# In situ synchrotron X-ray diffraction analysis of two-way shape memory effect in Nitinol

Zifan Wang, Yunlan Zhang, Konstantinos Liogas, Jingwei Chen, Gavin B.M. Vaughan, Radim Kocich, Lenka Kunčická, Fatih Uzun, Zhong You, Alexander M. Korsunsky

► To cite this version:

Zifan Wang, Yunlan Zhang, Konstantinos Liogas, Jingwei Chen, Gavin B.M. Vaughan, et al. In situ synchrotron X-ray diffraction analysis of two-way shape memory effect in Nitinol. Materials Science and Engineering: A, 2023, 878, pp.145226. 10.1016/j.msea.2023.145226. hal-05095274

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# *In situ* synchrotron X-ray diffraction analysis of two-way shape memory effect in Nitinol

<figure><img src="image_2.png" /></figure>

Zifan Wang<sup>a, b, *</sup>, Yunlan Zhang<sup>b, c</sup>, Konstantinos Liogas<sup>b</sup>, Jingwei Chen<sup>b</sup>, Gavin B.M. Vaughan<sup>d</sup>, Radim Kocich<sup>e, f</sup>, Lenka Kunčická<sup>e</sup>, Fatih Uzun<sup>b</sup>, Zhong You<sup>b</sup>, Alexander M. Korsunsky<sup>b, **</sup>

## ARTICLE INFO

### Keywords:

Two-way shape memory effect

*In situ* synchrotron X-ray diffraction

Nitinol

Micromechanics

## ABSTRACT

Despite the fact that the Two-Way Shape Memory Effect (TWSME) has been demonstrated in most Shape Memory Alloys, the effective application of this unique functional behaviour is hindered by the lack of a proper training methodology and understanding of its mechanisms. In this study, a novel training routine has been established together with a home-designed device, enabling TWSME of customised spline curvature to be produced. An *in situ* high energy synchrotron X-ray diffraction experiment has been performed on Nitinol, followed by comprehensive analysis to reveal the micromechanics of TWSME. Multiple mainstream hypotheses have been examined. The important findings are: (1) The training process has negligible influence on the texture of parent phase; (2) The preferred variant of the B19' phase exhibits tension/compression asymmetry in TWSME; (3) (100) compound twin is the preferred deformation mode for compression TWSME; (4) The mesoscale residual strain field is the dominant factor that induces TWSME; (5) Lattice defects (dislocations) are spatially rearranged after training; (6) Compression TWSME training retards the B2 to B19' transformation, whilst tension has the opposite effect. The implications of these findings are further discussed.

## 1. Introduction and objectives

Shape Memory Alloys (SMAs), probably the most important category of Shape Memory Materials, have extensive applications in the medical, aerospace, and industrial sectors [1,2]. Two extensively utilised functional behaviours are the Shape Memory Effect [3] and Superelasticity [4], which originate from the reversible thermally activated phase transformation between high temperature austenite phase and low temperature martensite phase. The austenite phase is also known as the parent phase, and presents the original designated shape of the material. The martensite phase is a configurable state, and can be induced by low temperature (in Shape Memory Effect mode) or applied stress (in Superelasticity mode). The stress-induced martensitic phase transformation brings about macroscopic deformation of the material, whilst temperature-induced transformation does not due to the formation of

self-accommodated twinning [3].

Nevertheless, a specific thermomechanical process can be employed to endow SMAs with a novel functional behaviour called the Two-Way Shape Memory Effect (TWSME), namely, the material exhibits spontaneous shape change during martensitic phase transformation without any intervention of applied stress, and upon the reverse phase transformation to austenite by heating, it recovers its designated shape. In other words, the material can toggle between two shapes via only temperature control. This particular thermomechanical process is termed as TWSME training [5].

Widely discovered in many SMAs, however, TWSME is still not as well utilised as other functional behaviour due to the ambiguity in its driving mechanisms: why is the material able to memorize a unique shape instead of forming self-accommodated twins after TWSME training?

