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The low temperature specific heat of Lu-Cu-Y metallic glasses
Journal of Magnetism and Magnetic Materials 65 (1987) 15-20 North-Holland, Amsterdam
15
T H E LOW TEMPERATURE SPECIFIC HEAT OF L u - C u - Y M E T A L L I C G L A S S E S K.A. M O H A M M E D t and P.C. L A N C H E S T E R Department of Physics, The University, Southampton, S09 5NH, UK Received 29 August 1986
The specific heat of a series of amorphous metallic alloys of the form LUxCUo.37Yo.63-x (x = 0, 0.1, 0.3 and 0.4) has been
measured between 2 and 50 K, primarily in order to be able to determine the non-magneticcontributions to the specific heat in magnetic RE-Cu-Y amorphous alloys. The data at low temperature fit the simple form Cp = y T + fiT 3 from which values of y and 0D(0) have been determined. Consideration is given to the error that arises if Y is used rather than Lu or La in forming non-magnetic rare earth intermetallics for purposes of determining the non-magnetic contributions to the specific heat of magnetic samples. A simple procedure is described that allows a useful improvement in accuracy in estimating non-magnetic contributions below 20 K if Y is used. The method may also be useful if only a restricted range of compositions using Lu is possible.
1. Introduction Recently we have made a systematic study of the specific heats of a series of amorphous G d - C u - Y alloys with particular emphasis on the determination of the magnetic specific heats [1,2]. A basic problem in obtaining the magnetic specific heat arises from the difficulty of determining independently the non-magnetic contributions due to the electronic and lattice excitations. One possibility is to measure the specific heat of non-magnetic samples with very similar electronic and lattice properties which have been prepared by substituting Lu, La or Y for a magnetically active rare earth component. All these substitutes have the same outer electronic structure and form similar crystal structures, the main difference between them being their atomic weights. In this regard Lu should be best for the heavy rare earths and La for the light rare earths. Gd lies in the middle of the series and there is little to choose between them. Unfortunately, however, La is unsuited to the melt-spinning process due to its reactivity with air, and we have therefore used Lu as a non-magnetic t Present address: Department of Physics, College of Education, University of Mosul, Mosul, Iraq.
substitute for Gd, despite the very high cost involved. In fact, probably because of the cost factor, and despite the large difference in atomic weight, many workers tend to use Y rather than La or Lu. The present results reveal that Y is a very poor substitute for the rare earths. However we have found that it is possible to improve the value of Y as a substitute by modifying the temperature scale of the results. This is discussed in section 3.
2. Experimental Amorphous ribbons of LuxCu0.37Y0.63_ x alloys where x = 0, 0.1, 0.3, 0.4, were prepared using the well established melt-spinning technique in which rapid cooling of a molten alloy is achieved by expelling the melt against a rapidly spinning copper wheel. In our case the wheel had a diameter of 15 cm and was rotating at 4000 to 5000 rpm. Amorphicity of the resultant ribbons was checked by studying the X-ray diffraction pattern and by a simple mechanical (180 ° bend) test that has been described previously [2]. Samples of about 0.75 g were prepared by winding lengths of ribbon edgewise onto a sample
0304-8853/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
16
K.A. Mohammed, P.C. Lanchester / Specific heat of Lu- Cu- Y metallic glasses
temperature was first analysed assuming the form;
holder as described in refs. [1,3]. The specific heat of the samples was then measured using a modified adiabatic continuous heating technique full details of which can also be found in refs. [1-3].
3. Results
and
which has commonly been found to describe the low temperature specific heat of amorphous alloys [4]. The linear term represents the contribution from the electrons and possibly other non-electronic contributions which are often found in glasses. The second and third terms represent the lattice contributions to the specific heat. In fact it was found from the initial fits that the 8T 5 contributions are relatively insignificant and subsequently only the first two terms were included in the fitting equation. The resultant values of ~, and fl are summarised in table 1, and V is shown plotted against Lu concentration in fig. 3a. The magnitudes observed for -/ are typical for electrons in normal crystalline metals and it is therefore tempting to assume that the linear term is purely electronic in origin. Even so it is difficult to arrive at any firm conclusions because ~, is notoriously difficult to calculate with any accu-
discussion
The results of our measurements are shown plotted as a function of temperature between 2 and 50 K in fig. 1. As expected, as the concentration of the relatively massive Lu increases, the Debye temperature falls and the specific heat at a given temperature increases. The data below 7 K are replotted in fig. 2 as C p / T versus T 2. A noticeable upturn is apparent in this plot at the low temperature end. The magnitude of this deviation from the fitted straight line increases with Lu concentration. The origin of this has not been established with certainty but is thought to be due to magnetic impurities in the Lu start material. Ignoring the upturn, the specific heat at low
15
i
i
i
(1)
C = ' y T + flT3 + ~ T 5
i
i
i
i
i
i
1/+ 13 12 :.,.." • -......
