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Study of R-phase transformation in a Ti–50.7at%Ni alloy by in-situ transmission electron microscopy observations
Materials Science and Engineering A273 – 275 (1999) 186 – 189 www.elsevier.com/locate/msea
Study of R-phase transformation in a Ti–50.7at%Ni alloy by in-situ transmission electron microscopy observations W. Cai a, Y. Murakami b, K. Otsuka a,* b
a Institute of Materials Science, Uni6ersity of Tsukuba, Tsukuba, Ibaraki 305 -8573, Japan Institute for Ad6anced Materials Processing, Tohoku Uni6ersity, Katahira, Sendai 980 -77, Japan
Abstract The R-phase transformation in a Ti–50.7at%Ni alloy was investigated by in-situ transmission electron microscopy (TEM) observations using double-tilt cooling stages, and the incommensurability of 1/3 diffuse scattering in the process of the transformation was examined by using imaging plates. It is shown that the incommensurate diffuse scattering exists in the parent phase within a wide temperature range above the Rs temperature and that the incommensurability decreases with decreasing temperature. The R-phase transformation starts at the Rs temperature where the electrical resistance starts to increase and the R-phase is commensurate even in the state just after formation. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Martensite; R-phase; Ni–Ti; Incommensurability
1. Introduction The R-phase transformation with a small temperature hysteresis in Ti – Ni alloys has attracted considerable attention, since it is very useful for actuator applications. In order to understand its transformation mechanism, many studies have been carried out using various techniques. The transformation sequence in Ti –Ni alloys during cooling has been believed for a long time to be as follows [1 – 3]: B2 parent (P)- incommensurate (IC)- commensurate (R), and the R-phase transformation was tentatively explained in terms of a charge density wave [1] or modulated lattice relaxation model [4]. The R-phase transformation was first found by Dautovich and Purdy [5], and then characterized well by Sandrock and Hehemann [6] by the sharp increase of the electrical resistivity and appearance of superlattice reflections at 1/3 position along 110* in X-ray and electron diffraction. Thereafter, many investigations have been made in order to clarify the R-phase transformation process by Wayman’s group [1 – 3], who carried out systematic experiments for Ti – Ni – Fe alloys by * Corresponding author. Tel.: +81-298-535294; fax: + 81-298557440. E-mail address: [email protected] (K. Otsuka)
using neutron and X-ray diffraction, electron microscopy, electrical resistivity and magnetic susceptibility measurements etc. They found that the superlattice reflections appear at an incommensurate position first, and the incommensurability decreases with decreasing temperature until it locks-in to a commensurate phase at lower temperature. The temperature where the incommensurate superlattice reflections start to appear (TI) coincides with that where the resistivity starts to rise. The lock-in temperature Tr from incommensurate to commensurate coincides with the temperature where dr/dT becomes maximum. The temperature difference between TI and Tr in the case of a Ti–46.8Ni– 3.2Fe(at%) single crystal is 8 K. Based on their experimental results, they ascribed the R-phase transformation to the formation of charge density waves (CDW). On the other hand, Shapiro et al. [7] made a detailed study on the incommensurability by the X-ray diffraction technique using a linear position sensitive detector, and reported that the incommensurate displacement in reciprocal space is neither regular nor periodic. Thus, they denied the interpretation by CDW. Later Yamada [4] proposed a modulated lattice relaxation model for the incommensurate state of the parent phase. Recently, Saburi’s group [8,9] made a qualitative study on R-phase transformation in a Ti–48Ni–
0921-5093/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 9 9 ) 0 0 3 6 7 - 6
W. Cai et al. / Materials Science and Engineering A273–275 (1999) 186–189
2Al(at%) alloy by electron microscopy. They observed that the R-phase nucleates from lattice defects such as dislocations and grows during cooling. Therefore, they claimed that the transformation is first order. Furthermore, they interpreted the transformation such that the specimen is in a diffuse incommensurate state above the temperature where the resistivity starts to increase. Thus, their interpretation is different from that of Wayman’s group. Very recently, Tamiya and Otsuka et al. [10] studied the R-phase transformation in a Ti – 48Ni – 2Fe(at%) alloy by in-situ electron microscopy with double-tilt cooling stages and examined accurately the incommensurability in the early stages of the transformation by using imaging plates. They found that the R-phase transformation starts at the temperature Rs from the B2 parent phase with weak diffuse scattering to the commensurate R-phase with a sharp interface. Thus, they pointed out that the transformation is of first order and the temperature hysteresis represents the two-phase region of parent and the commensurate Rphase. Therefore, we can see that the origin of R-phase transformation is not well understood, and the incommensurability associated with the transformation is even controversial. So, in the present work we studied the R-phase transformation in an aged Ti – 50.7at%Ni alloy and paid special emphasis on the incommensurability in the process of the transformation.
