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Antiphase boundary-like structure of B19′ martensite via R-phase transformation in Ti–Ni–Fe alloy
Journal of Alloys and Compounds 586 (2014) 87–93
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Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom
Antiphase boundary-like structure of B190 martensite via R-phase transformation in Ti–Ni–Fe alloy M. Matsuda a,⇑, R. Yamashita a, S. Tsurekawa a, K. Takashima a, M. Mitsuhara b, M. Nishida b a b
Department of Materials Science and Engineering, Kumamoto University, 2-39-1 Kurokami, Kumamoto 860-8555, Japan Department of Engineering Sciences for Electronics and Materials, Kyushu University, Kasuga, Fukuoka 816-8580, Japan
a r t i c l e
i n f o
Article history: Received 22 August 2013 Received in revised form 2 October 2013 Accepted 3 October 2013 Available online 14 October 2013 Keywords: Metals and alloys Microstructure Phase transitions Transmission electron microscopy, TEM Shape memory
a b s t r a c t The antiphase boundary (APB)-like structure of B190 martensite via R-phase transformation in a Ti–Ni–Fe alloy was investigated by means of transmission electron microscopy. The APB-like structure exhibited shifts along the (0 1 0)B190 , (0 0 1)B190 , and (1 0 0)B190 planes; that is, it exhibited facets composed of those planes at the atomic level. This atomic displacement reflects the atomic movement stemming from the R-phase transformation. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Near equiatomic Ti–Ni and Ti–Pd alloys undergo thermoelastic martensitic transformation from the B2 to B190 (monoclinic) and B19 (orthorhombic) structures upon cooling, respectively. The Ti–Ni alloy is a technologically important material with superior shape memory effect and superelasticity [1]. The Ti–Pd alloy is a candidate for high-temperature shape memory material because its transformation temperature is approximately 800 K [2]. We recently discovered an antiphase boundary (APB)-like contrast of the martensite in Ti–Ni and Ti–Pd shape memory alloys [3,4]. We characterized those APB-like structures as a kind of stacking fault, with an APB-like morphology that is induced by the martensitic transformation. The characterization of the APB-like structure reveals details of the atomic movements during martensitic transformation, resulting in a further understanding of the shape memory behavior. Recently, Inamura et al. discovered an APB-like structure in a00 -martensite of a b-Ti shape memory alloy [5]. The displacement vector was determined as a transformation-induced APB, with an additional small displacement stemming from a specific variant of the pre-existing athermal x-phase. As atomic displacements before a martensitic transformation from the B2 parent phase, it is well known that the athermal x-phase transformation forms during quenching of b-Ti alloys and that R-phase transformation ⇑ Corresponding author. Tel.: +81 96 342 3718; fax: +81 96 342 3710. E-mail address: [email protected] (M. Matsuda). 0925-8388/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2013.10.015
in Ti–Ni-based alloys occurs. Concerning the R-phase transformation, a B2–R–B190 two-step transformation has been observed in Ti–Ni–Fe alloys and aged Ni-rich Ti–Ni alloys with Ti3Ni4 precipitates [1]. Hwang et al. [6] and Murakami and Shindo [7] analyzed the peculiar APB-like contrast in the R-phase in a Ti–Ni–Fe alloy. Their results indicate that different subvariants can grow upon cooling and then impinge against neighboring subvariants, forming boundaries [7]. However, the relationship between APB-like structures induced by martensitic transformation and R-phase transformation itself has not been clarified. The purpose of the present paper is to investigate the crystallography and morphology of the APB-like structure in B190 martensite via R-phase transformation in a Ti–Ni–Fe alloy by conventional transmission electron microscopy (CTEM) and high-resolution transmission electron microscopy (HRTEM). Furthermore, high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) is applied to analyze the interface of the APB-like structure at the atomic level, by which the relatively heavy atom positions are identified by bright contrast in the image as a result of atomic number (Z) contrast [8,9].
2. Experimental procedure A Ti–47.75 at.% Ni–1.5 at.% Fe alloy was prepared from 99.7% Ti, 99.7% Ni, and 99.5% Fe (mass%) by arc melting in an argon atmosphere. A Ti–50.0 at.% Ni alloy was also fabricated as a specimen for comparison. The ingots were homogenized in an argon atmosphere at 1273 K for 86.4 ks. Subsequently, the samples were solution treated in an argon atmosphere at 1273 K for 3.6 ks and then quenched in ice water. Differential scanning calorimetry (DSC) measurements were performed
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using a calorimeter (DSC-60, Shimadzu) at a cooling and heating rate of 0.17 K/s. The TEM specimens were electropolished to perforation in a Fischione Model-110 operated at 8 V, 0.1 A, and 223 K in an electrolyte solution consisting of 25% HNO3 and 75% CH3OH by volume. CTEM and HRTEM observations were carried out with JEM-2000FX and FEI-Tecnai20F microscopes, respectively, which were both operated at 200 kV. The HAADF-STEM observation was performed by JEMARM200F (Cs-corrected 200 kV STEM). The electron probe size and current were 0.10 nm and approximately 20 PA, respectively. For the HAADF-STEM images, the annular detector was set to collect electrons scattered at angles between 90 and 170 mrad. The relationship between B2, B19, and B190 are illustrated schematically in Fig. 1 [1]. The following lattice parameters were used for the analysis of the monoclinic B190 martensite: aB190 = 0.2889 nm, bB190 = 0.4120 nm, cB190 = 0.4622 nm, and b = 96.8° [10].
