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Kinetics of crystallization of titanium based binary and ternary amorphous alloys
Journal of Non-Crystalline Solids 353 (2007) 2346–2349 www.elsevier.com/locate/jnoncrysol
Kinetics of crystallization of titanium based binary and ternary amorphous alloys Arun Pratap a
a,*
, T. Lilly Shanker Rao b, Kirit N. Lad a, Heena D. Dhurandhar
a
Condensed Matter Physics Laboratory, Applied Physics Department, Faculty of Technology and Engineering, The Maharaja Sayajirao University of Baroda, Vadodara 390 001, India b Electronics Department, Narmada College of Science and Commerce, Bharuch, India Received 17 August 2006; received in revised form 24 March 2007
Abstract Metallic glasses are kinetically metastable materials. These amorphous materials can be transformed into a crystalline state by both isothermal and isochronal methods. The study of this transformation, and hence the thermal stability of metallic glasses, are important from an application view-point. In the present work, the non-isothermal crystallization kinetics of two titanium-based amorphous alloys namely, Cu50Ti50 and Ti50Ni30Cu20, are reported. The activation energies for crystallization, Ec for both the systems have been evaluated using different non-isothermal methods viz. derived through Kissinger, Augis and Bennet and Ozawa. The values of Ec obtained using these methods are consistent for both the metallic glasses and it is found that Ec for the ternary metallic glass is considerably higher than the binary metallic glass. The increase in the activation energy on the substitution of Ni in the Cu–Ti metallic glass suggests the increase in the thermal stability. 2007 Elsevier B.V. All rights reserved. PACS: 81.05.Bx; 81.05.kf; 81.70.Pg; 82.20.Pm Keywords: Alloys; Nucleation; Calorimetry
1. Introduction The development of exotic materials is a strong motivating force for further progress in science and technology. The first metallic glasses were produced by direct quenching from the melt by Professor Paul Duwez and co-workers [1] at the Californian Institute of Technology. Consequently, great scientific effort has been made in last years in order to predict and control the crystallization processes of metallic glasses because of their various attractive properties. The amorphous state, which does not possess longrange crystalline order stimulated many researchers to study the thermo-dynamical, mechanical and magnetic properties. Metallic glasses exhibit high electrical resistiv*
Corresponding author. E-mail address: [email protected] (A. Pratap).
0022-3093/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2007.04.011
ity, high hardness and stiffness, soft ferromagnetism and high resistance to corrosion. Ti based alloys are technologically important materials, and among them, Ti–Ni alloys are best suited as shape memory alloys. Cu can be substituted up to 20 at.% for Ni and the Ti50Ni50xCux (x = 0– 20) alloys show the shape memory effect [2,3]. Due to the interest created by recently reported research on the Tibased amorphous metallic alloys [4,5], the authors carried out the study of crystallization kinetics of Cu50Ti50 [6,7] and a ternary system Ti50Cu20Ni30 [8]. In our earlier studies [6,7], we tried to understand the mechanism of crystallization through kinetic parameters such as the activation energy of crystallization (Ec), the dimensionality of growth (m) and Avrami exponent (n). In order to derive these parameters the single-heating rate thermal analysis methods like the Kolmogorov–Johnson–Mehl–Avrami (KJMA) [9–11] and the one proposed by Matusita and Sakka [12]
A. Pratap et al. / Journal of Non-Crystalline Solids 353 (2007) 2346–2349
were utilized. The advantage of these methods is that they provide the information of the kinetic parameters from a single scanning experiment. However, the single-heating rate methods are dependent on the reaction model. Also, there are some inherent uncertainties associated with the determination of the crystallized fraction. The multipleheating rate methods, on the other hand, are model-free and involve the shift in the onset-crystallization temperature (To)/peak crystallization temperature (Tp) with heating rate. Therefore, these methods are supposed to give consistent results for the kinetic parameters. This is also corroborated by our present study where three independent multiple-heating rate methods put forward by Kissinger [13], Ozawa [14] and Augis and Benett [15] have been utilized to determine the kinetic parameters of the crystallization process in Cu50Ti50 and Ti50Ni30Cu20. 2. Experimental Specimens of amorphous Ti50Cu20Ni30 and Cu50Ti50 ribbons were prepared by single roller melt spinning technique in an Argon atmosphere at the Institute of Materials Research, Tohoku University, Sendai, Japan. The amorphous nature of ribbons was confirmed by XRD and TEM. The as-quenched samples of Ti50Cu20Ni30 and Cu50Ti50 ribbons were heated in DSC (DSC-50, Shimadzu, Japan) at four linear heating rates from room temperature to 720 K in air. The DSC scans were recorded by a thermal analyzer (TA-50WSI, Shimadzu, Japan) interfaced to a computer. The detection sensitivity of the instrument is 10 lW. 3. Results The DSC curves of as-quenched samples at four heating rates give a single stage crystallization event as shown in Figs. 1 and 2. The crystallization peaks for different heating rates are given in Table 1 along with the corresponding onset temperatures of crystallization, To. These values of various characteristics temperatures involve an error
Fig. 1. DSC thermograms of Ti50Cu20Ni30 at different heating rates.