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the intensity and position of electron diffraction can be measured accurately.
3. Results and discussions
3.1. Obser6ation of R-phase transformation by electrical resistance measurements In order to determine the transformation temperatures of the R-phase transformation and to understand the transformation sequence well, the electrical resistance as a function of temperature was measured as shown in Fig. 1. The Rs temperature corresponding to the temperature where the resistivity starts to increase, represents the R-phase start temperature in our terminology. Thus, it coincides with the TI temperature of Hwang et al. [1]. The Rs temperature is 280 K for the present alloy. From Fig. 1, the temperature hysteresis associated with the R-phase transformation can be clearly seen although it is very small ( 1 K). This indicates that the R-phase transformation is of first order. The above result is consistent with the previous reports by Fukuda et al. [8] for a Ti–48Ni–2Al(at%) alloy and by Tamiya et al for a Ti–48Ni–2Fe(at%) alloy [10]. It should be noticed that no second order transformation ascribed by Wayman’s group [3] was observed in Fig. 1. It will be discussed in detail later.
3.2. Obser6ation of superlattice reflection changes with R-phase transformation 2. Experimental The specimens of nominal composition Ti– 50.7at%Ni were supplied by Furukawa Electric Co. Ltd. After spark cutting into proper sizes, the specimens were solution treated at 1273 K for 1 h in vacuum followed by quenching into ice water and then aged at 823 K for 25 h. Four terminal electrical resistance measurements were carried out with slow cooling and heating rate of 0.5 K min − 1. The specimens for electron microscopy were prepared by a twin-jet electro-polishing apparatus STRUERS TENUPOL3 with the solution of H2SO4 (20vol.%)+ CH3OH (80vol.%). In-situ transmission electron microscopy (TEM) observations were carried out using JEM 2000FX operating at 200 kV with a double-tilt cooling stage. The upper temperature limit for the cooling stage is about 353 K. The diffraction patterns were recorded by using Fuji FDL-URV imaging plates (IP). The size of IP was 8.2 ×11.8 cm2 and the onepixel-size was 25 mm. The sensitivity is 1000 times higher than that of the ordinary film, and the dynamic range is four digit wide. The information recorded on imaging plates was read out by an IP reader and then analyzed by a software called ‘Image Gauge’, by which
To examine the temperature dependence of superlattice reflections, the specimen was heated to 343 K, which is much higher than the Rs temperature, and then the change in diffraction pattern was observed during cooling from 343 to 276 K. When the temperature is higher than 276 K, the diffuse scattering is not
Fig. 1. Electric resistance vs. temperature curve for a Ti–50.7at%Ni alloy, which was solution-treated at 1273 K for 1 h and then aged at 823 K for 25 h.
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damental reflections of a higher angle is stronger than that at the lower angle and the diffuse scattering is almost invisible around transmitted beam (see Fig. 2(a)). The reason for this is unclear right now. Therefore, we select the diffuse scattering beside the (220) reflection instead of that beside the (110) reflection to measure the intensity and position of the diffuse scattering. We also notice that there is a small difference between the R-phase start temperature taken by TEM observation (276 K, as mentioned above) and that measured by electrical resistance measurement (280 K, as shown in Fig. 1). This is mainly due to the following two reasons. One is the thin film effect and another is the measurement method. The transformation temperature of the thin film used for TEM observations may be different from that of the bulk specimen used for electrical resistance measurement. On the other hand, for the TEM observations, the temperatures were measured by a Cu-constant thermocouple in the specimen holder, which may be a little different from that of the thin film portion of the specimen. Thus, the absolute value of the temperatures may not be accurate. However, the sequence in temperature must be correct. Therefore, in order to simplify the description of the experimental result, we also refer to the R-phase start temperature taken by TEM observation as Rs in the next section.