Mf
Ms R f R s
Heat flow (arb. unit)
Cooling
As
ARf
Heating
3. Results and discussion 200
Fig. 2 shows DSC curves for the quenched Ti–Ni–Fe alloy after solution treatment at 1273 K for 3.6 ks. There are two exothermic peaks corresponding to the B2 to R and R to B190 transformations during cooling. The Rs, Rf, Ms, and Mf temperatures are determined to be 303, 294, 269, and 215 K, respectively, where the notations of transformation temperatures are referred from the recent review of Otsuka and Ren [1]. Furthermore, there seem to be two peaks during heating, as has been previously reported [11]. The two endothermic peaks overlap during heating because the thermal hysteresis of the B190 to R and/or B2 transformation is larger than that of the R to B2 transformation. Therefore, the remaining transformation temperatures, As and ARf, were determined to be 281 and 313 K, respectively. The quenched specimen should consist of an R-phase because the specimen was quenched in ice water at about 273 K. However, the B190 phase was observed at room temperature by TEM observation when the specimen was electropolished below the Ms temperature. Therefore, it is apparent that the alloy used is suitable for TEM observations of the B190 martensite via R-phase transformation by controlling the electropolishing temperature. Fig. 3(a and b) shows the typical bright-field image and electron diffraction pattern, respectively, taken from the area marked B in (a) in the Ti–Ni–Fe alloy. The pattern in Fig. 3(b) consists of two 1 0]B190 zone axes. sets of reflections along the [1 0 1]B190 and [1 These patterns are consistent with those taken from h0 1 1iB190 type II twins, as discussed in our previous reports [12,13]. There were B190 type I twins also typical triangle-shaped variants and {1 1 1} with spear-like morphology in some places, although the micrographs are not included here. Therefore, the lattice invariant shear of the B190 martensite via the R-phase transformation is h0 1 1iB190 type II twinning, the same as that of the B190 martensite transformed directly from the B2 phase. It is notable that many line
(a)
250
300
350
Temperature, T/K Fig. 2. DSC curves for a Ti–47.75 at.% Ni–1.5 at.% Fe alloy.
(a)
(b)
Fig. 3. (a) Bright-field image of a Ti–47.75 at.% Ni–1.5 at.% Fe alloy and (b) Electron diffraction pattern taken from area B in (a).
contrasts are observed within the twin plates, as indicated by the arrow in Fig. 3(a). In order to analyze these planar defects, CTEM observations were carried out along the [1 0 0]B190 direction. HRTEM observations were also performed along this zone axis, as described below, because the atomic columns of Ti and Ni and/or Fe in the B190 structure can easily be distinguished. Fig. 4(a and b) shows the bright-field image and corresponding electron diffraction pattern, respectively, of the [1 0 0]B190 zone axis. Some APB-like structures with curved and wide contrasts are ob-
(b)
Fig. 1. (a) Lattice correspondence between the B2 parent phase and the B19 martensite. Dashed and solid lines indicate the B2 and B19 structures, respectively. (b) B2. Monoclinic martensite B190 , viewed as a B19 structure sheared by a nonbasal shear (0 0 1)[110]
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(b)
(a)
020
001 000
200nm
(c)
g
EB // [100]B19’
(d)
200nm
g
(e)
200nm
g
200nm
served in martensitic plates of the Ti–Ni–Fe alloy, as indicated by the arrows in Fig. 4(a), whereas APB-like structures with angular looped contrasts are observed in large martensitic plates of the Ti–Ni alloy [3]. Fig. 4(c and d) shows dark-field images taken using 0 0 1B190 and 0 0 2B190 reflections, in which APB-like contrasts are observed. It has been widely recognized that p contrast of APB induced by order–disorder transformations can be observed using superlattice reflections for the ordered structure, whereas no contrast is observed using fundamental reflections. The APB-like contrast is observed when both the 0 0 1B190 superlattice and 0 0 2B190 fundamental reflections for the B190 structure are used. These facts indicate that the APB-like contrast does not correspond to p contrast; they do, however, correspond to stacking faults with an APB-like morphology induced by the martensitic transformation, as expected from Ti–Ni [3] and Ti–Pd [4] alloys. The 0 2 0*B190 reflection is used because the 0 1 0*B190 reflection is forbidden according to the extinction rule of the B190 structure [14]. It is noteworthy that APB-like contrasts are faintly observed on using the 0 2 0*B190 reflection, as indicated by the double arrow of Fig. 4(e), although no contrast is observed when using the 0 2 0*B190 reflection in the Ti–Ni alloy. This phenomenon will be discussed later. In order to analyze the APB-like contrast at the atomic level, HRTEM observations were carried out along the [1 0 0]B190 zone axis. Fig. 5 shows the two-dimensional lattice image of the APBlike structure. We can identify the shift of bright spots along both the (0 1 0)B190 and (0 0 1)B190 planes, as shown by the arrows of Fig. 5. Here, the APB-like structure does not show any sharp interface structure because the APB-like structure would consist of twodimensional interfaces in a three-dimensional crystal; that is, the boundary would be curved in the projected direction. This supports the results of the CTEM observations shown in Fig. 4. The HAADF-STEM technique using Z contrast was performed to determine the positions of the atomic columns at the interface. Fig. 6(a) shows an HAADF-STEM image of the APB-like structure along the [1 0 0]B190 zone axis. Fig. 6(b) shows the image intensity profile taken along the white line X–Y in Fig. 6(a). It has been
(001)
Fig. 4. (a) Bright-field image and (b) corresponding electron diffraction pattern of a Ti–47.75 at.% Ni–1.5 at.% Fe alloy along the [1 0 0]B190 zone axis. (c–e) Dark-field images of the area shown in (a); APB-like structure in contrast: g = (c) 0 0 1, (d) 0 0 2, and (e) 0 2 0 with EB near [1 0 0]B190 .
(010)
2nm
Fig. 5. Two-dimensional lattice image of the APB-like structure in a Ti–47.75 at.% Ni–1.5 at.% Fe alloy along the [1 0 0]B190 zone axis.
reported that Fe atoms can be located by electron channelingenhanced microanalysis at the Ni atom sites preferentially in a Ti48.5Ni48.5Fe3 alloy [15]. Therefore, the higher intensity profile indicates Ni (Z = 28) and/or Fe (Z = 26) columns because of the nature of Z contrast, whereas the lower intensity profile indicates Ti (Z = 22) columns. Thus, the bright and dim spots in Fig. 6(a) correspond to the Ni and/or Fe and Ti atomic columns, respectively. The Fourier filter-processed image around the interface between the arrows in Fig. 6(a) is presented in Fig. 6(c), and the atomic arrangements in Fig. 6(c) are schematically illustrated in Fig. 6(d). The open and solid circles indicate Ni and/or Fe and Ti atom columns, respectively. We can see the shifts along both the (0 1 0)B190 and (0 0 1)B190 planes by the positions of the Ni and/or Fe atomic columns, indicated by open circles in Fig. 6(c). That is to say, the APB-like structure is a gradual change in the orientation of the interface and consists of facets composed of both (0 1 0)B190 and (0 0 1)B190 planes at an atomic level, as indicated by the line
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(a)
(b)
(001) (010)
1nm
(c)
Ni, Fe
Ni, Fe
Y Intensity (arbit. unit)
X
X
Ti
Ni, Fe Ti
1nm
Ti
Y
(001)
(d)
(010)
1nm
Ti Ni, Fe
Fig. 6. (a) A HAADF-STEM image of the APB-like structure in a Ti–47.75 at.% Ni–1.5 at.% Fe alloy along the [1 0 0]B190 zone axis. (b) Image intensity profile taken along the white line X–Y in (a). (c) Fourier filter-processed HAADF-STEM image around the APB-like interface. The open circles indicate the Ni and/or Fe atomic columns. (d) Schematic illustration of the atomic arrangements in (c).
