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# Characteristics of martensitic and strain-glass transitions of the Fe-substituted TiNi shape memory alloys probed by transport and thermal measurements

## Abstract

The electrical resistivity, Seebeck coefficient, thermal conductivity, and specific heat of Ti50Ni50-x Fe x (x = 2.0–10.0 at.%) shape memory alloys (SMAs) were measured to investigate the influence of point defects (Fe) on the martensitic transformation characteristics. Our results show that the Ti50Ni48Fe2 and Ti50Ni47Fe3 SMAs have a two-step martensitic transformation (B2 → R and R → B19′), while the Ti50Ni46Fe4, Ti50Ni44.5Fe5.5, and Ti50Ni44Fe6 SMAs display a one-step martensitic transition (B2 → R). However, the compounds Ti50Ni42Fe8 and Ti50Ni40Fe10 show strain glass features (frozen strain-ordered state). Importantly, the induced point defects significantly alter the martensitic transformation characteristics, namely transition temperature and width of thermal hysteresis during the transition. This can be explained by the stabilization of austenite B2 phase upon Fe substitution, which ultimately leads to the decrease in enthalpy that associated to the martensitic transition. To determine the boundary composition that separates the R-phase and strain glass systems in this series of SMAs, a Ni-rich specimen Ti49Ni45Fe6 was fabricated. Remarkably, a slight change in Ti/Ni ratio converts Ti49Ni45Fe6 SMA into a strain glass system. Overall, the evolution of phase transformation in the Fe-substituted TiNi SMAs is presumably caused by the changes in local lattice structure via the induced local strain fields by Fe point defects.

## Introduction

The TiNi-based shape memory alloys (SMAs) are one of the most studied functional materials because they have superior properties such as thermal and mechanical memory1,2,3,4. For instance, an equiatomic TiNi (Ti50Ni50) alloy undergoes a first-order phase transition from the cubic austenite phase (B2) to a monoclinic martensite phase (B19′) during the cooling process. In general, the martensite state is defined as the long-range strain-ordered ferroelastic state below martensitic transition5. That is, the martensite state is analogous to the long-range ordering of electric dipoles and magnetic spins in ferroelectrics and ferromagnets, respectively6,7. It is well-established that the introduction of point defects plays an important role in modifying and controlling the properties of ferroelastics4,8. In addition to the two normal states of austenite (paraelastic) and martensite (ferroelastic), point defects in the SMAs can create two abnormal states such as precursor state and strain-glass state in the ferroelastic system9,10,11,12,13,14. These abnormal states are referred as the non-ideal strain states of ferroelastics13. Notably, the precursor state has been studied extensively in recent years10,11,12,13,14,15,16,17,18. This is because the precursor state is neither a fully disordered strain state like austenite nor a fully ordered strain state like martensite13,15,16. However, the precursor state is ergodic, although it is not a frozen glass state18. On the other hand, strain glass is known as a frozen-disordered strain state caused by fluctuations of randomly distributed point defects.

Typically, point defects are induced via alloying/substituting of equiatomic TiNi SMA with various elements including Fe, Co, Cr, Mn, Ni, and Cu4,11,12,13,19,20,21,22,23,24,25,26. All these substituents (except Cu) induce the R-martensite ordering into the TiNi SMA together with a complete suppression of martensite B19′ phase. Most importantly, the strain glass features emerge in these substituted SMAs when the substitution exceeds a critical concentration, x c . Particularly, the Co-substituted TiNi SMAs has a higher x c value (~9 at.%) than that of other substituted SMAs (≤6 at.%). The x c values are about 6.0, 4.5, and 5.5 at.% for the Fe-, Cr-, and Mn-substituted TiNi SMAs, respectively19,20,22,23,24. However, excess Ni content has a strong influence on the martensitic transformation features of Ti50-x Ni50+x SMA, as the martensitic transition remains intact for x < 1.3 and the martensitic transition is suppressed for x ≥1.323,26. In our earlier works27,28, we showed that low-T aging/annealing also results in a significant change in the martensitic transformation features of Ti48.7Ni51.3 SMA. That is, the strain glass order in as-quenched Ti48.7Ni51.3 is transformed to the R-martensite order by the aging process27. This is mainly due to the local lattice deformations which induced by the aging created Ti3Ni4 precipitates. Interestingly, the element Cu has a unique nature that it can be substituted for Ni up to 30 at.% and still exhibits shape memory effects24,25. Recently, Frenzel et al.24 observed a linear variation of martensitic transition temperature (M s ) in the Ti50Ni45Cu5 SMA with a small variation in Ni content. This work confirmed that the stoichiometry of Ni atoms also plays a key role in the martensitic transformation of the substituted TiNi SMAs4,23,24,26.

