1. Introduction
Ti–Ni based alloys, known as shape memory alloys (SMAs), are widely used for industrial and medical applications. For Ti50−xNi50+x alloys, while the martensitic transformation from the B2 ($Pm\bar{3}m$) to the B19′ (P21/m) phase occurs directly,1,2) the transformation temperature drastically decreases with increasing Ni content and suddenly disappears at x ≈ 1.4.3,4) The addition of a third element has been used to change the martensitic transformation behavior in Ti–Ni based alloys.5–7) Ti50Ni50−xCux alloys with 7.5 ≤ x ≤ 15 show a two-step martensitic transformation from the B2 to the B19′ phase via the B19 (Pmma) phase,8–11) whereas Ti50Ni50−xFex alloys with 1 ≤ x ≤ 3 show a successive martensitic transformation from the B2 to the B19′ phase via the R ($P\bar{3}$) phase.12–14) The B2/R martensitic transformation is a first-order phase transition, involving a small latent heat and a small thermal hysteresis in the forward and reverse transformations. In the Ti50Ni50−xFex alloys, the temperatures of both the B2/R and the successive R/B19′ transformations decrease monotonically with increasing Fe content,15–17) and a negative temperature dependence of electrical resistivity (ER) appears in the parent-phase region of relatively high Fe alloys.17) Choi et al. also reported that in a 6 at% Fe alloy, in which no B2/R phase transformation is detected, a broad endothermic peak due to a commensurate-incommensurate (C-IC) transition appears in the heating curve of the specific heat measurement.17)
The C-IC transition was first reported in a Ti50Ni47Fe3 alloy by Hwang et al. in 1983,12) and they repeatedly discussed the existence of a 1/3 110 diffuse scattering, recognized as a precursor state to the B2/R phase transition.12) The IC state is characterized by the diffuse scattering reflections at offset positions near the 1/3 110 reflection. In the C-IC transition during cooling, the reflections shift and finally lock onto the exact 1/3 position on transforming to C state. Recently, Shindo et al. and Murakami et al. examined the 1/3 110 diffuse scattering and its dark-field microstructure in a Ti50Ni48Fe2 alloy18,19) by in situ transmission electron microscopy (TEM) observation, where the characteristics of the microstructural evolutions during the C-IC and successive B2/R phase transformations were clarified. According to their works, a nanodomain microstructure, which can be divided into different variants, was found in the C and IC states, and the crystallographic characteristics of the C state was obviously different from that of the R phase showing long-range order.
Furthermore, Ren et al. reported the strain glass phenomenon related to the C-IC transition in Ni-rich TiNi alloys,20,21) Fe-doped TiNi alloys,22,23) and Cu-doped TiNi alloys,24) where the strain glass phenomenon was described as a frozen state with disordered local strain. It was reported that the storage modulus and internal friction (tan δ) show frequency dependence in the region where the strain glass phenomenon appears. Furthermore, a cluster-like microstructure was also observed in the strain glass state and its morphology is similar to that of C state during the C-IC transition.
So far, the B2/R and the C-IC transformations have mainly been investigated in ternary alloys with a composition fixed at 50 at% Ti. It is well known that in the Ni-rich TiNi binary single-phase alloys quenched from high temperatures, the B2/B19′ transformation temperature drastically decreases with increasing Ni content, and the C-IC transition appears in regimes of higher Ni content.25) Niitsu et al.25) also reported that, in some Ni-rich TiNi binary alloys, as in Ti50Ni44Fe6, a broad peak presumably due to the C-IC transition appeared in the specific heat curves, and that the entropy change (ΔS) of the B2/B19′ transformation was significantly reduced after the C-IC transition. Similar experimental results were also found for the B2/B19 phase transformation in Ti50−xNi40+xCu10 alloys.26) For the alloys, the C state, which was called “Intermediate (I) phase” in the paper, showed a sharper endothermic peak in the specific heat curves and its influence on the martensitic transformation was more significant. Actually, the C-IC (denoted as B2/I hereafter) phase transformation affects not only the ΔS but also the transformation temperatures in both the B19 and B19′ martensitic transformations. However, the influences of the B2/I transition on the R phase transformation are still unknown.
In this study, Ti50−xNi47+xFe3 alloys, in which the R-phase is detectable even at x = 0,12) were selected in order to examine the influence of the B2/I phase transition on the R phase transformation.
