Achievement of Room Temperature Superelasticity in Ti-Mo-Al Alloy System via Manipulation of ω Phase Stability

The achievement of room-temperature (RT) superelasticity in a Ti-Mo-Al ternary alloy system through the addition of a relatively high concentration of Al to manipulate the phase stability of the ω phase is realized in this study. The composition of the Ti-6 mol% Mo (Ti-11.34 mass% Mo) alloy was designated as the starting alloy, while 5 mol% Al (=2.71 mass% Al) and 10 mol% Al (=5.54 mass% Al) were introduced to promote their superelastic behavior. Among the alloys, Ti-6 mol% Mo-10 mol% Al alloy, which was investigated for the very first time in this work, performed the best in terms of superelasticity. On the other hand, Ti-6 mol% Mo and Ti-6 mol% Mo-5 mol% Al alloys exhibited a shape memory effect upon heating. It is worth mentioning that in the transmission electron microscopy observation, ω phase, which appeared along with β-parent phase, was significantly suppressed as Al concentration was elevated up to 10 mol%. Therefore, the conventional difficulties of the inhibited RT superelasticity were successfully revealed by regulating the number density of the ω phase below a threshold.


Introduction
Shape memory alloys (SMAs) have been extensively investigated owing to their functional properties, such as shape memory effect (SME) and superelasticity. In particular, the β-Ti-based SMAs are considered as promising candidates for the biomedical and biomaterial communities due to the aforementioned functionalities (i.e., SME and superelasticity) and good biocompatibility [1,2].
In Ti alloys, additives are classified into α (hcp)-stabilizing and β (bcc)-stabilizing elements. Al, known as a typical one, is a standard element for the calculation of Alequivalent as other α-stabilizing elements are used, while Mo is also used for the calculation of Mo-equivalent [3]. Therefore, Ti-Mo-Al alloy, which contains Al, a typical α-stabilizing element and Mo, a typical β-stabilizing element, is a basic and standard model for Tialloys, and is a crucial system for fundamental research of Ti-alloys. The achievement of superelasticity in this Ti-Mo-Al basic model, which is considered as a prototype of SMA, could be a guideline for the development of various types of other β-Ti-based SMAs via the equivalent calculations. The β-type Ti-Mo-Al system was thus prepared in this study for studying its superelasticity at room temperature (RT).
The SME of β-Ti-based alloys originates from phase transformation between β (bcc) parent and α" (orthorhombic) martensite phases. The Lattice deformation strain of Ti-Mo alloys between β and α" phases of about 9.5% is comparable to well-known Ti-Ni alloys even when Mo was introduced to lower martensitic transformation (MT) temperature to RT [4]. Therefore, SME of Ti-Mo-based alloys has been widely investigated [5][6][7][8]. Our group also succeeded in developing RT superelasticity via MT temperature regulation by alloying Zr and Sn to Ti-3 mol% Mo specimens [9]. Besides Ti-Mo alloys, the SME of Ti-Cr-Al [10] and Ti-Ta-Al [11] as well as superelasticity of Ti-Nb-Al [12][13][14] containing Al, have been explored.
Ijaz et al. discovered that stress hysteresis (∆σ) of superelastic Ti-Nb-Mo alloys was alleviated via Sn addition, which suppresses formations of the ω phase [17]. Here, ∆σ is the difference between the stress for inducing MT of β phase (σ β-α" ) during loading and the stress for finishing of reverse MT (σ α"-β ) during unloading. In certain cases, reverse MT is not triggered even when applied stress is fully released in reverse MT due to a large ∆σ, whereby superelasticity deteriorates or vanishes. To achieve superelasticity, ∆σ must be reduced sufficiently for the commencement of reverse MT. It is also known that Al also mitigates formations of ω phases in a similar manner as Sn [10,[18][19][20]. Williams et al. studied the effects of Al on formations of the ω phase in Ti-6 mol% Mo alloys and stated that volume fraction (VF) of the ω phase was reduced with Al [21].