<footnote><sup>a</sup> Department of Engineering, University of Cambridge, Cambridge, CB2 1PZ, UK</footnote>

<footnote><sup>b</sup> Department of Engineering Science, University of Oxford, Oxford, OX1 3PJ, UK</footnote>

<footnote><sup>c</sup> Department of Civil, Architectural and Environmental Engineering, The University of Texas at Austin, Austin, 78712, USA</footnote>

<footnote><sup>d</sup> ESRF - the European Synchrotron, 71 avenue des Martyrs, CS40220, 38043, Grenoble, France</footnote>

<footnote><sup>e</sup> Faculty of Materials Science and Technology, VSB-Technical University of Ostrava, Ostrava 8, Czech Republic</footnote>

<footnote><sup>f</sup> Faculty of Mechanical Engineering, Brno University of Technology, Technická 2896/2, Brno 61669, Czech Republic</footnote>

<footnote>* Corresponding author. Department of Engineering, University of Cambridge, Cambridge, CB2 1PZ, UK.</footnote>

<footnote>** Corresponding author.
E-mail addresses: zw421@cam.ac.uk, zifan.w@outlook.com (Z. Wang), alexander.korsunsky@eng.ox.ac.uk (A.M. Korsunsky).</footnote>
Various mechanisms for the TWSME have been proposed. (1) Microscale residual stress fields around dislocation arrays [6] and Ni₄Ti₃ precipitates [5,7] that are rearranged during the training process induces the formation of preferred martensitic variants. (2) A macroscale residual stress field caused by plastic deformation causes the directional deformation during the cooling process [8]. (3) The increase in micro-strain (which is associated with lattice defect) during the training process is fundamental to improve the generation of TWSME [9]. (4) Certain martensite variants retained after the training process can assist the stability and efficacy of TWSME [10]. Despite the development of these theories, their corresponding experimental validation is rare and localised. Most evidences have been obtained by microscopy-based methods, such as TEM and SEM. The field of view of such methods is on the magnitude of a few microns. Given the sample size at millimetre scale, local nanoscale observations are inescapably unrepresentative.

Moreover, the TWSME training methods proposed in current works so far are simple deformation modes, namely, uniaxial tension/ compression, and single curvature bending. Therefore, the trained SMA product exhibits TWSME that toggles between two simple shapes, e.g. from a straight line to a curve [11], or elongation and retraction along a straight line [5,6,12], which has limited usefulness in practical applications. Hence a TWSME training method that can produce complex shape change is verily needed to utilise this functional behaviour.

In situ synchrotron high energy X-ray transmission diffraction (HE-XRD) has been acknowledged as probably the most advanced technique in probing the microstructure of polycrystalline materials at the meso- and microscale. Careful analysis of a diffraction pattern provides comprehensive crystallographic information involving lattice defect density (microstrain), presence of minor phases, phase fraction, preferred orientation (texture), and lattice strain (elastic strain). This gives the potential to test the hypotheses that are introduced above.

Having identified the dilemma in existing studies and the significance of TWSME in engineering applications, in the present work, we seek to develop an advanced TWSME training method that can deliver a complex shape change between a straight line and a customised spline curvature. The training method is universally applicable, which gives the possibility to manufacture Shape Memory Materials with the desired TWSME behaviour. A readily available and still in sale commercial Nitinol (near-equiatomic Nickel–Titanium SMA) product is chosen to demonstrate the general applicability of the method. An in situ HE-XRD experiment has been carried out on a Nitinol sample produced by such a training method, to analyse the microstructural evolution during TWSME behaviour. Multiple mechanisms proposed in previous studies, including dislocation arrays (also known as lattice defect density), macro-mesoscale residual strain field, martensite variants, and parent phase texture, have been examined and evaluated.

This work is probably the first study to demonstrate a highly practical TWSME training method, as well as the most comprehensive experimental evidence on the mechanisms of TWSME in SMA. The training method will vastly broaden the application scenarios of TWSME, and the insight into the TWSME mechanisms gives indicative guidance for optimising the performance.

