Martensitic Transformation and Superelasticity of Ti-Nb-Pt Alloys

Transcription

1 Materials Transactions, Vol. 48, No. 3 (27) pp. 4 to 46 Special Issue on Smart and Harmonic Biomaterials #27 The Japan Institute of Metals Martensitic Transformation and Superelasticity of Ti-Nb-Pt Alloys Hee Young Kim 1; *, Naomi Oshika 1, Jae Il Kim 2, Tomonari Inamura 3, Hideki Hosoda 3 and Shuichi Miyazaki 1; * 1 Institute of Materials Science, University of Tsukuba, Tsukuba 3-873, Japan 2 Department of Materials Science, Dong-A University, Pusan , Korea 3 Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama , Japan Shape memory properties and martensitic transformation of Ti-Nb-Pt alloys were investigated in order to develop Ni-free biomedical superelastic alloys. The effect of Pt addition on the transformation strain was investigated by measuring the lattice constants of the parent and martensite phases of Ti-Nb-Pt alloys. The Ti-Nb-Pt alloys were fabricated by arc melting. The ingots were cold-rolled up to 99% reduction in thickness. The cold-rolled specimens were heat treated at 873 K for.6 ks. The shape memory effect and/or superelastic behavior were observed in the Ti-Nb-Pt alloys. The martensitic transformation temperature decreases by about 16 K with a 1 at% increase of Pt in the Ti-Nb-Pt alloys. The addition of Pt as a substitute of Nb was effective to increase the transformation strain when compared with compositions which reveal similar transformation temperatures. An aging treatment at 73 K was effective for increasing the stress for inducing the martensitic transformation and the critical stress for plastic deformation, resulting in good superelasticity. [doi:1.232/matertrans.48.4] (Received October 26, 26; Accepted December 18, 26; Published February 2, 27) Keywords: shape memory alloy, superelasticity, biomaterial, smart material, titanium base alloy 1. Introduction Development of low modulus alloy with high strength is strongly required for implant materials in order to reduce the modulus difference between implants and bones. -type Tibase alloys have been developed for biomedical applications because of their low Young s modulus and good biocompatibility. 1) Superelastic Ti-Ni alloys have also been successfully applied for many medical devices such as stents, guide wires and dental wires. 2) In addition, Ti-Ni alloys are considered as one of the attractive candidates for orthopedic implant applications, since effective modulus of Ti-Ni alloys is extremely low when considering their superelastic effect. However, concerns about hypersensitivity associated with dissolution of Ni ions have restricted the use of Ti-Ni alloys as an implant material. Recently, -type Ti-base alloys composed of non-toxic elements have attracted attention as new biomedical superelastic materials. It has been reported that Ti-Mo base multicomponent alloys such as -Cez(Ti-Al-2Sn-4Zr-4Mo-2Cr- 1Fe (mass%)), 3) Ti-(8-1)Mo-4Nb-2V-3Al (mass%), 4) Ti- Mo-Ga ) and Ti-Mo-Sn 6) exhibit superelasticity at room temperature. Superelastic behavior has also been observed in Ti-Nb binary alloys 7,8) and ternary alloys, e.g., Ti-Nb-Sn, 9) Ti-Nb-Al, 1) Ti-Nb-O, 11) Ti-Nb-Ta 12,13) and Ti-Nb-Zr. 14,1) It has been confirmed that addition of ternary alloying elements, such as Sn, Al, Zr and O, is effective in stabilizing the superelastic properties in Ti-Nb base alloys. Other attractive candidates for the third element is noble metal elements such as Pt, Au and Pd, because of their excellent corrosion resistance and good biocompatibility. In addition, they are strong stabilizer and exhibit eutectoid decomposition. However, the effect of noble metal elements on martensitic transformation and shape memory behavior has not been reported yet. In this study, martensitic transformation and shape *Corresponding authors, miyazaki@ims.tsukuba.ac.jp, heeykim@ims.tsukuba.ac.jp. memory behavior of Ti-Nb-Pt alloys were investigated. The effect of Pt addition on transformation strain was investigated by measuring the lattice constants of the parent and martensite phases of Ti-Nb-Pt alloys. The effect of aging at 73 K on the microstructure and superelastic behavior was also investigated. 