Some studies revealed the SME of the Ti-Mo-Al alloys [15,16]; however, there is still a lack of research regarding superelasticity of this system at RT. For various applications, it is critical to put both SME and superelasticity into practice in the most fundamental β-Ti-based SMAs, such as the Ti-Mo-Al in this study, since it can be a potential tool for the preparation of various types of the β-Ti-based SMAs via the Mo-and Al-equivalent calculations, as mentioned. Additionally, judging from the literature, it was concluded that by means of the already-studied Al composition range (i.e., less than 8 mol%) in Ti-Mo-Al alloys, it is insufficient to inhibit the formation of ω phase; consequently, superelasticity was not unveiled due to a large ∆σ. Therefore, it is assumed that relatively high Al addition is necessary for the development of RT superelasticity in the Ti-Mo-Al system. Based on this assumption, RT superelasticity is expected to be imposed in Ti-Mo-Al alloys as Al concentration is beyond 8 mol%, which is higher than those in the literature.
In this work, to verify this hypothesis about the aforementioned Al addition concentration, the Ti-6 mol% Mo alloy, which allows the formation of the β phase at RT through quenching followed by solution-treatment, was chosen as the prototype specimen. Furthermore, specific Al concentrations of 5 mol% (i.e., within the range studied by literature) and 10 mol% (i.e., out of the literature range) were designed, respectively, to certify the speculation. The correlation between deformation behaviors and formations of ω phase in Ti-Mo-Al alloys was further investigated.

Materials and Methods
High purity Ti (99.99%), Mo (99.9%), and Al (99.99%) were used for the preparation of Ti-6Mo-(0, 5, and 10) Al (mol%) alloys. Ingots of 8 g were fabricated by arc-melting in an Ar-1 mol% H 2 atmosphere. Specimens are abbreviated as 0Al, 5Al, and 10Al, unless otherwise stated. Arc-melted ingots were sealed in quartz tubes under an Ar atmosphere, homogenized at 1273 K for 7.2 ks, quenched in iced-water, and cold-rolled into sheets. Specimens used for measurements were cut by electro-discharge machining, solutiontreated at 1273 K for 1.8 ks in Ar atmosphere, followed by iced-water quenching.
For phase identification, X-ray diffraction (XRD; X Pert-PRO-MPD, Malvern PANalytical, Malvern, UK) measurements were conducted by CuKα radiation within 2θ = 20-120 • at RT (295 ± 2 K). Scanning electron microscopy (SEM; SU5000, Hitachi High-Tech Corporation, Tokyo, Japan) and transmission electron microscopy (TEM; JEM-2100, JEOL Ltd., Tokyo, Japan) were undertaken with acceleration voltages of 15 kV and 200 kV, respectively. Prior to TEM observations, thin foil specimens were processed by twin-jet polishing. Tensile tests were performed by an Instron universal testing machine (Autograph AG-Xplus 5 kN, Shimadzu Corporation, Kyoto, Japan) on 20 mm (length) × 2 mm (width) × 0.2 mm (thickness) specimens at RT. The tensile tests were conducted along the rolling direction of specimens at a strain rate of 8.3 × 10 −4 s −1 and specimens were unloaded after approximately 4% strain deformation. Those specimens did not perform superelastic recovery, were subjected to heat-treatments up to 500 K ± 20 K after unloading, and shape recoveries were recorded to investigate SME.

Results and Discussion
All alloys possessed the β phase in XRD profiles (Figure 1a), and as shown in the inset, a small peak was observed in 0Al, which could be indexed as ω phase. Equiaxed grains of about 200 µm were observed in OM images ( Figure S1 in the Supplementary Materials) and no secondary phase was discerned in SEM images (Figure 1b-d).
× 0.2 mm (thickness) specimens at RT. The tensile tests were conducted along the rolling direction of specimens at a strain rate of 8.3 × 10 −4 s −1 and specimens were unloaded after approximately 4% strain deformation. Those specimens did not perform superelastic recovery, were subjected to heat-treatments up to 500 K ± 20 K after unloading, and shape recoveries were recorded to investigate SME.

Results and Discussion
All alloys possessed the β phase in XRD profiles (Figure 1a), and as shown in the inset, a small peak was observed in 0Al, which could be indexed as ω phase. Equiaxed grains of about 200 μm were observed in OM images ( Figure S1 in the Supplementary Materials) and no secondary phase was discerned in SEM images (Figure 1b  (a) XRD profiles of 0Al, 5Al, and 10Al solution-treated alloys (magnified X-ray diffraction patterns for three specimens from 2θ = 64° to 68° are inserted in the top-right corner of (a) to reveal the diffraction peaks of ω phase). SEM images of (b) 0Al, (c) 5Al, and (d) 10Al.
