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[Xin Ji](https://orcid.org/0000-0002-4758-5910), [Satoshi Emura](https://orcid.org/0000-0001-5789-6408), [Koichi Tsuchiya](https://orcid.org/0000-0003-0267-2727)

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[A unique {332}<113> twin to α″ martensite transition during twin propagation in a Ti-12wt.% Mo alloy with micro-segregation](https://mdr.nims.go.jp/datasets/41620070-5a5e-4dd2-b03b-8b33d54d9d40)

## Fulltext

1 A unique {332}<113> twin to α" martensite transition during twin propagation in a Ti-12wt.% Mo alloy with micro-segregation  Xin Jia,*,1, Satoshi Emuraa, Koichi Tsuchiyaa,b, *  aResearch Center for Structural Materials, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan bGraduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan *Corresponding authors: jixin0814@gmail.com (Xin Ji),  TSUCHIYA.Koichi@nims.go.jp (Koichi Tsuchiya) 1Present address: Technical Research Center, Nippon Yakin Kogyo Co., Ltd., Kawasaki, Kanagawa 210-8558, Japan   Abstract     In this study, the propagation behavior of {332}<113>β twins was investigated in a Ti-12Mo (wt.%) alloy with micro-segregation bands (Mo content ranging from 10 to 13 wt.%). A unique transition from {332}<113>β twins to α"-martensite was observed when those twins propagated across the Mo-lean bands inside the grain. A deflection angle of ~18 º was found between the twin boundary and the α"-martensite plate. This transition was more frequently found at relatively higher stresses. Thermodynamic analysis revealed that the Mo content together with the applied stress govern the required mechanical work for triggering α" martensitic phase transformation. The stress-induced α" martensitic phase transformation was easier to trigger in the Mo-lean bands, with a spontaneous interruption of the {332}<113>β twin propagation. The present chemically segregated microstructure provides a novel approach to comprehensively characterize the variable deformation modes in metastable β titanium alloys.  Keywords: Ti-12Mo, twin propagation, α"-martensite, Mo content, β phase stability     mailto:jixin0814@gmail.commailto:TSUCHIYA.Koichi@nims.go.jp2 In β-Ti alloys, several deformation modes including stress-induced martensitic (SIM) transformation (bcc-β → orthorhombic-α"), {332}<113>β twinning and dislocation slip, have been frequently reported, depending on the β phase stability of the alloy [1–5]. Molybdenum equivalency ([Mo]eq), as a function of the alloying element contents (Mo, Al, V, Fe, etc.) [Mo]eq= [Mo] + 2.9 [Fe] + 0.67 [V] + 0.44 [W] + 0.22 [Ta] + 1.6 [Cr] – [Al], in wt.% is commonly used to quantify the β phase stability [6]. Based on a large number of experimental results, it has been empirically suggested that SIM α" is the dominant deformation mechanism in β-Ti alloys with 7.4~12 wt.% [Mo]eq [3,7-8], whereas  {332}<113>β twinning takes over at a [Mo]eq range of 10~18 wt.% [Mo]eq [9-11]. In highly stable β-Ti alloys with [Mo]eq > 20 wt.% [12], dislocation slip becomes the major deformation mode. In particular, the coexistence of different deformation modes has been suggested to improve the mechanical performances of β-Ti alloys [3,13]. For instance, Sun et al. [3,14] reported a superior combination of strength and work-hardening in a Ti-12Mo (wt.%) alloy, due to the simultaneous occurrence of SIM α", {332}<113>β twins and dislocation slip.  {332}<113>β twinning is known as a unique twinning mode in metastable β-Ti alloys [15]. Several mechanisms  have been proposed for the nucleation of {332}<113>β twins, such as shear and shuffle [16,17], partial dislocation [18] and α" martensite-assisted [19] mechanisms. In contrast, relatively less attention has been paid to the propagation behavior of {332}<113>β twins, which also plays a critical role in affecting the work hardening behavior and uniform elongation of the material [20]. Recently, a novel approach of developing chemically heterogeneous microstructure in β-Ti alloys enabled a comprehensive investigation of the solute effects on phase transformation [21,22], precipitation kinetics [23] and twin propagation behaviors [24,25]. For example, in a multilayered Ti-10Mo-xFe (x = 1~3, wt.%) alloy processed by hot rolling, the propagation of {332}<113>β twin was interrupted at the boundary of highly stabilized β matrix ([Mo]eq > 15.8 wt.%) with a higher Fe content. This was explained by a higher stress required for twin propagation in high Fe concentration regions [24,25]. Similarly, Mo-segregation bands were also reported in a Ti-12wt.