2. Experimental The Ti-Nb-Pt alloy ingots were prepared using the Ar arc melting method. Table 1 provides a list of alloys fabricated in this study. Chemical analysis was not carried out, because the weight change before and after the arc-melting was less than.1 mass%. The concentration of oxygen was analyzed using some ingots and determined to be.3.4 mass%. The ingots were sealed in vacuum in a quartz tube and homogenized at 1273 K for 7.2 ks, and then cold-rolled with a reduction of 99% in thickness. Specimens for X-ray diffraction (XRD) measurements, mechanical tests and TEM observation were cut using an electro-discharge machine. The damaged surface was removed by mechanical polishing and chemical etching. The specimens were cleaned with ethanol, wrapped in Ti foils and encapsulated in quartz tubes under a 3.3 kpa partial pressure of high-purity Ar, and then annealed at 873 K for.6 ks. The specimens were quenched into water by breaking the quartz tubes. After annealing, some specimens were aged at 73 K. XRD measurements were conducted at room temperature with Cu K radiation. Tensile tests were carried out at a strain rate of 1: s 1. The gage length of specimens was 2 mm. Specimens for TEM observation were prepared by a conventional twin-jet polishing technique. TEM observation was conducted using a JEOL21F instrument operated at 2 kv. 3. Results and Discussion 3.1 Effect of composition on shape memory effect in Ti-Nb-Pt alloys The shape memory effect and superelasticity of Ti-Nb-Pt

2 Martensitic Transformation and Superelasticity of Ti-Nb-Pt Alloys 41 4 Ti-17Nb-2Pt Ti-18Nb-2Pt Ti-19Nb-2Pt Ti-2Nb-2Pt Stress, σ / MPa Strain, ε (%) Fig. 1 Stress-strain curves obtained upon loading and unloading at room temperature for the Ti-(17-2)Nb-2Pt alloys. Table 1 Nominal composition of alloys fabricated in this study. Alloy Ti Nb Pt Ti-19Nb Bal. 19 Ti-2Nb Bal. 2 Ti-21Nb Bal. 21 Ti-22Nb Bal. 22 Ti-23Nb Bal. 23 Ti-24Nb Bal. 24 Ti-2Nb Bal. 2 Ti-26Nb Bal. 26 Ti-27Nb Bal. 27 Ti-28Nb Bal. 28 Ti-29Nb Bal. 29 Ti-1Nb-2Pt Bal. 1 2 Ti-12Nb-2Pt Bal Ti-14Nb-2Pt Bal Ti-16Nb-2Pt Bal Ti-17Nb-2Pt Bal Ti-18Nb-2Pt Bal Ti-19Nb-2Pt Bal Ti-2Nb-2Pt Bal. 2 2 Ti-21Nb-2Pt Bal Ti-22Nb-2Pt Bal Ti-16Nb-3Pt Bal Ti-18Nb-3Pt Bal Ti-2Nb-3Pt Bal. 2 3 Ti-12Nb-4Pt Bal Ti-14Nb-4Pt Bal Ti-16Nb-4Pt Bal Ti-18Nb-4Pt Bal Ti-2Nb-4Pt Bal. 2 4 Ti-14Nb-Pt Bal. 14 alloys were investigated by loading-unloading tensile tests at room temperature. For example, the stress strain curves of Ti- (17-2)Nb-2Pt (at%) alloys are shown in Fig. 1. The tensile stress was applied until the strain reached about 2.%, and then the stress was removed. After unloading, specimens which did not exhibit complete superelastic recovery were heated up to about K to investigate the shape memory effect. The Ti-17Nb-2Pt and Ti-(18-2)Nb-2Pt alloys exhibit Ti content (at%) shape memory effect and superelastic behavior, respectively. It is also seen that the apparent yield stress, which corresponds to the stress for inducing the martensitic transformation, increased with increasing Nb content in the Ti- (18-2)Nb-2Pt alloys. The parent phase becomes more stable with increasing temperature when the temperature is above Ms, thus a higher stress is required for inducing the martensitic transformation at a higher temperature, which is in accordance with the Clausius-Clapeyron relationship. On the other hand, when the test temperature is kept at room temperature, the stress for inducing the martensitic transformation increases with decreasing Ms of the specimen. Thus it is reasonable that the critical stress for inducing the martensitic transformation increases with increasing Nb content since the Ms decreases with increasing Nb content. The results of tensile tests of Ti-Nb-Pt alloys with various compositions are summarized in Fig. 2. Superelastic behavior and shape memory effect were observed at compositions marked by a solid circle and an open circle, respectively. 1 Pt content (at%) Fig. 2 Composition dependence of function of Ti-Nb-Pt at room temperature. : shape memory effect, : superelastic behavior, : no shape recovery. 1