between the arrows of Fig. 6(d). It is obvious that the APB-like interface in the Ti–Ni–Fe alloy also has obscure contrasts on the (0 1 0)B190 plane, indicated by the arrows in Fig. 6(c), as compared with the Fourier filter-processed image around the APB-like interface and its schematic illustration in the equiatomic Ti–Ni alloy of Fig. 7(a and b). This means that the APB-like interface with such a contrast in the Ti–Ni–Fe alloy is not perpendicular but rather tilted with respect to the direction normal to the foil [16]. That is to say, the APB-like contrast in the Ti–Ni–Fe alloy shows a displacement in its a-axis component. To confirm this, CTEM observations were carried out along the [0 1 0]B190 direction; these revealed the displacement along the a-axis on the a–c plane. Fig. 8(a and b) shows a bright-field image and the corresponding electron diffraction pattern, respectively, along the [0 1 0]B190 zone axis. Some APB-like
(b)
(001)
(a)
structures with angular contrasts are observed in large martensitic plates, as indicated by the arrows. Fig. 9(a) shows an HAADF-STEM image of the APB-like structure along the [0 1 0]B190 zone axis. Fig. 9(b) shows the image intensity profile taken along the white line X–Y in Fig. 9(a). The bright and dim spots in Fig. 9(a) correspond to the Ni and/or Fe and Ti atomic columns, respectively, because of the nature of Z contrast, as was found in Fig. 6(a). The Fourier filter-processed image around the interface between the arrows in Fig. 9(a) is presented in Fig. 9(c), and the atomic arrangements in Fig. 9(c) are schematically illustrated in Fig. 9(d). The open and solid circles indicate Ni and/or Fe and Ti atom columns, respectively. We can see the shifts along both the (0 0 1)B190 and (1 0 0)B190 planes by the double arrows and the positions of the Ni and/or Fe atomic columns, indicated by open circles in Fig. 9(c).
(010)
1nm
Ti Ni
Fig. 7. (a) Fourier filter-processed HAADF-STEM image around the APB-like interface in a Ti–50.0 at.% Ni alloy. The open circles indicate the Ni atomic columns. (b) Schematic illustration of the atomic arrangements in (a).
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(b)
(a)
100
002 000
EB // [010]B19’
100nm
Fig. 8. (a) Bright-field image and (b) corresponding electron diffraction pattern of a Ti–47.75 at.% Ni–1.5 at.% Fe alloy along the [010]B190 zone axis.
That is to say, the APB-like structure consists of facets composed of both (0 0 1)B190 and (1 0 0)B190 planes at an atomic level, as indicated by the line in Fig. 9(d). Furthermore, part of the APB-like boundary is not clear because it consists of facets composed of both (0 1 0)B190 and (0 0 1)B190 planes, as discussed above. On the basis of these observations, we discuss the atomic displacement of the APB-like structure in the present Ti–Ni–Fe alloy. We previously reported that the displacement vector of the APB-like structure on the B190 martensite in Ti–Ni alloy can be expressed as R = h0.1648 1/2 0.4328i. The value of R is equal to the displacement caused by atomic shuffling alone during the martensitic transformation to maintain the B190 structure between domains. Therefore, no APB-like contrast in the Ti–Ni alloy was observed using each g = (0 2n 0), where n is an integer, by the
relationship between the phase angle and R [17]. However, APBlike contrasts in the present Ti–Ni–Fe alloy are faintly observed upon using the 020*B190 reflection, as indicated by the double arrow in Fig. 4(e). This means that the atomic displacement along the b-axis is not ±1/2. Furthermore, the HAADF-STEM images along the [0 1 0]B190 zone axis indicate that the atomic displacement along the a-axis in the present Ti–Ni–Fe alloy seems to be larger than 0.1648, which is the a-axis component of R on the APB-like structure estimated from the conventional atomic coordinates of Ti and Ni in B190 martensite in binary Ti–Ni alloys, as indicated by the single arrows in Fig. 9(d). Consequently, it is apparent that the atomic displacement of the APB-like structure in the present Ti–Ni–Fe alloy is different from that in the Ti–Ni alloy, although the crystal structure of the martensite in both alloys has the same B190 structure. It is also evident from DSC measurements that the binary Ti–Ni alloy used in our previous report [3] has no R-phase transformation. The APB-like structure in the present Ti–Ni–Fe alloy also disappeared by heating in situ above the Af temperature, as it did in the Ti–Ni alloy, although the micrograph is not included here. This proves that the APB-like structure in the present Ti–Ni–Fe alloy is not related to the B2 ordered structure. Thus, it is likely that the atomic displacement of the APB-like structure in this alloy relates to the R-phase transformation itself, in addition to the displacement due to the atomic shuffling during the martensitic transformation directly from the B2 phase. The R-phase lattice can be described by stretching the B2 parent lattice along the h1 1 1iB2 diagonal directions. Since there are four h1 1 1iB2 orientations in the B2 parent lattice, four lattice correspondences are possible between the B2 parent lattice and the R-phase lattice [18–20]. There are also 12 lattice correspondences between the B2 parent and the B190 martensite [21]. These results
(b)
(a)
Ni, Fe
Intensity (arbit. unit)
Ni, Fe
(100)
1nm
(c)
X
Ni, Fe Ti
Ti
Ti
Y
1nm
(d)
(100)
1nm
Ti Ni, Fe
Fig. 9. (a) A HAADF-STEM image of the APB-like structure in a Ti–47.75 at.% Ni–1.5 at.% Fe alloy along the [0 1 0]B190 zone axis. (b) Image intensity profile taken along the white line X–Y in (a). (c) Fourier filter-processed HAADF-STEM image around the APB-like interface. The open circles indicate the Ni and/or Fe atomic columns. (d) Schematic illustration of the atomic arrangements in (c).
