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[Kodai Niitsu](https://orcid.org/0000-0002-0430-8868), Ryosuke Kainuma

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[Experimental determination of equilibrium stress in stress-induced martensitic transformation at low temperatures in Ni-rich TiNi](https://mdr.nims.go.jp/datasets/56e134e9-202d-442c-8976-2658f6603c7d)

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Experimental determination of equilibrium stress in stress-induced martensitic transformation at low temperatures in Ni-rich TiNiViewOnlineExportCitationRESEARCH ARTICLE |  DECEMBER 19 2025Experimental determination of equilibrium stress in stress-induced martensitic transformation at low temperatures inNi-rich TiNiKodai Niitsu   ; Ryosuke Kainuma Appl. Phys. Lett. 127, 241903 (2025)https://doi.org/10.1063/5.0301524Articles You May Be Interested InExtension of the iSoLF implicit-solvent coarse-grained model for multicomponent lipid bilayersJ. Chem. Phys. (August 2023) 22 December 2025 00:50:28https://pubs.aip.org/aip/apl/article/127/24/241903/3375272/Experimental-determination-of-equilibrium-stresshttps://pubs.aip.org/aip/apl/article/127/24/241903/3375272/Experimental-determination-of-equilibrium-stress?pdfCoverIconEvent=citejavascript:;https://orcid.org/0000-0002-0430-8868javascript:;https://orcid.org/0000-0003-0713-6106https://crossmark.crossref.org/dialog/?doi=10.1063/5.0301524&domain=pdf&date_stamp=2025-12-19https://doi.org/10.1063/5.0301524https://pubs.aip.org/aip/jcp/article/159/7/075101/2906650/Extension-of-the-iSoLF-implicit-solvent-coarsehttps://servedbyadbutler.com/redirect.spark?MID=188841&plid=3385069&setID=1044459&channelID=0&CID=1622678&banID=524192615&PID=0&textadID=0&tc=1&rnd=5622121246&scheduleID=3549797&adSize=1640x440&data_keys=%7B%22%22%3A%22%22%7D&metadata=%5B%5D&mt=1766364628155764&spr=1&referrer=http%3A%2F%2Fpubs.aip.org%2Faip%2Fapl%2Farticle-pdf%2Fdoi%2F10.1063%2F5.0301524%2F20844094%2F241903_1_5.0301524.pdf&request_uuid=9bf0fa53-3fb0-4965-8808-3bd36dc21cb4&hc=a76130812f1f94aa763c9ed99dc257fb1739c050&location=Experimental determination of equilibrium stressin stress-induced martensitic transformationat low temperatures in Ni-rich TiNiCite as: Appl. Phys. Lett. 127, 241903 (2025); doi: 10.1063/5.0301524Submitted: 9 September 2025 . Accepted: 4 December 2025 .Published Online: 19 December 2025Kodai Niitsu1,a) and Ryosuke Kainuma2AFFILIATIONS1Center for Basic Research on Materials, National Institute for Materials Science (NIMS), Tsukuba, Ibaraki 305-0047, Japan2Department of Materials Science, Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japana)Author to whom correspondence should be addressed: NIITSU.Kodai@nims.go.jp. Tel.: þ81-29-859-2566ABSTRACTThe exceptional broadening of superelastic stress hysteresis at low temperatures in Ni-rich Ti–Ni shape-memory alloys impedes their cryo-genic applications. This broadening arises from thermally activated habit plane glide. Traditionally, equilibrium stress has been assumed tolie at the midpoint between forward and reverse martensitic transformation (MT) stresses, assuming reciprocal kinetics. Here, we assess thisassumption using strain-rate jump tests, a simple method that detects the magnitude of stress change in response to strain-rate variation. Theobserved stress change is consistently larger during the forward MT than the reverse MT, indicating an asymmetric thermal activation and ashift in equilibrium stress toward the reverse MT stress. This result deviates from the classical midpoint approximation in systems with signif-icant hysteresis broadening. Strain-rate jump test is demonstrated to be a simple yet effective method for locating the equilibrium stress, evenwhen it is bracketed deep within a broadened stress hysteresis.VC 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0301524Shape-memory alloys (SMAs) are a class of alloys that undergo adiffusionless