11
.:g.- "...
'..
10 •,:..,' ~,..= . ='.:..
9
......:~::..%.?.. LU40CU37Y23~
O
~-r7
u
7
".. ":::'~.iL' T.I~"~':L---- CU37Y63
,,.~9~'.'!:::::~'-----'----~ Lu10cU37YS3 ,..L.-"...'--" .4:'~" ~.'.'
6
• ~fl.. >. ,:$.'
5
L U30 CU37 Y 33 ~ ~ - ~ "
z,
:.2::-;'
.,,,=#%--'"
3 •
2 I /
5
I
I
I
10
15
20
2~5
I
[
I
I
30
35
~.0
~-5
TEMP (K) Fig. 1. Specificheat of Lu-Cu-Y alloys as a function of temperature.
50
K.A. Mohammed, P. C Lanchester/ Specific heat of Lu- Cu- Y metallic glasses Table 1 Low temperature, specific heat data for amorphous L u - C u - Y alloys Composition
Cu37Y63 LUloCU37Y53 Lu 2oCu37Y43 Ltl 3oCu 37Y33 Lu 4oCu 37Y23
3'cxp (m J / mol K 2)
~FE
fl
#D(O)
(m J / tool K 2)
(m J / tool K 4)
(K)
3.62 3.09 2.85 2.61 2.34
0.99 1.00 1.02 1.03 1.04
0.399 0.459 0.524 0.550 0.639
170 162 156 150 145
racy. Nevertheless, we have calculated 7FE for each of our samples assuming the following result from a free electron model calculation [5] YFE = 0.136[ A / d ]2/3[ e/a ]1/3 m J / m o l K 2, where A is the average atomic mass of the alloy, d is the density, and e/a is the average number of free electrons per atom. These results are listed in table 1. Clearly the agreement with experiment is poor. The experimental values for ~/('/exp) are about three times greater than the calculated values (~FE) and the observed variation with composition is opposite to and much greater than that
~0
I
17
predicted. We conclude that the free electron theory is inapplicable, and that the enhanced "r values probably arise from peaks in the electron densities of states resulting from relatively narrow d bands, the position of which may be expected to be a sensitive function of the composition. Results for the lattice coefficient fl have been used to calculate the limiting values ( T ~ 0) of the Debye temperatures 0D(0 ) which are listed in table 1 and plotted as a function of Lu concentration in fig. 3b. The fall in 60(0 ) with increasing Lu concentration referred to earlier is clear. In the simplest possible description of these alloys at low temperatures we might expect that the force constants of the lattice should remain approximately independent of the Lu concentration, since the structure and the outer electronic configuration remain essentially essentially unchanged, but that the average mass ( M ) of the atoms will increase with increasing Lu concentration. If this is true then OD(0) should be simply proportional to ( M ) -1/2 w h e r e ( M ) is the mean atomic weight. As shown in fig. 4 the present results do indeed approximate this form. Since Y rather than La or Lu is so often used to form non-magnetic equivalents of rare earth al-
I
~
I
I
#
3'5
I
C5
35
3O 25 20
I-.-
15
5 5 5. 5 I
lo
2b
I
25
T~ ( K ~) Fig. 2. Cp/T versus T 2 for amorphous L u - C u - Y alloys.