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Fig. 2. DSC thermograms of Cu50Ti50 at different heating rates.
Table 1 Peak and onset temperatures of crystallization at different heating rates (b) Heating rate (b) (K/min) 2 4 8 10 16
Tp (K)
To (K)
Ti50Cu20Ni30
Cu50Ti50
Ti50Cu20Ni30
Cu50Ti50
– 711 718 719 725
618 632 639 – 651
– 697 706 707 712
598 612 616 – 625
of ±1. Various methods are available in the literature for the analysis of the experimental data obtained under non-isothermal conditions. We have selected the following methods to analyze the DSC data obtained under non-isothermal conditions. (i) Kissinger method: The shift in the crystallization peak with the heating rate can be utilized to determine the activation energy for crystallization Ec using Kissinger peak shift method [13], which relates the peak temperature Tp with heating rate (b) through the equation
Fig. 3. Kissinger plots for Cu50Ti50 and Ti50Cu20Ni30.
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A. Pratap et al. / Journal of Non-Crystalline Solids 353 (2007) 2346–2349
Table 2 Kinetic parameters derived using the three different methods Ti50Cu20Ni30
Methods
Ozawa Augis and Bennett Kissinger
A (s1)
Cu50Ti50
Ec (kJ/mol)
jrj
Ec (kJ/mol)
jrj
Ti50Cu20Ni30
Cu50Ti50
395 ± 3 423 ± 6 406 ± 3
0.99598 0.98439 0.99569
207 ± 2 191 ± 2 207 ± 2
0.99268 0.99506 0.99248
– 6.6 · 1028 4.3 · 1027
– 2.5 · 1013 6.7 · 1014
(ii) Ozawa’s method: The Ozawa’s equation which can be used to determine the activation energy from non-isothermal experiments is given by [14]; Ec þ const ð2Þ ln b ¼ 1:056 RT p Plot of lnb vs 1000/Tp gives the slope of 1.0516Ec/R (Fig. 4). The obtained activation energies are given in the Table 2. (iii) Augis and Bennett’s method: According to the method suggested by Augis and Bennett [15], ! b E ¼ c þ ln A ln ð3Þ RT p Tp To Fig. 4. Ozawa plots for Cu50Ti50 and Ti50Cu20Ni30.
From the slope of the plot (ln(b/(Tp To)) vs 1000/ Tp (Fig. 5), we have calculated Ec and the frequency factor A for both the samples and the values are given in Table 2. 4. Discussion
Fig. 5. Augis and Bennett plots for Cu50Ti50 and Ti50Cu20Ni30.
b ln T 2p
!
Ec AR þ ln ¼ Ec RT p
ð1Þ
where A is a fitting parameter, known as frequency factor and R is the universal gas constant. A plot of lnðb=T 2p Þ vs 1000/Tp (Fig. 3) gives an approximate straight line with a slope – Ec/R and an intercept ln(AR/Ec). The values of activation energy (Ec) and frequency factor (A) obtained from slope and intercept of the plot for both the samples along with correlation coefficient are given in Table 2.