## 2. Experimental and analytical details

### 2.1. Material preparation methodology

A commercially available spool of binary Nickel–Titanium (55Ni–45Ti wt.%) alloy wire (DYNALLOY Inc., 90 °C Flexinol Actuator Wire) of diameter 0.51 mm was used in this study. Multiple passes of cold drawing followed by heat treatment were applied to produce the final dimension of the material. The material density is measured to be 6.45 g/cm³. The cold drawing process yields strong fibre texture, which will be discussed in the ensuing Section 3.3. Segments of 2 mm length were cut out. The thermally-induced phase transformation behaviour was measured by TA DSC Q2000 in the wide temperature range between

-70 °C and 200 °C, covering the entire transformation region. The ramp rates for heating and cooling were 5 °C/min. Three cycles were repeated to ensure consistency [13]. The as-received material possesses only one-way Shape Memory Effect, namely, external force has to be applied to configure the material into the desired shape every time before heating to recover.

For the training of the Two-Way Shape Memory Effect (TWSME), sections of 50 mm length were segmented from the spool. A home-made device was manufactured for the training purpose. The device is capable of training the wire into a TWSME with a customised spline curve. The detailed description of the device is given in Appendix A. The TWSME training was performed according to the method described in Ref. [6]. The total of 40 thermal cycles under constant mechanical loading were completed to obtain a steady performance. The thermal cycles were conducted between 0 °C and 100 °C by using an ice-water mixture and boiling water as environment mediums. An example wire produced by our new TWSME training routine, which exhibits TWSME with a customised spline curve is demonstrated in the supplementary video. The quantification of the TWSME is described in Appendix B. Only a partial segment of the wire was trained to exhibit TWSME, while the remaining segment was kept in the untrained state for a comparative study as is elaborated below.

### 2.2. In situ synchrotron high energy X-ray transmission diffraction (HE-XRD)

The HE-XRD experiment was performed at the ID15A beamline at ESRF, France [14]. The setup overview is depicted in Fig. 1(a). Transmission diffraction mode was employed using a monochromatic beam energy of 96.93 keV with a focused spot size of 50 µm × 50 µm. The trained wire was mounted on the sample holder, adjacent to a heating gun. A thermocouple was attached to the wire for temperature control.

Two experimental conditions were investigated, namely, the high temperature (HT) and the low temperature (LT), as illustrated in Fig. 1 (b). In the HT configuration, the heat gun was operating to keep the wire at approximately 90 °C, hence the wire recovered and maintained its original straight shape. In the LT configuration, the wire was naturally cooled to room temperature, controlled at 22 °C. The trained segment at the upper part of the wire assumed a bent configuration due to the TWSME training. In both configurations, 2D mapping scans were carried out in the trained and untrained regions with the beam aligned with the bending axis.

Debye-Scherrer ring diffraction patterns were acquired by PerkinElmer XRD 1621 area detector. Diffraction data analysis was performed using GSAS II software [2–4,15–17]. Residual strain analysis is based on the strain model from Refs. [18–21]. The texture analysis routine is based on the technique from our previous works [1,4,15,22]. Example Rietveld refinement results are shown in Fig. 1(c) and (d), for pure B2 austenite (HT) and a mixture of B2 and B19' martensite (LT) configurations, respectively. The Crystallographic Information File of the two phases was obtained from ICSD database, corresponding to the index codes ICSD-166368 and ICSD-164156.

## 3. Results and discussion

### 3.1. Critical phase transformation temperatures

Critical phase transformation temperatures are essential parameters for TWSME training, since thermal cycling during the training process needs to cover the majority of the range between martensite finish temperature (*M*<sub>f</sub>) and austenite finish temperature (*A*<sub>f</sub>). The DSC results for the specimen are shown in Fig. 2. By convention [3,4,13], *M*<sub>f</sub> and *A*<sub>f</sub> are determined to be -40 °C and 90 °C respectively. Correspondingly, the training temperature range was chosen to be from 0 °C to 100 °C. It should be pointed out that, ideally the full temperature range of phase transformation should be covered during training to achieve the best
<figure><img src="image_3.png" /><figcaption>**Fig. 1.** (a) Setup overview with defined laboratory coordinate system. (b) Mapping scan scheme in high temperature (HT) and low temperature (LT) configurations, solid red line box is located at trained region, dashed green line box is located at untrained region. Examples of refined diffraction pattern for (c) only B2 phase (HT), (d) mixture of B2 and B19' phases (LT). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** DSC results revealing the critical phase transformation temperatures.</figcaption></figure>