3. Results and Discussion
3.1 Martensitic transformation behavior
All of the specimens presented herein were confirmed to show a single-phase microstructure by SEM observation at room temperature, though a small amount of tiny, dispersed oxide particles were found.
The results of the DSC cooling and heating curves are shown in Figs. 1(a) and 1(b), respectively. The noisy signals at around 275 K were caused by the melting of ice around the samples during the measurements. Hereafter, the martensitic transformation temperatures, i.e., the forward transformation peak temperature and the reverse transformation peak temperature between i and j phases, are indicated as $T_{\text{M}}^{i/j}$ and $T_{\text{A}}^{i/j}$, respectively. For x = 0.00, as indicated by the open-headed arrows, the transformation from B2 phase to R phase was detected ($T_{\text{M}}^{\text{B2/R}}$ and $T_{\text{A}}^{\text{B2/R}}$), where a similar behavior has also seen reported in the literature.12,27) It can be seen that the DSC peaks of the B2/R transformation become smaller with increasing Ni content. Broad peaks are clearly seen near 200 K in both the heating and cooling curves of x = 0.40 to 0.80, as indicated by solid squares in Fig. 1; these characteristics are not similar to that of the R phase transformations. The reaction associated with this feature is most likely to be caused by the B2/I transformation and a similar reaction has been reported in Ti-poor Ti–Ni–Cu26) alloys.
Figure 2 shows the differences of DSC heating curves, from which the heating curve of x = 1.00 showing no transformation is subtracted. It can be seen that both the areas of the peaks of B2/R and B2/I transformations, which correspond to the enthalpy change ΔHB2/R and ΔHB2/I, respectively, reduce with increasing x, whereas the $T_{\text{A}}^{\text{B2/I}}$ is almost constant. It is important to note that the curve of x = 0.40 shows both the sharp and the broad peaks, which means a clear two-stage process of B2/I and I/R transitions. For x = 0.45 and 0.50, though not as clear as that of x = 0.40, the subtracted DSC curves exhibit small bending behaviors at about 170 K. As to be demonstrated in ER measurements later, this behavior is also due to the I/R transition. In Fig. 2, as indicated by the two-headed arrows, the transformation temperatures for the B2/I transformation ($T_{\text{A}}^{\text{B2/I}}$) were determined as the peak points.
Figure 3 shows the temperature dependence of ER in the Ti50−xNi47+xFe3 alloys during both heating and cooling processes. For x = 0.00, the ER curve suddenly bends up at about 235 K due to the B2/R phase transformation accompanying a thermal hysteresis. With increasing x, the onset temperature decreases, and the ER change becomes less obvious. For the alloys with x ≥ 0.30, the ER starts to increase gradually with decreasing temperature in the temperature region below 240 K before the R phase transformation, while there is no thermal hysteresis in the temperature region between 220 and 240 K. A similar behavior has been reported in the Ni-rich Ti–Ni binary alloys20,25,28) and the Ti50(Ni+Fe)50 alloys.15–17)
It is worthy to note that the thermal hysteresis in the R phase transformation remains even in the alloy with x = 0.50, while gradually becoming less apparent with increasing x. Since direct determination of the R phase transformation temperature from the ER curves for the alloys with x ≥ 0.40 is difficult, the difference between heating (ρH) and cooling (ρC) curves, i.e., ρdiff ≡ ρH − ρC, was plotted for each sample as shown in Fig. 4; thus, the peaks are the results of thermal hysteresis.
The temperatures $T_{\text{M}}^{\text{B2/R}}$ (or $T_{\text{M}}^{\text{I/R}}$) and $T_{\text{A}}^{\text{B2/R}}$ (or $T_{\text{A}}^{\text{I/R}}$), corresponding to the peak temperatures in the DSC curves shown in Figs. 1 and 2, are also indicated with dashed and solid lines, respectively. For alloys with x = 0.00 to 0.50, the peak positions of the ρdiff curves are in a good agreement with the transformation temperatures determined by DSC. Especially, the onset points detected at about 170 K in the DSC measurement for the x = 0.45 and 0.50 alloys in Fig. 2 are precisely coincident with the peak positions in ρdiff, which is an evidence that these peaks correspond to the I/R transformation.
