , AI-Li-Cu, and Mackay-type A1-Ru-Cu and A1-Cu-V. The corresponding FK crystals were also prepared. The details of the sample preparation are described elsewhere [3-6]. Briefly, the QCs except for AI-Cu-V, A1-Li-Cu and A I - R u - C u were obtained as a metastable state by melt quenching, using a single-roll apparatus. In the case of AI-Cu-V, an amorphous single phase was first obtained and transformed into a QC phase upon heating. The thermodynamically stable AI-Li-Cu [4] and A I - R u - C u [5] QCs were prepared in the bulk form by slowly cooling the molten alloy under the equilibrium condition. The electronic specific heat coefficient V was determined from the lowtemperature specific heat measurements in the range 1.5-6 K. The resistivity and Hall coefficient were also measured using d.c. four- and five-terminal methods [3, 4]. Relevant numerical data are available in the literature [3-6] except those for the A1-Cu-V alloys, which are summarized in Table 1.
112 TABLE 1 Electron transport properties of amorphous and quasicrystalline phases in the A I - C u - V alloy system
Als0Cul0V.b Als0Cu.)V,~
A Q
AI75CulsVI0 AI75CulsV.I
A Q
Alv0Cu20Vl0 Al7oCu2oVlo
A A
7
a
O D
d
p
d
RH
( m J m o l - J K 2)
×10 2 (mJ mol J K -a)
(K)
x l 0 -4 (mJ m o l ] K -a)
(/~2-cm)
(gcm -3)
×10 -11 (m3A -l S-l)
130+7 163_+9
3.45
-5.1_+0.3 -14.0_+0.8
151-+5 221_+6
3.71
-5.4-+0.6 -5.3-+0.6
195 -+ 3 250-+ 4
3.93
-
1.30_+0.01 0.92-+0.01
2.6_+0.1 2.5+0.1
419_+4
425+4
-0.2-+0.1 0.7+0.2
4.9-+ 0.1 - 5.0_+ 0.6
A: amorphous phase; Q: quasicrystalline phase; y, a and 6 represent coefficients of low-temperature specific heats C = ~,T+ a T 3 + d T 5. OD is the Debye temperature, p the resistivity at 300 K and RH the Hall coefficient at 300 K.
i 1.5
i
i
i
QC-Phase
OO
1.5
_
i ~ FK-Phase
i
iO_ / 0
.~
•
t~
I
I 2.2
I
I
Ot 2.0
2.4
I
e/a
I I 2.2 e/a
I 2.4
Fig. 1. The ratio ~/exp/71:of the electronic specific heat coefficient over the corresponding free-electron value as a function of the number of electrons per atom e/a in (A) sp-electron quasicrystals and (B) Frank-Kasper crystals. Symbols are as follows; ~z: Mg-A1-Ag, o: Mg-A1-Cu, zx: Mg-AI-Zn, D: M g - Z n - G a and Or:A1-Li-Cu.
1.5
I
I
Mg-AI-Cu
A Mg.Zn-Ga
-g
[]
l.O
(3
Mg-AI-Ag --
O
E
Mg-Zn-Ga AI-Cu-V ( after anealing)
[]
0.5
AI-Li-Cu
3. Electronic specific heat coefficient Figure 1 depicts the electron concentration dependence of 7exp/YVfor both QCs and the FK crystals [6]. It is seen that both sets of data are identical to each other within the accuracy. This suggests that the orientationally ordered structure in a QC yields singularities in the density of states as a result of the Fermi surface-Brillouin zone interaction just like in the FK crystal [6, 7]. An insulating QC or FK phase is expected to occur at e/a = 2.0, but the attempt to fabricate such alloys has been so far unsuccessful [6]. The value of e/a for the Mackay-type A I - C u - V and A I - C u - R u cannot be unambiguously defined. To allow the discussion for both triacontahedron- and Mackay-type QCs on the same footing, we plotted in Fig. 2 the value of Yexp against the half-width of the strongest X-ray diffraction peak, which may be taken as a rough measure for the quasicrystallinity. Indeed, the thermodynamically stable QC is characterized by a small half-width. The value of Yexpis found to decrease sharply when the quasicrystallinity or the stability of a QC is enhanced. A reducing value of y is attributable to the sharpening of the structure-induced minimum, at which the Fermi level happens to fall.