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(b)
(001)
(a)
(010)
1nm
Ti Ni, Fe
Fig. 10. (a) Fourier filter-processed HAADF-STEM image around the APB-like interface in a Ti–47.75 at.% Ni–1.5 at.% Fe alloy. The open circles indicate the Ni and/or Fe atomic columns. (b) Schematic illustration of the atomic arrangements in (a).
suggest that the displacement along h1 1 1iB2 direction of the B2 parent phase stemming from the R-phase transformation corresponds to either the h1 0 1iB190 direction on the (0 1 0)B190 plane or the h1 1 0iB190 direction on the (0 0 1)B190 plane for the B190 martensitic lattice, as shown in Fig. 1. That is to say, these displacements can be expressed as Rxz = hdx 0 dziB190 and Rxy = hdx dy 0iB190 , respectively. The Rxz displacement supports both the obscure contrasts on the (0 1 0)B190 plane in the HAADF-STEM image along the [1 0 0]B190 zone axis of Fig. 6 and the atomic displacement, which is larger than 0.1648, along the a-axis along the [0 1 0]B190 zone axis, as indicated by the arrows of Fig. 9(d). A Fourier filterprocessed HAADF-STEM image along the [1 0 0]B190 zone axis of another APB-like structure differing from Fig. 6 in the present Ti–Ni–Fe alloy is shown in Fig. 10(a). The APB-like interface indicated by the line between the arrows of Fig. 10(b) consists of facets composed of both (0 1 0)B190 and (0 0 1)B190 planes, similar to that shown in Fig. 6. The presence of the atomic shifts along the b-axis as indicated by the arrows in Fig. 10(a) should be noted. This displacement corresponds to the Rxy stemming from the R-phase transformation, as described above. Thus, it is apparent that the atomic displacement of the APB-like structure of the martensite via the R-phase in the Ti–Ni–Fe alloy reflects the atomic movement stemming from R-phase transformation. From these observations, we conclude that the APB-like structure is affected not only by the atomic movements during martensitic transformation but also by the R-phase transformation. As described in the introduction, peculiar APB-like contrasts are present within the R-phase variants in Ti–Ni–Fe alloys [6,7]. The boundary is formed by impingement against the growth of neighboring subvariants, and the stacking phase is shifted at the boundaries. If the APB-like structure in the R-phase is inherited to that in martensite, the atomic-shifted amounts on the APB-like structure in B190 martensite according to the shifts of stacking planes in the R-phase should vary in different places. However, no irregularity in the atomic-shifted amounts on the APB-like structure in B190 martensite is recognized on the basis of the HAADF-STEM images of Figs. 6, 9 and 10. The morphology of the present APB-like structure in the B190 martensite is also quite different from that in the R-phase. We therefore expect at the present that the APB-like structure in the B190 martensite is not inherited from the APB-like contrasts in the R-phase. However, such an inheritance may be a potential route for formation of APB-like defects. To confirm this, we need to make observations of APB-like contrasts in the R-phase during cooling in situ before and after the martensitic transformation. Finally, we would like to make a comment concerning a formation of the APB-like structure. It is considered that the APB-like
structure is induced by a difference in the shear direction during martensitic transformation and/or the impingement with the growth of martensitic domains nucleated at various sites. In fact, APB-like structures are frequently observed in large martensitic plates. Therefore, one martensitic variant may contain more than one domain; that is, a martensitic nucleus. 4. Conclusions An APB-like structure of the B190 martensite via an R-phase transformation in a Ti–Ni–Fe alloy was investigated by means of CTEM, HRTEM, and HAADF-STEM. The APB-like structure exhibited shifts along the (0 1 0)B190 , (0 0 1)B190 , and (1 0 0)B190 planes; that is, facets composed of those planes at the atomic level. The atomic displacement on the APB-like structure of the martensite via an R-phase transformation in the Ti–Ni–Fe alloy reflects the atomic movement stemming from the R-phase transformation itself, in addition to the displacement due to the atomic shuffling during the transformation directly from the B2 parent phase to B190 martensite. Acknowledgments This work was supported by JSPS KAKENHI Grant No. 24656417. The authors would like to express their sincere gratitude to Professor Y. Morizono of Kumamoto University for his support in the arc melting and for his valuable comments. References [1] K. Otsuka, X. Ren, Prog. Mater. Sci. 50 (2005) 511–678. [2] H.C. Donkersloot, J.H.N. Van Vucht, J. Less-Common Met. 20 (1970) 83–91. [3] M. Matsuda, K. Kuramoto, Y. Morizono, S. Tsurekawa, E. Okunishi, T. Hara, M. Nishida, Acta Mater. 59 (2011) 133–140. [4] M. Matsuda, T. Hara, M. Nishida, Mater. Trans. 49 (2008) 461–465. [5] T. Inamura, H. Hosoda, H.Y. Kim, S. Miyazaki, Philos. Mag. 90 (2010) 3475– 3498. [6] C.M. Hwang, M. Meichle, M.B. Salamon, C.M. Wayman, Philos. Mag. A 47 (1983) 9–30. [7] Y. Murakami, D. Shindo, Mater. Trans. 46 (2005) 743–755. [8] S.J. Pennycook, D.E. Jesson, Acta Metall. Mater. 40 (1992) S149–S159. [9] T. Kogure, E. Okunishi, J. Electron. Microsc. 59 (2010) 263–271. [10] K. Otsuka, T. Sawamura, K. Shimizu, Phys. Status Solidi 5 (1971) 457–470. [11] T. Nishiura, M. Nishida, Mater. Trans. 50 (2009) 1219–1224. [12] M. Nishida, K. Yamauchi, A. Chiba, Y. Higashi, in: Proceedings of ICOMAT-92, Monterey Inst. Adv. Studies (1993) 881–886. [13] M. Nishida, H. Ohgi, I. Itai, A. Chiba, K. Yamauchi, Acta Metall. Mater. 43 (1995) 1219–1227. [14] Y. Kudoh, M. Tokonami, S. Miyazaki, K. Otsuka, Acta Metall. 33 (1985) 2049– 2056. [15] Y. Nakata, T. Tadaki, K. Shimizu, Mater. Trans. 32 (1991) 1120–1127. [16] M.J. Whelan, P.B. Hirsch, Philos. Mag. 2 (1957) 1121–1142.