5o
18
K.A. Mohammed, P.C. Lanchester / Specific heat of L u - C u - Y metallic glasses i
(a)
proximately true except at very low temperatures. However it is reasonable to suppose that a set of closely related materials such as those of interest here will fit the same function of (T/OD(O) over a reasonable wide temperature range. In order to check this supposition the results for all our sampies were plotted in the form c versus T/OD(O) and were indeed found to lie reasonably accurately on a single curve, at least up to about 20 to 25 K. This observation suggests that results obtained with Y can be corrected so that they correspond to the results that would be obtained with a heavier rare earth element, say Lu, simply by scaling the temperature, i.e. by plotting the result for the Y alloy at a temperature T at a temperature T ' where
i
od
T
1
0 18C
i
i
,
i
(b)
16C
T'= TOD(O)[Lu]/OD(O)[Y].
0 15C
130
o
1~
2b
30J
~0
50
fiONC. ( AT % LU ) Fig. 3. (a) Electronic specific heat coefficient 3' versus Lu concentration; (b) Debye temperature 0D(0) versus Lu con centration. loys, it is of interest to consider the error that arises in so doing. In fact our non-magnetic samples based on Lu and Y are ideally suited to this exercise because the error that results from substituting Y for Lu can be observed simply by comparing the results for the Lu samples with that for the Cu0.37Y0.63 = YxCu0.37Y0.63_xsample. It is immediately clear from such comparisons that the error is substantial, amounting to more than 20% for the 30% Lu alloy at 20 K. We must conclude that Y is really rather a poor substitute for Lu. It is however possible to improve matters by scaling the results obtained with Y having regard to the difference in mass between Y and the element for which it is substituted. According to the Debye theory the lattice specific heat of all solids should fit a universal function of (T/OD(O)). In practice this is well known to be only ap-
Clearly it is necessary to be able to estimate 0D(0 ) for the fictitious Lu alloy and this can be done by using the approximate result noted earlier that 0D(0 ) cc ( M ) - 1 / 2 . The result of carrying out this process in order to estimate the lattice specific heat of Lu0.30Cu0.37Y0.33 from the result for Cu 0.3vY0.63 is shown in fig. 5. Clearly the estimated result lies significantly closer to the known experimental result for the Lu alloy than does the result for the uncorrected Y alloy. (The residual difference is due almost entirely to the error in estimating 0D(0 ) for the Lu alloy.) We conclude that our technique can be used to improve the accuracy of determining the magnetic contribution to the specific heat of rare earth alloys when Y is used as a non-magnetic substitute. One further situation in which the method we have described could be useful is when results for a series of Lu compositions are required but the cost of the samples is prohibitive. In this case it should be possible to measure just two samples, one at each end of the composition range, and to interpolate the results for intermediate compositions. Measurement of two samples should allow a much better determination of the variation of 0D(0 ) with Lu composition which in turn should lead to much more accurate estimations of the lattice contributions at intermediate compositions than would be possible with just a single sample.
K.A. Mohammea~ P.C. Lanchester / Specific heat of L u - Cu- Y metallic glasses 200
!
1
i
r
i
i
i
=
~
i
I
I
I
I
i
I
I
I
I
2
3
/,
5
6
7
8
9
10
11
12
19
I
180 160 140 120 v'
100
E:I 80 60 ~0 2(3 i
1
I
13
14
15
M -½ [ £~&,H/MOLE -l"z x 10 .2 ] Fig. 4. Debye temperature versus square root inverse of average atomic mass for L u - C u - Y alloys.
3,0
// LU30CU37Y33 (exp)
2,5
LU30CU37Y33 - ESTIMATED USINGCU3"/Y63 RESULT~ . . ~ / /
//
2,0
0
.~
1,5
O1,0
0,5
5
10
15
TEMP (K) Fig. 5. Specific heat of Lu30Cu37Y33 versus temperature.
20
20
K.A. Mohammed, P.C. Lanchester / Specific heat of L u - C u - Y metallic glasses
Acknowledgements W e are grateful to Professor B.D. R a i n f o r d a n d to Professor B.R. Coles for useful discussions. Dr. K.A. M o h a m m e d acknowledges financial s u p p o r t from the Iraqi g o v e r n m e n t .
References [1] K.A. Mohammed, PhD thesis, Southampton University (1985).
[2] K.A. Mohammed and P.C. Lanchester, J. Magn. Magn. Mat. 60 (1986) 275. [3] P.C. Lanchester and K.A. Mohammed, J. Phys. E 18 (1985) 581. [4] B. Golding, B.G. Baley and F.S.L. Hsu, Phys. Rev. Lett. 29 (1972) 68. [5] U. Mizutani, Prog. Mater. Sci. 28 (1983) 97.
