- Email: [email protected]
Martensitic phase transformations in nanocrystalline NiTi studied by TEM
Acta Materialia 52 (2004) 137–147 www.actamat-journals.com
Martensitic phase transformations in nanocrystalline NiTi studied by TEM T. Waitz *, V. Kazykhanov 1, H.P. Karnthaler Institute of Materials Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria Received 16 June 2003; accepted 22 August 2003
Abstract By high pressure torsion (HPT) deformation almost complete amorphization is obtained in bulk Ni–50.3at.%Ti containing B190 martensite. During low temperature annealing tiny crystallites retained after the HPT deformation are acting as nuclei and trigger the nanocrystallization of B2 austenite. It is shown that the density of the nuclei is a function of the HPT strain and determines together with the annealing temperature the grain size of the nanocrystals ranging from 5 to 350 nm. Upon cooling the nanostructures transform to B190 partially since the grain boundaries hinder the autocatalytic formation of martensite. The large transformation strains of B190 are reduced by very fine (0 0 1) compound twins. With decreasing grain size an increasing energy barrier arises and the martensitic transformation is completely suppressed in grains smaller than 60 nm. The R-phase transformation causing only small transformation strains is observed in grains between 15 and 60 nm. Whereas in grains below 15 nm B2 remains indicating that no transformation occurs at all. Ó 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: High pressure torsion; Bulk amorphous materials; Nanocrystallization; Martensitic phase transformation; High-resolution electron microscopy
1. Introduction In the intermetallic compound NiTi the shape memory effect and superelastic properties are related to a martensitic phase transformation being of considerable interest both from a scientific and a technological point of view. In addition, in NiTi amorphization can be induced applying various solid state processes such as particle irradiation [1] and strong mechanical deformation by cold rolling [2] and mechanical alloying [3]. Recently severe plastic deformation by high pressure torsion (HPT) methods was applied to NiTi achieving amorphization; followed by a suitable heat treatment a nanocrystalline phase can obtained in bulk HPT alloys by devitrification of the amorphous phase [4]. Still, the *
Corresponding author. Fax: +43-1-4277-51316. E-mail address: [email protected] (T. Waitz). URL: http://www.univie.ac.at/Materialphysik/EM. 1 On leave from the Institute of Advanced Materials, Ufa State Aviation Technical University, 12 K. Marksa Street, 450000 Ufa, Russian Federation.
cause of the nanocrystallization in the HPT deformed alloys remained unclear. As the martensitic transformation occurring in nanocrystalline NiTi is concerned there are contradictory results presented in the literature. In Ni–49.8at.%Ti subjected to cold rolling crystal refinement and partial amorphization was achieved and the martensitic transformation was suppressed even after cooling to )150 °C [5,6]. The reason for the observed change in the transformation seems to be unclear; it was proposed that dislocations induced by the cold rolling may stabilize the parent B2 austenite. Contrary to this, it was reported that the martensite start temperature Ms increases with decreasing grain size in a bulk nanocrystalline material obtained by annealing a shock compacted amorphous Ni–49.12at.%Ti powder. The increase of Ms seems to be unclear; it was proposed that enhanced nucleation is facilitated by internal stresses caused by the nanograins or by effects of the shock compression [7]. Since contradictory results of the martensitic transformation presented in the literature may be attributed to
1359-6454/$30.00 Ó 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2003.08.036
138
T. Waitz et al. / Acta Materialia 52 (2004) 137–147
stresses caused by lattice defects rather than to the ultrafine grain size it is the aim of the present study to carry out a systematic investigation. Therefore a nanocrystalline NiTi alloy was investigated containing little lattice strains and almost no dislocations and having a broad range of grain sizes (from about 5 to 350 nm). In a first step, the NiTi alloy showing the monoclinic B190 martensite phase at room temperature (RT) was subjected to HPT deformation achieving a bulk amorphous alloy. As compared to mechanically amorphized powders no further compaction or densification is necessary and contrary to cold rolling almost complete amorphization can be achieved by the HPT method. In a second step, a nanocrystalline microstructure was obtained by annealing the alloy close to the crystallization temperature. To investigate the nanocrystallization, two different degrees of HPT deformation were carried out and the microstructures were analysed carefully prior and after the devitrification. In addition, at RT the transformation induced microstructure and its dependence on the grain size was investigated in detail using both transmission electron microscopy (TEM) and high resolution transmission electron microscopy (HRTEM) methods.
2. Experimental procedure In the present study a binary NiTi alloy with a nominal composition Ni–50.3at.%Ti was used. The details of the alloy preparation and the transformation temperatures are given by [8]: the initial coarse grained alloy shows a single step transformation from B2 austenite to monoclinic B190 martensite (the martensite finish temperature Mf is in the range from 22 to 45 °C depending on the thermo-mechanical treatment prior to the transformation). The alloy was quenched from 800 °C in water below Mf and used to prepare HPT discs applying 10 turns at a pressure of 6 GPa. The as-processed HPT discs had a diameter of 12 mm and a thickness of about 0.2 mm. From the HPT discs specimens with a diameter of 2.3 mm were punched by spark erosion using very low power to avoid any heating. To study the influence of strain on the amorphization specimens were taken at two different distances from the centre of the HPT discs: about 2.5 and 4.3 mm; this corresponds to true logarithmic strains S of about 6.7 and 7.3, respectively, at the central area of the TEM specimens. To achieve different grain sizes two different heat treatments were carried out: the specimens were annealed either at 340 °C for 5 h or at 450 °C for 1 h under vacuum. The heat treatment was followed by cooling to RT and by quenching either into methanol at a temperature of )25 °C or into liquid nitrogen. The peak temperature Tp and the onset temperature Tx of the crystallization were measured by differential scanning calorimetry (DSC) at a heating rate
of 40 °C/min in flowing nitrogen gas using a Perkin– Elmer DSC 7. The specimens were used to prepare TEM foils by twin-jet polishing. The thinning was done in a Tenupol 3 with a solution of 75% CH3 OH and 25% HNO3 ()22 °C and 15 V). The different phases were analyzed by selected area (SA) diffraction applying different beam directions (BD) in a TEM (Philips CM 200 operating at 200 kV). Afterwards a HRTEM analysis was carried out using a Philips CM30 ST (operating at 250 and 300 kV) equipped with a Gatan slow scan CCD camera.
3. Experimental results 3.1. The nanostructured amorphous phase after HPT of different strains Fig. 1 shows a TEM study of a specimen immediately after the HPT deformation at a strain of S ¼ 6:7. As seen in Fig. 1(a) (bright field image) the specimen contains heterogeneously distributed nanocrystals (spots of dark contrast) that are embedded in an amorphous matrix and have a size between 5 and 30 nm. As analyzed by HRTEM and SA diffraction methods most of the larger nanocrystals contain B190 martensite whereas the smaller crystallites have the B2 structure. The contrast is reversed in the dark field image of Fig. 1(b) that was achieved by placing an objective aperture over part of the h1 1 0iB2 , h1 1 1iB190 and h0 2 0iB190 diffraction rings of the nanocrystals. A band shaped area that contains only a very small volume fraction (<1%) of crystallites that have a diameter in the range of 5–15 nm is marked by L; an area containing a higher density of mainly larger crystals is marked by H. In the diffraction pattern of Fig. 1(c) the amorphous phase gives rise to diffuse rings superimposed by the rather sharp diffraction rings of the crystallites. As seen in Fig. 2 almost the entire volume of the specimens deformed at the higher strain S ¼ 7:3 is amorphous. A low density (less than about 1%) of nanocrystals is observed in bright and dark field images (cf. Figs. 2(a) and (b)). Their analysis shows that the nanocrystals are heterogeneously distributed; areas are observed containing a higher density of nanocrystals (e.g. near H) whereas other areas are almost free of them (e.g. near L). The crystallites have a size of less than about 15 nm and using HRTEM methods some of them with a diameter of only 3 nm were analyzed. In the diffraction pattern (see Fig. 2(c)) diffuse rings are observed; the radius of the inner, bright ring corresponds to 4.7 nm1 and therefore to the reflection g110 of the NiTi B2 lattice; additional rings being weak and broad correspond to g211 and g220 (as indicated in Fig. 2(c)). The analysis of several diffraction patterns shows that frequently the first diffuse ring is superimposed by weak h1 1 0iB2 reflection spots of the nanocrystals. In addition
T. Waitz et al. / Acta Materialia 52 (2004) 137–147
Fig. 1. Ni–50.3at.%Ti after HPT deformation; strain S ¼ 6:7. (a) TEM bright field image. The amorphous matrix contains retained nanocrystals showing dark contrast. P marks a coarse particle of the Ti2Ni lattice. (b) TEM dark field image of the heterogeneously distributed crystallites showing bright contrast (H and L mark areas containing a high and low density of them). (c) In the diffraction pattern broad diffuse rings of the amorphous phase are superimposed with rings containing B2 and B190 diffraction spots of the nanocrystallites.
139
Fig. 2. Ni–50.3at.%Ti after HPT deformation; strain S ¼ 7:3. (a) TEM bright field image. The amorphous matrix contains a volume fraction of retained nanocrystals of less than about 1%. (b) Crystallites having a diameter of less than about 15 nm show up as bright spots in the corresponding TEM dark field image. H marks a higher density of nanocrystals whereas in the area marked L there are almost no nanocrystals. (c) SA diffraction pattern showing broad diffuse rings of the amorphous phase having radii that correspond to the length of the diffraction vectors h1 1 0i, h2 1 1i and h2 2 0i of the B2 lattice.