M. Matsuda et al. / Journal of Alloys and Compounds 586 (2014) 87–93 [17] M.J. Marchinkowski, Theory and direct observation of antiphase boundaries and dislocations in superlattice, in: G. Thomas, J. Washburn (Eds.), Electron microscopy and strength of crystals, Interscience, New York, 1963, pp. 333– 440. [18] E. Goo, R. Sinclair, Acta Metall. 33 (1985) 1717–1723.
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Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom
Antiphase boundary-like structure of B190 martensite via R-phase transformation in Ti–Ni–Fe alloy M. Matsuda a,⇑, R. Yamashita a, S. Tsurekawa a, K. Takashima a, M. Mitsuhara b, M. Nishida b a b
Department of Materials Science and Engineering, Kumamoto University, 2-39-1 Kurokami, Kumamoto 860-8555, Japan Department of Engineering Sciences for Electronics and Materials, Kyushu University, Kasuga, Fukuoka 816-8580, Japan
a r t i c l e
i n f o
Article history: Received 22 August 2013 Received in revised form 2 October 2013 Accepted 3 October 2013 Available online 14 October 2013 Keywords: Metals and alloys Microstructure Phase transitions Transmission electron microscopy, TEM Shape memory
a b s t r a c t The antiphase boundary (APB)-like structure of B190 martensite via R-phase transformation in a Ti–Ni–Fe alloy was investigated by means of transmission electron microscopy. The APB-like structure exhibited shifts along the (0 1 0)B190 , (0 0 1)B190 , and (1 0 0)B190 planes; that is, it exhibited facets composed of those planes at the atomic level. This atomic displacement reflects the atomic movement stemming from the R-phase transformation. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Near equiatomic Ti–Ni and Ti–Pd alloys undergo thermoelastic martensitic transformation from the B2 to B190 (monoclinic) and B19 (orthorhombic) structures upon cooling, respectively. The Ti–Ni alloy is a technologically important material with superior shape memory effect and superelasticity [1]. The Ti–Pd alloy is a candidate for high-temperature shape memory material because its transformation temperature is approximately 800 K [2]. We recently discovered an antiphase boundary (APB)-like contrast of the martensite in Ti–Ni and Ti–Pd shape memory alloys [3,4]. We characterized those APB-like structures as a kind of stacking fault, with an APB-like morphology that is induced by the martensitic transformation. The characterization of the APB-like structure reveals details of the atomic movements during martensitic transformation, resulting in a further understanding of the shape memory behavior. Recently, Inamura et al. discovered an APB-like structure in a00 -martensite of a b-Ti shape memory alloy [5]. The displacement vector was determined as a transformation-induced APB, with an additional small displacement stemming from a specific variant of the pre-existing athermal x-phase. As atomic displacements before a martensitic transformation from the B2 parent phase, it is well known that the athermal x-phase transformation forms during quenching of b-Ti alloys and that R-phase transformation ⇑ Corresponding author. Tel.: +81 96 342 3718; fax: +81 96 342 3710. E-mail address: [email protected] (M. Matsuda). 0925-8388/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2013.10.015
in Ti–Ni-based alloys occurs. Concerning the R-phase transformation, a B2–R–B190 two-step transformation has been observed in Ti–Ni–Fe alloys and aged Ni-rich Ti–Ni alloys with Ti3Ni4 precipitates [1]. Hwang et al. [6] and Murakami and Shindo [7] analyzed the peculiar APB-like contrast in the R-phase in a Ti–Ni–Fe alloy. Their results indicate that different subvariants can grow upon cooling and then impinge against neighboring subvariants, forming boundaries [7]. However, the relationship between APB-like structures induced by martensitic transformation and R-phase transformation itself has not been clarified. The purpose of the present paper is to investigate the crystallography and morphology of the APB-like structure in B190 martensite via R-phase transformation in a Ti–Ni–Fe alloy by conventional transmission electron microscopy (CTEM) and high-resolution transmission electron microscopy (HRTEM). Furthermore, high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) is applied to analyze the interface of the APB-like structure at the atomic level, by which the relatively heavy atom positions are identified by bright contrast in the image as a result of atomic number (Z) contrast [8,9].
2. Experimental procedure A Ti–47.75 at.% Ni–1.5 at.% Fe alloy was prepared from 99.7% Ti, 99.7% Ni, and 99.5% Fe (mass%) by arc melting in an argon atmosphere. A Ti–50.0 at.% Ni alloy was also fabricated as a specimen for comparison. The ingots were homogenized in an argon atmosphere at 1273 K for 86.4 ks. Subsequently, the samples were solution treated in an argon atmosphere at 1273 K for 3.6 ks and then quenched in ice water. Differential scanning calorimetry (DSC) measurements were performed
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using a calorimeter (DSC-60, Shimadzu) at a cooling and heating rate of 0.17 K/s. The TEM specimens were electropolished to perforation in a Fischione Model-110 operated at 8 V, 0.1 A, and 223 K in an electrolyte solution consisting of 25% HNO3 and 75% CH3OH by volume. CTEM and HRTEM observations were carried out with JEM-2000FX and FEI-Tecnai20F microscopes, respectively, which were both operated at 200 kV. The HAADF-STEM observation was performed by JEMARM200F (Cs-corrected 200 kV STEM). The electron probe size and current were 0.10 nm and approximately 20 PA, respectively. For the HAADF-STEM images, the annular detector was set to collect electrons scattered at angles between 90 and 170 mrad. The relationship between B2, B19, and B190 are illustrated schematically in Fig. 1 [1]. The following lattice parameters were used for the analysis of the monoclinic B190 martensite: aB190 = 0.2889 nm, bB190 = 0.4120 nm, cB190 = 0.4622 nm, and b = 96.8° [10].