Among the third element substituted TiNi systems, the Fe-substituted TiNi (Ti50Ni50-x Fe x ) SMAs are extremely interesting materials for fundamental and applied research4,11,12,13,14,15,19,20,23,25. Remarkably, a generic phase diagram using the data of the Ti50Ni50-x Fe x SMAs has been proposed to describe the relationships among all strain states in ferroelastics13,20. That is, the Ti50Ni50-x Fe x SMAs have a two-step martensitic transformation (B2 → R and R → B19′) below x = 3.0, while a one-step R-phase transformation (B2 → R) is observed for 3.0 ≤ x ≤ 5.0. For x ≥ 6.0, strain glass features emerge13,20. A recent calculation by Niu and Geng using the density functional theory showed that the substitution of Fe into the TiNi lattice induces anti-precursor effects29. This is because the Fe atom triggers a drastic atomic-scale local lattice distortion, which leads to the intermediate structure between the B2 and R phases. As a result, the formation of precipitates is unlikely in the Ti50Ni1-x Fe x SMAs29.

Moreover, a study by Wang et al.30 revealed that the non-martensitic Ti48.5Ni51.5 alloy (which goes through the strain glass transition) has both shape memory effect and superelasticity. These effects have developed primarily due to the stress-induced transformation from a short-range strain-state to a long-range strain-ordered martensite and vice versa. Therefore, it will be very informative to carry out a thorough study on the transport and thermal properties of the Fe-substituted TiNi SMAs, Ti50Ni50-x Fe x . In particular, the highly sensitive Seebeck coefficient and thermal conductivity measurements on the Ti50Ni50-x Fe x SMAs will be crucial to explore their thermal transport properties, which have not yet been fully explored. In this respect, we recently reported the electrical and thermal transport properties of the Ti50Ni48.5Fe1.5 and Ti50Ni46Fe4 SMAs27,31. From these studies, it was shown that both the Fermi energy (E F ) and the density of states (DOS) of TiNi SMAs vary considerably with the Fe concentration (x). In addition, the phonon-electron coupling is noticeably weakened by Fe substitution, which leads to the change in the transformation features of these SMAs27,31.

With the background of these earlier works, we performed a comprehensive study on the transport and thermal properties of the Ti50Ni50-x Fe x (x = 2.0–10.0) SMAs to investigate the impact of Fe substitution on the characteristics of martensitic transformation in TiNi SMA. In the study, we observed that the Ti50Ni48Fe2 and Ti50Ni47Fe3 SMAs display a two-step martensitic transformation (B2 → R and R → B19′), while the Ti50Ni50-x Fe x SMAs with x = 4.0–6.0 have a one-step transition (B2 → R). However, the characteristics of strain glass transition are seen for the Ti50Ni42Fe8 and Ti50Ni40Fe10 SMAs. Most importantly, we decisively confirm that Ti50Ni44Fe6 is the boundary composition for the studied Ti50Ni50-x Fe x SMAs, which dividing the martensite (x ≤ 6.0) and strain glass (x > 6.0) state SMAs. Here, a careful comparison of the crossover composition SMA Ti50Ni44Fe6 with a slightly Ni-rich alloy Ti49Ni45Fe6 was made. Markedly, a small amount of excess Ni transforms the martensitic R-phase transition in Ti50Ni44Fe6 to a strain glass transition in Ti49Ni45Fe6. Such an observation suggests that the excess Ni atoms are likely occupying (as antisite defects) the vacancy sites of Ti atoms, as in the case of Ni-rich Ti50-x Ni50+x SMAs.