solid–solid phase transformation known as martensitictransformation (MT). Their hallmark functionalities—the shape-memory effect and superelasticity—have long attracted significant atten-tion in the field of materials science and engineering.1,2 Among them,Nitinol, a Ti–Ni-based alloy has served as a benchmark SMA owing toits good cold-workability and prominent fatigue resistance, enabling itswidespread application at temperatures above ambient.3–8 At low tem-peratures, however, these functionalities become difficult to operate dueto the pronounced broadening of the transformation hysteresis.9 Thishysteresis broadening originates from the thermally activated glide ofhabit planes.10 A kinetic description of thermally activated habit planeglide extensively explains the viscous nature of low-temperature MTs,11which is manifested as the isothermal MT,12–14 the kinetic arrest,15 thestrain glass behavior (vanishingMT),16 and the broken ergodicity.17The extent to which the low-temperature MT dynamics is gov-erned by thermal activation is material-dependent. A characteristicmeasure is the 0K-extrapolated thermal activation component of thestress hysteresis, which informs the intrinsic barrier associated withthermal activation. Reported values vary widely across alloy systems:747–1074MPa in a Ni-rich Ti–Ni,9–11 628MPa in a Ti–Ni–Cu,18�1150MPa in a nanocrystalline Ti–Ni–Fe,19 �480MPa in a Ti–Al–Cr,20 125MPa in a Co–Cr–Al–Si,21 110MPa in a Ni–Co–Mn–In,22and �0MPa in a Cu–Al–Mn23 and a Fe–Mn–Al–Cr–Ni.24 Amongthese, Ni-rich Ti–Ni exhibits exceptionally significant thermal activa-tion, making its low-temperature operation particularly challenging.To uncover the nature of this pronounced thermal activation in thissystem, it is essential to decompose the total hysteresis into its compo-nents to drive the habit plane forward and backward—in other words,to determine the equilibrium stress.A widely used approximation assumes that thermodynamic equi-librium is achieved at the midpoint between the start temperature of theforward MT (TM) and the finish temperature of the reverse MT (TA).25This approximation has been extended to other external variables—stress, magnetic field, and composition—and is often treated as self-evident. However, are these approximations truly valid—and if so, towhat extent? This question may appear trivial at temperatures above theambient temperature, where the thermally activated nature of the MT isfully diminished and vibrational entropy shows little temperaturedependence. At lower temperatures, however, where the thermal activa-tion becomes pronounced and vibrational entropy notably depends ontemperature, the validity of such approximationsmay warrant scrutiny.Appl. Phys. Lett. 127, 241903 (2025); doi: 10.1063/5.0301524 127, 241903-1VC Author(s) 2025Applied Physics Letters ARTICLE pubs.aip.org/aip/apl 22 December 2025 00:50:28https://doi.org/10.1063/5.0301524https://doi.org/10.1063/5.0301524https://www.pubs.aip.org/action/showCitFormats?type=show&doi=10.1063/5.0301524http://crossmark.crossref.org/dialog/?doi=10.1063/5.0301524&domain=pdf&date_stamp=2025-12-19https://orcid.org/0000-0002-0430-8868https://orcid.org/0000-0003-0713-6106mailto:NIITSU.Kodai@nims.go.jphttps://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://doi.org/10.1063/5.0301524pubs.aip.org/aip/aplIndeed, this concern has been examined for the case of metamag-netic (magnetic field-induced) MTs in a Ni–Co–Mn–In alloy,26 reveal-ing that the equilibrium magnetic field is biased toward the fieldrequired to complete the reverse MT. This suggests that the thermalactivation nature is more pronounced in the forward MT than inthe reverse MT. A similar trend has also been confirmed in asystem exhibiting a magnetic field-induced first-order ferrimagnetic–antiferromagnetic transformation with substantial hysteresis broaden-ing.27 In these studies, the equilibrium magnetic field was estimated bymeasuring the