The values of activation energy obtained 207 ± 2 kJ/mol (Ozawa method), 191 ± 1.6 kJ/mol (Augis and Bennett method) and 207 ± 4 kJ/mol (Kissinger method) for Cu50Ti50 are lower than the value (270 kJ/mol) reported for Cu40Ti60 [16,17]. This difference may be attributed to the difference in the composition. Further, the values of Ec obtained for the ternary system using the above three methods come out to be 395 ± 3, 423 ± 6 and 406 ± 3 kJ/ mol, respectively. These Ec values are consistent with the one reported by Schlossmacher et al. [4] for Ti50Cu25Ni25 (374 kJ/mol). The higher value of activation energy for the ternary system can be understood with the help of ‘confusion principle’ [18]. According to this principle; the metallic liquid melt with increasing number of elements, when subjected to rapid cooling, involves competition among constituent elements for crystallization and it results into the confusion leading to formation of glass. The metallic liquid alloy with three or more elements is shown to exhibit good glass-forming ability. Such multicomponent metallic glasses possess large undercooled liquid region. The larger undercooled region suggests a higher activation energy for crystallization. This becomes evident when we compare the values of Ec and the frequency factor (A) for the binary and the ternary systems (Table 2). The values of Ec for Ti50Cu20Ni30 is approxi-
A. Pratap et al. / Journal of Non-Crystalline Solids 353 (2007) 2346–2349
mately twice the value for Cu50Ti50 whereas A is more than 10 orders higher in magnitude. The frequency factor could be physically interpreted as the number of attempts made by nuclei to cross the activation barrier. The larger value of A then evidentially suggests larger width of activation barrier. If we consider the variation in atomic radius, a mixture of elements leads to dense packing in the liquid state and the resulting stability favors glass formation over crystallization [19]. In another way the material forms a structure which is the key to its large glass forming ability. To explain this clearly, we may need further investigation with different concentration of Ni in this alloy. 5. Conclusion Crystallization kinetics of amorphous Cu50Ti50 and Ti50Cu20Ni30 is studied using DSC. The kinetic parameters (Ec and A) obtained using different methods hint at the effect of the addition of Ni into a binary alloy Cu–Ti. In agreement with the confusion principle, the addition of Ni results into the increased glass-forming ability and it subsequently suggests increase in Ec and A. Acknowledgement T. Lilly Shanker Rao (UGC Teacher Fellow) acknowledges the support given by UGC New Delhi for the Teacher Fellowship.
2349
References [1] W. Clemens, R.H. Willens, P. Duwez, Nature 187 (1960) 869. [2] T.H. Nam, T. Saburi, Y. Kawamura, K. Shimizu, Mater. Trans. Jpn. Inst. Met. 31 (1990) 262. [3] T.H. Nam, T. Saburi, K. Shimizu, Mater. Trans. Jpn. Inst. Met. 31 (1990) 959. [4] P. Schlossmacher, N. Boucharat, H. Rosner, G. Wilde, A.V. Shelyakov, J. Phys. IV France 112 (2003) 731. [5] Y. Li, S.C. Ng, Z.P. Lu, Y.P. Feng, K. Lu, Philos. Mag. Lett. 78 (1998) 213. [6] A. Pratap, K.N. Lad, T.L.S. Rao, P. Majmudar, N.S. Saxena, J. Non-Cryst. Solids 345&346 (2004) 178. [7] T.L.S. Rao, K.N. Lad, A. Pratap, J. Therm. Anal. Cal. 78 (2004) 769. [8] K.G. Raval, K.N. Lad, A. Pratap, A.M. Awasthi, S. Bhardwaj, Thermochim. Acta 425 (2005) 47. [9] A.N. Kolmogorov, Bull. Acad. Sci. USSR, Phys. Ser. 1 (1937) 355. [10] W.A. Johnson, P.A. Mehl, Trans. Inst. Min. Metall. Pet. Eng. 135 (1939) 416. [11] M. Avrami, J. Chem. Phys. 7 (1939) 1103; M. Avrami, J. Chem. Phys. 8 (1940) 212; M. Avrami, J. Chem. Phys. 9 (1941) 177. [12] K. Matusita, S. Sakka, Phys. Chem. Glasses 20 (1979) 77. [13] H.E. Kissinger, Anal. Chem. 29 (1957) 1702. [14] T. Ozawa, Bull. Chem. Soc. Jpn. 38 (1965) 1881. [15] J.A. Augis, J.E. Bennett, J. Therm. Anal. 13 (1978) 283. [16] K.H.J. Buschow, Acta Metall. 31 (1983) 155. [17] W.F. Miao, J.T. Wang, S.L. Li, B.Z. Ding, J. Non-Cryst. Solids 117&118 (1990) 230. [18] A. Lindsay Greer, Nature 366 (1993) 303. [19] T. Zhang, A. Inoue, T. Masumoto, Mater. Trans., JIM 32 (1991) 1005.