% Mo model alloy processed by conventional hot rolling method. This begs the question of whether and how the propagation behavior of {332}<113>β twins will be affected at the chemically heterogeneous interfaces, and if so, what the underlying mechanism for this effect.     A Ti-12Mo (wt.%) ingot was prepared by cold crucible levitation melting. The chemically heterogeneous microstructure was produced by hot forging at 1273 K, and then hot rolling at 923 K into a 14.3 mm square bar followed by air-cooling. The material was solution-treated at 1073 K for 1 hour in the single β phase region followed by water quenching. Both the forging and rolling temperatures were deliberately chosen to be lower than those required (forging temperature: 1473 K and rolling temperature: 1423 K, based on our previous study [26]) to fully homogenize Mo element. In addition, no homogenization treatment was carried out in this study. Tensile specimens with a gauge geometry of 18 mm (length) × 4 mm (width) × 2 mm 3 (thickness) were machined with the tensile axis (TA) parallel to rolling direction (RD). Interrupted tensile tests up to a strain (ε) of 4.5% were performed in an INSTRON 5581 testing machine with an initial strain rate of 2.8×10-4 s-1 at ambient temperature. Microstructural characterization was performed on the same region of the sample at each interrupted strain by backscattered electron (BSE) imaging and electron backscatter diffraction (EBSD). BSE imaging was carried out on a Zeiss  scanning electron microscope (SEM). EBSD measurements were conducted on a JEOL JSM-7001F field emission gun-SEM equipped with a TSL OIM EBSD system operated at 20 kV and the step size of 0.1μm. Distribution of Mo was measured by JEOL JXA-8900F electron probe micro-analyzer (EPMA).  Fig. 1 (a) BSE image of the microstructure prior to deformation. The tensile axis (TA) is parallel to the rolling direction (RD), as shown in the image. (b) BSE image of identical area as (a) after a strain of 4.5%. (c) Inverse pole figure (IPF) map of the deformed microstructure. (d) Boundary map (red line: {332}<113> twin boundary, black line: high angle grain boundary with a misorientation angle θ >15°) of the deformed microstructure, in which α" phase was indicated by green color.      A BSE image of the chemically heterogenous microstructure before tensile deformation is shown in Fig. 1(a). The alternating dark and bright bands aligned parallel to RD correspond the Mo-lean (~ 10 wt.% Mo) and Mo-rich (~ 13 wt.% Mo) regions, respectively [27]. These micro-segregation bands are about 20~40 m in thickness. A BSE image of the same area after tensile deformation (by a strain of 4.5%) is shown in Fig. 1(b), in which numerous plate-like deformation products can be observed. It is interesting to note that 4 some of the plates (indicated by the white arrows in Fig. 1(b)) are not exactly straight, and instead, are deflected when propagating through the micro-segregation bands within the grain. Inverse pole figure (IPF) map and boundary map (red line: {332}<113>β twin boundary, black line: high angle grain boundary and green colored region: α" phase) of the deformed microstructure are shown in Fig. 1(c) and (d), respectively. Most of the plate-like deformation products were identified to be {332}<113>β deformation twins (red lines in Fig. 1(d)), except for a few SIM α" (regions with green color in Fig. 1(d)) that mainly located at the deflection points where {332}<113>β deformation twins propagated across the Mo-lean bands (indicated by black arrows in Fig. 1(d)). This indicates a transition of deformation mode from {332}<113>β twinning to SIM α" transformation (β-twin → α"-martensite) at the chemical interface between the Mo-lean and Mo-rich regions. Although the propagation of deformation twins was generally deflected or even blocked at high angle grain boundaries, to the best of the authors ’knowledge, such a transition of deformation mode in the grain interior was reported for the first time in metastable β titanium alloys. It should also be noted that the propagation of {332}<113>β twins did not change the direction when propagating through the Mo-rich regions.  A more detailed analysis of this transition (β-twin → α"-martensite) was carried out for a single β grain containing Mo-segregation bands (Fig. 2). BSE image and grain boundary map (red line: {332}<113>β twin boundary, green colored region: α" phase) of this grain after a plastic strain of 4.5% are shown in Fig. 2(a) and (b), respectively. The corresponding Mo mapping obtained by EPMA is shown in Fig. 2(c). A good correlation can be found between the dark bands (Fig. 2(a)), α"-martensite plates (Fig. 2(b)) and Mo-lean regions with 10~11 wt.