A. Compressive stress–strain curves

Figure 1 presents the σ–ε curves at the initial stage of superelasticity (SE) at various temperatures for various x values. The stress-induced forward/reverse transformation starting/finishing stresses, σ_Ms and σ_Af, respectively, were difficult to define using the former definition ^{Reference Niitsu, Omori and Kainuma8} for some of the σ–ε curves, especially for large x alloys, because of the irreversible behavior in the elastic deformation region. Instead, we herein defined σ_M and σ_A as the 0.2% proof stresses for the loading and unloading curves, respectively, as shown in Fig. 1(d). The values determined for the present alloys and for x = 1.75 in the previous paper ^{Reference Niitsu, Omori and Kainuma8} are plotted in Fig. 2(a) as a function of temperature together with their σ₀ values, which were approximated as the average of σ_M and σ_A. Overall, the curve for σ_M was concave, and σ_A and σ₀ decreased with decreasing temperature. The gradient of σ₀ gradually approached zero as temperature decreases. Similar behavior was reported for various types of MTs induced not only by one-dimensional stress ^{Reference Kimura, Xu, Niitsu, Omori and Kainuma12,Reference Niitsu15–Reference Xu, Ito, Umetsu, Kainuma and Ishida17} but also by applying magnetic fields. ^{Reference Ito, Ito, Umetsu, Kainuma, Koyama, Watanabe, Fujita, Oikawa, Ishida and Kanomata18} The temperature dependence of σ₀ allows us to see ΔS _SE ^B2–B19′ by Eq. (3). Further discussions on σ₀ will be provided in terms of ΔS in Sec. III.F.

FIG. 1.

Stress–strain curves obtained by compression tests at various temperatures ranging from 7 to 300 K for polycrystalline Ti–(50 + x)Ni alloys for x = (a) 0.92, (b) 1.30, (c) 1.54, (d) 1.63, and (e) 1.89.

FIG. 2.

Temperature dependences of (a) σ_M, σ_A, and σ₀ and (b) σ_hys for x = 0.92, 1.30, 1.54, 1.63, 1.75, ^{Reference Niitsu, Omori and Kainuma8} and 1.89.

The transformation stress hysteresis, σ_hys (≡ σ_M − σ_A), is plotted as a function of temperature in Fig. 2(b). σ_hys starts to drastically increase with decreasing temperature from approximately 150 K. This behavior is considered to be caused by a type of thermal activation process in the migration of B2/B19′ phase boundaries during stress-induced B2/B19′ MT, as discussed in our previous works. ^{Reference Niitsu, Omori and Kainuma8,Reference Niitsu15,Reference Niitsu, Xu, Umetsu and Kainuma16} In addition, it is important to note that all the σ_hys curves are almost coincident, which suggests the insensitivity of the thermal activation process to the alloy composition.

In the σ–ε curve at 7 K for x = 1.30, a serrated flow of SE was observed. Such behavior has also been confirmed in Ni–Co–Mn–In at 4.2 and 7 K. ^{Reference Niitsu, Xu, Umetsu and Kainuma16} The origin of this phenomenon may be explained in analogous to a serrated flow in plastic deformation, which is also observed in the cryogenic region; at cryogenic temperatures, a release of dissipated energy locally and adiabatically heats the moving habit plane itself because of extremely small specific heat and thermal conductivity, whereby the motion of habit planes occurs discontinuously. Such a phenomenon is supposed to be typical in the alloy systems showing a dramatic increase in σ_hys upon cooling.

B. DSC measurements

Figures 3(a1)–3(d1) present the h-DSC measurements for the alloys for various x values. For x = 0.71, exothermic and endothermic peaks attributed to the forward and reverse B2/B19′ MTs, respectively, were clearly observed, where T _Ms and T _Af (the B2/B19′ reverse MT finishing temperature) were designated by filled triangles. For x = 0.92, however, the intensities of these peaks were significantly suppressed and consecutive tails widely arose at the onsets of the high-temperature sides, high-temperature terminals of which were represented as T*_M and T*_A (open triangles). Furthermore, a very small peak is observed for x = 1.09, and no peaks are present for x = 1.23.

FIG. 3.

(a1)–(d1) h-DSC measurements for cooling (blue) and heating (red). Only the heating curves (red lines) were calibrated with respect to their baselines; therefore, the inserted scale bars are valid only for the heating curves. The forward/reverse B2/B19′ MT starting/finishing temperatures, T _Ms and T _Af, are marked with filled triangles, and the high-temperature terminals of the small tails detected for x = 0.92 are represented as T*_M and T*_A, as indicated by the open triangles in (b1), respectively. The inset of (d1) presents the DSC cooling curve obtained with a much larger specimen. The sweeping rates were 10 K/min. (a2)–(d2) Lower columns: c _P and fitting curves to the c _P plots at temperatures below the ending of the peak and/or hump. Upper columns: Difference between the experimental c _P and fitting curves. The c _P measurements were performed in a cooling sequence using the relaxation method with three repetitions and a 2% temperature increase. The plots are an average of three repetitions. (e) Lower column: S as a function of temperature for x = 0.71, 0.92, 1.09, and 1.23. Upper column: The difference ΔS _cp ^B2–B19′ between S for x = 0.71 (the B19′ phase) and x = 1.09 (the B2 phase).