## Results

### Electrical resistivity

Figure 1 displays the normalized electrical resistivity, ρ(T)/ρ 293K versus temperature for the Ti50Ni50-x Fe x (x = 2.0–10.0) SMAs, which measured during the warming cycle. It is noted that the Ti50Ni48Fe2 and Ti50Ni47Fe3 SMAs showed a two-step martensitic transformation19,32. Especially, the Ti50Ni47Fe3 SMA has a noticeable thermal hysteresis temperature (ΔT H ) of about 15 K and 45 K for the transitions B2 → R and R → B19′, respectively (see inset of Fig. 1). In contrast, the Ti50Ni46Fe4 and Ti50Ni44.5Fe5.5 SMAs displayed a one-step R-phase martensitic transition (B2 → R) with a much smaller ΔT H value of less than 6 K, while ΔT H is negligible (less than 1 K) for Ti50Ni44Fe6. This observation is in agreement with the literature that the one-step R-phase transition in the TiNi-based SMAs has a less pronounced thermal hysteretic behavior than that of the two-step one27. However, the Ti50Ni50-x Fe x SMAs with x > 6 (Ti50Ni42Fe8 and Ti50Ni40Fe10) show the features of strain glass (short-range strain order)19,20.

Using the resistivity data, the characteristic temperatures such as the martensitic start temperature M s and the T min (the temperature at which the resistivity minimum occurs) of the strain glass compounds are obtained and listed in Table 1. These data showed that the characteristic temperature decreases with an increasing Fe content (x), which is consistent with the literature19,20. In particular, the M s value decreases considerably with x > 3.0. In addition, the transformation width (ΔT) of the B2 → R transition is estimated to be above 70 K for x > 3.0 (Table 1), much larger than the Ti50Ni48Fe2 and Ti50Ni47Fe3 SMAs (<30 K). The pronounced change in characteristic temperature and transformation width with Fe substitution (x > 3.0) can be clearly seen in the inset of Fig. 1. Such a finding demonstrates that the Fe substitution into the Ni sites of TiNi SMA has a strong influence on the characteristics of martensitic transformation when the substitution level is beyond x = 3.024.

Upon Fe substitution, the value of ρ 293K decreases substantially above x = 3.0. For example, the ρ 293K value decreases to <90 μΩ cm (for x ≥ 4.0) from about 147 μΩ cm of Ti50Ni47Fe3. However, it becomes nearly constant above x = 6.0, i.e. their ρ 293K values lie in the range of 67.0–70.0 μΩ cm. However, the low-T resistivity (ρ 10K) increases with Fe content up to x = 8.0 and then it decreases for x = 10.0. Surprisingly, the Ti50Ni40Fe10 SMA displays a positive temperature coefficient of resistivity below 30 K, which shown by an arrow in Fig. 1. This feature of Ti50Ni40Fe10 may be attributed to the induced metallic character by heavy Fe substitution. This will be further examined using the highly sensitive Seebeck coefficient, which presented in the Seebeck coefficient section.

We also investigated the Ni-rich Fe-substituted SMA Ti49Ni45Fe6 to explore the influence of excess Ni on the boundary composition (x = 6) of the Ti50Ni50-x Fe x system19,20. In fact, Wang et al. showed the existence of strain glass beyond a critical content of 5.0 < x c  < 6.020. Here, we plotted the resistivity data of Ti49Ni45Fe6 SMA together with the Ti50Ni44Fe6 SMAs in Fig. 2 to a compare the nature of their strain state ordering. Evidently, a slight excess Ni (about 1 at.%) in Ti49Ni45Fe6 SMA has transformed the system to a short-range strain ordering from the long-range R-martensite ordering of the Ti50Ni44Fe6 SMA. This observation reveals that the Ni/Ti ratio also plays a key role in determining the critical content, x c . Interestingly, the studied strain glass alloys (Ti49Ni45Fe6, Ti50Ni42Fe8, and Ti50Ni40Fe10) in the present work have a positive and negative temperature coefficient of resistivity at high and low temperatures (see Figs 1 and 2), respectively. However, this observation is distinct from the positive temperature coefficient behavior over the entire temperature range of 10–300 K for the Ni-rich Ti50-x Ni50+x (x ≥ 1.3) SMAs26. Besides, we estimated the inflection point (T 0) using the ρ(T) data for two strain glass samples Ti50Ni40Fe10 and Ti49Ni45Fe6 of the present work and their T 0 values are about 92 and 124 K, respectively. This finding indicates that the strain-glass transition temperature of these Fe-substituted TiNi SMAs is much lower than the Ni-rich SMAs Ti48.7Ni51.3 and Ti48.4Ni51.6 (>175 K)26. In order to further explore the martensitic transformation features of these Fe-substituted TiNi SMAs, we carried out the Seebeck coefficient measurement (see Figs 3 and 4). The Seebeck coefficient is a highly sensitive probe for the phenomenon that involves the changes in Fermi level DOS such as the phase transition. Recently, Kustov et al.33 revealed that the estimation of the exact value of martensitic temperatures (M S ) using the resistivity data is rather difficult, due to the anelastic effects during the heating and cooling cycles. Hence, the Seebeck coefficient measurement may provide an alternative way to determine M S with better accuracy.