15
T H E LOW TEMPERATURE SPECIFIC HEAT OF L u - C u - Y M E T A L L I C G L A S S E S K.A. M O H A M M E D t and P.C. L A N C H E S T E R Department of Physics, The University, Southampton, S09 5NH, UK Received 29 August 1986
The specific heat of a series of amorphous metallic alloys of the form LUxCUo.37Yo.63-x (x = 0, 0.1, 0.3 and 0.4) has been
measured between 2 and 50 K, primarily in order to be able to determine the non-magneticcontributions to the specific heat in magnetic RE-Cu-Y amorphous alloys. The data at low temperature fit the simple form Cp = y T + fiT 3 from which values of y and 0D(0) have been determined. Consideration is given to the error that arises if Y is used rather than Lu or La in forming non-magnetic rare earth intermetallics for purposes of determining the non-magnetic contributions to the specific heat of magnetic samples. A simple procedure is described that allows a useful improvement in accuracy in estimating non-magnetic contributions below 20 K if Y is used. The method may also be useful if only a restricted range of compositions using Lu is possible.
1. Introduction Recently we have made a systematic study of the specific heats of a series of amorphous G d - C u - Y alloys with particular emphasis on the determination of the magnetic specific heats [1,2]. A basic problem in obtaining the magnetic specific heat arises from the difficulty of determining independently the non-magnetic contributions due to the electronic and lattice excitations. One possibility is to measure the specific heat of non-magnetic samples with very similar electronic and lattice properties which have been prepared by substituting Lu, La or Y for a magnetically active rare earth component. All these substitutes have the same outer electronic structure and form similar crystal structures, the main difference between them being their atomic weights. In this regard Lu should be best for the heavy rare earths and La for the light rare earths. Gd lies in the middle of the series and there is little to choose between them. Unfortunately, however, La is unsuited to the melt-spinning process due to its reactivity with air, and we have therefore used Lu as a non-magnetic t Present address: Department of Physics, College of Education, University of Mosul, Mosul, Iraq.
substitute for Gd, despite the very high cost involved. In fact, probably because of the cost factor, and despite the large difference in atomic weight, many workers tend to use Y rather than La or Lu. The present results reveal that Y is a very poor substitute for the rare earths. However we have found that it is possible to improve the value of Y as a substitute by modifying the temperature scale of the results. This is discussed in section 3.
2. Experimental Amorphous ribbons of LuxCu0.37Y0.63_ x alloys where x = 0, 0.1, 0.3, 0.4, were prepared using the well established melt-spinning technique in which rapid cooling of a molten alloy is achieved by expelling the melt against a rapidly spinning copper wheel. In our case the wheel had a diameter of 15 cm and was rotating at 4000 to 5000 rpm. Amorphicity of the resultant ribbons was checked by studying the X-ray diffraction pattern and by a simple mechanical (180 ° bend) test that has been described previously [2]. Samples of about 0.75 g were prepared by winding lengths of ribbon edgewise onto a sample
0304-8853/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
16
K.A. Mohammed, P.C. Lanchester / Specific heat of Lu- Cu- Y metallic glasses
temperature was first analysed assuming the form;
holder as described in refs. [1,3]. The specific heat of the samples was then measured using a modified adiabatic continuous heating technique full details of which can also be found in refs. [1-3].
3. Results
and
which has commonly been found to describe the low temperature specific heat of amorphous alloys [4]. The linear term represents the contribution from the electrons and possibly other non-electronic contributions which are often found in glasses. The second and third terms represent the lattice contributions to the specific heat. In fact it was found from the initial fits that the 8T 5 contributions are relatively insignificant and subsequently only the first two terms were included in the fitting equation. The resultant values of ~, and fl are summarised in table 1, and V is shown plotted against Lu concentration in fig. 3a. The magnitudes observed for -/ are typical for electrons in normal crystalline metals and it is therefore tempting to assume that the linear term is purely electronic in origin. Even so it is difficult to arrive at any firm conclusions because ~, is notoriously difficult to calculate with any accu-
discussion
The results of our measurements are shown plotted as a function of temperature between 2 and 50 K in fig. 1. As expected, as the concentration of the relatively massive Lu increases, the Debye temperature falls and the specific heat at a given temperature increases. The data below 7 K are replotted in fig. 2 as C p / T versus T 2. A noticeable upturn is apparent in this plot at the low temperature end. The magnitude of this deviation from the fitted straight line increases with Lu concentration. The origin of this has not been established with certainty but is thought to be due to magnetic impurities in the Lu start material. Ignoring the upturn, the specific heat at low
15
i
i
i
(1)
C = ' y T + flT3 + ~ T 5
i
i
i
i
i
i
1/+ 13 12 :.,.." • -......