Dark-field (DF) images along with corresponding selected area diffraction patterns (SADPs) from the [110]β direction are shown in Figure 2 and a fine secondary phase was identified. Besides diffraction spots of the β phase, notwithstanding the Al amount, spots of the ω phase were further observed at 1/3 and 2/3 positions along the <112>*β direction in all SADPs. This ω phase was recognized as athermal ω (ωath), whose area fraction (AF) and size were evaluated by ImageJ 1.51k. Not surprisingly, the highest AF of 12.5% possessing a major axis of approximately 6.9 nm and a minor axis of approximately 2.3 nm of ωath phase, was found in 0Al ( Figure 2a). AF of 5.9% with an average size of 3.3 nm and AF of 2.8% with an average size of 3.1 nm of the ωath phase were found in 5Al ( Figure 2b) and 10Al (Figure 2c), respectively. It was thus concluded that the size and AF of the ωath phase could be diminished with Al introduction. Moreover, spots of the ωath phase in 0Al was observed distinctly and sharply; conversely, spots turned diffuse and faint with the Al introduction (i.e., 5Al and 10Al), indicating that SADPs results agreed well with DF images. Figure 1. (a) XRD profiles of 0Al, 5Al, and 10Al solution-treated alloys (magnified X-ray diffraction patterns for three specimens from 2θ = 64 • to 68 • are inserted in the top-right corner of (a) to reveal the diffraction peaks of ω phase). SEM images of (b) 0Al, (c) 5Al, and (d) 10Al.
Dark-field (DF) images along with corresponding selected area diffraction patterns (SADPs) from the [110] β direction are shown in Figure 2 and a fine secondary phase was identified. Besides diffraction spots of the β phase, notwithstanding the Al amount, spots of the ω phase were further observed at 1/3 and 2/3 positions along the <112>* β direction in all SADPs. This ω phase was recognized as athermal ω (ω ath ), whose area fraction (AF) and size were evaluated by ImageJ 1.51k. Not surprisingly, the highest AF of 12.5% possessing a major axis of approximately 6.9 nm and a minor axis of approximately 2.3 nm of ω ath phase, was found in 0Al ( Figure 2a). AF of 5.9% with an average size of 3.3 nm and AF of 2.8% with an average size of 3.1 nm of the ω ath phase were found in 5Al ( Figure 2b) and 10Al (Figure 2c), respectively. It was thus concluded that the size and AF of the ω ath phase could be diminished with Al introduction. Moreover, spots of the ω ath phase in 0Al was observed distinctly and sharply; conversely, spots turned diffuse and faint with the Al introduction (i.e., 5Al and 10Al), indicating that SADPs results agreed well with DF images. The ratio of Iω/Iβ of ωath spot intensity to β spot intensity (black bars with error bars) and relative number density (ρN) of ωath-particles (red solid circles) for each alloy. Note that the relative ρN for each alloy is normalized by taking 0Al as a standard.
Since it is crucial to take specimen thickness into account, the total amount of ωath phase was further estimated by the Iω/Iβ measure of the spot intensity ratio of the ωath phase (Iω) to β phase (Iβ) (Figure 2d), which was calculated from the integrated intensity profiles of SADPs along <112>*β [22]. Iω/Iβ, which is equivalent to VF, are approximately at 25%, 4%, and 1% for 0Al, 5Al, and 10Al, respectively. The subsided spot intensity of ωath phase, suggesting the diminished VF of the ωath phase originated from elevated Al. A remarkable suppression of the ωath phase was especially found in 10Al (i.e., the highest Al) and the results are consistent with literature [20,21]. The quantification of the SADPs can be difficult; nevertheless, it is apparent that the diffraction spots of the ωath phase gradually turned weak and diffuse from 0Al to 10Al.