¢r AI-Ru-Cu
0
O
4. Electrical resistivity I
I
I
2
AKp/Kp(%)
Fig. 2. The measured electronic specific heat coefficient Yex~ as a function of AKp/Kp for both triacontahedron- and Mackay-type quasicrystals. The quasicrystals AI-Li-Cu and AI-Ru-Cu are thermodynamically stable, whereas the quasicrystal Mg39.sZn40.0Ga:05 is stable up to the melting point [3].
The temperature dependence of the electrical resistivity for the amorphous A175Cu15V10 alloy above 300 K is shown in Fig. 3, together with the low-temperature data in its inset. It can be seen that the resistivity jumps up almost 30% at about 730 K upon transformation into the QC phase. As is listed in Table 1, the resistivity in the QC
113
2.0
I
I
I
• ,
,[
.
,
, .I,
-OOl. !
.
1.6
'°° 1.4
,oo
~ ~ . ~ - 7 " ~
',,
I O0
\\
\\',
- ?o' A -" o
(B) .........
',
1
eo
aS
~\
\\
T (K) /
1.2
~L o
200
~
0,o
d ~
o
TCK~ ~ o
\~
° oo--
c
0o o ° ~ he ~"~-Yx~ o oo0 o
(A)
t Tx
,oo
0.8 I J I 600 700 800 900 T (K) Fig. 3. Temperature dependence of the electrical resistivity for the amorphous A17sCulsVi0 alloy. It jumps at Tx as a result of the transformation into the quasicrystalline phase (B). The inset shows the temperature dependence of the electrical resistivity in the range 2 - 3 0 0 K for the amorphous and quasicrystalline phases. 0.6 300
0
o_
1.0
\
a ".
?
(2..
i
oU:'
1.8 ~ i(11 o_ [
,
400
i 500
phase is higher than that in the amorphous phase. As another notable feature for the resistivity of a QC, we point to the fact that the resistivity increases by about 8% when the quasicrystallinity in the stable M g - G a - Z n QC is improved upon heating [3]. This is at variance with our experience for crystalline metals, in which the resistivity decreases as the degree of order enhances due to annealing. The electron transport properties of spelectron amorphous alloys have been often discussed in terms of the generalized Faber-Ziman theory, in which structural information is introduced in the form of the structure factor S(Q) in the range 0 - < Q < 2 k F. The S(Q) for a QC possesses an overall feature similar to that for an amorphous phase but with a series of Bragg peaks as in crystals [8]. Therefore, the Faber-Ziman theory, which assumes the scattering to occur only once on the spherical Fermi surface without Bragg reflections, needs to be reconsidered. We believe that the effect of Bragg-like reflections in a QC should be critically important as evidenced from the same e/a dependence of Y between QC and FK phases shown in Fig. 1. 5. Interrelation b e t w e e n V and p
As is listed in Table 1, an increase in p is accompanied by a reduction in y when the amor-
°°b
o
OD
0
40 0
i
[
I
J
1
I
2
3
4
5
y ( m J m o 1 - 1 K -2) Fig. 4. Interrelation between the resistivity at 300 K and the electronic specific heat coefficient 7e× for sp-electron quasicrystals. The data for sp-, (sp + d)- anc(d-electron amorphous alloys are also incorporated. Symbols are as follows; A: Mg-A1-Ag, O: Mg-AI-Cu, v : M g - A I - Z n , n: M g - G a - Z n , O : AI-Cu-V, *: AI-Li-Cu, 4: A1-Ru-Cu and o: amorphous alloys. Inset shows the p - T characteristics observed in both quasicrystals and amorphous alloys. Types (a)-(e) appear in this alphabetical sequence with increasing p in nonperiodic and nonmagnetic systems. A dashed curve represents a possible high-resistivity limiting curve [2, 4].