140
T. Waitz et al. / Acta Materialia 52 (2004) 137–147
to the amorphous rings weak h2 0 0iB2 reflections were observed. It should be mentioned that a volume fraction of about 5% corresponds to coarse spherical particles of the Ti2 Ni lattice that have survived the HPT in both cases S ¼ 6:7 and 7.3 (cf. P in Fig. 1(a)). 3.2. Nanocrystallization after different heat treatments The onset of the crystallization was measured by DSC (cf. Fig. 3). The analysis of the DSC curve of the HPT specimen with the lower strain (S ¼ 6:7) yields that both the crystallization temperature and the crystallization enthalpy are lower than in the case of S ¼ 7:3. Tx (Tp ) are 352 °C (374 °C) and 362 °C (379 °C) in the case of S ¼ 6:7 and 7.3, respectively. The crystallization enthalpies DH 6:7 and DH 7:3 are about )1.4 and )1.7 kJ/ mol corresponding to S ¼ 6:7 and 7.3, respectively. Fig. 4 shows TEM bright field images of annealed specimens. Figs. 4(a) and (b) correspond to the deformations S ¼ 6:7 and S ¼ 7:3, respectively; in addition the specimens were isothermally annealed at a temperature
Fig. 3. DSC curves of the crystallization of HPT deformed Ni– 50.3at.%Ti. (heating rate 40 °C/min). (a) S ¼ 6:7. An exothermic peak occurs at Tp ¼ 374 °C; the crystallization temperature Tx ¼ 352 °C is indicated. (b) S ¼ 7:3. The crystallization occurs at a higher temperature (Tp ¼ 379 °C, Tx ¼ 362 °C).
Fig. 4. Nanocrystalline phase formed after isothermal annealing of HPT deformed amorphous Ni–50.3at.%Ti. TEM bright field images. (a) S ¼ 6:7 after annealing at 340 °C for 5 h. Most of the grains are smaller than about 50 nm containing both B2 and R-phase. (b) S ¼ 7:3 after annealing at 340 °C for 5 h. Frequently areas are observed that contain mainly smaller grains (e.g. near S) and are adjacent to areas where larger grains are dominating (e.g. near M). B2 phase and R-phase are found in the smaller grains near S. R marks a grain of the R-phase. Martensite occurs in the grains near M having a diameter of about 120 nm. (c) S ¼ 7:3 after annealing at 450 °C for 1 h. Almost all grains larger than about 150 nm contain martensite.
T. Waitz et al. / Acta Materialia 52 (2004) 137–147
of 340 °C for 5 h followed by cooling to RT and quenching to )25 °C. Fig. 4(c) shows a specimen with S ¼ 7:3 annealed at a higher temperature (450 °C) for 1 h. In all cases the crystallization is complete since the diffraction patterns do not contain diffuse rings any more corresponding to the amorphous phase. Sharp and rather flat grain boundaries were observed both by TEM bright field and HRTEM images. It is important to point out that within the grains almost no dislocations were observed and most of the grains show only weak strain contrast. Additional TEM bright and dark field images were taken to measure the size distribution of the grains; the results are summarized in Fig. 5. In the case of S ¼ 6:7 annealed at 340 °C the grains have a diameter in the range of about 5–90 nm; only few of them are larger than about 50 nm (as shown in Fig. 5(a)). In the case of S ¼ 7:3 annealed at 340 °C there is a broad range of grain diameters ranging from 5 to 140 nm (cf. Fig. 5(b)). Their distribution seems to be non-uniform since frequently areas are observed mainly containing grains of small diameters (mean diameter of about 25 nm, e.g. near S in Fig. 4(b)) whereas other areas that are adjacent to them contain mainly larger grains (mean diameter about 70 nm, e.g. near M in Fig. 4(b)). In the case of S ¼ 7:3 and an annealing temperature of 450 °C most of the grains are larger than about 100 nm (cf. Fig. 5(c)). SA diffraction patterns were taken to analyze the crystalline phases occurring in the grains of different diameter. It is interesting to note that grains smaller than about 15 nm show reflections of the B2 phase only. When the grain size is between 15 and 60 nm reflections of the B2 phase and the R-phase were observed whereas no reflections corresponding to the martensite were encountered. When the grains are larger than about 60 nm they contain R-phase (cf. the grain marked by R in Fig. 4(b)) and B190 martensite (cf. the area near M in Fig. 4(b)) and in this case the B2 phase is hardly observed. Finally, grains larger than about 150 nm contain mainly martensite (cf. Fig. 4(c)). The volume fraction transformed to martensite by quenching to )25 °C was estimated to be less than about 30% (cf. fig 4(b)) and more than about 80% (cf. Fig. 4(c)) in the specimens having a maximum grain size of about 140 and 350 nm (cf. Figs. 5(b) and (c)), respectively. It should be noted that no martensite could be detected in grains smaller than about 60 nm even when the specimens were quenched in liquid nitrogen. In this case the volume fraction of R-phase seems to increase and only very small grains (less than about 15 nm diameter) contain residual austenite. The results of this analysis are summarized in Table 1. 3.3. The martensitic transformations in the nanostructures In the specimens annealed at 340 °C for 5 h followed by cooling to RT and quenching to )25 °C the R-phase
141
Fig. 5. Histograms of the size distributions of the grains after crystallization (cf. Fig. 4(a)).) S ¼ 6:7 after annealing at 340 °C for 5 h is leading to a mean grain size of 30 nm. (b) S ¼ 7:3 after annealing at 340 °C for 5 h. The dashed bars correspond to areas containing mainly smaller and larger grains (mean 25 and 70 nm), respectively. (c) S ¼ 7:3 after annealing at 450 °C for 1 h. Almost all grains are larger than 100 nm.
and the B190 martensite were analyzed in detail using both SA diffraction and HRTEM methods. As illustrated in Fig. 6 the grains containing the R-phase and
142
T. Waitz et al. / Acta Materialia 52 (2004) 137–147
Table 1 Grain size dependence of the observed phases Grain size (nm)
B2
< 15 15–60 60–150 >150
* *
R-phase * *
B190
* (<0.3) * (>0.8)
The occurrence of B2, R-phase and B190 is indicated by *. An estimate of the volume fraction of B190 is given in parentheses.
having a size larger than about 50–70 nm are frequently twinned and show some strain contrast; the width of the twins is about 20–50 nm (cf. Fig. 6(a)). Fig. 6(b) shows a HRTEM micrograph of two twin related R-phase variants RT1 and RT2; they are contained in a grain having a diameter of about 70 nm. The ð1 1 0 0ÞR lattice planes of both variants are indicated and they are corresponding to the ð1 0 1ÞB2 and ð0 1 1ÞB2 planes of the initial B2 lattice (in the case of the R-phase a hexagonal unit cell is used; BD runs along a common ½2 2 4 3R ½1 1 1B2 direction). The planar twin boundary is edge on in the TEM projection and runs along ð1 1 0ÞB2 . The rhombohedral angle aR of the R-phase was measured tilting a grain containing two twin related variants to a common BD ½1 0 1 0R (cf. Fig. 6(c)). In this case, the diffraction pattern contains both the ð0 0 0 1ÞR and ð1 2 1 0ÞR reflections. The corresponding lattice spacing d0001 and d1210 were measured and used to calculate the ratio of the hexagonal unit cell parameters cR and aR : cR /aR ¼ 1.39 0.01 and 1.38 0.01 leading to aR ¼ 88:5° 0.6° and 87.8° 0.6° in the case of RT1 and RT2, respectively. Fig. 7 shows typical diffraction patterns corresponding to B190 martensite. The pattern of Fig. 7(a) contains diffraction spots of two martensite twins MT1 and MT2 that are related by a rotation of p around ½0 0 1B190 (BD ½ 1 1 0MT1 ½1 1 0MT2 ). Most of the grains smaller than about 100–120 nm seem to contain only a single variant of the twinned martensite. In larger grains two or more martensite variants twinned on ð0 0 1ÞB190 planes were frequently observed (cf. Fig. 7(b)). It should be noted that the reflections ½1 1 1MT1;2 and ½ 1 1 1MT1;2 are strongly elongated along ½0 0 1B190 and streaks are running along the ½0 0 1B190 direction indicating a very small width of the twins. In addition, the streaks contain a regular sequence of closely spaced intensity maxima with an average spacing of 0:3 nm1 indicating a fairly constant spacing of the twin boundaries of about 3 nm. Fig. 8(a) shows a TEM bright field image that can be used to measure the width of the twins. The average width is d1 ¼ 1:7 and d2 ¼ 2:0 nm for MT1 and MT2 twins, respectively; the average relative twin period k ¼ d1 =ðd1 þ d2 Þ is 0.46 (cf. Fig. 8(b)). Almost all martensite grains contain ð0 0 1ÞB190 twins that have a width of less than 10 nm. As illustrated in Fig. 9 the width of very narrow twins can be determined on an atomic level
Fig. 6. Ni–50.3at.%Ti. Nanocrystalline structure; R-phase. (a) Bright field image of a twinned grain. Twin boundaries are indicated by arrows; near S strain contrast is visible. (b) HRTEM image of a grain containing two twin related variants. The twin boundary and the ð1 1 0 0ÞRT1;2 lattice planes of the variants RT1 and RT2 are indicated (BD ½2 2 4 3RT1;2 ) (c) Diffraction pattern showing two twin related R-phase variants (BD ½1 0 1 0 RT1;2 ) used to measure the rhombohedral angle.
using HRTEM images; the minimum width was measured to be 4 ð0 0 2ÞB190 atomic planes (0.9 nm) only (near A in Fig. 9).