specific heat under different static magnetic fields, whilethe critical fields for the forward and reverse transformations weredetermined by sweeping the field. This approach requires the stabiliza-tion of single-phase states of both competing phases within the tem-perature window of interest; thus, specific heat measurements areperformed under different static magnetic fields. For stress-inducedMTs, however, this approach is not feasible as performing specific heatmeasurements under uniaxial stress remains technically challenging.To locate the equilibrium stress bracketed by the stress hysteresis,we performed a strain-rate jump test. This technique is commonlyemployed to evaluate the activation volume associated with dislocationglide during plastic deformation. In this sense, the change in superelas-tic flow stress in response to a strain-rate jump is a direct measure ofthe manifestation of thermally activated habit plane glides. Even better,this method allows simultaneous extraction of the equilibrium stressand the critical stresses for starting/finishing the forward/reverse MTswith a single test. Applying this method to a benchmark Ni-richTi–Ni, an essential difference in the thermal activation characteristicsof the forward and reverse MTs can be disclosed.A Ti–51.7Ni (at.%) alloy was fabricated by arc melting. At thiscomposition, thermally induced MT is completely suppressed in theabsence of external stress.9 The as-cast polycrystalline button washomogenized at 1173K for 24 h, followed by quenching in water. A2.5� 2.5� 7.0-mm specimen was cut from the button for mechanicaltesting. The specimen is polycrystalline with an average radius of approx-imately 18lm containing small amounts of intergranular Ti4Ni2O inclu-sions, the microstructure of which is presented in the supplementarymaterial, Sec. S1. Compression tests were conducted over the tempera-ture range of 20–180K and strain rates ranging from 1.2� 10�6 to5.0� 10�2 s�1. Strain-rate jump tests were performed between5.0� 10�4 and 5.0� 10�5 s�1 at a strain interval of approximately0.3%–0.4%. It has been confirmed that a steady state is reached withinseveral seconds (< 0.1% in strain) after the strain rate changes. It isimportant to note that these strain rates were selected to obtain an appar-ent response of flow stress while sufficiently reducing any thermal effects.According to our previous study,10 it is recommended that strain-ratetests be performed in the range of 10�6–10�3 s�1. Strain was recordedby an extensometer attached to the compression jigs, with a samplingrate of 1000Hz. We note that all mechanical tests were conducted on asingle specimen. Functional fatigue of superelasticity28 tested on anotherrectangular specimen is presented in the supplementary material, Sec.S2. The overall change in critical stresses during the successive 11 cycles,which is required for obtaining the temperature-variable stress–straincurves, does not exceed 25MPa, which is small enough compared to theintrinsic temperature dependence of the critical stresses.Figure 1(a) presents the stress–strain curves obtained from thestrain-rate jump tests. Strain-rate jumps were repeatedly appliedFIG. 1. Superelastic behaviors at various temperatures and strain rates. (a) Stress–strain curves obtained from strain-rate jump tests. The strain rate was initially set at5.0� 10�4 s�1 and intermittently reduced to 5.0� 10�5 s�1 during both the forward and reverse superelastic flow (see inset). (b) Stress–strain curves obtained at constantstrain rates ranging from 1.2� 10–6 to 5.0� 10–2 s�1 at 80 K. (c) and (d) Stress–VM (martensite volume fraction) relationships converted from the data in (a) and (b),respectively.Applied Physics Letters ARTICLE pubs.aip.org/aip/aplAppl. Phys. Lett. 127, 241903 (2025); doi: 10.1063/5.0301524 127, 241903-2VC Author(s) 2025 22 December 2025 