Fig. 2. Diffraction patterns in [11( 1] B2 zone taken at 300 K (a) and at 258 K (b), by using imaging plates.
observed on the screen of TEM with naked eyes. Fortunately, they can be recorded by IPs under appropriate exposure time. Fig. 2(a – b) show the typical diffraction patterns in the [11( 1] zone taken at 300 K (in parent phase) and at 258 K (in R-phase),respectively, and Fig. 3 shows a line profile beside the (220) fundamental reflection as a function of temperature. From Fig. 3 the diffuse scattering is observed within the entire temperature range of the present experiment, even at 343 K. Their intensities increase with decreasing temperature. When the temperature is down to 276 K, the R-phase starts to form and at the same time the sharp superlattice reflections are abruptly visible in the screen even by the eyes. We can clearly see that the diffuse scattering is very weak in the parent phase and the superlattice reflections in the R-phase are quite sharp by comparing Fig. 2(a–b). By carefully observing the diffraction patterns in the parent phase taken at different temperatures, we notice that the intensity of diffuse scattering around the fun-
Fig. 3. Line profile along ll0 as a function of temperature.
W. Cai et al. / Materials Science and Engineering A273–275 (1999) 186–189
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4. Conclusions
Fig. 4. Temperature dependence of superlattice peak position, i.e. incommensurability in the parent phase.
The R-phase transformation was investigated by insitu TEM observations and electrical resistance measurements. The following conclusions were obtained. (1) The incommensurate diffuse scattering was observed in the parent phase in a wide temperature range above the Rs temperature and their incommensurability decreased during cooling. (2) The R-phase transformation starts at the Rs temperature, where the electrical resistance starts to increase and the R-phase is commensurate even at the beginning of its formation. (3) The R-phase transformation is of first order with a small temperature hysteresis, which represents a twophase region of parent and commensurate R-phase.
Acknowledgements
3.3. The temperature dependence of the position of the superlattice reflection Fig. 4 shows a peak position of the superlattice reflection in Fig. 3, which is plotted as a function of temperature. It is seen that the peak position is incommensurate within the temperature range above the Rs temperature and shifts to the commensurate position (exact 1/3 position) at Rs. When the temperature decreases to the Rs temperature the peak position changes to a commensurate position and keeps unchanged during further cooling. The above experimental results clearly show that the parent phase is in an incommensurate state within a wide temperature range above the Rs temperature. The R-phase is commensurate even in the R-phase just after the formation. The temperature, at which the incommensurate state just changes to the commensurate state, coincides with the Rs temperature, and thus the B2-incommensurate transition ascribed by Hwang et al. [1] was not found in the test temperature range. Thus, we describe the R-phase transformation as follows: in a temperature range above Rs, the incommensurate diffuse scattering exists in the parent phase and the incommensurability decreases during cooling. The R-phase transformation starts at the Rs temperature, where the electrical resistance starts to rise. This interpretation is similar to that by Saburi et al. [9] and Tamiya et al. [10], and is obviously different from that by Wayman’s group.
.
The authors would like to express their appreciation to Professor D. Shindo, Drs X. Ren and T. Hara, and T. Tamiya, J. Zhang, T. Ishii and M. Inami for their help and useful discussion in the present experiment. This work was supported by a Grant-in-Aid for Research on Priority Area on Phase Transformations from the Ministry of Education, Science and Culture of Japan (1997–1999). W. Cai is a recipient of the JSPS Fellowship.
References [1] C.M. Hwang, M.E. Meichle, M.B. Salamon, C.M. Wayman, Philos. Mag. A47 (1983) 9. [2] M.B. Salamon, M.E. Meichle, C.M. Wayman, Phys. Rev. B31 (1985) 7306. [3] M.E. Meichle, Ph.D. thesis, University of Illinois, 1980. [4] Y. Yamada, Proceedings of the International Conference on Martensitic Transformations (ICOMAT-86), JIM, Sendai, 1986, p. 89. [5] D.P. Dautovich, G.R. Purdy, Can. Metall. Q4 (1965) 129. [6] G.D. Sandrock, A.J. Perkins, R.F. Hehemann, Metall. Trans. 2 (1971) 2769. [7] S.M. Shapiro, Y. Noda, Y. Fujii, Y. Yamada, Phys. Rev. B30 (1984) 4314. [8] T. Fukuda, T. Saburi, K. Doi, S. Nenno, Mater. Trans. JIM 33 (1992) 271. [9] T. Saburi, Proceedings of the Conference on Martensitic Transformations (ICOMAT-92), Monterey, Institute of Advanced Studies (1993), p. 875. [10] T. Tamiya, D. Shindo, Y. Murukami, Y. Bando, K. Otsuka, Mater. Trans. JIM 7 (1998) 714.