Kinetics of crystallization of titanium based binary and ternary amorphous alloys Arun Pratap a
a,*
, T. Lilly Shanker Rao b, Kirit N. Lad a, Heena D. Dhurandhar
a
Condensed Matter Physics Laboratory, Applied Physics Department, Faculty of Technology and Engineering, The Maharaja Sayajirao University of Baroda, Vadodara 390 001, India b Electronics Department, Narmada College of Science and Commerce, Bharuch, India Received 17 August 2006; received in revised form 24 March 2007
Abstract Metallic glasses are kinetically metastable materials. These amorphous materials can be transformed into a crystalline state by both isothermal and isochronal methods. The study of this transformation, and hence the thermal stability of metallic glasses, are important from an application view-point. In the present work, the non-isothermal crystallization kinetics of two titanium-based amorphous alloys namely, Cu50Ti50 and Ti50Ni30Cu20, are reported. The activation energies for crystallization, Ec for both the systems have been evaluated using different non-isothermal methods viz. derived through Kissinger, Augis and Bennet and Ozawa. The values of Ec obtained using these methods are consistent for both the metallic glasses and it is found that Ec for the ternary metallic glass is considerably higher than the binary metallic glass. The increase in the activation energy on the substitution of Ni in the Cu–Ti metallic glass suggests the increase in the thermal stability. 2007 Elsevier B.V. All rights reserved. PACS: 81.05.Bx; 81.05.kf; 81.70.Pg; 82.20.Pm Keywords: Alloys; Nucleation; Calorimetry
1. Introduction The development of exotic materials is a strong motivating force for further progress in science and technology. The first metallic glasses were produced by direct quenching from the melt by Professor Paul Duwez and co-workers [1] at the Californian Institute of Technology. Consequently, great scientific effort has been made in last years in order to predict and control the crystallization processes of metallic glasses because of their various attractive properties. The amorphous state, which does not possess longrange crystalline order stimulated many researchers to study the thermo-dynamical, mechanical and magnetic properties. Metallic glasses exhibit high electrical resistiv*
Corresponding author. E-mail address: [email protected] (A. Pratap).
0022-3093/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2007.04.011
ity, high hardness and stiffness, soft ferromagnetism and high resistance to corrosion. Ti based alloys are technologically important materials, and among them, Ti–Ni alloys are best suited as shape memory alloys. Cu can be substituted up to 20 at.% for Ni and the Ti50Ni50xCux (x = 0– 20) alloys show the shape memory effect [2,3]. Due to the interest created by recently reported research on the Tibased amorphous metallic alloys [4,5], the authors carried out the study of crystallization kinetics of Cu50Ti50 [6,7] and a ternary system Ti50Cu20Ni30 [8]. In our earlier studies [6,7], we tried to understand the mechanism of crystallization through kinetic parameters such as the activation energy of crystallization (Ec), the dimensionality of growth (m) and Avrami exponent (n). In order to derive these parameters the single-heating rate thermal analysis methods like the Kolmogorov–Johnson–Mehl–Avrami (KJMA) [9–11] and the one proposed by Matusita and Sakka [12]
A. Pratap et al. / Journal of Non-Crystalline Solids 353 (2007) 2346–2349
were utilized. The advantage of these methods is that they provide the information of the kinetic parameters from a single scanning experiment. However, the single-heating rate methods are dependent on the reaction model. Also, there are some inherent uncertainties associated with the determination of the crystallized fraction. The multipleheating rate methods, on the other hand, are model-free and involve the shift in the onset-crystallization temperature (To)/peak crystallization temperature (Tp) with heating rate. Therefore, these methods are supposed to give consistent results for the kinetic parameters. This is also corroborated by our present study where three independent multiple-heating rate methods put forward by Kissinger [13], Ozawa [14] and Augis and Benett [15] have been utilized to determine the kinetic parameters of the crystallization process in Cu50Ti50 and Ti50Ni30Cu20. 2. Experimental Specimens of amorphous Ti50Cu20Ni30 and Cu50Ti50 ribbons were prepared by single roller melt spinning technique in an Argon atmosphere at the Institute of Materials Research, Tohoku University, Sendai, Japan. The amorphous nature of ribbons was confirmed by XRD and TEM. The as-quenched samples of Ti50Cu20Ni30 and Cu50Ti50 ribbons were heated in DSC (DSC-50, Shimadzu, Japan) at four linear heating rates from room temperature to 720 K in air. The DSC scans were recorded by a thermal analyzer (TA-50WSI, Shimadzu, Japan) interfaced to a computer. The detection sensitivity of the instrument is 10 lW. 3. Results The DSC curves of as-quenched samples at four heating rates give a single stage crystallization event as shown in Figs. 1 and 2. The crystallization peaks for different heating rates are given in Table 1 along with the corresponding onset temperatures of crystallization, To. These values of various characteristics temperatures involve an error
Fig. 1. DSC thermograms of Ti50Cu20Ni30 at different heating rates.