00:50:28https://doi.org/10.60893/figshare.apl.c.8184881https://doi.org/10.60893/figshare.apl.c.8184881https://doi.org/10.60893/figshare.apl.c.8184881pubs.aip.org/aip/aplduring both the forward and reverse superelastic flow, as highlightedin the inset of Fig. 1(a). This test was carried out sequentially from180K down to lower temperatures. Note that the residual, unrecoveredsuperelastic strain, which becomes pronounced below 80K due to hys-teresis broadening, was fully recovered by subsequent annealing above100K. The hysteresis broadening with decreasing temperature is astraightforward manifestation of the thermally activated nature ofhabit plane glide. As shown in the inset of Fig. 1(a), the change (inabsolute value) in forward superelastic flow stress, DrFWD, in responseto the strain-rate change from 5.0� 10�4 to 5.0� 10�5 s�1 is down-ward, which follows the same trend typically observed in dislocationglides; but the counterpart in the reverse flow, DrREV, is upward.As elucidated in our previous studies, the thermal activation ofhabit plane glide is manifested not only in the temperature dependenceof stress hysteresis but also in the strain-rate dependence of stress hys-teresis10 and the isothermal development of the forward and reverseMTs.11 At 80K, compression tests were performed at various constantstrain rates, and the resulting stress–strain curves are presented inFig. 1(b). The forward and reverse superelastic flow stresses exhibitmonotonic trends with strain rate: the forward stress decreases, whilethe reverse stress increases with decreasing strain rate. These opposingtrends persist throughout the tested strain-rate range; however, theirmagnitudes appear to differ. Although temperature fluctuations due tothe thermal effects should be taken into account at higher strain rates,the result sheds light on a potential inequivalence in the degree of ther-mal activation governing the forward and reverse habit plane glides.The magnitude of superelastic (anelastic) strain is a direct mea-sure of the volume fraction of transformed martensite VM.Nevertheless, the strain in the experimental stress–strain curve involvesthe superelastic strain as well as the elastic strain of the parent andmartensite phases, and thus conveys less information on the evolutionof MTs. The stress–strain curves in Figs. 1(a) and 1(b) were convertedto stress–VM curves, as shown in Figs. 1(c) and 1(d), respectively,where the details of this mathematical conversion are described in thesupplementary material, Sec. S3. The critical stresses rM/rA for start-ing/finishing the forward/reverse MTs are defined as the intercepts atVM¼ 0 of the linear extrapolations of the forward and reverse supere-lastic plateaus, as illustrated in Fig. 1(c). They are plotted in Fig. 3(c) asa function of temperature, the discussion of which will be given later.The results of strain-rate jump tests provide detailed insights intothe thermally activated dynamics of MTs. The values of DrFWD andDrREV, arbitrarily obtained at various levels of VM, are presented inthe bottom panels of Figs. 2(a) and 2(b), respectively. These values aredependent on VM, as well as temperature. In the case of dislocationglides, the magnitude of shear stress drop in response to a strain-ratejump depends on accumulated plastic strain, reflecting interactionsbetweenmoving dislocations and evolving substructures or themselves.Therein, in BCC metals, the stress drop typically increases withFIG. 