phous A1-Cu-V alloy transforms to a QC phase. A reduction in 7 coupled with an increase in p is also observed in the stable M g - G a - Z n QC [3]. Thermodynamically stable A1-Li-Cu [4] and A1-Ru-Cu [5] QCs are characterized in common by the values of a reduced Y and a very high p. As shown in Fig. 4, one finds that an increase in p with decreasing 7 is a universal feature for nonperiodic sp-electron systems, including both QCs and amorphous alloys. The interrelation between the 7 and p has been discussed in detail on the basis of the conductivity formula a =/9 - 1= (e2/3) AFvv N(E v ), where A v is the mean free path, vF is the Fermi velocity and N(Ev) is the density of states at the Fermi level or the value of y [2-5]. Briefly, it has been claimed that the observed steep rise of/9 with decreasing y is caused by two simultaneously occurring effects: a reduction in carrier density or the value of Y itself and a reduction in A v [2]. As indicated in the inset to Fig. 4, a systematic change in the p - T characteristics from type
114
(a) through (e) is observed in common for both amorphous alloys [2] and QCs [3-5]. A change from type (a) to (c) in the alphabetical sequence with increasing p has been attributed to a decrease in A F with increasing resistivity. It has been shown that the types (d) and (e) observed in high-resistivity AI-Li-Cu and A1-Ru-Cu QCs are the consequence of the weak localization effect [4, 5]. This conclusion has been also drawn for the nonmagnetic amorphous alloys [2]. In conclusion, an amorphous phase can be viewed as being disordered with respect to the translational and orientational symmetries whereas the QC phase as being ordered orientationally without satisfying the translational symmetry. The breakdown of the Bloch condition is, therefore, common in two cases. This yields the same ~, versus p relation and /9-T characteristics. But the observed similarity in the 7 versus e/a dependence between the QCs and the
FK crystals is taken as evidence for the presence of the Fermi surface-Brillouin zone interaction as in typical crystals. References 1 U. Mizutani, Prog. Mater. Sci., 28 (1983) 97; U. Mizutani, Mater. Sci. Eng., 99(1988) 165. 2 U. Mizutani, S. Ohashi, T. Matsuda, K. Fukamichi and K: Tanaka, J. Phys.: Condens. Matter, 2(1990) 541. 3 U. Mizutani, Y. Sakabe and T. Matsuda, J. Phys.: Condens. Matter, 2 (1990) 6153. 4 K.. Kimura, H. Iwahashi, T. Hashimoto, S. Takeuchi, U. Mizutani, S. Ohashi and G. Itoh, J. Phys. Soc. Jpn., 58 (1989) 2472. 5 U. Mizutani, Y. Sakabe, T. Shibuya, K. Kishi, K. Kimura and S. Takeuchi, J. Phys.: Condens. Matter, 2 (1990) 6169. 6 U. Mizutani, A. Kamiya, T. Matsuda, K. Kishi and S. Takeuchi, J. Phys.: Condens. Matter, 2 (1990) (submitted). 7 J. L. Wagner, B. D. Biggs and S. J. Poon, Phys. Rev. Let., 65 (1990) 203. 8 M. Itoh, A. Ishida, H. Sato, T. Matsuda, T. Fukunaga, A. Kamiya and U. Mizutani, presented at this conference.
111
Electronic structure and transport properties of sp-electron quasicrystals in comparison with the Frank-Kasper crystals and amorphous alloys Uichiro Mizutani and A. Kamiya Department of Crystalline Materials Science, Nagoya University, Faro-cho, Chikusa-ku, Nagoya 464-01 (Japan)
T. Matsuda Department of Physics, Aichi University of Education, Kariya-shi, 448 (Japan)
S. Takeuchi Institute for Solid State Physics, The University of Tokyo, Roppongi, Minato-ku, Tokyo 106 (Japan)
Abstract The electron transport properties and the density of states at E v have been studied on various spelectron quasicrystals (QC) and Frank-Kasper (FK) crystals. A comparison was made with the data for sp-electron amorphous alloys. A similarity with amorphous alloys is found in the magnitude of p, the interrelation between ), and p and the p - T dependence. This is attributed to the breakdown of the Bloch condition. On the other hand, a similarity with the FK crystals is found in the 7 versus e/a relation. A Fermi sufface-Brillouin zone interaction similar to that in FK crystals is suggested. It is concluded that QCs exhibit features characteristic of an amorphous alloy or of a crystal, depending on the electronic properties studied.