3 42 H. Y. Kim et al..33 (a).33 (b) a (nm).32 a' (nm) (c). (d) b' (nm).48 c' (nm) Fig. 3 Nb content dependence of the lattice constants of the and phases in Ti-Nb-2Pt alloys. Neither shape memory effect nor superelastic behavior was observed in the alloy marked by. Compositions exhibiting shape memory effect and superelasticity are separated by a dashed line. And the boundary between compositions exhibiting superelasticity and no shape recovery was represented by a solid line. For the binary Ti-Nb alloys, superelastic behavior was observed when the Nb content is between at%. 16) It is seen that the Nb content showing superelastic behavior decreases with increasing Pt content, indicating that Pt decreases transformation temperatures. For Ti-Nb-2Pt alloys, superelastic behavior was observed when the Nb content is between 18 2 at%, indicating that the effect of 2 at%pt in decreasing transformation temperature is equivalent to that of 8 at%nb. It has been reported that Ms decreased by 4 K with increasing Nb content by 1 at% for Ti-(2-28)Nb alloys. As a result, it is suggested that the Ms decreases by about 16 K with an increase of 1 at%pt. 3.2 Lattice constants and transformation strain in Ti- Nb-Pt alloys The transformation strain is determined by the lattice correspondence between martensite and parent phases and their lattice constants. Therefore, in order to develop superelastic alloys with a larger recovery strain, it is needed to investigate the lattice constants of martensite and parent phases as well as transformation temperatures. The lattice constant of the parent phase in Ti-(16-22)Nb-2Pt alloys was measured at room temperature, since no distinct peak of parent phase was observed when the Nb content is less than 16 at%. On the other hand, the lattice constants of the orthorhombic martensite phase were measured in Ti-(1-17)Nb-2Pt alloys, since the XRD profiles of the Ti-(18-22)Nb-2Pt alloys exhibited a single parent phase. It is seen from Fig. 3(a) that the lattice constant a of the phase is insensitive to Nb content. The Nb dependence of the lattice constants a, b and c of the orthorhombic martensite phase is shown in Fig. 3(b) (d), respectively. The lattice constants of the phase change linearly with increasing Nb content in the Ti-(1-17)Nb-2Pt alloys: a increases by 1: nm and b decreases by 1: nm with an increase of 1 at%nb. The change of c is small when compared with those of a and b, i.e., : nm/ 1 at%nb. The Nb content dependence of the lattice constants is consistent with that of Ti-Nb binary alloys. 8) The orientation relationship between and orthorhombic phases are expressed approximately as follows: 17) ½1Š == ½1Š ; ½1Š == ½11Š ; ½1Š == ½11Š : Therefore, the lattice deformation strains ( 1, 2 and 3 ) needed to form the phase from the phase along the three principal axes of ½1Š, ½1Š and ½1Š are given as follows:

4 Martensitic Transformation and Superelasticity of Ti-Nb-Pt Alloys 43 Transformation strain, ε (%) 1 - η 2 η 3 η 1 [111] (1.%) 2.% 2.% 3.% 3.% Fig. 4 Nb content dependence of the lattice deformation strains needed to form the from the along the three principal axes of the phase. pffiffiffi 1 ¼ a a ; 2 ¼ b 2 p a pffiffiffi ; 3 ¼ c ffiffiffi 2 a pffiffi : a 2 a 2 a Figure 4 shows 1, 2 and 3 which were calculated from the measured lattice constants of the parent and martensite phases. The lattice constant of the phase for the Ti-(1-17)Nb-2Pt alloys was determined by extrapolation using the linear dependence of lattice constant on Nb content as shown in Fig. 3(a). Figure 4 reveals that two principal lattice strains ( 1 and 2 ) are approximately equal and opposite in sign, and their absolute values decrease with increasing Nb content. Not only the magnitude but also Nb dependence of lattice strain 3 is relatively small when compared with 1 and 2. The Nb content dependence of the lattice deformation strains is almost the same as that of Ti-Nb binary alloys. 