11
.:g.- "...
'..
10 •,:..,' ~,..= . ='.:..
9
......:~::..%.?.. LU40CU37Y23~
O
~-r7
u
7
".. ":::'~.iL' T.I~"~':L---- CU37Y63
,,.~9~'.'!:::::~'-----'----~ Lu10cU37YS3 ,..L.-"...'--" .4:'~" ~.'.'
6
• ~fl.. >. ,:$.'
5
L U30 CU37 Y 33 ~ ~ - ~ "
z,
:.2::-;'
.,,,=#%--'"
3 •
2 I /
5
I
I
I
10
15
20
2~5
I
[
I
I
30
35
~.0
~-5
TEMP (K) Fig. 1. Specificheat of Lu-Cu-Y alloys as a function of temperature.
50
K.A. Mohammed, P. C Lanchester/ Specific heat of Lu- Cu- Y metallic glasses Table 1 Low temperature, specific heat data for amorphous L u - C u - Y alloys Composition
Cu37Y63 LUloCU37Y53 Lu 2oCu37Y43 Ltl 3oCu 37Y33 Lu 4oCu 37Y23
3'cxp (m J / mol K 2)
~FE
fl
#D(O)
(m J / tool K 2)
(m J / tool K 4)
(K)
3.62 3.09 2.85 2.61 2.34
0.99 1.00 1.02 1.03 1.04
0.399 0.459 0.524 0.550 0.639
170 162 156 150 145
racy. Nevertheless, we have calculated 7FE for each of our samples assuming the following result from a free electron model calculation [5] YFE = 0.136[ A / d ]2/3[ e/a ]1/3 m J / m o l K 2, where A is the average atomic mass of the alloy, d is the density, and e/a is the average number of free electrons per atom. These results are listed in table 1. Clearly the agreement with experiment is poor. The experimental values for ~/('/exp) are about three times greater than the calculated values (~FE) and the observed variation with composition is opposite to and much greater than that
~0
I
17
predicted. We conclude that the free electron theory is inapplicable, and that the enhanced "r values probably arise from peaks in the electron densities of states resulting from relatively narrow d bands, the position of which may be expected to be a sensitive function of the composition. Results for the lattice coefficient fl have been used to calculate the limiting values ( T ~ 0) of the Debye temperatures 0D(0 ) which are listed in table 1 and plotted as a function of Lu concentration in fig. 3b. The fall in 60(0 ) with increasing Lu concentration referred to earlier is clear. In the simplest possible description of these alloys at low temperatures we might expect that the force constants of the lattice should remain approximately independent of the Lu concentration, since the structure and the outer electronic configuration remain essentially essentially unchanged, but that the average mass ( M ) of the atoms will increase with increasing Lu concentration. If this is true then OD(0) should be simply proportional to ( M ) -1/2 w h e r e ( M ) is the mean atomic weight. As shown in fig. 4 the present results do indeed approximate this form. Since Y rather than La or Lu is so often used to form non-magnetic equivalents of rare earth al-
I
~
I
I
#
3'5
I
C5
35
3O 25 20
I-.-
15
5 5 5. 5 I
lo
2b
I
25
T~ ( K ~) Fig. 2. Cp/T versus T 2 for amorphous L u - C u - Y alloys.
5o
18
K.A. Mohammed, P.C. Lanchester / Specific heat of L u - C u - Y metallic glasses i
(a)
proximately true except at very low temperatures. However it is reasonable to suppose that a set of closely related materials such as those of interest here will fit the same function of (T/OD(O) over a reasonable wide temperature range. In order to check this supposition the results for all our sampies were plotted in the form c versus T/OD(O) and were indeed found to lie reasonably accurately on a single curve, at least up to about 20 to 25 K. This observation suggests that results obtained with Y can be corrected so that they correspond to the results that would be obtained with a heavier rare earth element, say Lu, simply by scaling the temperature, i.e. by plotting the result for the Y alloy at a temperature T at a temperature T ' where
i
od
T
1
0 18C
i
i
,
i
(b)
16C
T'= TOD(O)[Lu]/OD(O)[Y].