result. Nevertheless, the training temperature range in this study is constrained due to the fact that water is used as the temperature control medium. Despite that, this partial overlap between the two temperature ranges has been proved effective (see Section 3.2). No intermediate phase exists between austenite and martensite during martensitic phase transformation, as demonstrated in diffraction analysis in Appendix C.

## 3.2. TWSME of the trained wire

The dynamic TWSME behaviour of a trained wire is shown in the supplementary video. Water was used as the environment for temperature control. The wire is seen to toggle between two shape profiles at the two temperatures, namely 0 °C and 95 °C. At 95 °C, the wire recovers to
a straight shape, whilst at 0 °C, the wire exhibits a customised spline curve. The switch between the two shapes is swift due to the rapid cooling/heating of the wire. The observation can be made that the TWSME, like the normal SME, has negligible time-dependent retardation, and therefore is a temperature-dependent process.

The changing of curvature (1/radius) of a trained wire is shown in Fig. 3. In the cooling process, the shape memory effect takes place gradually until 15 °C. On the contrary, shape recovery does not happen until 50 °C. The critical temperatures of TWSME match well with those from DSC analysis before training, inferring that the particular training process used in this work (though there are many other training routines [12]) does not significantly change the critical phase transformation temperatures.

### 3.3. Texture evolution during TWSME

Since the B2 cubic phase is considered to be parent phase, the wire segment was heated to a high temperature (HT) of 90 °C as the start configuration. Texture analysis has been carried out at various locations, as shown in Fig. 4. Pole figures of {111} HKL plane are plotted. In both the trained and untrained regions, three figures have been produced: two at the edges (subplot 1,3,4,6) and one in the middle (subplot 2,5) of the wire. The pole figures are corrected by taking into account the small amount of irrecoverable plastic deformation (bending angle $\theta = 15.57^{\circ}$) induced by the training process, the determination of which is elaborated in Section 3.4.

The texture of the untrained region exhibits the initial crystal orientation of the wire. There is a significant difference between the centre and the edges. A strong concentration of <111> directions can be observed parallel to the lateral direction across the thickness, while the concentration in the axial direction varies in such a way that the centre texture is much weaker than that of the edges. This implies that a certain degree of orientation heterogeneity exists in the initial product, likely being induced by the thermomechanical history in production, despite its relatively small dimension (0.51 mm diameter).

Comparing Fig. 4 subplot 1 and 4, 2 and 5, 3 and 6, similar textures are observed, hence the TWSME training process does not noticeably modify the texture of the parent phase. Though not the same effect, this is counterintuitive from the theory of phase transformation strain for the Superelasticity and the one-way Shape Memory Effect, which states that the phase transformation strain is dependent on the texture of parent phase [3,4,23]. Given the compressive and tensile strain state on left and right edge of the wire when it is in low temperature phase, the textures

of the parent phase are supposed to be different, nevertheless, the present result contradicts this assumption.

Following the heating process, the wire was cooled to 20 °C to present the morphing configuration. Pole figures of the B19' phase {001} HKL plane are given in Fig. 5 in the same plotting format.

The textures in the untrained region have a high resemblance, regardless of the clear distinction in their parent phase in Fig. 4. This indicates that the B19' texture is not highly dependent on its parent B2 texture.

Comparing between Fig. 5 subplot 1 and 4, 2 and 5, 3 and 6, the texture of subplot 1 shows a dramatic change from the others, with the concentration of {001} plane normal in the lateral direction significantly higher than those of the others, increased from 1.2 to 2 MRD. Meanwhile the concentration decreased from 1.7 to 1.2 MRD in the axial direction. On the contrary, the texture of subplot 3 shows a noticeable change in the lateral direction, whose concentration decreased from 1.2 to 0.8 MRD.