8) The transformation strain was calculated as a function of crystal orientation for the Ti-Nb-Pt alloys using the lattice constants. For example, the calculated result of the transformation strains for the Ti-17Nb-2Pt alloy is shown in Fig.. A detailed description of the calculation method for the transformation strain has been reported in previous papers. 8,12) The dependence of the transformation strain on a crystal direction of the Ti-Nb-Pt alloys is essentially similar to those of other Ti-Nb base alloys: 8,1,12) the largest transformation strain is obtained along the [11] direction and the transformation strain decreases with changing direction from [11] toward the directions of [1] and ½111Š, respectively. Since the -Ti alloy specimens were severely cold-rolled with a reduction of 99%, they reveal a strong deformation texture of f1gh11i and a strong recrystallization texture of f112gh11i, the rolling direction being h11i for both the textures. 12) This means that the transformation strain along the rolling direction is close to that along the [11] direction. The transformation strain along the [11] direction " ½11Š M is plotted as a function of Nb content in Fig. 6. The results in Ti-Nb binary alloys are also shown for reference. The " ½11Š M decreases with a slope of :34%/Nb in Ti-Nb and :3%/ Nb in Ti-Nb-Pt, respectively. It is also seen that the addition of Pt decreases transformation strain when compared with the [1] [11] (2.2%) 4.% (4.1%) Fig. Orientation dependence of the calculated transformation strain associated with the martensitic transformation from the to in the Ti- 17Nb-2Pt alloy. Transformation strain, ε (%) Ti-xNb Ti-xNb-2Pt Nb content(at%) Fig. 6 Nb content dependence of the transformation strain in Ti-Nb and Ti-Nb-2Pt alloys. results of the binary Ti-Nb alloys with same Nb composition. For example, the " ½11Š M decreases from.2% to 3.3% by the addition of 2 at%pt in the Ti-19Nb alloy, indicating that the " ½11Š M decreases by about 1.% with an increase of 1 at%pt. However, it should be noted that the addition of Pt increases the " ½11Š M when comparing different composition alloys which reveal similar Ms. For example, the " ½11Š M strains of the Ti- 19Nb-2Pt and Ti-27Nb alloys which show superelastic behavior at room temperature are 3.3% and 2.%, respectively. This seems reasonable because Pt is four times more effective for decreasing Ms than Nb, while Pt is only three times more effective for decreasing transformation strain than Nb, indicating that the addition of Pt as a substitute of Nb is effective to increase the transformation strain of Ti-Nb base superelastic alloys with similar Ms. 3.3 Shape memory and superelastic behavior Strain increment cyclic tensile tests were carried out for

5 44 H. Y. Kim et al. Stress, σ / MPa Ti-19Nb-2Pt Ti-27Nb Recovery strain, ε (%) Ti-19Nb-2Pt Ti-27Nb Ti-19Nb-2Pt Ti-27Nb ε r ε tr εr ε tr 1 Strain, ε (%) Fig. 7 Stress-strain curves obtained by cyclic loading-unloading tensile tests for the Ti-19Nb-2Pt and Ti-27Nb alloys annealed at 873 K for.6 ks. the Ti-19Nb-2Pt subjected to annealing at 873 K for.6 ks which exhibits superelastic behavior at room temperature, and the results are shown in Fig. 7. The results for the binary Ti-27Nb specimen which shows similar superelastic behavior are also shown for reference. 16) At the first cycle, tensile stress was applied until strain reached about 1.%, and then the stress was removed in the specimen. The similar measurement was repeated by increasing the maximum strain by.