T. Waitz et al. / Acta Materialia 52 (2004) 137–147
Fig. 7. Ni–50.3at.%Ti. Nanocrystalline structure; martensite. (a) SA diffraction pattern of a grain containing twinned martensite; (0 0 1) compound twinning is indicated by twin reflections (marked by MT1 and MT2) related by a rotation of p around ½0 0 1. Streaks and elongated reflections along ½0 0 1MT1;2 are caused by the very small width of the twins (BD ½ 1 1 0MT1 ½1 1 0MT2 ) (b) Two martensite variants M1 and M2 that are twinned on (0 0 1) occur within one grain (BD ½1 1 0M1;2 ).
4. Discussion 4.1. HPT induced amorphization The results of Figs. 1 and 2 show that by HPT deformation Ni–50.3at.%Ti transforms from B190 martensite to a nanostructured amorphous phase. It is proposed that a localized deformation process proceeds the transformation by leading to a nanocrystalline structure. The latter is fragmented by bands of an amorphous phase (cf. Fig. 1; S ¼ 6:7). Similar, after cold
143
Fig. 8. Ni–50.3at.%Ti. Nanocrystalline structure; martensite. (a) TEM bright field image of a grain containing a high density of (0 0 1) compound twins. The twin lamellae show bright and dark contrast. (b) Histogram of the observed twin widths.
rolling of NiTi a martensite microstructure refined by dislocation accumulation and strain induced twinning was observed containing numerous intersecting bands of nanocrystalline and amorphous phase arising locally by a shear strain instability [5,6,9,10]. As compared to cold rolling the HPT strain is much higher and dominated by a shear deformation [11] causing shear bands and strong crystal refinement [12]. Therefore, the HPT deformation of NiTi facilitates both the crystal refinement and the continuous accumulation of amorphous shear bands. When S increases the crystalline volume fraction
144
T. Waitz et al. / Acta Materialia 52 (2004) 137–147
Fig. 9. Ni–50.3at.%Ti. Nanocrystalline structure; martensite. HRTEM image showing (0 0 1) compound twins having a minimum width of 4 lattice planes (0.9 nm) only (near A). The ð0 0 1ÞMT1;2 twin boundary plane and the ð1 0 1ÞMT1;2 planes of the twin related martensite variants MT1 and MT2 are indicated by a dashed and a full line, respectively (BD ½0 1 0MT1;2 ).
gradually decreases until only isolated nanocrystals are left embedded heterogeneously in an amorphous matrix. Finally, caused by the plastic deformation of the amorphous matrix the retained nanocrystals dissolve in the amorphous phase until at S ¼ 7:3 only a few very small nanocrystals survive. Since most of them have the B2 structure it is concluded that the austenite is more stable against amorphization than the B190 martensite. This is in agreement with previous results [13]. In the present case it is concluded that the nanocrystalline debris contains austenite that was retained during the thermally induced B2 to B190 transformation [14] prior to HPT. Still their might be another explanation: the observed B2 nanocrystals could be formed by a stress induced reverse transformation B190 to B2 during HPT. That might be caused by a local increase of temperature exceeding the austenite start temperature (As 110 °C in the present case). Similar results of a deformation induced reverse transformation were reported by [15]. 4.2. Nanocrystallization The results of Figs. 3 and 4 show that during annealing in HPT induced amorphous Ni–50.3at.%Ti alloys heterogeneous polymorphous crystallization of the B2 phase occurs about 150 °C lower as compared to thin amorphous NiTi films processed by sputtering or melt spinning (Tx 510 °C [16]). It is concluded that the low thermal stability of the amorphous phase formed by HPT is caused by the retained nanocrystalline debris triggering crystallization (see Figs. 1 and 2). Therefore, already at an annealing temperature as low as Ta ¼
340 °C nanocrystallization occurs since the retained crystallites can act as heterogeneous nucleation sites leading to a high nucleation rate although the rate of growth is low since Ta =Tm ¼ 0:39 is small (Tm melting temperature). In agreement with the present conclusion it was proposed that the devitrification process should proceed with the largest nucleation rate and slowest growth rate to obtain a nanocrystalline structure; during low temperature annealing retained crystallites embedded in the amorphous phase can act as nuclei since they do not dissolve and can exceed the critical size for heterogeneous nucleation [17]. It is concluded that the nucleation rate depends on the HPT strain and decreases with increasing S (as can be seen by an increase of Tx and Tp ; cf. Fig. 3). This is explained as follows: in the alloy deformed up to S ¼ 7:3 the nucleation rate is lower since a only a small volume fraction <1% of tiny crystallites <15 nm is retained (cf. Fig. 2). Contrary to this, in the case of S ¼ 6:7 nucleation is triggered by numerous retained crystallites with a diameter up to about 30 nm having a high nucleation potency (cf. Fig. 1; a retained crystalline volume fraction Vcr of about 18% is deduced using Vcr ¼ 1 ðDH6:7 = DH7:3 Þ. In the amorphous matrix the growth of the nuclei ceases when the advancing interfaces of neighboring crystallites impinge on each other leading to grain boundaries. As the density of the nuclei increases their mean separation and therefore the final grain size will decrease. Since the density of the nuclei is lower in the case of S ¼ 7:3 annealing at Ta ¼ 340 °C is leading to a larger grain size as compared to the alloy deformed up
T. Waitz et al. / Acta Materialia 52 (2004) 137–147
to S ¼ 6:7 and annealed at the same temperature (cf. Figs. 4 and 5). In addition, when the retained crystallites are not distributed uniformly a nanocrystalline phase with a heterogeneous distribution of the grain sizes arises after crystallization (as shown at S and M in Fig. 4(b)). Finally, as compared to an annealing temperature of 340 °C the growth rate is expected to be higher at Ta ¼ 450 °C ðTa =Tm ¼ 0:46Þ leading to larger grain sizes (compare Figs. 4(b) and (c)). 4.3. Phase transformations occurring in the nanocrystalline grains Based on the results of the TEM analysis summarized in Table 1 it is concluded that in the nanocrystalline Ni– 50.3at.%Ti alloy the martensitic transformation is suppressed with decreasing grain size. This means, the transformed volume fraction decreases with decreasing grain size and the onset of the martensitic transformation is shifted towards lower temperatures. Therefore, Ms drops below the transformation temperature of the R-phase (TR ) in grains smaller than about 150 nm leading to a two step transformation from the B2 austenite via the R-phase to the B190 martensite. Finally, in grains smaller than about 60 nm the martensitic phase transformation is completely suppressed. Similar results of suppressing Ms were reported in the case of a cold rolled Ni–49.8Ti alloy containing a nanocrystalline phase [5]. A decrease of Ms below TR is also observed in coarse grained NiTi alloys and could be caused by a high density of dislocations induced during rolling [18] or coherent precipitates induced by aging [19]. It was proposed that in a nanocrystalline NiTi alloy the martensitic transformation could be suppressed in different ways: by the introduction of elastic strains, by lattice defects or by crystal refinement [5,6]. In the present investigation almost no dislocations and little elastic strains were encountered in the grains (cf. Fig. 4). Therefore it is concluded that the grain refinement leads to the suppression of the transformation. In this context aspects concerning nucleation sites, grain boundaries, twinning and the R-phase transformation are discussed in the following paragraphs. 4.3.1. Nucleation sites in the nanograins Specific dislocation configurations as dislocation walls or dislocation pile-ups are generally considered as possible nucleation sites [20,21]; in coarse grained NiTi alloys there is direct experimental evidence that martensite is nucleating at dislocations tangles in the matrix and near grain boundary dislocations [22]. Since in the present case almost no dislocations occur within the nanograins it is concluded that the grain boundaries act as the heterogeneous nucleation sites. This is in agreement with experimental results indicating that in NiTi the grain boundaries can favour the martensitic transformation [23].