0 15C
130
o
1~
2b
30J
~0
50
fiONC. ( AT % LU ) Fig. 3. (a) Electronic specific heat coefficient 3' versus Lu concentration; (b) Debye temperature 0D(0) versus Lu con centration. loys, it is of interest to consider the error that arises in so doing. In fact our non-magnetic samples based on Lu and Y are ideally suited to this exercise because the error that results from substituting Y for Lu can be observed simply by comparing the results for the Lu samples with that for the Cu0.37Y0.63 = YxCu0.37Y0.63_xsample. It is immediately clear from such comparisons that the error is substantial, amounting to more than 20% for the 30% Lu alloy at 20 K. We must conclude that Y is really rather a poor substitute for Lu. It is however possible to improve matters by scaling the results obtained with Y having regard to the difference in mass between Y and the element for which it is substituted. According to the Debye theory the lattice specific heat of all solids should fit a universal function of (T/OD(O)). In practice this is well known to be only ap-
Clearly it is necessary to be able to estimate 0D(0 ) for the fictitious Lu alloy and this can be done by using the approximate result noted earlier that 0D(0 ) cc ( M ) - 1 / 2 . The result of carrying out this process in order to estimate the lattice specific heat of Lu0.30Cu0.37Y0.33 from the result for Cu 0.3vY0.63 is shown in fig. 5. Clearly the estimated result lies significantly closer to the known experimental result for the Lu alloy than does the result for the uncorrected Y alloy. (The residual difference is due almost entirely to the error in estimating 0D(0 ) for the Lu alloy.) We conclude that our technique can be used to improve the accuracy of determining the magnetic contribution to the specific heat of rare earth alloys when Y is used as a non-magnetic substitute. One further situation in which the method we have described could be useful is when results for a series of Lu compositions are required but the cost of the samples is prohibitive. In this case it should be possible to measure just two samples, one at each end of the composition range, and to interpolate the results for intermediate compositions. Measurement of two samples should allow a much better determination of the variation of 0D(0 ) with Lu composition which in turn should lead to much more accurate estimations of the lattice contributions at intermediate compositions than would be possible with just a single sample.
K.A. Mohammea~ P.C. Lanchester / Specific heat of L u - Cu- Y metallic glasses 200
!
1
i
r
i
i
i
=
~
i
I
I
I
I
i
I
I
I
I
2
3
/,
5
6
7
8
9
10
11
12
19
I
180 160 140 120 v'
100
E:I 80 60 ~0 2(3 i
1
I
13
14
15
M -½ [ £~&,H/MOLE -l"z x 10 .2 ] Fig. 4. Debye temperature versus square root inverse of average atomic mass for L u - C u - Y alloys.
3,0
// LU30CU37Y33 (exp)
2,5
LU30CU37Y33 - ESTIMATED USINGCU3"/Y63 RESULT~ . . ~ / /
//
2,0
0
.~
1,5
O1,0
0,5
5
10
15
TEMP (K) Fig. 5. Specific heat of Lu30Cu37Y33 versus temperature.
20
20
K.A. Mohammed, P.C. Lanchester / Specific heat of L u - C u - Y metallic glasses
Acknowledgements W e are grateful to Professor B.D. R a i n f o r d a n d to Professor B.R. Coles for useful discussions. Dr. K.A. M o h a m m e d acknowledges financial s u p p o r t from the Iraqi g o v e r n m e n t .
References [1] K.A. Mohammed, PhD thesis, Southampton University (1985).
[2] K.A. Mohammed and P.C. Lanchester, J. Magn. Magn. Mat. 60 (1986) 275. [3] P.C. Lanchester and K.A. Mohammed, J. Phys. E 18 (1985) 581. [4] B. Golding, B.G. Baley and F.S.L. Hsu, Phys. Rev. Lett. 29 (1972) 68. [5] U. Mizutani, Prog. Mater. Sci. 28 (1983) 97.