% Mo (Fig. 2(c)), thereby unambiguously confirming that α"-martensite plates preferentially formed when {332}<113>β twins propagated to the Mo-lean regions (white arrows in Fig. 2(b)). In the Mo-rich regions with 11~13 wt.% Mo, on the other hand, the propagation of {332}<113>β twins was straight and no transition was observed. One local region (marked by rectangle in Fig. 2(a)) containing such transition is zoomed in, as shown in the BSE image of Fig. 2(d). The angle between the traces of {332}<113>β twin boundary (red dashed line) and the α"-martensite plate (green dashed line) was measured to be ~18 º, which was related to the different habit planes of {332}<113>β twin and α"-martensite ({344}β [28]) with respect to the β matrix. Thin martensitic twin plates with a thickness of 50~150 nm were clearly observed inside the α" plate, which was believed to accommodate the β-α" phase transformation strain [28]. The Mo content profile along the blue line (parallel to the {332}<113>β twin boundary) is shown in Fig. 2(e), in which the occurrence ranges of {332}<113>β twins and α"-martensite were indicated by red and black arrows, respectively. It can be seen that, {332}<113>β twins existed in the Mo content range of 11.2~12.5 wt.%, whereas α"-martensite were detected at the Mo content range of 10.5~11.7 wt.%. At the intermediate Mo range (11.2~11.7 wt.%), both deformation modes coexisted, which indirectly suggests that 5 α"-martensite could probably nucleates from the interface between {332}<113>β twin tip and the parent β phase, a region generally associated with a high stress concentration [29, 30].   Fig. 2 (a) BSE image of one specific β grain exhibiting the ‘{332} <113>β twin → α"-martensite transition’. (b) EBSD image quality map of the same area, in which α′′ phase and {332} <113>β twin boundaries were shown by green color and red lines. (c) EPMA Mo-mapping of the same area, according to the scale bar on the right. (d) BSE image of the marked region shown in (a). (e) EPMA line analysis of Mo along the blue line in (d), where the ranges of where {332} <113>β twins and α"-martensite occurs are indicated by red and blue arrows, respectively.   It should also be mentioned that some {332} <113>β twins propagated through the Mo-lean bands without any noticeable morphological change, especially for those close to the grain boundary. To explain this phenomenon, the twin propagation behaviors in the same grain as in Fig. 2(a) at the early stages (from  = 0.2% to  = 2.6%) of plastic deformation were revisited (Fig. 3). Boundary maps (with the same illustration method as in Fig. 2(b)) of the identical area at interrupted plastic strains are shown in Fig. 3(b)~(d), respectively. Two types of twin propagation was defined, namely type A without β-twin → α"-martensite transition and type B with β-twin → α"-martensite transition. A total of 9 twin propagation events (labelled by numbers) were analyzed, together with the stress and strain at which the event occurred (as summarized in the table of Fig. 3). It was revealed by this semi-quantitative analysis that type A twin 6 propagation (without transition) typically occurred at lower applied stress (~515 MPa), whereas type B twin propagation (with transition) was more dominant at relatively higher applied stress (~561 MPa).   Fig. 3 (a)-(d) EBSD image quality (IQ) maps showing the evolution of twin propagation events at different interrupted plastic strains in one grain investigated. The summary of two types (type A: without transition, type B: with transition) of twin propagation events at different interrupted strains () and applied stresses () is shown in the table.   These findings indicate that both Mo content and the applied stresses  play a key role in the propagation of {332}<113>β twins as well as its transition to α"-martensite. Solute atoms can affect the twin propagation behavior by influencing the twinning stress, i.e., the critical stress to propagate twin plates, which scales with the stacking fault energy [31]. However, the Mo content variations in this study (10~13 wt.