### Seebeck coefficient

The temperature-dependent Seebeck coefficient S(T) of Ti50Ni50-x Fe x (x = 2.0–6.0) SMAs is presented in Fig. 3. It is observed that Ti50Ni48Fe2 and Ti50Ni47Fe3 SMAs display a pronounced two-step martensitic transformation above 250 K with a noticeable thermal hysteresis (Fig. 3a). Whereas, a step-like feature or a slope change was observed below 250 K for the Ti50Ni50-x Fe x SMAs with x = 4.0–6.0 (Fig. 3b), which is associated to the R → B2 transition. Notably, the transition temperature M s decreases noticeably with Fe content above x = 3.0 (Table 1). These observations are consistent with the resistivity data. However, we noticed that the estimated M s values for these SMAs from the S(T) data are lower than the values that deduced from the resistivity data. This finding suggests that the transition temperature (M s ) of these SMAs in the resistivity data is slightly shifted to a higher temperature than its actual value. This is presumably due to the structural anelasticity of the TiNi-based SMAs during the thermal cycles33. In addition, the Seebeck coefficient measurement is not as sensitive to the grain boundaries and defects as the resistivity measurement26. Thus, we argue that the Seebeck coefficient measurement is a more reliable probe for the evaluation of the martensitic temperatures of the TiNi-based SMAs.

Conversely, no noticeable anomalous features can be detected in the S(T) data for the samples Ti49Ni45Fe6, Ti50Ni42Fe8, and Ti50Ni40Fe10 (Fig. 4), similar to the behavior of the Ni-rich Ti48.7Ni51.3 and Ti48.4Ni51.6 SMAs26. In addition, all the samples show positive S values over the entire temperature range, indicating that the dominant charge carriers are holes (p-type carriers) in the Ti50Ni50-x Fe x systems. It is worth mentioning here that the excess Fe point defects alter the strain state of Ti50Ni42Fe8 and Ti50Ni40Fe10 alloys to short-range strain (strain-glass) state from the R-martensite state of Ti50Ni44Fe6 SMA, while the excess Ni atoms at Ti-sites induce the strain glass ordering in the Ni-rich alloy Ti49Ni45Fe6 from that of same SMA Ti50Ni44Fe6.

Below the transition temperature, the S(T) data of the Ti50Ni50-x Fe x SMAs show a typical metallic diffusive behavior. Particularly, a hump-like feature below 40 K was observed as a result of the phonon-drag effect (indicated by the arrows in Figs 3 and 4)25,26,27. At high temperatures above the transition, the measured S(T) varies rather linearly with temperature. This is generally observed for the TiNi-based SMAs with the diffusive thermoelectric transport25,26,27,31. That is, the linear variation of S with temperature is expected for metals according to Mott’s formula, $$S=\frac{{\pi }^{2}{k}_{B}^{2}}{2e{E}_{F}}T=bT$$, where k B is the Boltzmann constant and E F is the Fermi energy. The linear fits to the high-T S(T) data of the Ti50Ni50-x Fe x SMAs using Mott’s equation are illustrated as solid lines in Figs 3 and 4, and the deduced E F values are given in Table 1. We found a significant decrease in the E F value from Ti50Ni47Fe3 to Ti50Ni46Fe4, possibly due to the different type of transition which may alter the DOS near Fermi level. In addition, the E F value increases substantially with x > 6.0 as the samples enter the strain glass state. This may also relate to the change of the transition nature together with a higher content Fe substitution. In general, the point defect (Fe) induces a noticeable change in the E F and the Fermi level DOS of TiNi SMA25,26,27. Hence, the characteristics of martensitic transformation in TiNi SMA are altered considerably with Fe substitution (see Table 1). Besides, the Ni-rich Ti49Ni45Fe6 has a comparable E F value (2.4 eV) to that of Ti50Ni44Fe6 (E F  2.3 eV), although they show different types of transition at low temperatures. Such a behavior indicates that there could be other factors such as Ni antisite defects also affecting the DOS near Fermi level in the Fe-substituted TiNi SMAs, which warrants further investigation.