145
It should be noted that a suppression of a martensitic phase transformation was also observed in small particles and it was proposed that the fraction of particles containing a lattice defect suitable for heterogeneous nucleation is decreasing with decreasing grain size [24]. However, these statistical arguments seem to fail in the case of FeNi nanoparticles (size from 10–200 nm) since the particles easily transform above RT although both experimental observations and calculations indicate that heterogeneous nucleation sites are not contained within the particles; therefore it was proposed that heterogeneous nucleation sites are provided by the surfaces of the nanoparticles [25]. Similar, in the present case it is concluded that in the nanocrystalline NiTi alloy the martensitic transformation is not suppressed by a lack of nucleation sites as the density of heterogeneous nucleation sites provided by the grain boundaries may even increase with increasing grain boundary area and decreasing grain size. 4.3.2. Constraints arising by the grain boundaries It is proposed that the grain boundaries impose constraints on the growth of the martensite confining the transformed volume fraction in the nanocrystalline structure. A martensite plate nucleated within a grain will be stopped at the grain boundaries acting as obstacles. To propagate the transformation the plate has to exert stresses that are sufficient to stimulate nucleation and growth of favourable martensite variants in the adjacent grains [22]. However, little stresses are expected to occur ahead of a small plate bound within an nanograin that has a size of less than 100 nm [26]. In addition, as deduced from TEM observations in NiTi a restriction was proposed for the autocatalytic nucleation of self accommodating plate groups [27]. This is based on a twin relation of all the martensite variants in the group which is possible only within a single grain since martensite variants occurring in adjacent grains have not the required orientation relationship. Therefore, in the present case it is concluded that in a volume containing many small grains the ability of spreading the transformation by autocatalytic nucleation decreases with increasing grain boundary area in agreement with the observed decrease of the martensite volume fraction. 4.3.3. (0 0 1) Compound twinning As outlined by [28] a martensitic phase transformation will follow a path of almost complete accommodation of the transformation shape strains. In coarse grained NiTi two different mechanisms occurring at different length scales facilitate the strain accommodation: Firstly, twinning by h0 1 1i type II or ð1 1 1Þ type I twins (at scale of 30–100 nm) leading to an invariant plane strain; secondly, at a scale far exceeding 100 nm self-accommodation of groups of different habit plane variants arises [27,29]. In the present case of the
146
T. Waitz et al. / Acta Materialia 52 (2004) 137–147
nanocrystalline NiTi the mean grain size (30–160 nm, cf. Figs. 4 and 5) represents a length scale of the same order as that of the twinning period and smaller than that of the self-accommodating groups in a coarse grained alloy. Therefore, in the nanograins the constraints of the grain boundaries suppress the formation of self-accommodating variants. As a consequence within the nanograins a different path of the transformation occurs that is leading to the required decrease of the transformation strains by the formation of very fine (0 0 1) compound twins (cf. Figs. 7–9). This is outlined as follows: it was proposed that (0 0 1) compound twinning leads to a smaller strain energy as compared to h0 1 1i type II twinning [29,30]. In addition, a decrease of the twinning period d1 + d2 decreases the elastic energy Dwe (strain energy per unit transformed volume) [31]. However, with decreasing d the twin boundary area At and therefore the twin boundary energy At ct of the transformed volume increase. From the observed very small twinning period it can be concluded that the specific twin boundary energy ct of the (0 0 1) compound twins must be very small. It should be mentioned that in the present case (cf. Fig. 9) the thinnest lamellae of the compound twins contain two martensite unit cells (i.e. four (0 0 2) lattice planes yielding d ¼ 0:9 nm). Since the separations of the twin boundaries are comparable to the interatomic distance the nanotwinned martensite may be regarded as an adaptive martensite phase as proposed by [28]. Finally, experimental results found in the literature [29,30,32] indicate that a variety of constraints as dislocations, grain boundaries and precipitates that may inhibit self-accommodation lead to the same preferred mode of the transformation involving (0 0 1) compound twinning to decrease the strain energy. The experimental results show that in grains smaller than 60nm (cf. Table 1) no thermally induced martensitic phase transformation occurs. It is proposed that this is caused by the decrease of self-accommodation with decreasing grain size since per unit of transformed volume an increasing chemical driving force )Dgc (<0) i.e. a larger undercooling is required to overcome an increasing energy barrier Dgnc (>0) including elastic (Dwe ) and surface (At ct ) energy. The present conclusions are in agreement with calculations of Dgnc carried out for ZrO2 nanoparticles containing twinned martensite [33]. Similar to the present case smaller particles are more stable against the martensitic transformation than larger ones. It should be mentioned that previously (0 0 1) compound twins of the martensitic phase were considered as deformation twins only since they do not agree with the phenomenological theory of the B2 to B190 transformation in NiTi as no invariant habit plane can occur [29]. In the nanocrystalline alloy the presence of an invariant habit plane is less important for the transformation since the B190 phase will mainly occur attached
to grain boundaries. Also the grain boundaries might even trigger the formation of twins [34]. Finally, it was proposed recently that during the Rphase to B190 transformation (0 0 1) compound twinning could give rise to an invariant plane strain under the condition of a critical value aR 6 86:2° [29]. In the present case the martensitic transformation is preceded by the formation of R-phase as required for (0 0 1) compound twinning acting as lattice invariant strain. As deduced from Fig. 6(c) the measured RT values of aR (88.5° 0.6° and 87.8° 0.6°) are somewhat larger than the calculated critical angle but the agreement is better than in the case of annealed coarse grained NiTi where aR P 89° [35]. 4.3.4. R-phase transformation It is concluded that the constraints of the grain boundaries should have little effect on the B2 to R-phase transformation since in this case the transformation shape strain is significantly smaller (roughly 1% as compared to 10% in the case of the B2 to B190 transformation). This is in agreement with the present results since on cooling the R-phase precedes the martensite in the small grains. The critical diameter of nuclei of the Rphase was estimated to be about 4–8 nm by in situ TEM analysis [36]. Therefore, the R-phase transformation is expected to be completely suppressed in very small grains as shown in Table 1. In grains having a size in the range from 15 to 50 nm small strains could be present prior to the transformation that may help to accommodate a single variant of the R-phase elastically. In the grains larger than 50 nm, however, the shape strains have to be accommodated by twins that have a small width to decrease Dwe (cf. Fig. 6(a)). Therefore as expected, caused by the constraints of the grain boundaries the width of the twins (20–50 nm) is significantly smaller in the nanograins as compared to that of about 300 nm measured in coarse grained NiTi alloys [37].
5. Conclusions 1. A NiTi alloy was subjected to HPT deformation leading to amorphization. Nanocrystalline debris is retained in the amorphous phase; the size and the number of the retained crystallites is decreasing with increasing HPT strain. 2. The amorphous phase shows low thermal stability. It is concluded that heterogeneous crystallization is triggered by the retained crystallites that have survived the HPT deformation. 3. Isothermal annealing is leading to nanocrystalline structures with grain sizes in the range of 5–350 nm depending on the annealing temperature and the density of the heterogeneous nucleation sites present in the amorphous phase. This leads to the conclusion that the strain of the HPT deformation determines
T. Waitz et al. / Acta Materialia 52 (2004) 137–147
the number of retained crystals in the amorphous phase and therefore the grain size of the nanocrystalline structure formed by annealing. 4. The martensitic transformation is suppressed in the ultrafine grains. It is concluded that forced by the constraints of the grain boundaries the R-phase precedes the martensite and that atomic scale (0 0 1) compound twinning occurs in the martensite facilitating the accommodation of the transformation strains. 5. In grains smaller than 60 nm no thermally induced martensitic transformation is observed. Therefore it is concluded that with decreasing grain size and decreasing twin separation both the strain energy and the twin interfacial energy are leading to an increasing energy barrier. Acknowledgements The authors thank Professor A.C. Kneissl for the kind provision of the NiTi alloy and Professor W. Pfeiler for his help with the DSC measurements. One of us (V.K.) thanks Professor R.Z. Valiev for the provision of laboratory facilities. Financial support from the Austrian Science Fund (FWF) is acknowledged. References [1] [2] [3] [4]
Thomas G, Mori H, Fujita H, Sinclair R. Scr Metall 1982;16:589. Koike J, Parkin DM, Nastasi M. J Mater Res 1990;5:1414. Schwarz RB, Koch CC. Appl Phys Lett 1986;49:146. Sergueeva AV, Song C, Valiev RZ, Mukherjee AK. Mater Sci Eng A 2003;A339:159. [5] Nakayama H, Tsuchiya K, Umemoto M. Scr Mater 2001;44:1781. [6] Nakayama H, Tsuchiya K, Liu ZG, Umemoto M, Morii K, Shimizu T. Mater Trans 2001;42:1987.
147
[7] Xu X, Thadhani N. Scr Mater 2001;44:2477. [8] Prader P, Kneissl AC. Z Metallkd 1997;88:410. [9] Tatyanin EV, Borovnikov NF, Kurdyumov VG. Phys Solid State 1997;39:1997. [10] Koike J, Parkin DM, Nastasi M. Philos Mag Lett 1990;62: 257. [11] Kim HS. J Mater Process Technol 2001;113:617. [12] Tyumentsev AN, Pinzhin YP, Tretjak MV, et al. Theoret Appl Fract Mech 2001;35:155. [13] Ewert JC, B€ ohm I, Peter R, Haider F. Acta Mater 1997;45: 2197. [14] Crevoiserat S, Gotthard R. Mater Sci Eng A 1999;A273–275: 357. [15] Lopez HF, Salinas A, Calderon H. Met Mater Trans A 2001;32A:717. [16] Chen JZ, Wu SK. J Non-Cryst Sol 2001;288:159. [17] Kulik T. J Non-Cryst Sol 2001;287:145. [18] Chrobak D, Morawiec H. Scr Mater 2001;44:725. [19] Khahil AJ, Ren X, Eggeler G. Acta Mater 2000;50:793. [20] Olson GB. Metall Trans A 1976;7A:1969. [21] Chen IW, Chiao YH. Acta Metall 1985;33:1827. [22] Saburi T, Nenno S. In: Tamura I, editor. Proceedings of the International Conference on Martensitic Transformations. Japan: The Japan Inst Metals, Japan; 1986. p. 671. [23] Gil FJ, Manero JM, Planell JA. J Mater Sci 1995;30:2526. [24] Chen IW, Chiao YH, Tsuzaki K. Acta Metall 1985;33:1847. [25] Kajiwara S, Ohno S, Honma K. Philos Mag A 1991;63:625. [26] Ling HC, Owen WS. Acta Metall 1981;29:1721. [27] Madangopal K. Acta Mater 1997;45:1997. [28] Khachaturyan AG, Shapiro SM, Semenovskaya S. Mater Trans JIM 1992;33:278. [29] Krishnan M, Singh JB. Acta Mater 2000;48:1325. [30] Nishida M, Itai I, Kitamura K, Chiba A, Yamauchi K. J Phys 1995;5:C8–635. [31] Evans AG, Burlingame N, Drory M, Kriven WM. Acta Metall 1981;29:447. [32] Zhang JX, Sato M, Ishida A. Acta Mater 2001;49:3001. [33] Yan WJ, Reisner G, Fischer FD. Acta Mater 1997;45:1997. [34] Fischer FD, Appel F, Clemens H. Acta Mater 2003;51:1249. [35] Ling HC, Kaplow R. Metall Trans A 1981;12A:2101. [36] Murakami Y, Shindo D. Philos Mag Lett 2001;81:631. [37] Miyazaki S, Wayman CM. Acta Metall 1988;36:181.