The observations from Fig. 5 can be further summarised as illustrations in Fig. 6. Two laterals of the wire were subjected to compression and tension respectively. At the compression side, the {001} plane normal tends to rotate from the axial direction to the lateral. Whilst on the tension side, rotation happens in the opposite way, as depicted in Fig. 6(b). It should be noted that it is uncertain how the texture is exactly aligned in the space since only the {001} plane normal is known, while the crystal is still unconstrained and can freely rotate around the [001] axis.

To solve this lack of information, inverse pole figures with respect to the axial direction are given in Fig. 7. The orientation concentrations in the untrained region are highly similar along the lateral direction, as can be seen from subplots 4, 5, and 6. At the compression side, namely subplot 1, the concentration distribution is clearly different compared to the rest, in that the intensity of {010} plane normal is much higher. Meanwhile, the concentration of {001} plane normal is weaker in subplot 1, which well corresponds to the observation in Fig. 5. Nevertheless, there is no obvious distinction between subplot 3 and those subplots from the untrained region.

Given that now the orientations of two axes of the crystal structure are known, the texture reorientation is clear at the compression side, as depicted in Fig. 8. The a axis of the structure aligns with the lateral direction, whilst the c axis aligns with axial direction. This orientation describes the general tendency of the crystal reorientation at the compression side when the wire is morphing to the low temperature configuration. In this particular crystal orientation, the shear direction of (100) compound twin, as is described and discussed in Refs. [3,24], is parallel to the compression direction. Hence this observation implies that (100) compound twin can be the preferred deformation mode for compression TWSME. On the other hand, the exact crystal reorientation at the tension side is not explicitly resolved, hence the twining mode remains unknown.

### 3.4. Residual strain field

The residual strain is equivalent to elastic strain, sometimes also called lattice strain. Elastic strain can be quantified from the shifting of diffraction peaks from their zero strain positions. Three components of the elastic strain tensor can be resolved from 2D diffraction pattern, namely, two principal and one shear strain. Detailed description of the quantification method refers to Ref. [18]. The mesoscale residual strain field in the parent B2 phase is shown in Fig. 9.

In reality, the TWSME training process causes a small degree of plastic deformation in the structure [12]. In the case of bending, there is a short segment of curvature at the trained region that cannot recover to straight at high temperature. The angle of this uncoverable curvature can be accurately quantified by direct measurement, and further verified by the subplot 1 $\epsilon_{12}$ in Fig. 9, as indicated by a clear inclined black band in the plot. Correction on the strain error brought by this tilt has been

<figure><img src="image_5.png" /><figcaption>Fig. 3. TWSME: Curvature of customised spline curve as a function of temperature.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Pole figures showing the texture of B2 phase along the lateral direction in trained (red solid line boxes) and untrained (green dashed line boxes) regions. Coordinate notations are given for the sample and subplots: axial and lateral directions. The orientation distribution unit is in Multiples of Random Distribution (MRD). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Fig. 5.** Pole figures showing texture of B19' phase. Refer to Fig. 4 for detailed description of the figure format.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Texture evolution on two laterals of the wire. (a) Crystal structure of B19' phase (a = 2.89 Å, b = 4.63 Å, c = 4.16 Å, α = β = 90°, γ = 96.8°). (b) Crystal reorientation according to observation from Fig. 5.</figcaption></figure>

done by employing the Mohr circle for plane strain.

Very low residual strain exists in the untrained region, as the three strain fields in subplot 2 exhibit relatively homogenous distributions.

However strong local variation is observed in the lateral direction in the trained region, as indicated by subplot 1. Bending deformation of the wire causes a large amount of strain in the axial direction, therefore ε₂₂
<figure><img src="image_9.png" /><figcaption>**Fig. 7.** Inverse pole figures showing orientation distribution in the axial direction in trained and untrained regions. {HKL} plane notations are given in subplot 1, those of the others are the same.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Fig. 8.** Crystal reorientation at the compression side, according to the observations from Figs. 5 and 7.</figcaption></figure>

and $\epsilon_{12}$ have relatively higher local values than $\epsilon_{11}$. To precisely quantify this, the strain distribution along the lateral direction is plotted in Fig. 10.