As discussed later, in situ TEM observations during heating for x = 0.92 confirmed that the B19′ phase disappeared at approximately 230 K. This temperature agrees well with its T _Af and, thus, the main peaks most likely correspond to the B2/B19′ MT. All these critical temperatures are listed in Table I together with the equilibrium temperatures, T ₀ (≡ (T _Ms + T _Af)/2) and T*₀ (≡ (T*_M + T*_A)/2), and the transformation temperature hystereses, T _hys (≡ T _Af − T _Ms) and T*_hys (≡ T*_A – T*_M). Overall, the T _hys values in this work are larger than those previously determined by electrical resistivity (ER) measurements. ^{Reference Niitsu, Kimura, Xu and Kainuma5} The transformation hysteresis is known to increase with increasing sweeping rate in the low-temperature region where the thermal activation nature is developed. ^{Reference Xu, Kihara, Tokunaga, Matsuo, Ito, Umetsu, Kindo and Kainuma19} Because the sweeping rate used for the h-DSC measurements was 10 K/min, which is 5 times larger than that used for the ER measurements, the B2/B19′ MT behavior may be more strongly arrested, thereby resulting in the larger T _hys values in this work.

TABLE I.

Transformation temperatures and entropy changes of the Ti–(50 + x)Ni alloys.

Sweeping rates of ER, and DSC and h-DSC measurements were 2 K/min and 10 K/min, respectively.

C. Specific heat measurements

The c _P values for these alloys are presented in the lower columns of Figs. 3(a2)–3(d2). All the measurements were performed in a cooling sequence using the relaxation method. Therefore, in principle, the latent heats associated with the class of first-order transformations could not be detected or, if detected, were significantly suppressed in magnitude. Indeed, although a peak appeared at approximately 260 K for x = 0.71 in response to the B2/B19′ MT [Fig. 3(a2)], its magnitude was less than one-tenth of that detected by h-DSC. As observed in Fig. 3(b2), the peak of x = 0.92 broadened similar to that in the h-DSC curve. Furthermore, this peak disappeared and was replaced by a broad hump for x = 1.09 and 1.23. We applied the hybrid function of the Einstein and Debye models as a fitting function of the phonon term of c _P to the fitting curves [black lines in Figs. 3(a2)–3(d2)], in line with the precedent study. ^{Reference Lashley, Drymiotis, Safarik and Smith20} The difference between the fitting curves and measured plots (Δc _P) is presented in the upper columns. The Δc _P curves facilitate the visualization of the degrees of deviation from the c _P components which are reasonably expected to exist in terms of the contributions of phonon and electrons, e.g., the deviation caused by the B2/B19′ MT is highlighted for x = 0.71. An anomalous hump over a very wide temperature window is clearly visible for the two most Ni-rich alloys. Their peak temperatures are ∼220 K and appear to be insensitive to x, whereas the peak magnitudes appear to be somewhat suppressed with increasing x. These features are mostly undetectable in the h-DSC curves and thus distinct from the peak attributed to the B2/B19′ MT. Only the DSC cooling curve taken with a larger sample of x = 1.23 [see the inset of Fig. 3(d1)] shows a similar tendency with an inflection point at ∼205 K, very close to the peak temperature of the hump. In the h-DSC measurements, such a hump with wide tails over the entire measured temperature region would be difficult to clearly detect because of the uncertain baseline. Considering the similarity of c _P for Ti–Ni–Fe, ^{Reference Fukuda, Choi, Kakeshita and Ohba21} the origin of the hump is most likely linked to the second-order C–IC transition and/or related precursor phenomena. Further research on microstructural developments within these alloys will be presented in the near future.