Martensitic phase transformations in nanocrystalline NiTi studied by TEM T. Waitz *, V. Kazykhanov 1, H.P. Karnthaler Institute of Materials Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria Received 16 June 2003; accepted 22 August 2003
Abstract By high pressure torsion (HPT) deformation almost complete amorphization is obtained in bulk Ni–50.3at.%Ti containing B190 martensite. During low temperature annealing tiny crystallites retained after the HPT deformation are acting as nuclei and trigger the nanocrystallization of B2 austenite. It is shown that the density of the nuclei is a function of the HPT strain and determines together with the annealing temperature the grain size of the nanocrystals ranging from 5 to 350 nm. Upon cooling the nanostructures transform to B190 partially since the grain boundaries hinder the autocatalytic formation of martensite. The large transformation strains of B190 are reduced by very fine (0 0 1) compound twins. With decreasing grain size an increasing energy barrier arises and the martensitic transformation is completely suppressed in grains smaller than 60 nm. The R-phase transformation causing only small transformation strains is observed in grains between 15 and 60 nm. Whereas in grains below 15 nm B2 remains indicating that no transformation occurs at all. Ó 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: High pressure torsion; Bulk amorphous materials; Nanocrystallization; Martensitic phase transformation; High-resolution electron microscopy
1. Introduction In the intermetallic compound NiTi the shape memory effect and superelastic properties are related to a martensitic phase transformation being of considerable interest both from a scientific and a technological point of view. In addition, in NiTi amorphization can be induced applying various solid state processes such as particle irradiation [1] and strong mechanical deformation by cold rolling [2] and mechanical alloying [3]. Recently severe plastic deformation by high pressure torsion (HPT) methods was applied to NiTi achieving amorphization; followed by a suitable heat treatment a nanocrystalline phase can obtained in bulk HPT alloys by devitrification of the amorphous phase [4]. Still, the *
Corresponding author. Fax: +43-1-4277-51316. E-mail address: [email protected] (T. Waitz). URL: http://www.univie.ac.at/Materialphysik/EM. 1 On leave from the Institute of Advanced Materials, Ufa State Aviation Technical University, 12 K. Marksa Street, 450000 Ufa, Russian Federation.
cause of the nanocrystallization in the HPT deformed alloys remained unclear. As the martensitic transformation occurring in nanocrystalline NiTi is concerned there are contradictory results presented in the literature. In Ni–49.8at.%Ti subjected to cold rolling crystal refinement and partial amorphization was achieved and the martensitic transformation was suppressed even after cooling to )150 °C [5,6]. The reason for the observed change in the transformation seems to be unclear; it was proposed that dislocations induced by the cold rolling may stabilize the parent B2 austenite. Contrary to this, it was reported that the martensite start temperature Ms increases with decreasing grain size in a bulk nanocrystalline material obtained by annealing a shock compacted amorphous Ni–49.12at.%Ti powder. The increase of Ms seems to be unclear; it was proposed that enhanced nucleation is facilitated by internal stresses caused by the nanograins or by effects of the shock compression [7]. Since contradictory results of the martensitic transformation presented in the literature may be attributed to
1359-6454/$30.00 Ó 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2003.08.036
138
T. Waitz et al. / Acta Materialia 52 (2004) 137–147
stresses caused by lattice defects rather than to the ultrafine grain size it is the aim of the present study to carry out a systematic investigation. Therefore a nanocrystalline NiTi alloy was investigated containing little lattice strains and almost no dislocations and having a broad range of grain sizes (from about 5 to 350 nm). In a first step, the NiTi alloy showing the monoclinic B190 martensite phase at room temperature (RT) was subjected to HPT deformation achieving a bulk amorphous alloy. As compared to mechanically amorphized powders no further compaction or densification is necessary and contrary to cold rolling almost complete amorphization can be achieved by the HPT method. In a second step, a nanocrystalline microstructure was obtained by annealing the alloy close to the crystallization temperature. To investigate the nanocrystallization, two different degrees of HPT deformation were carried out and the microstructures were analysed carefully prior and after the devitrification. In addition, at RT the transformation induced microstructure and its dependence on the grain size was investigated in detail using both transmission electron microscopy (TEM) and high resolution transmission electron microscopy (HRTEM) methods.
2. Experimental procedure In the present study a binary NiTi alloy with a nominal composition Ni–50.3at.%Ti was used. The details of the alloy preparation and the transformation temperatures are given by [8]: the initial coarse grained alloy shows a single step transformation from B2 austenite to monoclinic B190 martensite (the martensite finish temperature Mf is in the range from 22 to 45 °C depending on the thermo-mechanical treatment prior to the transformation). The alloy was quenched from 800 °C in water below Mf and used to prepare HPT discs applying 10 turns at a pressure of 6 GPa. The as-processed HPT discs had a diameter of 12 mm and a thickness of about 0.2 mm. From the HPT discs specimens with a diameter of 2.3 mm were punched by spark erosion using very low power to avoid any heating. To study the influence of strain on the amorphization specimens were taken at two different distances from the centre of the HPT discs: about 2.5 and 4.3 mm; this corresponds to true logarithmic strains S of about 6.7 and 7.3, respectively, at the central area of the TEM specimens. To achieve different grain sizes two different heat treatments were carried out: the specimens were annealed either at 340 °C for 5 h or at 450 °C for 1 h under vacuum. The heat treatment was followed by cooling to RT and by quenching either into methanol at a temperature of )25 °C or into liquid nitrogen. The peak temperature Tp and the onset temperature Tx of the crystallization were measured by differential scanning calorimetry (DSC) at a heating rate
of 40 °C/min in flowing nitrogen gas using a Perkin– Elmer DSC 7. The specimens were used to prepare TEM foils by twin-jet polishing. The thinning was done in a Tenupol 3 with a solution of 75% CH3 OH and 25% HNO3 ()22 °C and 15 V). The different phases were analyzed by selected area (SA) diffraction applying different beam directions (BD) in a TEM (Philips CM 200 operating at 200 kV). Afterwards a HRTEM analysis was carried out using a Philips CM30 ST (operating at 250 and 300 kV) equipped with a Gatan slow scan CCD camera.
3. Experimental results 3.1. The nanostructured amorphous phase after HPT of different strains Fig. 1 shows a TEM study of a specimen immediately after the HPT deformation at a strain of S ¼ 6:7. As seen in Fig. 1(a) (bright field image) the specimen contains heterogeneously distributed nanocrystals (spots of dark contrast) that are embedded in an amorphous matrix and have a size between 5 and 30 nm. As analyzed by HRTEM and SA diffraction methods most of the larger nanocrystals contain B190 martensite whereas the smaller crystallites have the B2 structure. The contrast is reversed in the dark field image of Fig. 1(b) that was achieved by placing an objective aperture over part of the h1 1 0iB2 , h1 1 1iB190 and h0 2 0iB190 diffraction rings of the nanocrystals. A band shaped area that contains only a very small volume fraction (<1%) of crystallites that have a diameter in the range of 5–15 nm is marked by L; an area containing a higher density of mainly larger crystals is marked by H. In the diffraction pattern of Fig. 1(c) the amorphous phase gives rise to diffuse rings superimposed by the rather sharp diffraction rings of the crystallites. As seen in Fig. 2 almost the entire volume of the specimens deformed at the higher strain S ¼ 7:3 is amorphous. A low density (less than about 1%) of nanocrystals is observed in bright and dark field images (cf. Figs. 2(a) and (b)). Their analysis shows that the nanocrystals are heterogeneously distributed; areas are observed containing a higher density of nanocrystals (e.g. near H) whereas other areas are almost free of them (e.g. near L). The crystallites have a size of less than about 15 nm and using HRTEM methods some of them with a diameter of only 3 nm were analyzed. In the diffraction pattern (see Fig. 2(c)) diffuse rings are observed; the radius of the inner, bright ring corresponds to 4.7 nm1 and therefore to the reflection g110 of the NiTi B2 lattice; additional rings being weak and broad correspond to g211 and g220 (as indicated in Fig. 2(c)). The analysis of several diffraction patterns shows that frequently the first diffuse ring is superimposed by weak h1 1 0iB2 reflection spots of the nanocrystals. In addition
T. Waitz et al. / Acta Materialia 52 (2004) 137–147
Fig. 1. Ni–50.3at.%Ti after HPT deformation; strain S ¼ 6:7. (a) TEM bright field image. The amorphous matrix contains retained nanocrystals showing dark contrast. P marks a coarse particle of the Ti2Ni lattice. (b) TEM dark field image of the heterogeneously distributed crystallites showing bright contrast (H and L mark areas containing a high and low density of them). (c) In the diffraction pattern broad diffuse rings of the amorphous phase are superimposed with rings containing B2 and B190 diffraction spots of the nanocrystallites.
139
Fig. 2. Ni–50.3at.%Ti after HPT deformation; strain S ¼ 7:3. (a) TEM bright field image. The amorphous matrix contains a volume fraction of retained nanocrystals of less than about 1%. (b) Crystallites having a diameter of less than about 15 nm show up as bright spots in the corresponding TEM dark field image. H marks a higher density of nanocrystals whereas in the area marked L there are almost no nanocrystals. (c) SA diffraction pattern showing broad diffuse rings of the amorphous phase having radii that correspond to the length of the diffraction vectors h1 1 0i, h2 1 1i and h2 2 0i of the B2 lattice.