Study of R-phase transformation in a Ti–50.7at%Ni alloy by in-situ transmission electron microscopy observations W. Cai a, Y. Murakami b, K. Otsuka a,* b
a Institute of Materials Science, Uni6ersity of Tsukuba, Tsukuba, Ibaraki 305 -8573, Japan Institute for Ad6anced Materials Processing, Tohoku Uni6ersity, Katahira, Sendai 980 -77, Japan
Abstract The R-phase transformation in a Ti–50.7at%Ni alloy was investigated by in-situ transmission electron microscopy (TEM) observations using double-tilt cooling stages, and the incommensurability of 1/3 diffuse scattering in the process of the transformation was examined by using imaging plates. It is shown that the incommensurate diffuse scattering exists in the parent phase within a wide temperature range above the Rs temperature and that the incommensurability decreases with decreasing temperature. The R-phase transformation starts at the Rs temperature where the electrical resistance starts to increase and the R-phase is commensurate even in the state just after formation. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Martensite; R-phase; Ni–Ti; Incommensurability
1. Introduction The R-phase transformation with a small temperature hysteresis in Ti – Ni alloys has attracted considerable attention, since it is very useful for actuator applications. In order to understand its transformation mechanism, many studies have been carried out using various techniques. The transformation sequence in Ti –Ni alloys during cooling has been believed for a long time to be as follows [1 – 3]: B2 parent (P)- incommensurate (IC)- commensurate (R), and the R-phase transformation was tentatively explained in terms of a charge density wave [1] or modulated lattice relaxation model [4]. The R-phase transformation was first found by Dautovich and Purdy [5], and then characterized well by Sandrock and Hehemann [6] by the sharp increase of the electrical resistivity and appearance of superlattice reflections at 1/3 position along 110* in X-ray and electron diffraction. Thereafter, many investigations have been made in order to clarify the R-phase transformation process by Wayman’s group [1 – 3], who carried out systematic experiments for Ti – Ni – Fe alloys by * Corresponding author. Tel.: +81-298-535294; fax: + 81-298557440. E-mail address: [email protected] (K. Otsuka)
using neutron and X-ray diffraction, electron microscopy, electrical resistivity and magnetic susceptibility measurements etc. They found that the superlattice reflections appear at an incommensurate position first, and the incommensurability decreases with decreasing temperature until it locks-in to a commensurate phase at lower temperature. The temperature where the incommensurate superlattice reflections start to appear (TI) coincides with that where the resistivity starts to rise. The lock-in temperature Tr from incommensurate to commensurate coincides with the temperature where dr/dT becomes maximum. The temperature difference between TI and Tr in the case of a Ti–46.8Ni– 3.2Fe(at%) single crystal is 8 K. Based on their experimental results, they ascribed the R-phase transformation to the formation of charge density waves (CDW). On the other hand, Shapiro et al. [7] made a detailed study on the incommensurability by the X-ray diffraction technique using a linear position sensitive detector, and reported that the incommensurate displacement in reciprocal space is neither regular nor periodic. Thus, they denied the interpretation by CDW. Later Yamada [4] proposed a modulated lattice relaxation model for the incommensurate state of the parent phase. Recently, Saburi’s group [8,9] made a qualitative study on R-phase transformation in a Ti–48Ni–
0921-5093/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 9 9 ) 0 0 3 6 7 - 6
W. Cai et al. / Materials Science and Engineering A273–275 (1999) 186–189
2Al(at%) alloy by electron microscopy. They observed that the R-phase nucleates from lattice defects such as dislocations and grows during cooling. Therefore, they claimed that the transformation is first order. Furthermore, they interpreted the transformation such that the specimen is in a diffuse incommensurate state above the temperature where the resistivity starts to increase. Thus, their interpretation is different from that of Wayman’s group. Very recently, Tamiya and Otsuka et al. [10] studied the R-phase transformation in a Ti – 48Ni – 2Fe(at%) alloy by in-situ electron microscopy with double-tilt cooling stages and examined accurately the incommensurability in the early stages of the transformation by using imaging plates. They found that the R-phase transformation starts at the temperature Rs from the B2 parent phase with weak diffuse scattering to the commensurate R-phase with a sharp interface. Thus, they pointed out that the transformation is of first order and the temperature hysteresis represents the two-phase region of parent and the commensurate Rphase. Therefore, we can see that the origin of R-phase transformation is not well understood, and the incommensurability associated with the transformation is even controversial. So, in the present work we studied the R-phase transformation in an aged Ti – 50.7at%Ni alloy and paid special emphasis on the incommensurability in the process of the transformation.