Mf
Ms R f R s
Heat flow (arb. unit)
Cooling
As
ARf
Heating
3. Results and discussion 200
Fig. 2 shows DSC curves for the quenched Ti–Ni–Fe alloy after solution treatment at 1273 K for 3.6 ks. There are two exothermic peaks corresponding to the B2 to R and R to B190 transformations during cooling. The Rs, Rf, Ms, and Mf temperatures are determined to be 303, 294, 269, and 215 K, respectively, where the notations of transformation temperatures are referred from the recent review of Otsuka and Ren [1]. Furthermore, there seem to be two peaks during heating, as has been previously reported [11]. The two endothermic peaks overlap during heating because the thermal hysteresis of the B190 to R and/or B2 transformation is larger than that of the R to B2 transformation. Therefore, the remaining transformation temperatures, As and ARf, were determined to be 281 and 313 K, respectively. The quenched specimen should consist of an R-phase because the specimen was quenched in ice water at about 273 K. However, the B190 phase was observed at room temperature by TEM observation when the specimen was electropolished below the Ms temperature. Therefore, it is apparent that the alloy used is suitable for TEM observations of the B190 martensite via R-phase transformation by controlling the electropolishing temperature. Fig. 3(a and b) shows the typical bright-field image and electron diffraction pattern, respectively, taken from the area marked B in (a) in the Ti–Ni–Fe alloy. The pattern in Fig. 3(b) consists of two 1 0]B190 zone axes. sets of reflections along the [1 0 1]B190 and [1 These patterns are consistent with those taken from h0 1 1iB190 type II twins, as discussed in our previous reports [12,13]. There were B190 type I twins also typical triangle-shaped variants and {1 1 1} with spear-like morphology in some places, although the micrographs are not included here. Therefore, the lattice invariant shear of the B190 martensite via the R-phase transformation is h0 1 1iB190 type II twinning, the same as that of the B190 martensite transformed directly from the B2 phase. It is notable that many line
(a)
250
300
350
Temperature, T/K Fig. 2. DSC curves for a Ti–47.75 at.% Ni–1.5 at.% Fe alloy.
(a)
(b)
Fig. 3. (a) Bright-field image of a Ti–47.75 at.% Ni–1.5 at.% Fe alloy and (b) Electron diffraction pattern taken from area B in (a).
contrasts are observed within the twin plates, as indicated by the arrow in Fig. 3(a). In order to analyze these planar defects, CTEM observations were carried out along the [1 0 0]B190 direction. HRTEM observations were also performed along this zone axis, as described below, because the atomic columns of Ti and Ni and/or Fe in the B190 structure can easily be distinguished. Fig. 4(a and b) shows the bright-field image and corresponding electron diffraction pattern, respectively, of the [1 0 0]B190 zone axis. Some APB-like structures with curved and wide contrasts are ob-
(b)
Fig. 1. (a) Lattice correspondence between the B2 parent phase and the B19 martensite. Dashed and solid lines indicate the B2 and B19 structures, respectively. (b) B2. Monoclinic martensite B190 , viewed as a B19 structure sheared by a nonbasal shear (0 0 1)[110]
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(b)
(a)
020
001 000
200nm
(c)
g
EB // [100]B19’
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g
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g
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served in martensitic plates of the Ti–Ni–Fe alloy, as indicated by the arrows in Fig. 4(a), whereas APB-like structures with angular looped contrasts are observed in large martensitic plates of the Ti–Ni alloy [3]. Fig. 4(c and d) shows dark-field images taken using 0 0 1B190 and 0 0 2B190 reflections, in which APB-like contrasts are observed. It has been widely recognized that p contrast of APB induced by order–disorder transformations can be observed using superlattice reflections for the ordered structure, whereas no contrast is observed using fundamental reflections. The APB-like contrast is observed when both the 0 0 1B190 superlattice and 0 0 2B190 fundamental reflections for the B190 structure are used. These facts indicate that the APB-like contrast does not correspond to p contrast; they do, however, correspond to stacking faults with an APB-like morphology induced by the martensitic transformation, as expected from Ti–Ni [3] and Ti–Pd [4] alloys. The 0 2 0*B190 reflection is used because the 0 1 0*B190 reflection is forbidden according to the extinction rule of the B190 structure [14]. It is noteworthy that APB-like contrasts are faintly observed on using the 0 2 0*B190 reflection, as indicated by the double arrow of Fig. 4(e), although no contrast is observed when using the 0 2 0*B190 reflection in the Ti–Ni alloy. This phenomenon will be discussed later. In order to analyze the APB-like contrast at the atomic level, HRTEM observations were carried out along the [1 0 0]B190 zone axis. Fig. 5 shows the two-dimensional lattice image of the APBlike structure. We can identify the shift of bright spots along both the (0 1 0)B190 and (0 0 1)B190 planes, as shown by the arrows of Fig. 5. Here, the APB-like structure does not show any sharp interface structure because the APB-like structure would consist of twodimensional interfaces in a three-dimensional crystal; that is, the boundary would be curved in the projected direction. This supports the results of the CTEM observations shown in Fig. 4. The HAADF-STEM technique using Z contrast was performed to determine the positions of the atomic columns at the interface. Fig. 6(a) shows an HAADF-STEM image of the APB-like structure along the [1 0 0]B190 zone axis. Fig. 6(b) shows the image intensity profile taken along the white line X–Y in Fig. 6(a). It has been
(001)
Fig. 4. (a) Bright-field image and (b) corresponding electron diffraction pattern of a Ti–47.75 at.% Ni–1.5 at.% Fe alloy along the [1 0 0]B190 zone axis. (c–e) Dark-field images of the area shown in (a); APB-like structure in contrast: g = (c) 0 0 1, (d) 0 0 2, and (e) 0 2 0 with EB near [1 0 0]B190 .
(010)
2nm
Fig. 5. Two-dimensional lattice image of the APB-like structure in a Ti–47.75 at.% Ni–1.5 at.% Fe alloy along the [1 0 0]B190 zone axis.
reported that Fe atoms can be located by electron channelingenhanced microanalysis at the Ni atom sites preferentially in a Ti48.5Ni48.5Fe3 alloy [15]. Therefore, the higher intensity profile indicates Ni (Z = 28) and/or Fe (Z = 26) columns because of the nature of Z contrast, whereas the lower intensity profile indicates Ti (Z = 22) columns. Thus, the bright and dim spots in Fig. 6(a) correspond to the Ni and/or Fe and Ti atomic columns, respectively. The Fourier filter-processed image around the interface between the arrows in Fig. 6(a) is presented in Fig. 6(c), and the atomic arrangements in Fig. 6(c) are schematically illustrated in Fig. 6(d). The open and solid circles indicate Ni and/or Fe and Ti atom columns, respectively. We can see the shifts along both the (0 1 0)B190 and (0 0 1)B190 planes by the positions of the Ni and/or Fe atomic columns, indicated by open circles in Fig. 6(c). That is to say, the APB-like structure is a gradual change in the orientation of the interface and consists of facets composed of both (0 1 0)B190 and (0 0 1)B190 planes at an atomic level, as indicated by the line
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(a)
(b)
(001) (010)
1nm
(c)
Ni, Fe
Ni, Fe
Y Intensity (arbit. unit)
X
X
Ti
Ni, Fe Ti
1nm
Ti
Y
(001)
(d)
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Ti Ni, Fe
Fig. 6. (a) A HAADF-STEM image of the APB-like structure in a Ti–47.75 at.% Ni–1.5 at.% Fe alloy along the [1 0 0]B190 zone axis. (b) Image intensity profile taken along the white line X–Y in (a). (c) Fourier filter-processed HAADF-STEM image around the APB-like interface. The open circles indicate the Ni and/or Fe atomic columns. (d) Schematic illustration of the atomic arrangements in (c).