The transformation temperatures $T_{\text{M}}^{\text{B2/R}}$, $T_{\text{A}}^{\text{B2/R}}$, $T_{\text{A}}^{\text{B2/I}}$, and $T_{\text{A}}^{\text{I/R}}$, which are experimentally determined from DSC data in Figs. 1 and 2, are plotted against composition in Fig. 5 and listed in Table 1. The temperatures $T_{\text{M}}^{i/j}$ and $T_{\text{A}}^{i/j}$ are indicated with open and closed symbols, respectively. The values of $T_{\text{A}}^{\text{B2/I}}$ in the alloys with x ≥ 0.40 are almost constant at about 200 K, and both $T_{\text{M}}^{\text{B2/R}}$ and $T_{\text{A}}^{\text{B2/R}}$ gradually decrease with increasing x. Moreover, when the B2/R transformation alters to I/R transformation at about x = 0.35, i.e., the product phase is identical whereas the parent phases are different, there is a sudden decline in the transformation temperature for $T_{\text{A}}^{\text{I/R}}$. This behavior can be considered as the relative thermodynamic destabilization of the R phase due to the appearance of the I phase. However, it is difficult to explain the origin of the composition-invariant behavior of $T_{\text{A}}^{\text{I/R}}$ for x = 0.45 and 0.50.
Table 1 Transformation temperatures obtained from peak temperatures in DSC curves and transformation enthalpy change, ΔHi/j and entropy change, ΔSi/j (i/j = B2/R, B2/I, or I/R transition) evaluated by DSC measurements, where ΔHTotal ≡ ΔHB2/I + ΔHI/R and ΔSTotal ≡ ΔSB2/I + ΔSI/R. An asterisk indicates the case where the transformation is qualitatively detected but the specific value cannot be quantitatively determined.
The transformation entropy change ΔS was extracted from the subtracted DSC curves in Fig. 2. The areas in the subtracted DSC curves correspond to the enthalpy change ΔHi/j in the transformation, and ΔSi/j is obtained by using the following relation,
| \begin{equation}
\Delta S^{i/j} = \Delta H^{i/j}/T_{\text{A}}^{i/j},
\end{equation}
| (1) |
where
i/
j indicates the type of transformation. As indicated in
Fig. 2, the enthalpy change corresponds to the B2/R transformation for
x = 0.00 to 0.35, the B2/I transformation for
x = 0.60 and 0.80, and a mixture of B2/I and I/R transformations (noted as Δ
HTotal ≡ Δ
HB2/I + Δ
HI/R) for
x = 0.40 to 0.50. These values of Δ
Si/j are listed in
Table 1 and plotted against the composition in
Fig. 6. It is observed that all the entropy changes monotonically decrease with increasing
x. It is seen that a large step at
x = 0.40 exists between Δ
STotal (≡ Δ
SB2/I + Δ
SI/R) and Δ
SB2/R. The present authors have investigated the transformation behaviors among B2, I, and B19 in Ti
50−xNi
40+xCu
10 alloys and reported that
$T_{\text{A}}^{\text{B2/B19}}$ (or
$T_{\text{A}}^{\text{I/B19}}$) is hardly affected by the presence of the I phase and that Δ
STotal ≡ Δ
SB2/I + Δ
SI/B19 at the critical composition is almost comparable to Δ
SB2/B19.
26) This suggests that the influence of the I phase on the R phase transformation is essentially different from that on the B19 phase. On the other hand, there is another large step at
x = 0.60 between Δ
STotal and Δ
SB2/I as shown in
Fig. 6. This suggests that the contribution of R phase transformation in the Δ
STotal is not small in comparison to that of the I phase transformation.
3.3 Crystal structure determination
The in situ X-ray diffraction patterns in the temperature range between 90 and 298 K for the x = 0.00, 0.35, and 0.40 alloys are shown in Fig. 7, where the measurements were performed during heating from 90 K, and the diffraction intensity below 35° is amplified by a factor of 5 for better visibility. The 100B2, 110B2, and 200B2 peaks were observed in all the samples at T = 298 K. For the x = 0.00 alloy, the 110B2 peak split into 112R and 300R peaks, and 110R, 202R, and 212R reflections from the R phase were also observed at T = 90 and 150 K, as shown in Fig. 7(a). At 200 K in the R phase region, while the faint 202R peak remained, the 110R peak almost disappeared. In the x = 0.35 and x = 0.40 alloys, although the 110B2 peaks do not split clearly, relatively large 110R reflections were detected at both T = 90 and 150 K, as shown in Figs. 7(b) and 7(c). In Fig. 7(c), at T = 200 K, which is in the I phase region of the x = 0.40 alloy, the XRD pattern shows no obvious difference from that of the B2 phase.