140
T. Waitz et al. / Acta Materialia 52 (2004) 137–147
to the amorphous rings weak h2 0 0iB2 reflections were observed. It should be mentioned that a volume fraction of about 5% corresponds to coarse spherical particles of the Ti2 Ni lattice that have survived the HPT in both cases S ¼ 6:7 and 7.3 (cf. P in Fig. 1(a)). 3.2. Nanocrystallization after different heat treatments The onset of the crystallization was measured by DSC (cf. Fig. 3). The analysis of the DSC curve of the HPT specimen with the lower strain (S ¼ 6:7) yields that both the crystallization temperature and the crystallization enthalpy are lower than in the case of S ¼ 7:3. Tx (Tp ) are 352 °C (374 °C) and 362 °C (379 °C) in the case of S ¼ 6:7 and 7.3, respectively. The crystallization enthalpies DH 6:7 and DH 7:3 are about )1.4 and )1.7 kJ/ mol corresponding to S ¼ 6:7 and 7.3, respectively. Fig. 4 shows TEM bright field images of annealed specimens. Figs. 4(a) and (b) correspond to the deformations S ¼ 6:7 and S ¼ 7:3, respectively; in addition the specimens were isothermally annealed at a temperature
Fig. 3. DSC curves of the crystallization of HPT deformed Ni– 50.3at.%Ti. (heating rate 40 °C/min). (a) S ¼ 6:7. An exothermic peak occurs at Tp ¼ 374 °C; the crystallization temperature Tx ¼ 352 °C is indicated. (b) S ¼ 7:3. The crystallization occurs at a higher temperature (Tp ¼ 379 °C, Tx ¼ 362 °C).
Fig. 4. Nanocrystalline phase formed after isothermal annealing of HPT deformed amorphous Ni–50.3at.%Ti. TEM bright field images. (a) S ¼ 6:7 after annealing at 340 °C for 5 h. Most of the grains are smaller than about 50 nm containing both B2 and R-phase. (b) S ¼ 7:3 after annealing at 340 °C for 5 h. Frequently areas are observed that contain mainly smaller grains (e.g. near S) and are adjacent to areas where larger grains are dominating (e.g. near M). B2 phase and R-phase are found in the smaller grains near S. R marks a grain of the R-phase. Martensite occurs in the grains near M having a diameter of about 120 nm. (c) S ¼ 7:3 after annealing at 450 °C for 1 h. Almost all grains larger than about 150 nm contain martensite.
T. Waitz et al. / Acta Materialia 52 (2004) 137–147
of 340 °C for 5 h followed by cooling to RT and quenching to )25 °C. Fig. 4(c) shows a specimen with S ¼ 7:3 annealed at a higher temperature (450 °C) for 1 h. In all cases the crystallization is complete since the diffraction patterns do not contain diffuse rings any more corresponding to the amorphous phase. Sharp and rather flat grain boundaries were observed both by TEM bright field and HRTEM images. It is important to point out that within the grains almost no dislocations were observed and most of the grains show only weak strain contrast. Additional TEM bright and dark field images were taken to measure the size distribution of the grains; the results are summarized in Fig. 5. In the case of S ¼ 6:7 annealed at 340 °C the grains have a diameter in the range of about 5–90 nm; only few of them are larger than about 50 nm (as shown in Fig. 5(a)). In the case of S ¼ 7:3 annealed at 340 °C there is a broad range of grain diameters ranging from 5 to 140 nm (cf. Fig. 5(b)). Their distribution seems to be non-uniform since frequently areas are observed mainly containing grains of small diameters (mean diameter of about 25 nm, e.g. near S in Fig. 4(b)) whereas other areas that are adjacent to them contain mainly larger grains (mean diameter about 70 nm, e.g. near M in Fig. 4(b)). In the case of S ¼ 7:3 and an annealing temperature of 450 °C most of the grains are larger than about 100 nm (cf. Fig. 5(c)). SA diffraction patterns were taken to analyze the crystalline phases occurring in the grains of different diameter. It is interesting to note that grains smaller than about 15 nm show reflections of the B2 phase only. When the grain size is between 15 and 60 nm reflections of the B2 phase and the R-phase were observed whereas no reflections corresponding to the martensite were encountered. When the grains are larger than about 60 nm they contain R-phase (cf. the grain marked by R in Fig. 4(b)) and B190 martensite (cf. the area near M in Fig. 4(b)) and in this case the B2 phase is hardly observed. Finally, grains larger than about 150 nm contain mainly martensite (cf. Fig. 4(c)). The volume fraction transformed to martensite by quenching to )25 °C was estimated to be less than about 30% (cf. fig 4(b)) and more than about 80% (cf. Fig. 4(c)) in the specimens having a maximum grain size of about 140 and 350 nm (cf. Figs. 5(b) and (c)), respectively. It should be noted that no martensite could be detected in grains smaller than about 60 nm even when the specimens were quenched in liquid nitrogen. In this case the volume fraction of R-phase seems to increase and only very small grains (less than about 15 nm diameter) contain residual austenite. The results of this analysis are summarized in Table 1. 3.3. The martensitic transformations in the nanostructures In the specimens annealed at 340 °C for 5 h followed by cooling to RT and quenching to )25 °C the R-phase
141
Fig. 5. Histograms of the size distributions of the grains after crystallization (cf. Fig. 4(a)).) S ¼ 6:7 after annealing at 340 °C for 5 h is leading to a mean grain size of 30 nm. (b) S ¼ 7:3 after annealing at 340 °C for 5 h. The dashed bars correspond to areas containing mainly smaller and larger grains (mean 25 and 70 nm), respectively. (c) S ¼ 7:3 after annealing at 450 °C for 1 h. Almost all grains are larger than 100 nm.
and the B190 martensite were analyzed in detail using both SA diffraction and HRTEM methods. As illustrated in Fig. 6 the grains containing the R-phase and
142
T. Waitz et al. / Acta Materialia 52 (2004) 137–147
Table 1 Grain size dependence of the observed phases Grain size (nm)
B2
< 15 15–60 60–150 >150
* *
R-phase * *
B190
* (<0.3) * (>0.8)
The occurrence of B2, R-phase and B190 is indicated by *. An estimate of the volume fraction of B190 is given in parentheses.
having a size larger than about 50–70 nm are frequently twinned and show some strain contrast; the width of the twins is about 20–50 nm (cf. Fig. 6(a)). Fig. 6(b) shows a HRTEM micrograph of two twin related R-phase variants RT1 and RT2; they are contained in a grain having a diameter of about 70 nm. The ð1 1 0 0ÞR lattice planes of both variants are indicated and they are corresponding to the ð1 0 1ÞB2 and ð0 1 1ÞB2 planes of the initial B2 lattice (in the case of the R-phase a hexagonal unit cell is used; BD runs along a common ½2 2 4 3R ½1 1 1B2 direction). The planar twin boundary is edge on in the TEM projection and runs along ð1 1 0ÞB2 . The rhombohedral angle aR of the R-phase was measured tilting a grain containing two twin related variants to a common BD ½1 0 1 0R (cf. Fig. 6(c)). In this case, the diffraction pattern contains both the ð0 0 0 1ÞR and ð1 2 1 0ÞR reflections. The corresponding lattice spacing d0001 and d1210 were measured and used to calculate the ratio of the hexagonal unit cell parameters cR and aR : cR /aR ¼ 1.39 0.01 and 1.38 0.01 leading to aR ¼ 88:5° 0.6° and 87.8° 0.6° in the case of RT1 and RT2, respectively. Fig. 7 shows typical diffraction patterns corresponding to B190 martensite. The pattern of Fig. 7(a) contains diffraction spots of two martensite twins MT1 and MT2 that are related by a rotation of p around ½0 0 1B190 (BD ½ 1 1 0MT1 ½1 1 0MT2 ). Most of the grains smaller than about 100–120 nm seem to contain only a single variant of the twinned martensite. In larger grains two or more martensite variants twinned on ð0 0 1ÞB190 planes were frequently observed (cf. Fig. 7(b)). It should be noted that the reflections ½1 1 1MT1;2 and ½ 1 1 1MT1;2 are strongly elongated along ½0 0 1B190 and streaks are running along the ½0 0 1B190 direction indicating a very small width of the twins. In addition, the streaks contain a regular sequence of closely spaced intensity maxima with an average spacing of 0:3 nm1 indicating a fairly constant spacing of the twin boundaries of about 3 nm. Fig. 8(a) shows a TEM bright field image that can be used to measure the width of the twins. The average width is d1 ¼ 1:7 and d2 ¼ 2:0 nm for MT1 and MT2 twins, respectively; the average relative twin period k ¼ d1 =ðd1 þ d2 Þ is 0.46 (cf. Fig. 8(b)). Almost all martensite grains contain ð0 0 1ÞB190 twins that have a width of less than 10 nm. As illustrated in Fig. 9 the width of very narrow twins can be determined on an atomic level
Fig. 6. Ni–50.3at.%Ti. Nanocrystalline structure; R-phase. (a) Bright field image of a twinned grain. Twin boundaries are indicated by arrows; near S strain contrast is visible. (b) HRTEM image of a grain containing two twin related variants. The twin boundary and the ð1 1 0 0ÞRT1;2 lattice planes of the variants RT1 and RT2 are indicated (BD ½2 2 4 3RT1;2 ) (c) Diffraction pattern showing two twin related R-phase variants (BD ½1 0 1 0 RT1;2 ) used to measure the rhombohedral angle.
using HRTEM images; the minimum width was measured to be 4 ð0 0 2ÞB190 atomic planes (0.9 nm) only (near A in Fig. 9).