2. Scalability of the stress changeamplitude DrFWD/REV. Top panels:Temperature-dependent profiles of dr/dVM during the forward (a) and reverse(b) strain flows. Bottom panels: Plots ofDrFWD (a) and DrREV (b) as a functionof VM, extracted from the strain-ratejump tests. dr/dVM are obtained from themathematically fitted r–VM curves (seeFig. S3). Rescaled plots of DrFWD (c) andDrREV (d) as a function of dr/dVM, show-ing linear correlations at respectivetemperatures.Applied Physics Letters ARTICLE pubs.aip.org/aip/aplAppl. Phys. Lett. 127, 241903 (2025); doi: 10.1063/5.0301524 127, 241903-3VC Author(s) 2025 22 December 2025 00:50:28https://doi.org/10.60893/figshare.apl.c.8184881pubs.aip.org/aip/aplincreasing plastic strain, which corresponds to a reduction in activationvolume due to dislocation forest hardening. In contrast, DrFWD andDrREV show non-monotonic variations with VM (analogous to thesuperelastic strain), reaching maxima near the point where thesuperelastic-hardening rate [identical to dr/dVM, see top panels of Figs.2(a) and 2(b)] reaches aminimum. This behavior suggests that themag-nitude of DrFWD and DrREV is uniquely scalable with the density ofmobile habit planes. This interpretation is plausible given that habitplanes do not intersect and the displacive atomic shear at the transfor-mation front is likely less influenced by interfacial interactions, unlikedislocations. The relationship between DrFWD/REV and dr/dVM is plot-ted in Figs. 2(c) and 2(d), showing linear correlation at eachtemperature.DrFWD and DrREV are now confirmed to scale with the densityof mobile habit planes. To be compared as a function of temperature,their extrapolated values at dr/dVM¼ 0, herein referred to as DrFWDoffand DrREVoff , were estimated via linear fits, as presented in Fig. 3(a).They reach maxima under conditions where the habit planes becomethermally mobile yet remain significantly arrested within the timescaleimposed by the given strain rate. Most importantly, DrREVoff is consis-tently smaller than DrFWDoff across the entire temperature range tested,and their peak temperatures differ. These findings highlight the differ-ent characteristics and magnitude of thermal activation processesinvolved in the forward and reverse MT pathways.To elucidate the different dynamics of the forward and reverseMTs, the overall hysteresis rhys was decomposed into effective compo-nents associated with eachMT pathway, rFWDeff and rREVeff , such thatrhys ¼ rFWDeff þ rREVeff : (1)They were further decomposed into athermal and isothermalterms such thatreff ¼ rl þ rTA 1� kBTDH0ln_e0_eSE� �� �1=q" #1=p; (2)where rl and rTA represent the athermal component and the 0K ther-mal activation offset for the overloading/underloading stressesrequired to drive the forward/reverse MTs, respectively; DH0 is theactivation enthalpy at 0K; kB is the Boltzmann constant; _e0 is a pre-exponential factor; _eSE is the superelastic strain rate; and p and q areadjustable parameters that shape the tail and top of the obstacle pro-file.10 The ranges of p and q are restricted to 0< p� 1 and 1� q� 2 toguarantee that the activation area increases continuously as the appliedstress decreases.29,30 Subscripts “FWD” and “REV” are omitted inEq. (2), but the parameters were independently determined for the for-ward and reverse MTs. Since DrFWD=REVoff is identical to the differencein rFWD=REVeff at _eSE¼ 5.0� 10�4 and 5.0� 10�5 s�1, the fitting toFIG. 3. Decomposition of transformationhysteresis and determination of equilib-rium stress. (a) Temperature dependenceof the extrapolated stress drop offsets,DrFWDoff and DrREVoff , derived from the datain Figs. 2(c) and 2(d). The solid curvesrepresent least squares fits using Eq. (2).(b) Temperature dependence of the effec-tive stresses for driving the forwardand reverse MTs, rFWDeff and rREVeff at_eSE ¼ 5.0� 10–5 s�1, derived usingEq. (2) with parameters tabulated in TableI. (c) Stress–temperature phase diagraminvolving equilibrium stress r0, forward/reverse MT starting/finishing stresses rM/rA,and their midpoint rmid. (d) Entropy changeDS estimated using r0 and rmid and fromspecific heat measurements.Applied Physics Letters ARTICLE pubs.aip.org/aip/aplAppl. Phys. Lett. 127, 241903 (2025); doi: 10.1063/5.0301524 127, 241903-4VC Author(s) 2025 22 December 2025 00:50:28pubs.aip.org/aip/aplDrFWD=REVoff plots can performed by least squares fitting using Eq. (2).The resultant fitting curves are presented in Fig. 3(a) and the values ofthe parameters