1. Introduction Experimental data on the electron transport properties of quasicrystals (abbreviated as QC) have been extensively accumulated in the last few years. This is because, among QCs fabricated after the discovery of the AI-Mn spin glass, a group of those possessing sp-electrons at the Fermi level has been recognized to be appropriate to extract information about the scattering mechanism of conduction electrons interacting with the quasiperiodic lattice. Indeed, the same guiding principle has been emphasized in the amorphous alloys [1]. In the present work, we discuss the electron transport properties in spelectron QCs with reference to the data available for the sp-electron amorphous alloys [2] and the Frank-Kasper (abbreviated as FK) crystals. 2. Experimental procedure and results The QCs studied in this work include triacontahedron-type Mg-Zn-AI, Mg-A1-Ag, Mg-A10921-5093/91/$3.50
Cu, M g - G a - Z n , AI-Li-Cu, and Mackay-type A1-Ru-Cu and A1-Cu-V. The corresponding FK crystals were also prepared. The details of the sample preparation are described elsewhere [3-6]. Briefly, the QCs except for AI-Cu-V, A1-Li-Cu and A I - R u - C u were obtained as a metastable state by melt quenching, using a single-roll apparatus. In the case of AI-Cu-V, an amorphous single phase was first obtained and transformed into a QC phase upon heating. The thermodynamically stable AI-Li-Cu [4] and A I - R u - C u [5] QCs were prepared in the bulk form by slowly cooling the molten alloy under the equilibrium condition. The electronic specific heat coefficient V was determined from the lowtemperature specific heat measurements in the range 1.5-6 K. The resistivity and Hall coefficient were also measured using d.c. four- and five-terminal methods [3, 4]. Relevant numerical data are available in the literature [3-6] except those for the A1-Cu-V alloys, which are summarized in Table 1.
112 TABLE 1 Electron transport properties of amorphous and quasicrystalline phases in the A I - C u - V alloy system
Als0Cul0V.b Als0Cu.)V,~
A Q
AI75CulsVI0 AI75CulsV.I
A Q
Alv0Cu20Vl0 Al7oCu2oVlo
A A
7
a
O D
d
p
d
RH
( m J m o l - J K 2)
×10 2 (mJ mol J K -a)
(K)
x l 0 -4 (mJ m o l ] K -a)
(/~2-cm)
(gcm -3)
×10 -11 (m3A -l S-l)
130+7 163_+9
3.45
-5.1_+0.3 -14.0_+0.8
151-+5 221_+6
3.71
-5.4-+0.6 -5.3-+0.6
195 -+ 3 250-+ 4
3.93
-
1.30_+0.01 0.92-+0.01
2.6_+0.1 2.5+0.1
419_+4
425+4
-0.2-+0.1 0.7+0.2
4.9-+ 0.1 - 5.0_+ 0.6
A: amorphous phase; Q: quasicrystalline phase; y, a and 6 represent coefficients of low-temperature specific heats C = ~,T+ a T 3 + d T 5. OD is the Debye temperature, p the resistivity at 300 K and RH the Hall coefficient at 300 K.
i 1.5
i
i
i
QC-Phase
OO
1.5
_
i ~ FK-Phase
i
iO_ / 0
.~
•
t~
I
I 2.2
I
I
Ot 2.0
2.4
I
e/a
I I 2.2 e/a
I 2.4
Fig. 1. The ratio ~/exp/71:of the electronic specific heat coefficient over the corresponding free-electron value as a function of the number of electrons per atom e/a in (A) sp-electron quasicrystals and (B) Frank-Kasper crystals. Symbols are as follows; ~z: Mg-A1-Ag, o: Mg-A1-Cu, zx: Mg-AI-Zn, D: M g - Z n - G a and Or:A1-Li-Cu.