The results in the in situ XRD measurements in Fig. 7 are used to obtain the lattice constants for B2 and R phases. The lattice constants of B2 and R phases are indicated with closed and open symbols, respectively. The results are listed in Table 2 and plotted in Fig. 8. Here, $a_{\text{R}}/\sqrt{6} $ and $c_{\text{R}}/\sqrt{3} $, where aR are cR are the lattice constants of the hexagonal R phase, are shown, corresponding to the lattice constant (aB2) of the B2 phase. The value of aB2 slightly decreases with increasing x and decreasing temperature. In the x = 0.00 and 0.35 alloys, as temperature increases, $a_{\text{R}}/\sqrt{6} $ increases and $c_{\text{R}}/\sqrt{3} $ decreases, accelerating to approach the aB2 (≈ 0.301 nm) at $T_{\text{A}}^{\text{B2/R}}$. Similar temperature dependences of lattice constants were reported by Choi et al. for some Ti50NiFe alloys.15) On the other hand, a quantitative evaluation of $a_{\text{R}}/\sqrt{6} $ and $c_{\text{R}}/\sqrt{3} $ was difficult for x = 0.40.
Table 2 Lattice constants for the B2 and R phases evaluated from XRD examinations performed at temperatures between 90 and 298 K.
Figure 9 shows the temperature dependence of the peak position (Δ2θ = 2θ − 2θ250K) and the full width at half maximum (Δw = w − w250K) using the 011B2 peak, where both the values were plotted as the difference from the value at T = 250 K for each sample. It is important to note that, due to the similarity of the crystal structures of B2 and I phases, the changes of both Δ2θ and Δw of the 011B2 peak can be hardly noticed around the transition temperatures $T_{\text{A}}^{\text{B2/I}}$. However, since the 011B2 peak is sensitive to the change in crystallographic symmetry at the B2/R phase transformation, both Δ2θ and Δw should drastically change at $T_{\text{A}}^{\text{B2/R}}$; an onset in both Δ2θ and Δw for x = 0.00 and 0.35 is actually observed at $T_{\text{A}}^{\text{B2/R}}$. For x = 0.40, while no changes in Δ2θ and Δw were detected around $T_{\text{A}}^{\text{B2/I}}$ (≈ 200 K), some obvious changes similar to those in the other alloys were detected at a temperature just below $T_{\text{A}}^{\text{I/R}}$ (≈ 170 K). This is caused by the fact that both the B2/R and I/R phase transitions are accompanied by the disappearance of cubic symmetry, although the transformation strain between B2 (or I) and R phases decreases with increasing Ni content.
In order to observe the influence on the microstructure of the R phase by the B2/I phase transformation, in situ TEM observations were carried out. The selected area diffraction pattern (SADP) taken from the $[1\bar{1}1]_{\text{B2}}$ incident beam direction at T = 87 K for the x = 0.00 alloy is shown in Fig. 10(a). In Fig. 10(b), the TEM specimen was tilted, so only 011-type reflections were excited. It is important to note that the n/3 011B2 diffractions remain, which is in accordance with the fact that the x = 0.00 alloy shows R phase at this temperature, which is also consistent with the literature.18,19) Figure 10(c) shows the dark-field image (DFI) taken from the 1/3 011B2 spot at T = 87 K for the x = 0.00 alloy, where the DFI exhibits a typical twin microstructure of the R phase.29–31) Note that, in the observed region in Fig. 10(a), limited variants with a twin structure appeared during the in situ TEM observation.
The SADPs taken from the $[1\bar{1}1]_{\text{B2}}$ incident beam direction and from a direction slightly tilted from the $[1\bar{1}1]_{\text{B2}}$ direction at T = 87 K for the x = 0.35 alloy are shown in Figs. 10(d) and 10(e), respectively. The obtained SADPs are very similar to those of the x = 0.00 alloy and indicate the existence of the limited variants of the R phase. In the x = 0.35 alloy, the characteristic twin microstructure of the R phase is also observed at T = 87 K, but a cluster-like structure exists in the twin microstructure, as shown in Fig. 10(f).