187
the intensity and position of electron diffraction can be measured accurately.
3. Results and discussions
3.1. Obser6ation of R-phase transformation by electrical resistance measurements In order to determine the transformation temperatures of the R-phase transformation and to understand the transformation sequence well, the electrical resistance as a function of temperature was measured as shown in Fig. 1. The Rs temperature corresponding to the temperature where the resistivity starts to increase, represents the R-phase start temperature in our terminology. Thus, it coincides with the TI temperature of Hwang et al. [1]. The Rs temperature is 280 K for the present alloy. From Fig. 1, the temperature hysteresis associated with the R-phase transformation can be clearly seen although it is very small ( 1 K). This indicates that the R-phase transformation is of first order. The above result is consistent with the previous reports by Fukuda et al. [8] for a Ti–48Ni–2Al(at%) alloy and by Tamiya et al for a Ti–48Ni–2Fe(at%) alloy [10]. It should be noticed that no second order transformation ascribed by Wayman’s group [3] was observed in Fig. 1. It will be discussed in detail later.
3.2. Obser6ation of superlattice reflection changes with R-phase transformation 2. Experimental The specimens of nominal composition Ti– 50.7at%Ni were supplied by Furukawa Electric Co. Ltd. After spark cutting into proper sizes, the specimens were solution treated at 1273 K for 1 h in vacuum followed by quenching into ice water and then aged at 823 K for 25 h. Four terminal electrical resistance measurements were carried out with slow cooling and heating rate of 0.5 K min − 1. The specimens for electron microscopy were prepared by a twin-jet electro-polishing apparatus STRUERS TENUPOL3 with the solution of H2SO4 (20vol.%)+ CH3OH (80vol.%). In-situ transmission electron microscopy (TEM) observations were carried out using JEM 2000FX operating at 200 kV with a double-tilt cooling stage. The upper temperature limit for the cooling stage is about 353 K. The diffraction patterns were recorded by using Fuji FDL-URV imaging plates (IP). The size of IP was 8.2 ×11.8 cm2 and the onepixel-size was 25 mm. The sensitivity is 1000 times higher than that of the ordinary film, and the dynamic range is four digit wide. The information recorded on imaging plates was read out by an IP reader and then analyzed by a software called ‘Image Gauge’, by which
To examine the temperature dependence of superlattice reflections, the specimen was heated to 343 K, which is much higher than the Rs temperature, and then the change in diffraction pattern was observed during cooling from 343 to 276 K. When the temperature is higher than 276 K, the diffuse scattering is not
Fig. 1. Electric resistance vs. temperature curve for a Ti–50.7at%Ni alloy, which was solution-treated at 1273 K for 1 h and then aged at 823 K for 25 h.
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W. Cai et al. / Materials Science and Engineering A273–275 (1999) 186–189
damental reflections of a higher angle is stronger than that at the lower angle and the diffuse scattering is almost invisible around transmitted beam (see Fig. 2(a)). The reason for this is unclear right now. Therefore, we select the diffuse scattering beside the (220) reflection instead of that beside the (110) reflection to measure the intensity and position of the diffuse scattering. We also notice that there is a small difference between the R-phase start temperature taken by TEM observation (276 K, as mentioned above) and that measured by electrical resistance measurement (280 K, as shown in Fig. 1). This is mainly due to the following two reasons. One is the thin film effect and another is the measurement method. The transformation temperature of the thin film used for TEM observations may be different from that of the bulk specimen used for electrical resistance measurement. On the other hand, for the TEM observations, the temperatures were measured by a Cu-constant thermocouple in the specimen holder, which may be a little different from that of the thin film portion of the specimen. Thus, the absolute value of the temperatures may not be accurate. However, the sequence in temperature must be correct. Therefore, in order to simplify the description of the experimental result, we also refer to the R-phase start temperature taken by TEM observation as Rs in the next section.