% upon loading using the same specimen. After unloading, the specimens which did not exhibit complete superelastic recovery were heated up to about K to measure shape recovery by heating. The starting points of the stress-strain curves are shifted in order to separate each curve. The Ti-19Nb-2Pt specimen reveals good superelasticity until the fourth cycle. With increasing applied tensile strain, the superelastic behavior became incomplete. It is seen that the residual strain was recovered by heating at the fifth cycle. Four types of strains were measured in each cycle: (1) the elastic strain " el recovered elastically upon unloading, (2) the recovered strain " tr due to the reverse transformation (which is equal to the sum of the transformation strain recovered superelastically upon unloading (" se ) and the strain recovered by heating (" sme )), (3) the total recovered strain " r consisting of " el and " tr, and (4) the permanently remained strain " p after unloading followed by the subsequent heating. Strains " r and " tr of Ti-19Nb-2Pt and Ti-27Nb are plotted as a function of tensile strain in Fig. 8. The difference between " r and " tr corresponds to " el. Both specimens exhibit similar trends up to about 3% tensile strain. It is also seen that " p indicated by the deviation of " r from the diagonal line increases with increasing tensile strain. For the Ti-27Nb specimen, the shape recovery rate decreases down to less than 9% when the tensile strain is 3.%. The maximum " r of 3.1% and maximum " tr of 2.1% were obtained for the Ti- 27Nb specimen. On the other hand, the recovery rate is higher than 9% even though the tensile strain is 4.% for the Ti-19Nb-2Pt specimen. It is also noted that the maximum " r of 3.8% and maximum " tr of 2.7% were obtained for the Ti- 2% Tensile strain, ε (%) Fig. 8 Total recovered strain (" r ) and transformation strain (" tr ) as a function of tensile strain obtained by cyclic loading-unloading tensile tests in Fig. 7. Stress, σ / MPa (a) (b) (c) Strain, ε (%) Fig. 9 Stress-strain curves obtained by cyclic loading-unloading tensile tests for the specimens aged at 73 K for (a) 1.8, (b) 3.6 and (c) 36 ks after annealing at 873 K for.6 ks. 19Nb-2Pt specimen. It is suggested that the lager " r of the Ti- 19Nb-2Pt is due to a larger transformation strain when compared with the Ti-27Nb as shown in Fig. 6. In order to investigate the effect of aging on superelastic behavior, strain increment cyclic tensile tests were carried out for the Ti-19Nb-2Pt specimens subjected to aging treatment at 73 K, and the results are shown in Fig. 9. The specimen aged at 73 K for 1.8 ks exhibits almost perfect superelasticity until the fifth cycle. It is seen that the critical 2%

6 Martensitic Transformation and Superelasticity of Ti-Nb-Pt Alloys 4 stress for the first yielding, which is the stress for inducing martensitic transformation, increased by aging at 73 K: the stress for the first yielding increased with increasing aging time. The maximum stress reached at each cycle also increased with increasing aging time. In order to evaluate the stability of superelasticity, the superelastically recovered strain, which is the sum of " el and " se, and the permanently retained plastic strain " p were measured at each cycle, and they are plotted as a function of maximum applied stress at each cycle in Fig. 1. Strain " p increased gradually with increasing applied stress. The critical stress for slip ( s )is defined as a stress inducing.% plastic strain in this study. For the specimen annealed at 873 K for.6 ks, s was determined as 4 MPa and the maximum superelastic strain of 3.% was obtained. Stress s and the maximum superelastic strain increased up to 1 MPa and 4.3%, respectively, by aging at 73 K for 1.8 ks. Stress s further increased by aging at 73 K for 3.6 ks, since " p was less than.% even if the applied stress reached 63 MPa. The stable superelasticity with a recovery strain of 3.3% was observed even though the maximum stress reached 63 MPa for the specimen aged at 73 K for 3.6 ks. However, it is noted that the maximum Strain (%) K/.6ks:superelastic strain 873K/.6ks:plastic strain 873K/.6ks+73K/1.8ks: superelastic strain 873K/.6ks+73K/1.8ks: plastic strain 873K/.6ks+73K/3.6ks: superelastic strain 873K/.6ks+73K/3.6ks: plastic strain Applied stress, σ/mpa Fig. 1 The superelastic strain and the remained plastic strain as a function of applied stress. (a) (b) 1nm 1nm (c) (d) 1nm 1nm Fig. 11 Dark-field TEM micrographs and the corresponding selected area diffraction patterns of (a) the specimen annealed at 873 K for.6 ks and the specimens subsequently aged at 73 K for (b) 1.8 ks, (c) 3.6 ks and (d) 36 ks.