between the arrows of Fig. 6(d). It is obvious that the APB-like interface in the Ti–Ni–Fe alloy also has obscure contrasts on the (0 1 0)B190 plane, indicated by the arrows in Fig. 6(c), as compared with the Fourier filter-processed image around the APB-like interface and its schematic illustration in the equiatomic Ti–Ni alloy of Fig. 7(a and b). This means that the APB-like interface with such a contrast in the Ti–Ni–Fe alloy is not perpendicular but rather tilted with respect to the direction normal to the foil [16]. That is to say, the APB-like contrast in the Ti–Ni–Fe alloy shows a displacement in its a-axis component. To confirm this, CTEM observations were carried out along the [0 1 0]B190 direction; these revealed the displacement along the a-axis on the a–c plane. Fig. 8(a and b) shows a bright-field image and the corresponding electron diffraction pattern, respectively, along the [0 1 0]B190 zone axis. Some APB-like
(b)
(001)
(a)
structures with angular contrasts are observed in large martensitic plates, as indicated by the arrows. Fig. 9(a) shows an HAADF-STEM image of the APB-like structure along the [0 1 0]B190 zone axis. Fig. 9(b) shows the image intensity profile taken along the white line X–Y in Fig. 9(a). The bright and dim spots in Fig. 9(a) correspond to the Ni and/or Fe and Ti atomic columns, respectively, because of the nature of Z contrast, as was found in Fig. 6(a). The Fourier filter-processed image around the interface between the arrows in Fig. 9(a) is presented in Fig. 9(c), and the atomic arrangements in Fig. 9(c) are schematically illustrated in Fig. 9(d). The open and solid circles indicate Ni and/or Fe and Ti atom columns, respectively. We can see the shifts along both the (0 0 1)B190 and (1 0 0)B190 planes by the double arrows and the positions of the Ni and/or Fe atomic columns, indicated by open circles in Fig. 9(c).
(010)
1nm
Ti Ni
Fig. 7. (a) Fourier filter-processed HAADF-STEM image around the APB-like interface in a Ti–50.0 at.% Ni alloy. The open circles indicate the Ni atomic columns. (b) Schematic illustration of the atomic arrangements in (a).
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(b)
(a)
100
002 000
EB // [010]B19’
100nm
Fig. 8. (a) Bright-field image and (b) corresponding electron diffraction pattern of a Ti–47.75 at.% Ni–1.5 at.% Fe alloy along the [010]B190 zone axis.
That is to say, the APB-like structure consists of facets composed of both (0 0 1)B190 and (1 0 0)B190 planes at an atomic level, as indicated by the line in Fig. 9(d). Furthermore, part of the APB-like boundary is not clear because it consists of facets composed of both (0 1 0)B190 and (0 0 1)B190 planes, as discussed above. On the basis of these observations, we discuss the atomic displacement of the APB-like structure in the present Ti–Ni–Fe alloy. We previously reported that the displacement vector of the APB-like structure on the B190 martensite in Ti–Ni alloy can be expressed as R = h0.1648 1/2 0.4328i. The value of R is equal to the displacement caused by atomic shuffling alone during the martensitic transformation to maintain the B190 structure between domains. Therefore, no APB-like contrast in the Ti–Ni alloy was observed using each g = (0 2n 0), where n is an integer, by the
relationship between the phase angle and R [17]. However, APBlike contrasts in the present Ti–Ni–Fe alloy are faintly observed upon using the 020*B190 reflection, as indicated by the double arrow in Fig. 4(e). This means that the atomic displacement along the b-axis is not ±1/2. Furthermore, the HAADF-STEM images along the [0 1 0]B190 zone axis indicate that the atomic displacement along the a-axis in the present Ti–Ni–Fe alloy seems to be larger than 0.1648, which is the a-axis component of R on the APB-like structure estimated from the conventional atomic coordinates of Ti and Ni in B190 martensite in binary Ti–Ni alloys, as indicated by the single arrows in Fig. 9(d). Consequently, it is apparent that the atomic displacement of the APB-like structure in the present Ti–Ni–Fe alloy is different from that in the Ti–Ni alloy, although the crystal structure of the martensite in both alloys has the same B190 structure. It is also evident from DSC measurements that the binary Ti–Ni alloy used in our previous report [3] has no R-phase transformation. The APB-like structure in the present Ti–Ni–Fe alloy also disappeared by heating in situ above the Af temperature, as it did in the Ti–Ni alloy, although the micrograph is not included here. This proves that the APB-like structure in the present Ti–Ni–Fe alloy is not related to the B2 ordered structure. Thus, it is likely that the atomic displacement of the APB-like structure in this alloy relates to the R-phase transformation itself, in addition to the displacement due to the atomic shuffling during the martensitic transformation directly from the B2 phase. The R-phase lattice can be described by stretching the B2 parent lattice along the h1 1 1iB2 diagonal directions. Since there are four h1 1 1iB2 orientations in the B2 parent lattice, four lattice correspondences are possible between the B2 parent lattice and the R-phase lattice [18–20]. There are also 12 lattice correspondences between the B2 parent and the B190 martensite [21]. These results
(b)
(a)
Ni, Fe
Intensity (arbit. unit)
Ni, Fe
(100)
1nm
(c)
X
Ni, Fe Ti
Ti
Ti
Y
1nm
(d)
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1nm
Ti Ni, Fe
Fig. 9. (a) A HAADF-STEM image of the APB-like structure in a Ti–47.75 at.% Ni–1.5 at.% Fe alloy along the [0 1 0]B190 zone axis. (b) Image intensity profile taken along the white line X–Y in (a). (c) Fourier filter-processed HAADF-STEM image around the APB-like interface. The open circles indicate the Ni and/or Fe atomic columns. (d) Schematic illustration of the atomic arrangements in (c).