D. Transformation behavior for x = 0.92

The transformation behavior for x = 0.92 was more complicated. The results of more detailed c _P measurements for this alloy, which were performed using different heating sequences, are presented in Fig. 4. For the heating sequence from 10 K, the c _P data of the first trial significantly deviated from those of the second and third trials, suggesting the occurrence of a first-order transformation with a temperature hysteresis larger than 2 K. Indeed, the first peak at 227 K is very close to T _Af. The second peak temperature is approximately 271 K. Notably, the heating sequence from 250 K also resulted in the appearance of a peak at 271 K even though this sequence did not cross T _Ms or T*_M. According to the aforementioned recent work, ^{Reference Ji, Wang, Ding, Otsuka and Ren7} isothermal holdings just above T ₀ in a 51.3 Ni alloy generate the R phase, the DSC heating curve of which was very similar to those presented in Figs. 3(b1) and 4. Indeed, an in situ TEM study for this alloy revealed that three types of microstructures coexist at 80 K: the B2 phase with a modulated fine contrast, the R-like phase with twin textures, and the B19′ phase, as shown in Figs. 5(a)–5(c), respectively. Here, the amount of the B2 phase and the R-like texture was very limited and coexisted only in the thinner area of the sample foil, which may be due to the additional stabilization of the B2 phase in the thinner region. During heating, the B19′ phase fully disappeared at approximately 230 K, whereas the R-like texture remained. During further heating to 300 K, the R-like texture was significantly diminished. Accordingly, it is deduced that the peak observed at 271 K in both heating sequences is likely related to the reverse B2/R transformation and that some of the R phase arises in an isothermal nature.

FIG. 4.

Detailed c _P measurements for x = 0.92. The gray data points are the same as those presented in Fig. 3(b2), the red data points represent the results for a heating sequence from 10 to 350 K, and the blue data points represent those for a heating sequence from 250 to 350 K. Above 200 K, the measurements were performed at intervals of ∼5 K. Three consecutive trials were performed for each measurement point with a temperature increase of 2 K.

FIG. 5.

Microstructures observed for x = 0.92 at 80 K: (a) B2 phase, (b) tweed-like texture, which is most likely the R phase, and (c) B19′ phase. The insets show the corresponding electron diffraction patterns obtained in the ${\left[ {\bar 11\bar 1} \right]_{{\rm{B}}2}}$ // ${\left[ {\bar 110} \right]_{{\rm{B}}19'}}$ beam direction. The scale bar is 200 nm.

E. Entropy difference between B2 and B19′ phases

S _cp ⁱ (T) for various x values are presented in Fig. 3(e). Note that S _cp ⁱ (T) for x = 0.71 and 0.92 was extrapolated toward higher temperatures in line with the fitting c _P curves represented with solid lines in Figs. 3(a2) and 3(b2). A noticeable difference was observed between S _cp ⁱ (T) for x = 0.92 and 1.09, especially at elevated temperature. This finding reasonably suggests that the B19′ phase is dominant for x = 0.92 below its B2/B19′ MT finishing temperature T _Mf of ∼172 K [see Fig. 3(b1)] while including small amounts of the residual B2 phase and possibly the isothermal R phase as well and that the B2 phase is dominant for x = 1.09 over the entire temperature range. For x = 1.09, the h-DSC cooling curve showed the B2/B19′ MT sign with T _Ms = 146 K [see Fig. 3(c1)] so that one may think that this alloy contains a large amount of the B19′ phase below its T _Ms. However, ΔS _DSC ^B2–B19′ associated with this MT was 0.24 J/mol K, about 10% of ΔS _DSC ^B2–B19′ for x = 0.92 (see Table I). As discussed later, this means that the B2/B19′ MT in x = 1.09 was mostly arrested, and in such a case, the c _P curve hardly shows any effects of the B2/B19′ MT, as shown in Fig. 3(c2). The upper column of Fig. 3(e) shows ΔS _cp ^B2–B19′ (= S _cp ^B2 − S _cp ^B19′), i.e. the difference between S _cp ⁱ (T) for x = 1.09 and 0.71 as being fully in the B2 and B19′ phases, respectively. The broken line corresponds to the ΔS _cp ^B2–B19′ derived under the assumption that no hump would exist in the B2 phase, as indicated by the black lines in Figs. 3(c2) and 3(d2). This result strikingly demonstrates that the B2 phase in this composition region is significantly stabilized by the presence of the anomalous hump.

F. Transformation entropy change

In Fig. 6(a), entropy changes between the B19′ and B2 phases are plotted for various Ti–Ni alloys for x ≥ 0 as a function of temperature. ^{Reference Zhang, Wang, Wang, Zhou, Otsuka and Ren2,Reference Niitsu, Kimura, Xu and Kainuma5,Reference Fukuda, Yoshida and Kakeshita6,Reference Wasilewski, Butler and Hanlon22–Reference Kim, Liu and Miyazaki26} For x = 0.92, the total area of the peak and consecutive tail in the h-DSC curve are regarded as ΔS _DSC ^B2–B19′. For the derivation of ΔS _SE ^B2–B19′, σ_A at elevated temperatures has a tendency to be underestimated because of the introduction of slip deformations and, thus, σ₀ is also reduced. Therefore, the ΔS _SE ^B2–B19′ values derived from dσ_M/dT, instead of dσ₀/dT, were plotted together for some σ–ε curves (open diamonds). Overall, the ΔS _SE ^B2–B19′ values were relatively close to the ΔS _cp ^B2–B19′ curve, whereas ΔS _DSC ^B2–B19′ exhibited a very different temperature dependency from both ΔS _cp ^B2–B19′ and ΔS _SE ^B2–B19′.