The highest distinction in residual strain between trained and untrained region is seen at the compression side for $\epsilon_{22}$ and $\epsilon_{12}$. While the strain values in the untrained region are within the range of $\pm 300$, $\epsilon_{22}$ and $\epsilon_{12}$ reach ~2200 at the leftmost of the wire where a large amount of compression takes place in the trained region. $\epsilon_{22}$ decreases to the negative at rightmost of the wire, indicating tensile residual strain, and there is also a rise in $\epsilon_{12}$ after crossing the neutral line.

The values of $\epsilon_{11}$ are negative in the trained region, but cannot be

reliably interpreted due to the relatively large error span.

In section 3.3, the texture of the parent B2 phase has been excluded from the main factors that cause the distinction of B19' phase texture between the trained and untrained region. Nevertheless, the observation in the present section suggests the mesoscale residual strain field as an important driving mechanism. The high residual strain field, either tension or compression, builds up a variant selection criterion in martensite phase transformation. Some martensitic variants are favoured in the tensile strain field, and by the same principle, some are favoured in the compressive strain field. This selective process results in the preferred orientation of the martensite phase, which in turn, brings about the phase transformation strain [25], which is finally observed as TWSME from the macroscopic point of view.

### 3.5. Lattice defect and residual B2 phase

The effect of TWSME training on the evolution of lattice defect density is revealed in Fig. 11. Lattice defect, also known as microstrain [9], is a discontinuity in the arrangement of atoms in crystalline solids. Dislocations is considered as the major contribution to microstrain. Microstrain information can be quantified from the broadening of diffraction peaks. A well-established quantification method [16], which is based on full width at half maximum (FWHM), is adopted in this study. As can be seen from Fig. 11(a), higher lattice defect density exists near the wire edges. The training process raised the overall density across the region, particularly at the compression side. On the other hand, the maximal value of lattice defect density only slightly increases. From the fit of the data points, a shift of lattice defects from the tension to the compression side can be observed in Fig. 11(b), namely, a special rearrangement of dislocations takes place, which partially supports the assumption of the TWSME training mechanism in Ref. [5].

Additionally, the residual B2 phase fraction upon martensitic phase transformation at low temperature has been analysed, and plotted in Fig. 12. In the untrained region, a relatively homogenous phase fraction distribution can be seen in subplot 1, compared to the trained region in subplot 2, Fig. 12(a). The line profile in Fig. 12(b) indicates that at low temperature, there is ~27% of B2 phase remaining in the untrained region. This is due to the fact that, as measured by DSC, the martensitic phase transformation completes fully only upon temperature reduction to -40 °C. Upon training, the residual B2 phase exhibits a linear distribution in lateral direction: a high fraction of 38% from the left-most of the compression side gradually decreases to 24% at the tension side. This result corresponds well with the role of lattice defects in the sense, that a high concentration of lattice defects hinders the phase transformation process. It also reveals the asymmetry of TWSME training in compression and tension mode: compression attracts the concentration of lattice
<figure><img src="image_11.png" /><figcaption>Fig. 9. Residual strain field in the parent B2 phase at high temperature. The values are on the order of $10^{-6}$. The lateral direction is parallel to the 11 direction, and the axial is parallel to the 22 direction of the strain tensor. Both trained and untrained regions are given. The two dash-dot lines indicate the area where the strain distribution is plotted in Fig. 10.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 10. Residual strain distribution along the lateral direction in banded areas in both trained and untrained regions in Fig. 9. The strain values are on the order of $10^{-6}$. The horizontal axis indicates the lateral position of each strain value, 0 µm is the left edge of the wire. Error bars are given individually for each point.</figcaption></figure>

defects, while tension has the opposite effect which promotes phase transformation.