2347
Fig. 2. DSC thermograms of Cu50Ti50 at different heating rates.
Table 1 Peak and onset temperatures of crystallization at different heating rates (b) Heating rate (b) (K/min) 2 4 8 10 16
Tp (K)
To (K)
Ti50Cu20Ni30
Cu50Ti50
Ti50Cu20Ni30
Cu50Ti50
– 711 718 719 725
618 632 639 – 651
– 697 706 707 712
598 612 616 – 625
of ±1. Various methods are available in the literature for the analysis of the experimental data obtained under non-isothermal conditions. We have selected the following methods to analyze the DSC data obtained under non-isothermal conditions. (i) Kissinger method: The shift in the crystallization peak with the heating rate can be utilized to determine the activation energy for crystallization Ec using Kissinger peak shift method [13], which relates the peak temperature Tp with heating rate (b) through the equation
Fig. 3. Kissinger plots for Cu50Ti50 and Ti50Cu20Ni30.
2348
A. Pratap et al. / Journal of Non-Crystalline Solids 353 (2007) 2346–2349
Table 2 Kinetic parameters derived using the three different methods Ti50Cu20Ni30
Methods
Ozawa Augis and Bennett Kissinger
A (s1)
Cu50Ti50
Ec (kJ/mol)
jrj
Ec (kJ/mol)
jrj
Ti50Cu20Ni30
Cu50Ti50
395 ± 3 423 ± 6 406 ± 3
0.99598 0.98439 0.99569
207 ± 2 191 ± 2 207 ± 2
0.99268 0.99506 0.99248
– 6.6 · 1028 4.3 · 1027
– 2.5 · 1013 6.7 · 1014
(ii) Ozawa’s method: The Ozawa’s equation which can be used to determine the activation energy from non-isothermal experiments is given by [14]; Ec þ const ð2Þ ln b ¼ 1:056 RT p Plot of lnb vs 1000/Tp gives the slope of 1.0516Ec/R (Fig. 4). The obtained activation energies are given in the Table 2. (iii) Augis and Bennett’s method: According to the method suggested by Augis and Bennett [15], ! b E ¼ c þ ln A ln ð3Þ RT p Tp To Fig. 4. Ozawa plots for Cu50Ti50 and Ti50Cu20Ni30.
From the slope of the plot (ln(b/(Tp To)) vs 1000/ Tp (Fig. 5), we have calculated Ec and the frequency factor A for both the samples and the values are given in Table 2. 4. Discussion
Fig. 5. Augis and Bennett plots for Cu50Ti50 and Ti50Cu20Ni30.
b ln T 2p
!
Ec AR þ ln ¼ Ec RT p
ð1Þ
where A is a fitting parameter, known as frequency factor and R is the universal gas constant. A plot of lnðb=T 2p Þ vs 1000/Tp (Fig. 3) gives an approximate straight line with a slope – Ec/R and an intercept ln(AR/Ec). The values of activation energy (Ec) and frequency factor (A) obtained from slope and intercept of the plot for both the samples along with correlation coefficient are given in Table 2.