FIG. 6.

ΔS _DSC ^B2–B19′ as a function of (a) temperature and (b) x. ^{Reference Zhang, Wang, Wang, Zhou, Otsuka and Ren2,Reference Niitsu, Kimura, Xu and Kainuma5,Reference Fukuda, Yoshida and Kakeshita6,Reference Berman, West and Rozner23–Reference Honma and Takei27} (c) T ₀ plots for various Ti–Ni alloys. ^{Reference Kakeshita, Fukuda, Tetsukawa, Saburi, Kindo, Takeuchi, Honda, Endo, Taniguchi and Miyako13,Reference Honma and Takei27–Reference Wang, Verlinden and Humbeeck29} The T ₀, T _Ms, and T _Af lines below 200 K refer to our precedent work. ^{Reference Niitsu, Kimura, Xu and Kainuma5} In (a), the ΔS _SE ^B2–B19′ values derived from dσ₀/dT and dσ_Ms/dT are plotted with open squares and diamonds, respectively. In (c), the color change in the B2 phase region represents the possible change in the degree of commensurability: denser contrast indicates higher commensurability. The references of ΔS _DSC ^B2–B19′ and T ₀ were limited to those of alloys quenched from the B2 single-phase region.

Figures 6(b) and 6(c) present the ΔS _DSC ^B2–B19′ and T ₀ values with respect to the change in x, respectively. ^{Reference Zhang, Wang, Wang, Zhou, Otsuka and Ren2,Reference Niitsu, Kimura, Xu and Kainuma5,Reference Fukuda, Yoshida and Kakeshita6,Reference Kakeshita, Fukuda, Tetsukawa, Saburi, Kindo, Takeuchi, Honda, Endo, Taniguchi and Miyako13,Reference Wasilewski, Butler and Hanlon22–Reference Wang, Verlinden and Humbeeck29} The ΔS _DSC ^B2–B19′ plots appear to be divided into three composition regions: Region I, x ≲ 0.8 (260 K ≲ T ₀), showing a static value in the range of 4–5 J/mol K, which is obviously larger than ΔS _cp ^B2–B19′; Region II, x ∼ 0.9 (T ₀ ∼ 235 K), exhibiting values comparable to ΔS _cp ^B2–B19′; and Region III, 0.95 ≲ x (T ₀ ≲ 225 K), possessing values much smaller than ΔS _cp ^B2–B19′. In our recent study, ^{Reference Niitsu, Kimura, Xu and Kainuma5} dT ₀/dx was expressed by

(4) $${{{\rm{d}}{T_0}} \over {{\rm{d}}x}} = - {{\Delta {\mu _{{\rm{Ti}}}} - \Delta {\mu _{{\rm{Ni}}}}} \over {\Delta {S^{{\rm{B}}2 - {\rm{B}}19'}}}}\quad ,$$

where Δμ _i represents the difference in the chemical potentials of the element i between the B2 and B19′ phases. By combining Eqs. (3) and (4) with respect to ΔS _SE ^B2–B19′, the T ₀ line in Fig. 6(c) was derived with the known dσ₀/dT for x = 1.75. ^{Reference Niitsu, Omori and Kainuma8} In addition, the T _Ms and T _Af lines could also be estimated from dσ_Ms/dT and dσ_Af/dT by analogy with dσ₀/dT, respectively. As observed in Fig. 6(c), these conversions reveal that the transformation hysteresis drastically widened with decreasing temperature. Therefore, the unreasonably small ΔS _DSC ^B2–B19′ in Region III can be explained by the kinetic arrest (i.e., partial transformation) in the B2/B19′ MT. However, it still appears unreasonable that the total amount of ΔS _DSC ^B2–B19′ (2.31 J/mol K) for x = 0.92 (Region II), which is given as the total amount of ΔS _DSC for the B2/B19′ MT including the partial B2/R transformation, remains much smaller than that (4.22 J/mol K) for the B2/B19′ MT of x = 0.71 (Region I). The origin of this remarkable discrepancy remains unclear but may be related to the precursor condition in the B2 phase. We guess that the following two factors, (i) change in the volume fraction of the precursor nanodomains and (ii) change in the degree of commensurability within the nanodomains, should be considered as the possible origin of the anomalous hump. It is possible that the B2 phase in Region I is additionally stabilized by both of the factors while in Region II (and possibly Region III as well) is stabilized by either one factor. Further studies on the microscopic changes of these alloys are in progress and will be provided in the near future.