### 3.6. TWSME mechanisms: further inferences

It is of no doubt that TWSME is a process dominated by many concurrent factors. The most significant ones being identified as texture reorientation, the residual strain field, and lattice defect rearrangement. The results obtained in the present study establish correlations between them.

Reorientation of the martensite variant is the direct cause of the shape morphing. The question remains that whether these preferred martensite variants still form twins? That is to say, the pseudo-plastic strain from TWSME morphing may come from two origins: (1) transformation strain via austenite to martensite [26] and (2) detwinning of martensite [3]. Additionally, the proportion of these two parts can be compression/tension asymmetric, viz. the detwinning is more favoured at the tension side, and vice versa. As noted from the data given above, the unit cell parameters of the B19' cell are $a = 2.89 Å, b = 4.63 Å, c = 4.16 Å, α = β = 90°, γ = 96.8°$, corresponding to a unit cell volume of $55.27 Å^3$. The B2 cubic unit cell has a side length of 3.003 Å, and a volume of $27.08 Å^3$. The volume ratio per atom between the two structures equals 1.02, i.e. corresponds to 2% shrinkage from B19' to B2. It is therefore possible to propose the following tentative explanation, that since the transformation is accompanied by 51% shrinkage, compressive strain on the concave side of the bending wire can be

accommodated by an increase in the B2 phase volume fraction, whilst tensile strain on the convex side of the wire could be accommodated by a decrease in the B2 phase volume fraction. This is consistent with the profiles shown in Fig. 12, which means that lattice defect accumulation (Fig. 11) is not the only reasoning for the retardation of B2 to B19' transformation at the compression side, as this is favoured thermodynamically as well.

The existence of the mesoscale residual strain field is a strong activator of the TWSME. The probed residual strain field in the full B2 phase state is in line with the bent configuration. Inarguably caused by plastic deformation, this is a joint result from the retained martensite [6] and conventional lattice slipping modes [8]. Nevertheless, the contribution of the retained martensite is limited, as no martensite hkl reflection is identified in the diffraction patterns in the high temperature full B2 state, which means the fraction of martensite is below a measurable level in the current experiment. The residual strain field, together with the rearranged lattice defect field, contribute to the formation of the preferred martensite variant.

Further developments in the understanding of TWSME are likely to require a thermodynamically and micromechanically based approach to phase transformation and internal stress modelling [27].

### 4. Summary and conclusions

The present work has addressed critical issues in Two-Way Shape Memory Effect (TWSME), from both practical and scientific aspects.
<figure><img src="image_13.png" /><figcaption>Fig. 11. (a) Lattice defect density maps in the trained and untrained regions. (b) Line profile along lateral direction in banded areas in subplot 1&2.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Fig. 12. (a) Residual B2 phase fraction maps in the trained and untrained regions at low temperature configuration. Subplot 2 has 21 by 21 scanning points. (b) Line profile along the lateral direction in banded areas in subplot 1&2.</figcaption></figure>

A novel training device has been designed and tested. The device is capable of training the Shape Memory Alloy wire into a customised spline curvature for TWSME. Conceptually, the device is universally applicable for TWSME training of any wire-shaped shape memory materials, which possess thermally activated phase transformations.

The proposed TWSME training method does not significantly alter the critical phase transformation temperature, and can produce

curvature radius of minimum 175 mm.

The texture of the parent B2 phase is not noticeably modified after the training process, therefore not the dominant underlying mechanism of TWSME.

Significant differences are seen on the texture of the B19' phase upon TWSME training, in which a compression/tension asymmetry is also observed. The reorientation at the compression side has a strong link
with (100) compound twins, suggesting the preferred deformation mode.

An intense mesoscale residual strain field is detected in the trained region, at both the compression and tension sides, which builds up a variant selection criterion in martensitic phase transformation.

Asymmetry of TWSME training in compression and tension mode is further revealed in aspects of lattice defect rearrangement and in the residual B2 phase fraction: the compression mode attracts lattice defect concentration, hence a higher fraction of residual B2 phase, whilst tension mode is the opposite.