The values of activation energy obtained 207 ± 2 kJ/mol (Ozawa method), 191 ± 1.6 kJ/mol (Augis and Bennett method) and 207 ± 4 kJ/mol (Kissinger method) for Cu50Ti50 are lower than the value (270 kJ/mol) reported for Cu40Ti60 [16,17]. This difference may be attributed to the difference in the composition. Further, the values of Ec obtained for the ternary system using the above three methods come out to be 395 ± 3, 423 ± 6 and 406 ± 3 kJ/ mol, respectively. These Ec values are consistent with the one reported by Schlossmacher et al. [4] for Ti50Cu25Ni25 (374 kJ/mol). The higher value of activation energy for the ternary system can be understood with the help of ‘confusion principle’ [18]. According to this principle; the metallic liquid melt with increasing number of elements, when subjected to rapid cooling, involves competition among constituent elements for crystallization and it results into the confusion leading to formation of glass. The metallic liquid alloy with three or more elements is shown to exhibit good glass-forming ability. Such multicomponent metallic glasses possess large undercooled liquid region. The larger undercooled region suggests a higher activation energy for crystallization. This becomes evident when we compare the values of Ec and the frequency factor (A) for the binary and the ternary systems (Table 2). The values of Ec for Ti50Cu20Ni30 is approxi-
A. Pratap et al. / Journal of Non-Crystalline Solids 353 (2007) 2346–2349
mately twice the value for Cu50Ti50 whereas A is more than 10 orders higher in magnitude. The frequency factor could be physically interpreted as the number of attempts made by nuclei to cross the activation barrier. The larger value of A then evidentially suggests larger width of activation barrier. If we consider the variation in atomic radius, a mixture of elements leads to dense packing in the liquid state and the resulting stability favors glass formation over crystallization [19]. In another way the material forms a structure which is the key to its large glass forming ability. To explain this clearly, we may need further investigation with different concentration of Ni in this alloy. 5. Conclusion Crystallization kinetics of amorphous Cu50Ti50 and Ti50Cu20Ni30 is studied using DSC. The kinetic parameters (Ec and A) obtained using different methods hint at the effect of the addition of Ni into a binary alloy Cu–Ti. In agreement with the confusion principle, the addition of Ni results into the increased glass-forming ability and it subsequently suggests increase in Ec and A. Acknowledgement T. Lilly Shanker Rao (UGC Teacher Fellow) acknowledges the support given by UGC New Delhi for the Teacher Fellowship.
2349
References [1] W. Clemens, R.H. Willens, P. Duwez, Nature 187 (1960) 869. [2] T.H. Nam, T. Saburi, Y. Kawamura, K. Shimizu, Mater. Trans. Jpn. Inst. Met. 31 (1990) 262. [3] T.H. Nam, T. Saburi, K. Shimizu, Mater. Trans. Jpn. Inst. Met. 31 (1990) 959. [4] P. Schlossmacher, N. Boucharat, H. Rosner, G. Wilde, A.V. Shelyakov, J. Phys. IV France 112 (2003) 731. [5] Y. Li, S.C. Ng, Z.P. Lu, Y.P. Feng, K. Lu, Philos. Mag. Lett. 78 (1998) 213. [6] A. Pratap, K.N. Lad, T.L.S. Rao, P. Majmudar, N.S. Saxena, J. Non-Cryst. Solids 345&346 (2004) 178. [7] T.L.S. Rao, K.N. Lad, A. Pratap, J. Therm. Anal. Cal. 78 (2004) 769. [8] K.G. Raval, K.N. Lad, A. Pratap, A.M. Awasthi, S. Bhardwaj, Thermochim. Acta 425 (2005) 47. [9] A.N. Kolmogorov, Bull. Acad. Sci. USSR, Phys. Ser. 1 (1937) 355. [10] W.A. Johnson, P.A. Mehl, Trans. Inst. Min. Metall. Pet. Eng. 135 (1939) 416. [11] M. Avrami, J. Chem. Phys. 7 (1939) 1103; M. Avrami, J. Chem. Phys. 8 (1940) 212; M. Avrami, J. Chem. Phys. 9 (1941) 177. [12] K. Matusita, S. Sakka, Phys. Chem. Glasses 20 (1979) 77. [13] H.E. Kissinger, Anal. Chem. 29 (1957) 1702. [14] T. Ozawa, Bull. Chem. Soc. Jpn. 38 (1965) 1881. [15] J.A. Augis, J.E. Bennett, J. Therm. Anal. 13 (1978) 283. [16] K.H.J. Buschow, Acta Metall. 31 (1983) 155. [17] W.F. Miao, J.T. Wang, S.L. Li, B.Z. Ding, J. Non-Cryst. Solids 117&118 (1990) 230. [18] A. Lindsay Greer, Nature 366 (1993) 303. [19] T. Zhang, A. Inoue, T. Masumoto, Mater. Trans., JIM 32 (1991) 1005.