1.5
I
I
Mg-AI-Cu
A Mg.Zn-Ga
-g
[]
l.O
(3
Mg-AI-Ag --
O
E
Mg-Zn-Ga AI-Cu-V ( after anealing)
[]
0.5
AI-Li-Cu
3. Electronic specific heat coefficient Figure 1 depicts the electron concentration dependence of 7exp/YVfor both QCs and the FK crystals [6]. It is seen that both sets of data are identical to each other within the accuracy. This suggests that the orientationally ordered structure in a QC yields singularities in the density of states as a result of the Fermi surface-Brillouin zone interaction just like in the FK crystal [6, 7]. An insulating QC or FK phase is expected to occur at e/a = 2.0, but the attempt to fabricate such alloys has been so far unsuccessful [6]. The value of e/a for the Mackay-type A I - C u - V and A I - C u - R u cannot be unambiguously defined. To allow the discussion for both triacontahedron- and Mackay-type QCs on the same footing, we plotted in Fig. 2 the value of Yexp against the half-width of the strongest X-ray diffraction peak, which may be taken as a rough measure for the quasicrystallinity. Indeed, the thermodynamically stable QC is characterized by a small half-width. The value of Yexpis found to decrease sharply when the quasicrystallinity or the stability of a QC is enhanced. A reducing value of y is attributable to the sharpening of the structure-induced minimum, at which the Fermi level happens to fall.
¢r AI-Ru-Cu
0
O
4. Electrical resistivity I
I
I
2
AKp/Kp(%)
Fig. 2. The measured electronic specific heat coefficient Yex~ as a function of AKp/Kp for both triacontahedron- and Mackay-type quasicrystals. The quasicrystals AI-Li-Cu and AI-Ru-Cu are thermodynamically stable, whereas the quasicrystal Mg39.sZn40.0Ga:05 is stable up to the melting point [3].
The temperature dependence of the electrical resistivity for the amorphous A175Cu15V10 alloy above 300 K is shown in Fig. 3, together with the low-temperature data in its inset. It can be seen that the resistivity jumps up almost 30% at about 730 K upon transformation into the QC phase. As is listed in Table 1, the resistivity in the QC
113
2.0
I
I
I
• ,
,[
.
,
, .I,
-OOl. !
.
1.6
'°° 1.4
,oo
~ ~ . ~ - 7 " ~
',,
I O0
\\
\\',
- ?o' A -" o
(B) .........
',
1
eo
aS
~\
\\
T (K) /
1.2
~L o
200
~
0,o
d ~
o
TCK~ ~ o
\~
° oo--
c
0o o ° ~ he ~"~-Yx~ o oo0 o
(A)
t Tx
,oo
0.8 I J I 600 700 800 900 T (K) Fig. 3. Temperature dependence of the electrical resistivity for the amorphous A17sCulsVi0 alloy. It jumps at Tx as a result of the transformation into the quasicrystalline phase (B). The inset shows the temperature dependence of the electrical resistivity in the range 2 - 3 0 0 K for the amorphous and quasicrystalline phases. 0.6 300
0
o_
1.0
\
a ".
?
(2..
i
oU:'
1.8 ~ i(11 o_ [
,
400
i 500
phase is higher than that in the amorphous phase. As another notable feature for the resistivity of a QC, we point to the fact that the resistivity increases by about 8% when the quasicrystallinity in the stable M g - G a - Z n QC is improved upon heating [3]. This is at variance with our experience for crystalline metals, in which the resistivity decreases as the degree of order enhances due to annealing. The electron transport properties of spelectron amorphous alloys have been often discussed in terms of the generalized Faber-Ziman theory, in which structural information is introduced in the form of the structure factor S(Q) in the range 0 - < Q < 2 k F. The S(Q) for a QC possesses an overall feature similar to that for an amorphous phase but with a series of Bragg peaks as in crystals [8]. Therefore, the Faber-Ziman theory, which assumes the scattering to occur only once on the spherical Fermi surface without Bragg reflections, needs to be reconsidered. We believe that the effect of Bragg-like reflections in a QC should be critically important as evidenced from the same e/a dependence of Y between QC and FK phases shown in Fig. 1. 5. Interrelation b e t w e e n V and p
As is listed in Table 1, an increase in p is accompanied by a reduction in y when the amor-
°°b
o
OD
0
40 0
i
[
I
J
1
I
2
3
4
5
y ( m J m o 1 - 1 K -2) Fig. 4. Interrelation between the resistivity at 300 K and the electronic specific heat coefficient 7e× for sp-electron quasicrystals. The data for sp-, (sp + d)- anc(d-electron amorphous alloys are also incorporated. Symbols are as follows; A: Mg-A1-Ag, O: Mg-AI-Cu, v : M g - A I - Z n , n: M g - G a - Z n , O : AI-Cu-V, *: AI-Li-Cu, 4: A1-Ru-Cu and o: amorphous alloys. Inset shows the p - T characteristics observed in both quasicrystals and amorphous alloys. Types (a)-(e) appear in this alphabetical sequence with increasing p in nonperiodic and nonmagnetic systems. A dashed curve represents a possible high-resistivity limiting curve [2, 4].