Precipitates of the ωath phase inhibiting stress-induced martensitic transformation (SIMT), increased the stress for β/α″ interface migration in a solid-solution strengtheninglike manner. Accordingly, intensified stress is reasonably speculated to correlate positively to number of pinning at the interface. First, it is assumed that ωath-particles are homogeneous in size and low-composition dependent in shape. Second, Iω/Iβ divided by the volume of one ωath-particle is proportional to the number density (ρN). A relative ρN, which is normalized by serving 0Al as the standard, is used and shown in Figure 2d. The highest and lowest relative ρN were found of 1.3 and 0.5 for 5Al and 10Al, respectively. It is thus concluded that size and Iω/Iβ (i.e., VF) were reduced with Al; by contrast, relative ρN does not show specific dependency. (d) The ratio of I ω /I β of ω ath spot intensity to β spot intensity (black bars with error bars) and relative number density (ρ N ) of ω ath -particles (red solid circles) for each alloy. Note that the relative ρ N for each alloy is normalized by taking 0Al as a standard.
Since it is crucial to take specimen thickness into account, the total amount of ω ath phase was further estimated by the I ω /I β measure of the spot intensity ratio of the ω ath phase (I ω ) to β phase (I β ) (Figure 2d), which was calculated from the integrated intensity profiles of SADPs along <112>* β [22]. I ω /I β , which is equivalent to VF, are approximately at 25%, 4%, and 1% for 0Al, 5Al, and 10Al, respectively. The subsided spot intensity of ω ath phase, suggesting the diminished VF of the ω ath phase originated from elevated Al. A remarkable suppression of the ω ath phase was especially found in 10Al (i.e., the highest Al) and the results are consistent with literature [20,21]. The quantification of the SADPs can be difficult; nevertheless, it is apparent that the diffraction spots of the ω ath phase gradually turned weak and diffuse from 0Al to 10Al.
Precipitates of the ω ath phase inhibiting stress-induced martensitic transformation (SIMT), increased the stress for β/α" interface migration in a solid-solution strengtheninglike manner. Accordingly, intensified stress is reasonably speculated to correlate positively to number of pinning at the interface. First, it is assumed that ω ath -particles are homogeneous in size and low-composition dependent in shape. Second, I ω /I β divided by the volume of one ω ath -particle is proportional to the number density (ρ N ). A relative ρ N , which is normalized by serving 0Al as the standard, is used and shown in Figure 2d. The highest and lowest relative ρ N were found of 1.3 and 0.5 for 5Al and 10Al, respectively. It is thus concluded that size and I ω /I β (i.e., VF) were reduced with Al; by contrast, relative ρ N does not show specific dependency.
Stress-strain curves and definitions are shown in Figure 3. First, yielding stress (σ y ) of 0Al was found at 340 MPa and the applied strain almost remained after unloading (Figure 3a). About 1/3 residual strain (i.e., 0.8%) of shape recovery took place upon heating due to SME (ε sme ). These results agreed well with Ti-6 mol% Mo and Ti-11 mass% Mo (= Ti-5.81 mol% Mo) alloys [23,24]. Additionally, Ti-11 mass% Mo alloy possessing proximate composition to 0Al was reported to undergo plastic deformation mainly by twinning deformation of the β phase [25,26] and was accompanied by SIMT simultaneously in the early stage [27][28][29][30]. Moreover, Oka et al. also reported that a slight SIMT occurred in 10% cold-rolled Ti-11 mass% Mo alloy [31]. It is thus concluded that twinning of the β phase is the major mechanism during deformation, while a minor amount of SIMT to the α" phase, which went along with it, led to shape recovery upon heating. Furthermore, since merely slight work-hardening was found in 0Al, σ y is considered to be equivalent to the stress for SIMT (σ SIMT ). Note that slight pseudoelastic recovery during unloading was attributed to twinning pseudoelasticity caused by stress-induced martensitic variants, which is often seen in Ti-Mo-based SMAs and others. Stress-strain curves and definitions are shown in Figure 3. First, yielding stress (σy) of 0Al was found at 340 MPa and the applied strain almost remained after unloading (Figure 3a). About 1/3 residual strain (i.e., 0.8%) of shape recovery took place upon heating due to SME (εsme). These results agreed well with Ti-6 mol% Mo and Ti-11 mass% Mo (= Ti-5.81 mol% Mo) alloys [23,24]. Additionally, Ti-11 mass% Mo alloy possessing