used are listed in Table I.Using the derived parameters, rFWDeff and rREVeff can be indepen-dently exploited; as a representative example, their temperature func-tions at _eSE ¼ 5.0� 10�5 s�1 are shown in Fig. 3(b). This presentationclearly shows that the transformation hysteresis is shaped by the differ-ent magnitudes of thermal activation between the forward and reverseMTs. The thermal activation offset at 0K for the forward MT, rFWDTA , isapproximately 2.3 times greater than that of the reverse MT, rREVTA .Furthermore, the thermal activation persists up to a higher limitingtemperature for the forward MT, 270K [¼ DH0kBln _eSE_e0� �], compared to166K for the reverse MT. The athermal component rl was estimatedunder the assumption rlFWD¼ rlREV (� rl). Although this approxi-mation is not self-evident, it has been demonstrated to be reasonablebased on thermodynamic analysis in a Ni–Co–Mn–In metamagneticSMA.26Once all components of rhys are broken down, r0 can be deter-mined such that the following factor D is minimized:D ¼ rM � r0 þ rFWDeff�   �2 þ rA � r0 � rREVeff�   �2: (3)The resultant r0 values are plotted in Fig. 3(c), alongside rM, rA,and their midpoint rmid. The black curve represents a polynomial fitto the r0 plots. The blue and red curves correspond to r0 þ rFWDeff andr0 � rREVeff , respectively. They closely trace the experimental rM andrA plots, corroborating that the mathematical handling of the resultsof the strain-rate jump tests makes sense. The deviation of r0 fromrmid becomes pronounced, and r0 biases toward rA with decreasingtemperature. This trend is consistent with previous investigations of ametamagnetic MT in Ni–Co–Mn–In26 and a first-order ferrimagnetic-to-antiferromagnetic transition in (Fe0.95Zn0.05)2Mo3O8,27 both of whichexhibit substantial hysteresis broadening. We note that this biasing ena-bles better reproduction of the different isothermal dynamics observedbetween the forward and reverseMT pathways, as discussed in Ref. 11.A straightforward benefit of properly assessing r0 is that it ena-bles an accurate evaluation of entropy change DS, which can be calcu-lated by the Clausius–Clapeyron equation given by@r0@T¼ � DSeSEVm; (4)where eSE is the full superelastic strain (¼ 0.05511) and DS is generallyestimated using the traditional approximation rmid¼ r0. However, asshown in Fig. 3(d), this approximation is not reliable at lower tempera-tures, eventually resulting in a sign reversal of DS.9,31 This study is noexception, and DS derived using rmid reverses its sign below 50K.Alternatively, DS evaluated using r0 can better reproduce the DS curveobtained directly from specific heat measurements.31In the realm of MT dynamics driven by thermally activated pro-cesses, it is revealed that the transformation stress hysteresis is shapedby inequivalent magnitudes of excess stresses for forwarding andreverting habit planes. This result, in conjunction with previous find-ings,26,27 strongly suggests that a larger driving force is required for thetransforming interface to propagate into the high-temperature parentphase. The kinetic driving force is scaled by the non-chemical freeenergy, which is primarily dictated by interfacial energy. Among vari-ous contributions, the stored elastic energy is considered a dominantsource for the present case. According to Kocks et al.,30 the adjustableparameters, p and q, in Eq. (2) inform the glide resistance overobstacles. The smaller p value for the forward MT suggests that alonger-range glide resistance acts during the propagation of the habitplane into the parent B2 phase. A promising source of the glide resis-tance is the internal stress arising from lattice mismatch. Indeed, Jamesand co-workers have revealed that highly compatible lattice corre-spondences can dramatically reduce thermal hysteresis.32–34 However,this context is, we think, primarily valid for the athermal componentof hysteresis and insufficient to explain the inequivalent driving forces.The possible differences in the generation or annihilation processes oflong-range lattice defects (such as dislocations and stacking faults) inthe forward and reverse MTs may be the origin of the observed non-reciprocal thermal activation.The classical approximation for the thermodynamic equilibriumtemperature,25 T0 ¼ ðTM þ TAÞ=2, is reevaluated here based onFig. 