phous A1-Cu-V alloy transforms to a QC phase. A reduction in 7 coupled with an increase in p is also observed in the stable M g - G a - Z n QC [3]. Thermodynamically stable A1-Li-Cu [4] and A1-Ru-Cu [5] QCs are characterized in common by the values of a reduced Y and a very high p. As shown in Fig. 4, one finds that an increase in p with decreasing 7 is a universal feature for nonperiodic sp-electron systems, including both QCs and amorphous alloys. The interrelation between the 7 and p has been discussed in detail on the basis of the conductivity formula a =/9 - 1= (e2/3) AFvv N(E v ), where A v is the mean free path, vF is the Fermi velocity and N(Ev) is the density of states at the Fermi level or the value of y [2-5]. Briefly, it has been claimed that the observed steep rise of/9 with decreasing y is caused by two simultaneously occurring effects: a reduction in carrier density or the value of Y itself and a reduction in A v [2]. As indicated in the inset to Fig. 4, a systematic change in the p - T characteristics from type
114
(a) through (e) is observed in common for both amorphous alloys [2] and QCs [3-5]. A change from type (a) to (c) in the alphabetical sequence with increasing p has been attributed to a decrease in A F with increasing resistivity. It has been shown that the types (d) and (e) observed in high-resistivity AI-Li-Cu and A1-Ru-Cu QCs are the consequence of the weak localization effect [4, 5]. This conclusion has been also drawn for the nonmagnetic amorphous alloys [2]. In conclusion, an amorphous phase can be viewed as being disordered with respect to the translational and orientational symmetries whereas the QC phase as being ordered orientationally without satisfying the translational symmetry. The breakdown of the Bloch condition is, therefore, common in two cases. This yields the same ~, versus p relation and /9-T characteristics. But the observed similarity in the 7 versus e/a dependence between the QCs and the
FK crystals is taken as evidence for the presence of the Fermi surface-Brillouin zone interaction as in typical crystals. References 1 U. Mizutani, Prog. Mater. Sci., 28 (1983) 97; U. Mizutani, Mater. Sci. Eng., 99(1988) 165. 2 U. Mizutani, S. Ohashi, T. Matsuda, K. Fukamichi and K: Tanaka, J. Phys.: Condens. Matter, 2(1990) 541. 3 U. Mizutani, Y. Sakabe and T. Matsuda, J. Phys.: Condens. Matter, 2 (1990) 6153. 4 K.. Kimura, H. Iwahashi, T. Hashimoto, S. Takeuchi, U. Mizutani, S. Ohashi and G. Itoh, J. Phys. Soc. Jpn., 58 (1989) 2472. 5 U. Mizutani, Y. Sakabe, T. Shibuya, K. Kishi, K. Kimura and S. Takeuchi, J. Phys.: Condens. Matter, 2 (1990) 6169. 6 U. Mizutani, A. Kamiya, T. Matsuda, K. Kishi and S. Takeuchi, J. Phys.: Condens. Matter, 2 (1990) (submitted). 7 J. L. Wagner, B. D. Biggs and S. J. Poon, Phys. Rev. Let., 65 (1990) 203. 8 M. Itoh, A. Ishida, H. Sato, T. Matsuda, T. Fukunaga, A. Kamiya and U. Mizutani, presented at this conference.