For the x = 0.40 alloy, the observation was performed at T = 87 and subsequently at 183 K, where the R phase and I phase, respectively, are expected to be detected. It is worth noting that all the variants of the R phase were observed in Fig. 10(g) for x = 0.40, unlike those for the x = 0.00 and 0.35 alloys. The SADP under two-beam excitation is shown in Fig. 10(h). Though the beam brightness is very low, the n/3 011B2 reflections still remain. In the DFI taken from the 1/3 011B2 spot at T = 87 K, however, a cluster-like microstructure without the twin microstructure was observed, as shown in Fig. 10(i). On the other hand, at T = 183 K in the I phase region, while the SADP in the $[1\bar{1}1]_{\text{B2}}$ direction shows weak n/3 011B2 reflections (Fig. 10(j)), no n/3 011B2 reflection was detected under two-beam excitation (Fig. 10(k)). Similar feature was observed in the parent phase prior to the R phase transformation in a Ti50Ni48Fe2 alloy.18,19) This result means that the crystal structure of the sample changes from the R phase to the I phase during heating, being consistent with the results from ER, DSC, and XRD measurements. It is seen that a cluster-like structure, which is similar to that of the R phase at T = 87 K, remains at T = 183 K in the I phase, as shown in Fig. 10(l), although the microstructure shows an image drift due to instability in the temperature control of the TEM cooling holder. By the similarity in the cluster-like structure between the I and R phases, it is deduced that the cluster regions in the I phase directly transform to the R phase, i.e., the I/R transition occurs in the only limited volume, but not the whole sample. The facts that the entropy change in the transition from the B2/R to I/R drastically decreases as shown in Fig. 6 seem to support this hypothesis. While we have performed no TEM observation, a similar transformation behavior is also expected for x = 0.45 and 0.50 samples showing the I/R transformation.
The temperature dependence of the positions of the 1/3 011B2 spot along the ⟨011⟩B2 direction for x = 0.00, 0.35, and 0.40 alloys is plotted in Fig. 11. For x = 0.00 and 0.35 alloys at T = 87 K, the position of the spot is almost exactly at ζ = 0.333, which is the feature of R phase. For x = 0.35 at 233 K, the position of the peak deviates from 0.333, which is the feature of IC phase. These results are in good agreement with previous studies in Ti–Ni–Fe alloys, where the value of ζ approaches 1/3 position with decreasing temperature and finally locks into the ζ = 1/3 position.15,17,18) For the x = 0.40 alloy, however, a different behavior was found. The position of the spot shows a value lower than 0.290 when the temperatures is 193 K, which is close to the B2/I transition temperatures. As the temperature decreases, this value suddenly rises up to about ζ = 0.309 at T = 183 K and then slightly increases to about ζ = 0.313 at T = 77 K but never reaches 1/3. Current authors provide two hypotheses why ζ = 1/3 was not obtained for the x = 0.40 alloy.
It is seen from TEM micrographs (Fig. 10(i)) that the microstructure, i.e., cluster-like feature, of R phase is strongly affected by the I phase transformation. One hypothesis for this phenomenon is that, only the cluster-like region of I phase transformed to R phase. As a result, at low temperatures, the cluster-like R phase (ζ = 1/3) with fine microstructure is surrounded by IC phase, which has the feature of ζ < 1/3. Moreover, the mixture of R and IC phases may have a gradual distribution of ζ, thus a ζ smaller than 1/3 as a whole was experimentally observed for the mixture. Another hypothesis is that the low-temperature phase for the x ≥ 0.40 alloys is actually not the R phase. It is true that being same to the R phase transformation, this transformation is also of the first order, as clearly seen by the thermal hysteresis in the electrical resistivity measurements (Fig. 3). However, with a variation of alloy composition, not only the transformation temperature (Fig. 5), but also the ΔS (Fig. 6) shows clear steps at the composition of x = 0.40. One can assume this transformation has a lower transformation strain than that of R phase, where a similar discussion has been carried out to distinguish the R and I phases by Choi et al.15) However, the current experimental results are not adequate to draw a final conclusion on this discussion, and thus further investigations are required to clarify this problem.