Taken together, these observations on the different aspects of the micro- and mesoscale structure create a complete picture of the synergetic forces at play in the TWSME, and point to ways to strengthen its performance.

### CRediT authorship contribution statement

**Zifan Wang:** Conceptualization, Methodology, Validation, Formal analysis, Investigation, Writing, Funding acquisition, Project administration, Supervision.
**Yunlan Zhang:** Conceptualization, Methodology.

**Konstantinos Liogas:** Investigation.
**Jingwei Chen:** Investigation.

**Gavin B.M. Vaughan:** Investigation, Writing.
**Radim Kocich:** Investigation.
**Lenka Kunčická:** Investigation.
**Fatih Uzun:** Investigation.

**Zhong You:** Funding acquisition, Supervision.
**Alexander M. Korsun- sky:** Funding acquisition, Project administration, Supervision.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Data availability

Data will be made available on request.

### Acknowledgements

AMK, ZW, and ZY wish to acknowledge the support from UK EPSRC IAA Doctoral Impact Scheme grant EP/R511742/1. ZW is grateful for the support from Mr. Weizhong Wang and Mrs. Yong Qian. This research was supported by project number SP2023/022 by VSB-Technical University of Ostrava. The authors would like to acknowledge the European Synchrotron Radiation Facility for allocation of beamtime MA-5202 at ID15A beamline.

## Appendix A. TWSME training machine

The training machine design is depicted in Figure A1. The machine consists of upper and lower panels, on which parallel sliding rails accommodates sliding blocks. The sliding blocks can freely side along the chosen rails; their positions are decided according to the desired spline curve of the wire. A pulley frame is attached to the side of the device. As illustrated in Figure A1(b), a free weight hung by a wire across the pulley system. The other end of the wire is attached to one of the two pillars of a sliding block.

Figure A1(d) demonstrates a practical configuration of the pulley system. Four sliding blocks are used, two of which are fixed, and the rest are set to slide freely. The two free sliding blocks are tied with ropes. Two pulley systems are installed beside the rails of these free sliding blocks. A weight is attached to one end of the rope, and the other end is tied to the sliding block. Therefore, in the current configuration, the weights pull the sliding blocks in opposite directions.

During the training process, half of the wire is clamped to the fixed blocks. The other half runs across the two free sliding blocks, hence a constant pulling force is applied to the wire. Water is used as the ambient environment to control the temperature of the whole system.

<figure><img src="image_15.png" /><figcaption>Fig. A1. Sketches on (a) top view, (b) lateral view, (c) isometric projection view. (d) Prototype photo.</figcaption></figure>
## Appendix B. TWSME bending curvature quantification

The TWSME trained wire was immersed in a water bath. A reference grid was put on the bath base. The temperature was monitored by a K-type thermocouple with a Fluke 54 II digital thermometer. The images of the wire were captured by a waterproof camera also immersed in the water bath. The series of photos in Figure B1 show the spontaneous bending process. Osculating circles were fit to the bending curvature, whose radii were quantified with respect to the grid.

<figure><img src="image_16.png" /><figcaption>Fig. B1. TWSME during cooling.</figcaption></figure>

## Appendix C. B2 austenite to B19' martensite transformation during cooling

DSC analysis in Fig. 2 shows an exceptional martensitic phase transformation process during cooling, which is unlike to those in other studies where a sharp peak is presented (e.g. Fig. 1 in Ref. [4]). To ensure that the training process does not involve any intermediate phase, *in situ* diffraction analysis has been carried out during the cooling process. The diffraction patterns are shown in Figure C1. During the cooling process from 80 °C to -60 °C, the intensity of B2 austenite peak decreased and finally vanished, which is contrary to that of B19' martensite peak. It is conclusive that in the entire process of martensitic phase transformation, no intermediate phase is presented.
<figure><img src="image_17.png" /><figcaption>Fig. C1. Diffraction spectrums during martensitic phase transformation from 80 °C to -60 °C. Two diffraction peaks, which belong to B2 austenite and B19' martensite respectively, are identified and marked by coloured arrows.</figcaption></figure>

## Appendix D. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.msea.2023.145226.

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