### Thermal conductivity

The thermal conductivity κ(T) of the Ti50Ni50-x Fe x (x = 2.0–6.0) SMAs during the warming cycle is illustrated in Fig. 5. It is noted that Fe substitution induces a reduction in the RT thermal conductivity (κ RT 11.0–15.0 W/m K) as compared to parent Ti50Ni50 (κ RT 17.0 W/m K)26. The Ti50Ni50-x Fe x SMAs with x = 2.0–6.0 display a step-like feature near the martensitic transition27,32. However, the strength of the step-like feature diminishes progressively with increasing x. However, this feature is completely different from a spike-shaped anomaly in the Ti50Ni50 and Ti50Ni48.5Fe1.5 SMAs26,31. This finding validates that the electron-phonon coupling near the martensitic transition is weakened by Fe substitution in the TiNi SMAs with x ≥ 2.0 that we examined here. This is due to the induced local lattice distortions by Fe point defects in the TiNi lattice27. Whereas the Ti50Ni42Fe8, Ti50Ni40Fe10, and Ti49Ni45Fe6 alloys do not show any anomalous features in the measured κ(T) data (Fig. 6), similar to the behavior of the strain glass Ni-rich TiNi SMAs26.

It is well-known that thermal conductivity measurements can give valuable information about various scattering processes of thermal carriers that are involved in solids. Hence, it is important to probe the role of charge and phonon carriers on the heat conduction of the Ti50Ni50-x Fe x SMAs. For the metallic compounds, the total thermal conductivity can be divided into the electronic thermal conductivity (κ e ) and the lattice thermal conductivity (κ L ). The electronic thermal conductivity κ e (T) of the studied SMAs is estimated by using the Wiedemann-Franz law: κ e ρ/T = L 0, where L 0 (=2.45 ×10−8 WΩK−2) is the Lorenz number, and the results are shown as solid lines in Fig. 5. The lattice thermal conductivity κ L (T) is then obtained by subtracting the κ e (T) from the measured κ(T) (see the inset of Fig. 6 for representative samples). It is clear from this estimation that κ e contributes more than half of the total κ for all studied samples at high temperatures (especially in the B2 phase), similar to the behavior of Cu- and Ni-substituted TiNi SMAs25,26,27. For instance, the contribution of κ e to total κ at 293 K increases considerably from less than 50% of the Ti50Ni47Fe3 SMA to larger than 60% for x ≥ 4.0 (Figs 5 and 6). Particularly, the κ e donates about 80.0% to total κ of the samples Ti50Ni42Fe8 and Ti50Ni40Fe10 at 293 K. This finding validates the complete weakening of the phonon-electron coupling in the TiNi-based SMA when Fe substituted beyond x = 6.0. Besides, two transitions (B2 → R and R → B19′) are clearly seen in the κ L (T) data of the Ti50Ni48Fe2 and Ti50Ni47Fe3 SMAs (see inset of Fig. 6). Remarkably, it is clearly seen in the inset of Fig. 6 that a slight increase of Fe content from x = 3.0 to x = 4.0 leads to a significant change in the martensitic transformation from a two-step transformation to a one-step transition (B2 → R).

It is obvious that the observed R-phase transition in the Ti50Ni44Fe6 SMA is mainly due to electronic contribution, as the slope change near the transition is much pronounced in the κ e (T) data than its κ L (T). However, the sample Ti49Ni45Fe6 does not show the noticeable anomalous feature in κ, presumably due to the excess Ni atoms that occupy the vacancy Ti sites as antisite defects26. Overall, a gradual weakening of electron-phonon coupling of the TiNi SMA occurs upon Fe substitution until x = 6.0, and finally, the coupling disappears completely beyond x = 6.0. Hence, no anomalous features are seen for the Ti50Ni50-x Fe x SMAs with x > 6.0. In addition, the introduction of a slight excess Ni into the Ti sites in Ti50Ni44Fe6 also weakens the electron-phonon coupling drastically in the compound Ti49Ni45Fe6, as the R-phase transition in Ti50Ni44Fe6 is completely suppressed.