T. Waitz et al. / Acta Materialia 52 (2004) 137–147
Fig. 7. Ni–50.3at.%Ti. Nanocrystalline structure; martensite. (a) SA diffraction pattern of a grain containing twinned martensite; (0 0 1) compound twinning is indicated by twin reflections (marked by MT1 and MT2) related by a rotation of p around ½0 0 1. Streaks and elongated reflections along ½0 0 1MT1;2 are caused by the very small width of the twins (BD ½ 1 1 0MT1 ½1 1 0MT2 ) (b) Two martensite variants M1 and M2 that are twinned on (0 0 1) occur within one grain (BD ½1 1 0M1;2 ).
4. Discussion 4.1. HPT induced amorphization The results of Figs. 1 and 2 show that by HPT deformation Ni–50.3at.%Ti transforms from B190 martensite to a nanostructured amorphous phase. It is proposed that a localized deformation process proceeds the transformation by leading to a nanocrystalline structure. The latter is fragmented by bands of an amorphous phase (cf. Fig. 1; S ¼ 6:7). Similar, after cold
143
Fig. 8. Ni–50.3at.%Ti. Nanocrystalline structure; martensite. (a) TEM bright field image of a grain containing a high density of (0 0 1) compound twins. The twin lamellae show bright and dark contrast. (b) Histogram of the observed twin widths.
rolling of NiTi a martensite microstructure refined by dislocation accumulation and strain induced twinning was observed containing numerous intersecting bands of nanocrystalline and amorphous phase arising locally by a shear strain instability [5,6,9,10]. As compared to cold rolling the HPT strain is much higher and dominated by a shear deformation [11] causing shear bands and strong crystal refinement [12]. Therefore, the HPT deformation of NiTi facilitates both the crystal refinement and the continuous accumulation of amorphous shear bands. When S increases the crystalline volume fraction
144
T. Waitz et al. / Acta Materialia 52 (2004) 137–147
Fig. 9. Ni–50.3at.%Ti. Nanocrystalline structure; martensite. HRTEM image showing (0 0 1) compound twins having a minimum width of 4 lattice planes (0.9 nm) only (near A). The ð0 0 1ÞMT1;2 twin boundary plane and the ð1 0 1ÞMT1;2 planes of the twin related martensite variants MT1 and MT2 are indicated by a dashed and a full line, respectively (BD ½0 1 0MT1;2 ).
gradually decreases until only isolated nanocrystals are left embedded heterogeneously in an amorphous matrix. Finally, caused by the plastic deformation of the amorphous matrix the retained nanocrystals dissolve in the amorphous phase until at S ¼ 7:3 only a few very small nanocrystals survive. Since most of them have the B2 structure it is concluded that the austenite is more stable against amorphization than the B190 martensite. This is in agreement with previous results [13]. In the present case it is concluded that the nanocrystalline debris contains austenite that was retained during the thermally induced B2 to B190 transformation [14] prior to HPT. Still their might be another explanation: the observed B2 nanocrystals could be formed by a stress induced reverse transformation B190 to B2 during HPT. That might be caused by a local increase of temperature exceeding the austenite start temperature (As 110 °C in the present case). Similar results of a deformation induced reverse transformation were reported by [15]. 4.2. Nanocrystallization The results of Figs. 3 and 4 show that during annealing in HPT induced amorphous Ni–50.3at.%Ti alloys heterogeneous polymorphous crystallization of the B2 phase occurs about 150 °C lower as compared to thin amorphous NiTi films processed by sputtering or melt spinning (Tx 510 °C [16]). It is concluded that the low thermal stability of the amorphous phase formed by HPT is caused by the retained nanocrystalline debris triggering crystallization (see Figs. 1 and 2). Therefore, already at an annealing temperature as low as Ta ¼
340 °C nanocrystallization occurs since the retained crystallites can act as heterogeneous nucleation sites leading to a high nucleation rate although the rate of growth is low since Ta =Tm ¼ 0:39 is small (Tm melting temperature). In agreement with the present conclusion it was proposed that the devitrification process should proceed with the largest nucleation rate and slowest growth rate to obtain a nanocrystalline structure; during low temperature annealing retained crystallites embedded in the amorphous phase can act as nuclei since they do not dissolve and can exceed the critical size for heterogeneous nucleation [17]. It is concluded that the nucleation rate depends on the HPT strain and decreases with increasing S (as can be seen by an increase of Tx and Tp ; cf. Fig. 3). This is explained as follows: in the alloy deformed up to S ¼ 7:3 the nucleation rate is lower since a only a small volume fraction <1% of tiny crystallites <15 nm is retained (cf. Fig. 2). Contrary to this, in the case of S ¼ 6:7 nucleation is triggered by numerous retained crystallites with a diameter up to about 30 nm having a high nucleation potency (cf. Fig. 1; a retained crystalline volume fraction Vcr of about 18% is deduced using Vcr ¼ 1 ðDH6:7 = DH7:3 Þ. In the amorphous matrix the growth of the nuclei ceases when the advancing interfaces of neighboring crystallites impinge on each other leading to grain boundaries. As the density of the nuclei increases their mean separation and therefore the final grain size will decrease. Since the density of the nuclei is lower in the case of S ¼ 7:3 annealing at Ta ¼ 340 °C is leading to a larger grain size as compared to the alloy deformed up
T. Waitz et al. / Acta Materialia 52 (2004) 137–147
to S ¼ 6:7 and annealed at the same temperature (cf. Figs. 4 and 5). In addition, when the retained crystallites are not distributed uniformly a nanocrystalline phase with a heterogeneous distribution of the grain sizes arises after crystallization (as shown at S and M in Fig. 4(b)). Finally, as compared to an annealing temperature of 340 °C the growth rate is expected to be higher at Ta ¼ 450 °C ðTa =Tm ¼ 0:46Þ leading to larger grain sizes (compare Figs. 4(b) and (c)). 4.3. Phase transformations occurring in the nanocrystalline grains Based on the results of the TEM analysis summarized in Table 1 it is concluded that in the nanocrystalline Ni– 50.3at.%Ti alloy the martensitic transformation is suppressed with decreasing grain size. This means, the transformed volume fraction decreases with decreasing grain size and the onset of the martensitic transformation is shifted towards lower temperatures. Therefore, Ms drops below the transformation temperature of the R-phase (TR ) in grains smaller than about 150 nm leading to a two step transformation from the B2 austenite via the R-phase to the B190 martensite. Finally, in grains smaller than about 60 nm the martensitic phase transformation is completely suppressed. Similar results of suppressing Ms were reported in the case of a cold rolled Ni–49.8Ti alloy containing a nanocrystalline phase [5]. A decrease of Ms below TR is also observed in coarse grained NiTi alloys and could be caused by a high density of dislocations induced during rolling [18] or coherent precipitates induced by aging [19]. It was proposed that in a nanocrystalline NiTi alloy the martensitic transformation could be suppressed in different ways: by the introduction of elastic strains, by lattice defects or by crystal refinement [5,6]. In the present investigation almost no dislocations and little elastic strains were encountered in the grains (cf. Fig. 4). Therefore it is concluded that the grain refinement leads to the suppression of the transformation. In this context aspects concerning nucleation sites, grain boundaries, twinning and the R-phase transformation are discussed in the following paragraphs. 4.3.1. Nucleation sites in the nanograins Specific dislocation configurations as dislocation walls or dislocation pile-ups are generally considered as possible nucleation sites [20,21]; in coarse grained NiTi alloys there is direct experimental evidence that martensite is nucleating at dislocations tangles in the matrix and near grain boundary dislocations [22]. Since in the present case almost no dislocations occur within the nanograins it is concluded that the grain boundaries act as the heterogeneous nucleation sites. This is in agreement with experimental results indicating that in NiTi the grain boundaries can favour the martensitic transformation [23].