%) is supposed to have a negligible effect on the twinning stress [9,32]. Therefore, we will rationalize the transition from a thermodynamic standpoint. At the testing temperature Tt, where Ms<Tt<T0 (Ms: martensitic transformation start temperature; T0: equilibrium temperature), the critical condition for triggering SIM transformation is described as follows [33, 34]:  ∆𝐺𝑚𝑐𝑟𝑖𝑡 = ∆𝐺𝑚𝑐ℎ + ∆𝐺𝑚𝜎                                                                      (1), where ∆𝐺𝑚𝑐𝑟𝑖𝑡 denotes the molar critical driving force, ∆𝐺𝑚𝑐ℎ is the chemical free energy difference (∆𝐺𝑚𝑐ℎ =𝐺𝑚𝑜𝑟𝑡ℎ𝑜 − 𝐺𝑚𝑏𝑐𝑐) and ∆𝐺𝑚𝜎  is the mechanical work caused by the applied stresses . The critical driving force (∆𝐺𝑚𝑐𝑟𝑖𝑡) equals the ∆𝐺𝑚ሺ𝑇=𝑀𝑠ሻ𝑐𝑟𝑖𝑡 at Ms without external stress. For SIM α" transformation at a given Tt, the value of ∆𝐺𝑚𝑐𝑟𝑖𝑡 is assumed invariable for β-Ti alloys with different Mo contents [35]. Thus, the required ∆𝐺𝑚𝜎  is closely related to the ∆𝐺𝑚𝑐ℎ , i.e., the chemical composition. In the present study, the chemical driving force ∆𝐺𝑚𝑐ℎ between β and α"-martensite at ambient temperature (298.15 K) is calculated using the TiGen model proposed by Yan and Olson [36]. This model provides thermodynamic data to describe the 7 kinetic of β → α" martensitic transformation for some binary and ternary Ti alloys. Based on the data, ∆𝐺𝑚𝑐ℎ was calculated.      In the calculation, the effect of orthorhombic distortion on thermodynamics was neglected and the crystal structure of α"-martensite was assumed to be the same with equilibrium hcp structure. The details of the calculation method are described in Ref. [36]. The results are shown in Fig. 4. It is seen that ∆𝐺𝑚𝑐ℎdecreases linearly with increasing Mo content. For instance, the difference between ∆𝐺𝑚𝑐ℎ for 10 wt.% Mo and 13 wt.% is estimated as -774.5 J/mol, which is quite comparable [36]. The required mechanical work ∆𝐺𝑚𝜎  to trigger SIM α" transformation is hence greatly reduced at the Mo-lean regions. This effect agrees with the present result, where the SIM α" plates mainly occur in Mo-lean micro-segregation bands, Fig.1 (b) and Fig. 2(a).   Fig. 4 Calculated molar chemical free energy of ∆𝐺𝑚𝑐ℎ(=𝐺𝑚𝑜𝑟𝑡ℎ𝑜 − 𝐺𝑚𝑏𝑐𝑐) together with 𝐺𝑚𝑜𝑟𝑡ℎ𝑜 and 𝐺𝑚𝑏𝑐𝑐 as a function of Mo content at ambient temperature (298.15K).       Moreover, the mechanical work term ∆𝐺𝑚𝜎  is proportional to the applied stress, according to Patch and Cohen’s model [33] of ∆𝐺𝑚𝜎 = 𝜏𝑠𝛾0 + 𝜎𝑛𝜀0 =12𝜎𝛾0 𝑠𝑖𝑛 2𝜃 +12𝜎𝜀0ሺ1 + 𝑐𝑜𝑠 2𝜃ሻ,where 𝜏𝑠𝛾0 and 𝜎𝑛𝜀0 represent the work done by the shear and normal stresses, respectively, 𝛾0 is the associated shear strain, 𝜀0 is the dilatational strain, and  is the angle between the stress axis and the normal to the habit plane. In this 8 context, a higher applied stress can increase the driving force for phase transformation, thus explaining a   more frequent occurrence of type B β-twin → α"-martensite transition at larger stress level, Fig.3 (c) and Fig. 3(d).   From the above thermodynamic analysis, we can now explain our observations (Fig. 5). In the analyzed grain with Mo gradient (10 - 13 wt.%), the required mechanical work ∆𝐺𝑚𝜎  to trigger the martensitic transformation varied during the twin propagation (Fig. 5(a)). At relatively higher applied stress, the transition of deformation modes (β-twin → α"-martensite) occurred during the twin propagation where ∆𝐺𝑚𝜎  is satisfied for specific Mo content (~12 wt.% in Fig.2 (e)) (Fig. 5(b)-(c)). Similarly, SIM α" transformation stopped at the Mo interface in the Mo-rich band where ∆𝐺𝑚𝜎   cannot be reached, followed by α"-martensite → β-twin deformation (Fig. 5(d)). It can be revealed that the transitions of deformation modes (β-twin → α"-martensite and further α"-martensite → β-twin) depending on the Mo content, namely, β phase stability.   Fig. 5 Schematically illustration of the deformation behaviors of a Ti-12Mo alloy with chemically heterogeneous microstructure. The gradient from black to white indicates increment of Mo content from 10 to 13 wt.%. The green and red color indicate α′′ and {332}<113> twin plates, respectively.  In summary, the propagation behavior of {332}<113>β twins in a chemically heterogeneous Ti-12.0 Mo alloy (with Mo content ranging from 10 to 13 wt.%) was investigated. The transition from {332}<113>β twinning to α" martensitic transformation occurred along the twin propagation path when the twins 9 propagated from the Mo-rich (11.2 ~12.5 wt.%) to Mo-lean (10.5~11.7 wt.%) region. This transition was preferentially found at relatively larger stress, along with a deflection angle of ~18°. By thermodynamic analysis, it is found that the stability of β phase, i.e. the local Mo content and applied stress governed the activation of α" martensitic transformation as well as the propagation of {332}<113>β twins.  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