### Specific heat

Figure 7 displays the temperature-dependent specific heat C P (T) of the Ti50Ni50-x Fe x (x = 2.0–6.0) SMAs during the warming cycle. The Ti50Ni48Fe2, Ti50Ni47Fe3, and Ti50Ni46Fe4 SMA samples have sharp transition features near the martensitic transition27,31. However, it is noted that the magnitude of the peak decreases gradually with x > 3.019. The two-step transitions (B2 → R and R → B19′) are clearly visible for the Ti50Ni47Fe3 SMA, as seen in its κ L (T) data (see inset of Fig. 6). In contrast, the slightly Ni-rich sample Ti49Ni45Fe6 does not show any detectable anomalous features associated with the strain glass transition in the C P (T) when compared to the Ti50Ni44Fe6 SMA (Fig. 8).

The entropy change ΔS during the R-phase martensitic transition can be evaluated from the specific heat jump ΔC P . First, the ΔC P value was estimated after subtracting a smooth lattice background (illustrated as a solid line in Fig. 7). This was done by fitting the C P (T) data far from the transition region27. The entropy change for the Ti50Ni50-x Fe x SMAs with x = 2.0–6.0 was then evaluated by integrating ΔC P /T across the transition (see the inset (a) of Fig. 8), and the deduced ΔS values are listed in Table 1. From this estimation, it is found that the ΔS value during the R-phase transition decreases gradually with increasing Fe content above x = 3.019,26,27. Likewise, the enthalpy change, ΔH, across the R-phase transition for these SMAs also decreases with increasing x (Table 1). The ΔH values of these SMAs were obtained by using the differential scanning calorimetry data32. These findings can be attributed to the lowering of the enthalpy difference between the martensite and austenite phases with the change in composition, as well as the stabilization of the B2 structure24. Markedly, the transition temperature (M s ) of the R-phase SMAs (x = 4.0–6.0) decreases linearly with decreasing ΔH (the inset (b) of Fig. 8, see left vertical axis). Similarly, the width of thermal hysteresis ΔT H of these SMAs also decreases linearly with ΔH (the inset (b) of Fig. 8, see right vertical axis). These observations are likely owing to the austenite and martensite phases getting more and more similar with increasing Fe content in these R-phase SMAs, as the R-martensite will be formed with a lower nucleation barrier energy24. Accordingly, a smaller width of thermal hysteresis (less than 1 K) is observed for the Ti50Ni44Fe6 due to a lower driving force is required for the formation of R-martensite in this SMA.

## Discussion

Our present study confirms that the introduction of point defects (Fe) into TiNi SMA leads to the stabilization (destabilization) of the B2 (B19′) phase13. As a result, a decrease in the transition temperature was observed for the Ti50Ni50-x Fe x (x ≥ 2) SMAs when compared to parent TiNi (M s  295 K). This is essentially due to the fluctuations of concentration associated with the induced point defects13. In other words, the Fe atoms destabilize the martensite B19′ phase, which ultimately reduces the transition temperature (see Table 1). This is because of the alteration in the global thermodynamic stability of the B19′ phase by Fe substitution13. In addition, the Fe atom also affects the local transition temperature of TiNi and thus the transformation width is altered accordingly (Table 1). This is due to the Fe induced divergent stress field at different Ni sites, which affects the local transition temperature via the induced local lattice distortions13,29. This means that Fe atoms introduce local strain fields into the B2 matrix that stabilize the R-martensite phase34,35,36. Hence, the examined SMAs including Ti50Ni46Fe4, Ti50Ni44.5Fe5.5, and Ti50Ni44Fe6 overcome local barriers to form the R-martensite4,27. These observations can be attributed to two major factors suggested by Frenzel et al.24: i) the alloying-driven change in geometry (i.e., the changes in bonding as a result of alloying) and ii) the alloying-induced defects that stabilize the B2 phase.

From a microscopic point of view13, at low-content defect concentrations of 2.0 ≤ x < 6.0, the nanodomains of martensite (R and B19′) are initially formed as a result of randomly distributed point defects. They are then transformed into a long-range strain-ordered state below the transition temperature. At high defect concentrations of x > 6.0, the martensitic transformation is completely suppressed and the strain glass (frozen-disordered strain state) features appear instead20,29. This is due to the local field effects induced by point defects that create local lattice distortions in the host TiNi lattice. Interestingly, the local field effect promotes the freezing of local strain ordering by preventing the formation of long-range and ordered martensitic twins13. In other words, the volume fraction of macro-sized martensite in the TiNi SMA diminishes gradually with increasing Fe content14. Hence, a progressive change in the phase transformation and the corresponding physical properties of the TiNi SMA with Fe substitution was observed (see Figs 18).