7 46 H. Y. Kim et al. superelastic strain of the specimen aged 73 K for 3.6 ks is smaller than that of the specimen aged for 1.8 ks. Furthermore, no shape recovery strain was obtained for the specimen aged for 36 ks. These are due to the fact that the stress for inducing martensitic transformation increases with increasing aging time. Figure 11(a) represents a dark field TEM micrograph and the corresponding selected area diffraction pattern of the specimen annealed at 873 K for.6 ks. The selected area diffraction pattern was obtained from the ½11Š zone axis. Diffuse scattering at 1/3 f112g positions corresponding to! phase is visible in the selected area diffraction pattern. The dark field image was obtained using the spot of! phase indicated by a circle. Very fine! particles with a dimension of 3 nm were observed in the specimen annealed at 873 K for.6 ks. These! particles are considered as the athermal! phase which was formed during quenching after annealing. The selected area diffraction patterns and dark field TEM micrographs obtained from the specimens aged at 73 K are also shown in Fig. 11(b) (d). It is clearly seen that the intensity of the reflections from! phase became strong on aging, and the size and volume fraction of! particles increased with increasing aging time although the size distribution of the! particles was quite broad: these! particles are considered as thermal! phase. This indicates that the substantial increases in the stress for inducing martensitic transformation and s after aging at 73 K are due to the growth of thermal! phase, which is consistent with the results obtained in the Ti-26Nb alloy. 8) It is noted that the specimen aged for 36 ks did not show shape recovery. This is due to the fact that the stress for inducing martensitic transformation increased drastically and became higher than s although s increased with increasing aging time. As a result, it is suggested that aging for 1.8 ks results in the largest superelastic recovery strain due to the higher critical stress for permanent deformation and relatively lower stress for inducing the martensitic transformation. 4. Conclusions (1) The shape memory effect and/or superelastic behavior were first observed in the Ti-Nb-Pt alloys. The martensitic transformation temperature decreases by about 16 K with an increase of 1 at%pt in the Ti-Nb-Pt alloys. (2) Transformation strains were calculated using the lattice constants of the and phases and the lattice correspondence between the two phases. The maximum transformation strain was obtained along the [11] direction of the phase. The addition of Pt as a substitute of Nb is effective to increase the transformation strain when comparing different composition alloys which reveal similar Ms. (3) An aging treatment at 73 K increased both of the critical stress for permanent deformation and the critical stress for inducing the martensitic transformation due to the growth of thermal! phase in the Ti-19Nb-2Pt alloy. Perfect superelastic behavior was obtained until the applied strain reached up to 3% in the alloy annealed at 873 K followed by subsequent aging at 73 K for 3.6 ks. Acknowledgments This work was partially supported by ILC Project from University of Tsukuba, the 21 Century Center of Excellence Program, the Iketani Foundation and the Grants-in-Aid for Fundamental Scientific Research (Kiban A(22-24), Wakate B(26-27)) from the Ministry of Education, Culture, Sports, Science and Technology, Japan. REFERENCES 1) M. Niinomi: Mater. Sci. Eng. A 243 (1998) ) T. Duerig, A. Pelton and D. Stockel: Mater. Sci. Eng. A (1999) ) T. Grosdidier and M. J. Philippe: Mater. Sci. Eng. A 291 (2) ) T. Zhou, M. Aindow, S. P. Alpay, M. J. Blackburn and M. H. Wu: Scr. Mater. (24) ) H. Y. Kim, Y. Ohmatsu, J. I. Kim, H. Hosoda and S. Miyazaki: Mater. Trans. 4 (24) ) T. Maeshima, S. Ushimaru, K. Yamauchi and M. Nishida: Mater. Trans. 47 (26) ) H. Y. Kim, S. Hashimoto, J. I. Kim, H. Hosoda and S. Miyazaki: Mater. Trans. 4 (24) ) H. Y. Kim, Y. Ikehara, J. I. Kim, H. Hosoda and S. Miyazaki: Acta Mater. 4 (26) ) E. Takahashi, T. Sakurai, S. Watanabe, N. Masahashi and S. Hanada: Mater. Trans. 43 (22) ) T. Inamura, Y. Fukui, H. Hosoda, K. Wakashima and S. Miyazaki: Mater. Trans. 4 (24) ) J. I. Kim, H. Y. Kim, H. Hosoda and S. Miyazaki: Mater. Trans. 46 (2) ) H. Y. Kim, T. Sasaki, K. Okutsu, J. I. Kim, T. Inamura, H. Hosoda and S. Miyazaki: Acta Mater. 4 (26) ) H. Y. Kim, S. Hashimoto, J. I. Kim, T. Inamura, H. Hosoda and S. Miyazaki: Mater. Sci. Eng. A 417 (24) ) J. I. Kim, H. Y. Kim, T. Inamura, H. Hosoda and S. Miyazaki: Mater. Sci. Eng. A 43 (2) ) J. I. Kim, H. Y. Kim, T. Inamura, H. Hosoda and S. Miyazaki: Mater. Trans. 47 (26) ) H. Y. Kim, J. I. Kim, T. Inamura, H. Hosoda and S. Miyazaki: Mater. Sci. Eng. A (26) ) B. A. Hatt and V. G. Rivlin: Brit. J. Appl. Phys. 1 (1968)