Fig. 2. Diffraction patterns in [11( 1] B2 zone taken at 300 K (a) and at 258 K (b), by using imaging plates.
observed on the screen of TEM with naked eyes. Fortunately, they can be recorded by IPs under appropriate exposure time. Fig. 2(a – b) show the typical diffraction patterns in the [11( 1] zone taken at 300 K (in parent phase) and at 258 K (in R-phase),respectively, and Fig. 3 shows a line profile beside the (220) fundamental reflection as a function of temperature. From Fig. 3 the diffuse scattering is observed within the entire temperature range of the present experiment, even at 343 K. Their intensities increase with decreasing temperature. When the temperature is down to 276 K, the R-phase starts to form and at the same time the sharp superlattice reflections are abruptly visible in the screen even by the eyes. We can clearly see that the diffuse scattering is very weak in the parent phase and the superlattice reflections in the R-phase are quite sharp by comparing Fig. 2(a–b). By carefully observing the diffraction patterns in the parent phase taken at different temperatures, we notice that the intensity of diffuse scattering around the fun-
Fig. 3. Line profile along ll0 as a function of temperature.
W. Cai et al. / Materials Science and Engineering A273–275 (1999) 186–189
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4. Conclusions
Fig. 4. Temperature dependence of superlattice peak position, i.e. incommensurability in the parent phase.
The R-phase transformation was investigated by insitu TEM observations and electrical resistance measurements. The following conclusions were obtained. (1) The incommensurate diffuse scattering was observed in the parent phase in a wide temperature range above the Rs temperature and their incommensurability decreased during cooling. (2) The R-phase transformation starts at the Rs temperature, where the electrical resistance starts to increase and the R-phase is commensurate even at the beginning of its formation. (3) The R-phase transformation is of first order with a small temperature hysteresis, which represents a twophase region of parent and commensurate R-phase.
Acknowledgements
3.3. The temperature dependence of the position of the superlattice reflection Fig. 4 shows a peak position of the superlattice reflection in Fig. 3, which is plotted as a function of temperature. It is seen that the peak position is incommensurate within the temperature range above the Rs temperature and shifts to the commensurate position (exact 1/3 position) at Rs. When the temperature decreases to the Rs temperature the peak position changes to a commensurate position and keeps unchanged during further cooling. The above experimental results clearly show that the parent phase is in an incommensurate state within a wide temperature range above the Rs temperature. The R-phase is commensurate even in the R-phase just after the formation. The temperature, at which the incommensurate state just changes to the commensurate state, coincides with the Rs temperature, and thus the B2-incommensurate transition ascribed by Hwang et al. [1] was not found in the test temperature range. Thus, we describe the R-phase transformation as follows: in a temperature range above Rs, the incommensurate diffuse scattering exists in the parent phase and the incommensurability decreases during cooling. The R-phase transformation starts at the Rs temperature, where the electrical resistance starts to rise. This interpretation is similar to that by Saburi et al. [9] and Tamiya et al. [10], and is obviously different from that by Wayman’s group.
.
The authors would like to express their appreciation to Professor D. Shindo, Drs X. Ren and T. Hara, and T. Tamiya, J. Zhang, T. Ishii and M. Inami for their help and useful discussion in the present experiment. This work was supported by a Grant-in-Aid for Research on Priority Area on Phase Transformations from the Ministry of Education, Science and Culture of Japan (1997–1999). W. Cai is a recipient of the JSPS Fellowship.
References [1] C.M. Hwang, M.E. Meichle, M.B. Salamon, C.M. Wayman, Philos. Mag. A47 (1983) 9. [2] M.B. Salamon, M.E. Meichle, C.M. Wayman, Phys. Rev. B31 (1985) 7306. [3] M.E. Meichle, Ph.D. thesis, University of Illinois, 1980. [4] Y. Yamada, Proceedings of the International Conference on Martensitic Transformations (ICOMAT-86), JIM, Sendai, 1986, p. 89. [5] D.P. Dautovich, G.R. Purdy, Can. Metall. Q4 (1965) 129. [6] G.D. Sandrock, A.J. Perkins, R.F. Hehemann, Metall. Trans. 2 (1971) 2769. [7] S.M. Shapiro, Y. Noda, Y. Fujii, Y. Yamada, Phys. Rev. B30 (1984) 4314. [8] T. Fukuda, T. Saburi, K. Doi, S. Nenno, Mater. Trans. JIM 33 (1992) 271. [9] T. Saburi, Proceedings of the Conference on Martensitic Transformations (ICOMAT-92), Monterey, Institute of Advanced Studies (1993), p. 875. [10] T. Tamiya, D. Shindo, Y. Murukami, Y. Bando, K. Otsuka, Mater. Trans. JIM 7 (1998) 714.