145
It should be noted that a suppression of a martensitic phase transformation was also observed in small particles and it was proposed that the fraction of particles containing a lattice defect suitable for heterogeneous nucleation is decreasing with decreasing grain size [24]. However, these statistical arguments seem to fail in the case of FeNi nanoparticles (size from 10–200 nm) since the particles easily transform above RT although both experimental observations and calculations indicate that heterogeneous nucleation sites are not contained within the particles; therefore it was proposed that heterogeneous nucleation sites are provided by the surfaces of the nanoparticles [25]. Similar, in the present case it is concluded that in the nanocrystalline NiTi alloy the martensitic transformation is not suppressed by a lack of nucleation sites as the density of heterogeneous nucleation sites provided by the grain boundaries may even increase with increasing grain boundary area and decreasing grain size. 4.3.2. Constraints arising by the grain boundaries It is proposed that the grain boundaries impose constraints on the growth of the martensite confining the transformed volume fraction in the nanocrystalline structure. A martensite plate nucleated within a grain will be stopped at the grain boundaries acting as obstacles. To propagate the transformation the plate has to exert stresses that are sufficient to stimulate nucleation and growth of favourable martensite variants in the adjacent grains [22]. However, little stresses are expected to occur ahead of a small plate bound within an nanograin that has a size of less than 100 nm [26]. In addition, as deduced from TEM observations in NiTi a restriction was proposed for the autocatalytic nucleation of self accommodating plate groups [27]. This is based on a twin relation of all the martensite variants in the group which is possible only within a single grain since martensite variants occurring in adjacent grains have not the required orientation relationship. Therefore, in the present case it is concluded that in a volume containing many small grains the ability of spreading the transformation by autocatalytic nucleation decreases with increasing grain boundary area in agreement with the observed decrease of the martensite volume fraction. 4.3.3. (0 0 1) Compound twinning As outlined by [28] a martensitic phase transformation will follow a path of almost complete accommodation of the transformation shape strains. In coarse grained NiTi two different mechanisms occurring at different length scales facilitate the strain accommodation: Firstly, twinning by h0 1 1i type II or ð1 1 1Þ type I twins (at scale of 30–100 nm) leading to an invariant plane strain; secondly, at a scale far exceeding 100 nm self-accommodation of groups of different habit plane variants arises [27,29]. In the present case of the
146
T. Waitz et al. / Acta Materialia 52 (2004) 137–147
nanocrystalline NiTi the mean grain size (30–160 nm, cf. Figs. 4 and 5) represents a length scale of the same order as that of the twinning period and smaller than that of the self-accommodating groups in a coarse grained alloy. Therefore, in the nanograins the constraints of the grain boundaries suppress the formation of self-accommodating variants. As a consequence within the nanograins a different path of the transformation occurs that is leading to the required decrease of the transformation strains by the formation of very fine (0 0 1) compound twins (cf. Figs. 7–9). This is outlined as follows: it was proposed that (0 0 1) compound twinning leads to a smaller strain energy as compared to h0 1 1i type II twinning [29,30]. In addition, a decrease of the twinning period d1 + d2 decreases the elastic energy Dwe (strain energy per unit transformed volume) [31]. However, with decreasing d the twin boundary area At and therefore the twin boundary energy At ct of the transformed volume increase. From the observed very small twinning period it can be concluded that the specific twin boundary energy ct of the (0 0 1) compound twins must be very small. It should be mentioned that in the present case (cf. Fig. 9) the thinnest lamellae of the compound twins contain two martensite unit cells (i.e. four (0 0 2) lattice planes yielding d ¼ 0:9 nm). Since the separations of the twin boundaries are comparable to the interatomic distance the nanotwinned martensite may be regarded as an adaptive martensite phase as proposed by [28]. Finally, experimental results found in the literature [29,30,32] indicate that a variety of constraints as dislocations, grain boundaries and precipitates that may inhibit self-accommodation lead to the same preferred mode of the transformation involving (0 0 1) compound twinning to decrease the strain energy. The experimental results show that in grains smaller than 60nm (cf. Table 1) no thermally induced martensitic phase transformation occurs. It is proposed that this is caused by the decrease of self-accommodation with decreasing grain size since per unit of transformed volume an increasing chemical driving force )Dgc (<0) i.e. a larger undercooling is required to overcome an increasing energy barrier Dgnc (>0) including elastic (Dwe ) and surface (At ct ) energy. The present conclusions are in agreement with calculations of Dgnc carried out for ZrO2 nanoparticles containing twinned martensite [33]. Similar to the present case smaller particles are more stable against the martensitic transformation than larger ones. It should be mentioned that previously (0 0 1) compound twins of the martensitic phase were considered as deformation twins only since they do not agree with the phenomenological theory of the B2 to B190 transformation in NiTi as no invariant habit plane can occur [29]. In the nanocrystalline alloy the presence of an invariant habit plane is less important for the transformation since the B190 phase will mainly occur attached
to grain boundaries. Also the grain boundaries might even trigger the formation of twins [34]. Finally, it was proposed recently that during the Rphase to B190 transformation (0 0 1) compound twinning could give rise to an invariant plane strain under the condition of a critical value aR 6 86:2° [29]. In the present case the martensitic transformation is preceded by the formation of R-phase as required for (0 0 1) compound twinning acting as lattice invariant strain. As deduced from Fig. 6(c) the measured RT values of aR (88.5° 0.6° and 87.8° 0.6°) are somewhat larger than the calculated critical angle but the agreement is better than in the case of annealed coarse grained NiTi where aR P 89° [35]. 4.3.4. R-phase transformation It is concluded that the constraints of the grain boundaries should have little effect on the B2 to R-phase transformation since in this case the transformation shape strain is significantly smaller (roughly 1% as compared to 10% in the case of the B2 to B190 transformation). This is in agreement with the present results since on cooling the R-phase precedes the martensite in the small grains. The critical diameter of nuclei of the Rphase was estimated to be about 4–8 nm by in situ TEM analysis [36]. Therefore, the R-phase transformation is expected to be completely suppressed in very small grains as shown in Table 1. In grains having a size in the range from 15 to 50 nm small strains could be present prior to the transformation that may help to accommodate a single variant of the R-phase elastically. In the grains larger than 50 nm, however, the shape strains have to be accommodated by twins that have a small width to decrease Dwe (cf. Fig. 6(a)). Therefore as expected, caused by the constraints of the grain boundaries the width of the twins (20–50 nm) is significantly smaller in the nanograins as compared to that of about 300 nm measured in coarse grained NiTi alloys [37].
5. Conclusions 1. A NiTi alloy was subjected to HPT deformation leading to amorphization. Nanocrystalline debris is retained in the amorphous phase; the size and the number of the retained crystallites is decreasing with increasing HPT strain. 2. The amorphous phase shows low thermal stability. It is concluded that heterogeneous crystallization is triggered by the retained crystallites that have survived the HPT deformation. 3. Isothermal annealing is leading to nanocrystalline structures with grain sizes in the range of 5–350 nm depending on the annealing temperature and the density of the heterogeneous nucleation sites present in the amorphous phase. This leads to the conclusion that the strain of the HPT deformation determines
T. Waitz et al. / Acta Materialia 52 (2004) 137–147
the number of retained crystals in the amorphous phase and therefore the grain size of the nanocrystalline structure formed by annealing. 4. The martensitic transformation is suppressed in the ultrafine grains. It is concluded that forced by the constraints of the grain boundaries the R-phase precedes the martensite and that atomic scale (0 0 1) compound twinning occurs in the martensite facilitating the accommodation of the transformation strains. 5. In grains smaller than 60 nm no thermally induced martensitic transformation is observed. Therefore it is concluded that with decreasing grain size and decreasing twin separation both the strain energy and the twin interfacial energy are leading to an increasing energy barrier. Acknowledgements The authors thank Professor A.C. Kneissl for the kind provision of the NiTi alloy and Professor W. Pfeiler for his help with the DSC measurements. One of us (V.K.) thanks Professor R.Z. Valiev for the provision of laboratory facilities. Financial support from the Austrian Science Fund (FWF) is acknowledged. References [1] [2] [3] [4]
Thomas G, Mori H, Fujita H, Sinclair R. Scr Metall 1982;16:589. Koike J, Parkin DM, Nastasi M. J Mater Res 1990;5:1414. Schwarz RB, Koch CC. Appl Phys Lett 1986;49:146. Sergueeva AV, Song C, Valiev RZ, Mukherjee AK. Mater Sci Eng A 2003;A339:159. [5] Nakayama H, Tsuchiya K, Umemoto M. Scr Mater 2001;44:1781. [6] Nakayama H, Tsuchiya K, Liu ZG, Umemoto M, Morii K, Shimizu T. Mater Trans 2001;42:1987.
147
[7] Xu X, Thadhani N. Scr Mater 2001;44:2477. [8] Prader P, Kneissl AC. Z Metallkd 1997;88:410. [9] Tatyanin EV, Borovnikov NF, Kurdyumov VG. Phys Solid State 1997;39:1997. [10] Koike J, Parkin DM, Nastasi M. Philos Mag Lett 1990;62: 257. [11] Kim HS. J Mater Process Technol 2001;113:617. [12] Tyumentsev AN, Pinzhin YP, Tretjak MV, et al. Theoret Appl Fract Mech 2001;35:155. [13] Ewert JC, B€ ohm I, Peter R, Haider F. Acta Mater 1997;45: 2197. [14] Crevoiserat S, Gotthard R. Mater Sci Eng A 1999;A273–275: 357. [15] Lopez HF, Salinas A, Calderon H. Met Mater Trans A 2001;32A:717. [16] Chen JZ, Wu SK. J Non-Cryst Sol 2001;288:159. [17] Kulik T. J Non-Cryst Sol 2001;287:145. [18] Chrobak D, Morawiec H. Scr Mater 2001;44:725. [19] Khahil AJ, Ren X, Eggeler G. Acta Mater 2000;50:793. [20] Olson GB. Metall Trans A 1976;7A:1969. [21] Chen IW, Chiao YH. Acta Metall 1985;33:1827. [22] Saburi T, Nenno S. In: Tamura I, editor. Proceedings of the International Conference on Martensitic Transformations. Japan: The Japan Inst Metals, Japan; 1986. p. 671. [23] Gil FJ, Manero JM, Planell JA. J Mater Sci 1995;30:2526. [24] Chen IW, Chiao YH, Tsuzaki K. Acta Metall 1985;33:1847. [25] Kajiwara S, Ohno S, Honma K. Philos Mag A 1991;63:625. [26] Ling HC, Owen WS. Acta Metall 1981;29:1721. [27] Madangopal K. Acta Mater 1997;45:1997. [28] Khachaturyan AG, Shapiro SM, Semenovskaya S. Mater Trans JIM 1992;33:278. [29] Krishnan M, Singh JB. Acta Mater 2000;48:1325. [30] Nishida M, Itai I, Kitamura K, Chiba A, Yamauchi K. J Phys 1995;5:C8–635. [31] Evans AG, Burlingame N, Drory M, Kriven WM. Acta Metall 1981;29:447. [32] Zhang JX, Sato M, Ishida A. Acta Mater 2001;49:3001. [33] Yan WJ, Reisner G, Fischer FD. Acta Mater 1997;45:1997. [34] Fischer FD, Appel F, Clemens H. Acta Mater 2003;51:1249. [35] Ling HC, Kaplow R. Metall Trans A 1981;12A:2101. [36] Murakami Y, Shindo D. Philos Mag Lett 2001;81:631. [37] Miyazaki S, Wayman CM. Acta Metall 1988;36:181.