Furthermore, our results show that the entropy change, ΔS, during the R-phase transition of the Ti50Ni50-x Fe x (x = 4.0–6.0) SMAs decreases with increasing x. This demonstrates that the transformation heat (proportional to ΔS) decreases with lowering transformation strain, according to the equation of Landau free energy (without applied stress)27,34: $$\Delta S=-A{e}_{M}^{2}$$. Here, A is the proportionality constant, e M is the transformation strain (or lattice distortion) at the transition temperature, and the minus sign indicates that the martensitic transformation always leads to a reduction in entropy. Generally, the induced point defects alter the local lattice structure of the TiNi SMA via induced local strain fields27,35. Thus, a noticeable entropy change of about ΔS < 1.4 J/mole K across the R-phase transition was observed for the Ti50Ni50-x Fe x SMAs with x = 4.0–6.0 (see Table 1)19,27. However, their value is much smaller than that of the B2 → B19′ transition in the Ti50Ni50 and Ti50Ni48.5Fe1.5 SMAs (>4.0 J/mole K)31. This is consistent with the observations in the literature4,27. Our present findings confirm that the Fe concentration has a major impact on the characteristics of the martensitic transformation in these Fe-substituted TiNi SMAs, and the observed features are analogous to those studies on the Ni-, Cu-, and Cr-substituted TiNi SMAs24,25,26.

Moreover, it is noticed that the κ L (T) of the Ti50Ni50-x Fe x SMAs with x = 2.0–6.0 do not follow the specific heat C P (T) behavior (the peak-shaped anomaly) across the martensitic transformation (see Figs 6 and 7). This means that the Fe-substituted TiNi SMAs do not obey the classical kinetic theory of lattice thermal conductivity (κ L  = C L νl) near the martensitic transition27,37. Here, C L ,ν, and l are the phonon specific heat, phonon drift velocity, and mean free path, respectively. Such an observation contradicts to the results found in the Ti50Ni50 and Ti50Ni48.5Fe1.5 SMAs that both samples show the peak-shaped anomalies in the C P (T) and κ L (T) across the B2 → B19′ transition31. This is most likely due to the absence of soft phonon modes in the Ti50Ni50-x Fe x system27,31. Such a finding is similar to the observations made in our recent work on the R-phase TiNi-based SMAs27. In conclusion, the Fe substitution induces a change in the crystal structure of the TiNi SMA which results in a gradual lessening of the difference between martensite and austenite lattices and hence the decrease in width of thermal hysteresis with increasing x is observed. In addition, the stabilization of B2 phase by Fe substitution is attributed to the variation in the electronic structure, which ultimately leads to the reduction in martensitic start temperature M s . Overall, the significant changes in martensitic transformation characteristics have emerged for TiNi SMA after Fe substitution. That is, the substituent concentration has a significant effect on the martensitic start temperature (M s ) and transformation width (ΔT) of the Ti50Ni50-x Fe x SMAs (Table 1), especially for the compounds with x > 3.0.

## Summary

The temperature-dependent thermal and transport properties of the Ti50Ni50-x Fe x (x = 2.0–10.0) SMAs were investigated by means of electrical resistivity, the Seebeck coefficient, thermal conductivity, and specific heat measurements. Our study revealed that the Ti50Ni48Fe2 and Ti50Ni47Fe3 SMAs undergo a two-step martensitic transition (B2 → R and R → B19′), which is distinct from a transition (B2 → B19′) that occurs in the parent TiNi. With further Fe substitution (4.0 ≤ x ≤ 6.0), a one-step B2 → R transition was observed for the Ti50Ni46Fe4, Ti50Ni44.5Fe5.5, and Ti50Ni44Fe6 SMAs, accompanied with a complete destabilization of the B19′ phase. The strain glass characteristics were seen for the alloys Ti50Ni42Fe8 and Ti50Ni40Fe10. These findings are essentially attributed to the induced change in the local lattice structure by Fe point defects. Most importantly, we decisively establish that Ti50Ni44Fe6 is the boundary composition SMA, which divides the martensite (x ≤ 6.0) and strain glass (x > 6.0) state compounds of the Ti50Ni50-x Fe x SMAs. This conclusion was validated by a careful comparison of the transition characteristics and physical properties between Ti50Ni44Fe6 and Ti49Ni45Fe6 SMAs. The variation in the characteristics of martensitic transformation in the TiNi SMA with Fe substitution (Ti50Ni50-x Fe x ) can be attributed to the induced local lattice deformations. This primarily resulted from the induced local strain fields by the Fe point defects. Most importantly, the transformation characteristics, such as martensitic start temperature (M s ) and width of thermal hysteresis (ΔT H ) decrease noticeably with increasing Fe content (x). Similarly, during the martensitic transition, both entropy change (ΔS) and enthalpy change (ΔH) were also found to decrease with Fe content. Remarkably, the M s and ΔT H values of the R-phase Ti50Ni50-x Fe x SMAs (4.0 ≤ x ≤ 6.0) decrease linearly with decreasing ΔH. Overall, the substituent concentration has a significant influence on the martensitic transformation characteristics of the Ti50Ni50-x Fe x SMAs, leading to a continuous evolution of phase transformation in the Fe-substituted TiNi SMAs.