3(c). TM and TA are defined as the temperatures intersecting therM and rA lines during cooling and heating, respectively, under agiven static stress. Under a high static stress (e.g., > 600MPa), whereboth TM and TA are largely athermal, the midpoint approximationholds reasonably. However, as the static stress decreases, the thermalactivation component becomes increasingly pronounced especially forthe forward MT, leading to a deviation of T0 from the midpoint. Mostnotably, there exists a stress range (approximately 200–450MPa) inwhich TM is not detectable, yet T0 remains well defined. This arisesfrom the pronounced time-dependent thermal activation. Hence, themidpoint approximation is only valid in regimes dominated by athe-rmal hysteresis. (Strictly speaking, differences in entropy changes atTM and TA disturb this approximation, even if fully athermal.) Thesame context can be applied to equilibrium stress, magnetic field, andcomposition, as the vertical axis of Fig. 3(c) can be converted analo-gously to magnetic field and composition.35To summarize, strain-rate jump tests were performed in thisstudy to locate the equilibrium stress for the stress-induced MTs in aNi-rich Ti–Ni alloy. Despite significant hysteresis broadening, theequilibrium stress could be determined and the assessed phase diagramreveals that the transformation hysteresis is shaped by different degreesof thermal activation between the forward and reverse MTs. The com-monly employed assumption that thermodynamic equilibrium lies atthe midpoint of the transformation hysteresis becomes increasinglyinvalid with lowering temperature. Our results indicate that the for-ward MT requires a greater kinetic driving force than the reverse MT,shedding light on the non-reciprocal propagation behavior of the habitplane.See the supplementary material for additional details on micro-structural characterization, cyclic fatigue of superelasticity, and themathematical conversion of stress–strain curves.TABLE I. Fitting parameters used in Eq. (2) for the forward and reverse MTs.rl(MPa)rTA(MPa)DH0(eV)_e0(s�1) p qForward MT 82 682 0.74 4.0� 1010 0.25 1.01Reverse MT 82 291 0.47 7.6� 1010 0.51 1.00Applied Physics Letters ARTICLE pubs.aip.org/aip/aplAppl. Phys. Lett. 127, 241903 (2025); doi: 10.1063/5.0301524 127, 241903-5VC Author(s) 2025 22 December 2025 00:50:28https://doi.org/10.60893/figshare.apl.c.8184881pubs.aip.org/aip/aplThe authors thank Dr. Oike and Dr. Suyama for helpfuldiscussions and technical assistance. This study was supported byJST PRESTO (Grant No. JPMJPR22Q6) and JSPS KAKENHI(Grant Nos. 23K04366 and 19H02418).AUTHOR DECLARATIONSConflict of InterestThe authors have no conflicts to disclose.Author ContributionsKodai Niitsu: Conceptualization (equal); Data curation (equal);Formal analysis (equal); Funding acquisition (equal); Investigation(equal); Methodology (equal); Project administration (equal);Resources (equal); Validation (equal); Visualization (equal); Writing –original draft (equal); Writing – review & editing (equal). RyosukeKainuma: Supervision (equal); Validation (equal); Writing – originaldraft (equal); Writing – review & editing (equal).DATA AVAILABILITYThe data that support the findings of this study are available fromthe corresponding author upon reasonable request.REFERENCES1V. Raghavan, Martensite (ASM International, Materials Park, OH, 1992).2K. Otsuka and C. M. Wayman, Shape Memory Materials (CambridgeUniversity Press, United Kingdom, 1998).3N. B. 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