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(b)
(001)
(a)
(010)
1nm
Ti Ni, Fe
Fig. 10. (a) Fourier filter-processed HAADF-STEM image around the APB-like interface in a Ti–47.75 at.% Ni–1.5 at.% Fe alloy. The open circles indicate the Ni and/or Fe atomic columns. (b) Schematic illustration of the atomic arrangements in (a).
suggest that the displacement along h1 1 1iB2 direction of the B2 parent phase stemming from the R-phase transformation corresponds to either the h1 0 1iB190 direction on the (0 1 0)B190 plane or the h1 1 0iB190 direction on the (0 0 1)B190 plane for the B190 martensitic lattice, as shown in Fig. 1. That is to say, these displacements can be expressed as Rxz = hdx 0 dziB190 and Rxy = hdx dy 0iB190 , respectively. The Rxz displacement supports both the obscure contrasts on the (0 1 0)B190 plane in the HAADF-STEM image along the [1 0 0]B190 zone axis of Fig. 6 and the atomic displacement, which is larger than 0.1648, along the a-axis along the [0 1 0]B190 zone axis, as indicated by the arrows of Fig. 9(d). A Fourier filterprocessed HAADF-STEM image along the [1 0 0]B190 zone axis of another APB-like structure differing from Fig. 6 in the present Ti–Ni–Fe alloy is shown in Fig. 10(a). The APB-like interface indicated by the line between the arrows of Fig. 10(b) consists of facets composed of both (0 1 0)B190 and (0 0 1)B190 planes, similar to that shown in Fig. 6. The presence of the atomic shifts along the b-axis as indicated by the arrows in Fig. 10(a) should be noted. This displacement corresponds to the Rxy stemming from the R-phase transformation, as described above. Thus, it is apparent that the atomic displacement of the APB-like structure of the martensite via the R-phase in the Ti–Ni–Fe alloy reflects the atomic movement stemming from R-phase transformation. From these observations, we conclude that the APB-like structure is affected not only by the atomic movements during martensitic transformation but also by the R-phase transformation. As described in the introduction, peculiar APB-like contrasts are present within the R-phase variants in Ti–Ni–Fe alloys [6,7]. The boundary is formed by impingement against the growth of neighboring subvariants, and the stacking phase is shifted at the boundaries. If the APB-like structure in the R-phase is inherited to that in martensite, the atomic-shifted amounts on the APB-like structure in B190 martensite according to the shifts of stacking planes in the R-phase should vary in different places. However, no irregularity in the atomic-shifted amounts on the APB-like structure in B190 martensite is recognized on the basis of the HAADF-STEM images of Figs. 6, 9 and 10. The morphology of the present APB-like structure in the B190 martensite is also quite different from that in the R-phase. We therefore expect at the present that the APB-like structure in the B190 martensite is not inherited from the APB-like contrasts in the R-phase. However, such an inheritance may be a potential route for formation of APB-like defects. To confirm this, we need to make observations of APB-like contrasts in the R-phase during cooling in situ before and after the martensitic transformation. Finally, we would like to make a comment concerning a formation of the APB-like structure. It is considered that the APB-like
structure is induced by a difference in the shear direction during martensitic transformation and/or the impingement with the growth of martensitic domains nucleated at various sites. In fact, APB-like structures are frequently observed in large martensitic plates. Therefore, one martensitic variant may contain more than one domain; that is, a martensitic nucleus. 4. Conclusions An APB-like structure of the B190 martensite via an R-phase transformation in a Ti–Ni–Fe alloy was investigated by means of CTEM, HRTEM, and HAADF-STEM. The APB-like structure exhibited shifts along the (0 1 0)B190 , (0 0 1)B190 , and (1 0 0)B190 planes; that is, facets composed of those planes at the atomic level. The atomic displacement on the APB-like structure of the martensite via an R-phase transformation in the Ti–Ni–Fe alloy reflects the atomic movement stemming from the R-phase transformation itself, in addition to the displacement due to the atomic shuffling during the transformation directly from the B2 parent phase to B190 martensite. Acknowledgments This work was supported by JSPS KAKENHI Grant No. 24656417. The authors would like to express their sincere gratitude to Professor Y. Morizono of Kumamoto University for his support in the arc melting and for his valuable comments. References [1] K. Otsuka, X. Ren, Prog. Mater. Sci. 50 (2005) 511–678. [2] H.C. Donkersloot, J.H.N. Van Vucht, J. Less-Common Met. 20 (1970) 83–91. [3] M. Matsuda, K. Kuramoto, Y. Morizono, S. Tsurekawa, E. Okunishi, T. Hara, M. Nishida, Acta Mater. 59 (2011) 133–140. [4] M. Matsuda, T. Hara, M. Nishida, Mater. Trans. 49 (2008) 461–465. [5] T. Inamura, H. Hosoda, H.Y. Kim, S. Miyazaki, Philos. Mag. 90 (2010) 3475– 3498. [6] C.M. Hwang, M. Meichle, M.B. Salamon, C.M. Wayman, Philos. Mag. A 47 (1983) 9–30. [7] Y. Murakami, D. Shindo, Mater. Trans. 46 (2005) 743–755. [8] S.J. Pennycook, D.E. Jesson, Acta Metall. Mater. 40 (1992) S149–S159. [9] T. Kogure, E. Okunishi, J. Electron. Microsc. 59 (2010) 263–271. [10] K. Otsuka, T. Sawamura, K. Shimizu, Phys. Status Solidi 5 (1971) 457–470. [11] T. Nishiura, M. Nishida, Mater. Trans. 50 (2009) 1219–1224. [12] M. Nishida, K. Yamauchi, A. Chiba, Y. Higashi, in: Proceedings of ICOMAT-92, Monterey Inst. Adv. Studies (1993) 881–886. [13] M. Nishida, H. Ohgi, I. Itai, A. Chiba, K. Yamauchi, Acta Metall. Mater. 43 (1995) 1219–1227. [14] Y. Kudoh, M. Tokonami, S. Miyazaki, K. Otsuka, Acta Metall. 33 (1985) 2049– 2056. [15] Y. Nakata, T. Tadaki, K. Shimizu, Mater. Trans. 32 (1991) 1120–1127. [16] M.J. Whelan, P.B. Hirsch, Philos. Mag. 2 (1957) 1121–1142.
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