## Methods

Samples of Ti50Ni50-x Fe x (x = 2.0–10.0 at.%) SMAs were fabricated using a vacuum arc re-melter, which described elsewhere32,33. Briefly, high-purity raw materials consisting of titanium (4 N), nickel (4 N), and iron (3 N) were melted six times using the re-melter to form ingots of the Ti50Ni50-x Fe x samples. Here, the weight loss for each ingot is less than 1 × 10−4. The ingots obtained were then hot-rolled individually at 1173 K into a plate with a thickness of about 2 mm using a commercial rolling machine (DBR150 × 200 2HI-MILL, Daito Seiki Co, Japan). Subsequently, the sample plates were solution heat-treated at 1173 K for 1 h, followed by water quenching to cool the samples to room temperature (RT). Finally, the surface oxide layer of the samples was removed using an etching solution of HF:HNO3:H2O (1:5:20 volumes). In addition, the Ni-rich Ti49Ni45Fe6 sample was prepared to explore the influence of excess Ni on the boundary composition (x ≤ 6.0) of the Ti50Ni50-x Fe x SMAs19,20.

For transport and thermal measurements, the sample plates were cut into a rectangular parallelepiped shape with dimensions of about 1.5 × 1.5 × 5.0 mm3 using a low-speed diamond cutter. The temperature-dependent electrical resistivity of the Ti50Ni50-x Fe x samples was measured using a standard four-probe method. The Seebeck coefficient and thermal conductivity measurements on the TiNi-based SMAs were carried out simultaneously in a closed-cycle refrigerator using a direct heat pulse technique. The specific heat data for these SMAs were obtained using a high-resolution ac calorimeter with chopped light as a heat source. More details about these measurement techniques can be obtained elsewhere25,26,27,28,38. The presented electrical and thermal measurement systems are all equipped with a calibrated silicon diode thermometer (Lake Shore model DT-470-SD) and all data presented in the manuscript were recorded with a slow heating rate of about 20 K/h and reproducibility better than 2%. The experimental errors in the temperature measurement, according to the manufactory specifications, are ±0.25 K from 2 to 100 K and ±0.50 K from 100 to 300 K.

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## Acknowledgements

Acknowledgement is made to the Ministry of Science and Technology (MOST) of Taiwan, for support of this research under Grant Nos MOST 103–2112-M-259–008-MY3 (YKK) and MOST 104–2221-E002–004, MOST 105–2221-E002–043-MY2 (SKW). SKW also acknowledges the support of this research from National Taiwan University (NTU) under the Grant Nos NTU103R891803 and NTU104R891803 (The NTU Excellence in Research Program).

## Author information

### Affiliations

1. #### Department of Physics, National Dong Hwa University, Hualien, 97401, Taiwan

• Balakrishnan Ramachandran
• , Pei-Chi Chang
•  & Yung-Kang Kuo
2. #### Department of Materials Science and Engineering, National Taiwan University, Taipei, 10617, Taiwan

• Chen Chien
•  & Shyi-Kaan Wu

### Contributions

Y.K.K. and S.K.W. initiated the project and designed the experiments. C.C. participated in the sample preparation and compositional characterization. P.C.C. carried out the transport and thermal measurements. B.R. compiled the data and drafted the manuscript. Y.K.K. and S.K.W. revised and edited the manuscript.

### Competing Interests

The authors declare that they have no competing interests.

### Corresponding author

Correspondence to Yung-Kang Kuo.