proximate composition to 0Al was reported to undergo plastic deformation mainly by twinning deformation of the β phase [25,26] and was accompanied by SIMT simultaneously in the early stage [27][28][29][30]. Moreover, Oka et al. also reported that a slight SIMT occurred in 10% cold-rolled Ti-11 mass% Mo alloy [31]. It is thus concluded that twinning of the β phase is the major mechanism during deformation, while a minor amount of SIMT to the α″ phase, which went along with it, led to shape recovery upon heating. Furthermore, since merely slight work-hardening was found in 0Al, σy is considered to be equivalent to the stress for SIMT (σSIMT). Note that slight pseudoelastic recovery during unloading was attributed to twinning pseudoelasticity caused by stress-induced martensitic variants, which is often seen in Ti-Mo-based SMAs and others. Second, in 5Al (Figure 3b), σy was identified at approximately 510 MPa, which is higher than 0Al. By contrast with 0Al, 5Al performed neither pseudoelastic nor superelastic recovery; instead, the elastic recovery was merely found during unloading. It is worth mentioning that followed by unloading, 100% shape recovery was realized upon heating performing a perfect SME. Accordingly, it is rational to infer that σy corresponds to σSIMT and these results are supported by literature [15].
Lastly, unexplored 10Al (Figure 3c), whose σy was at approximately 510 MPa, is similar to 5Al; nevertheless, a larger shape recovery than the amount brought by merely elastic recovery was recognized during unloading. This indicated that superelasticity was successfully revealed in 10Al showing a superelastic recovery strain εse of 0.9% while no SME (Open blue arrow symbols: strain originates from superelasticity during unloading (ε se ); solid red arrow symbols: strain brought by SME upon heating (ε sme ); ε sr : strain of overall shape recovery; ε p : strain by plastic deformation; σ y : yielding stress; applied strain = ε sr + ε p ).
Second, in 5Al (Figure 3b), σ y was identified at approximately 510 MPa, which is higher than 0Al. By contrast with 0Al, 5Al performed neither pseudoelastic nor superelastic recovery; instead, the elastic recovery was merely found during unloading. It is worth mentioning that followed by unloading, 100% shape recovery was realized upon heating performing a perfect SME. Accordingly, it is rational to infer that σ y corresponds to σ SIMT and these results are supported by literature [15].
Lastly, unexplored 10Al (Figure 3c), whose σ y was at approximately 510 MPa, is similar to 5Al; nevertheless, a larger shape recovery than the amount brought by merely elastic recovery was recognized during unloading. This indicated that superelasticity was successfully revealed in 10Al showing a superelastic recovery strain ε se of 0.9% while no SME was found in 10Al upon heating and the residual strain remained. It is considered that the residual strain could be ascribed to slip deformation, which originates from dislocation motions, and arises along with SIMT during loading. The RT superelasticity of 10Al was practiced for the very first time in this study. Judging from the results, σ y of 10Al is surmised to be both a critical stress for slip deformation and σ SIMT . In short, σ y of all specimens was accompanied with SIMT during loading in this study.
For further analysis of superelasticity of the 10Al, the cyclic loading-unloading tensile test was performed. Specimens were subjected to 1.5% stain in the first cycle followed by repeated 0.5% strain per cycle until they fractured. The stress-strain curves via the cyclic loading-unloading tensile test are shown in Figure 4a. The overall shape recovery strain (ε sr ), transformation strain of superelasticity (ε se ), and residual plastic strain (ε p ) of each cycle, which were evaluated from Figure 4a, are plotted as a function of applied strain in Figure 4b. It was found that ε sr and ε se increased linearly up to an applied strain of 6% before decreasing. The maximum ε se was 2.4% at an applied strain of 6%, and the maximum ε sr reached 4.8%. The obtained ε se in this 10Al surpassed that of 2.3% ε se of the greatly investigated Ti-26Nb (mol%) alloy [32]. It is expected that further manipulation of the alloy composition and/or heat-treatment could develop highly practical SMAs with promoted superelastic strain. Our research group is still working on the development of other related alloys, and improvements of the β-Ti-based SMAs will be published in future.
Materials 2022, 15, x FOR PEER REVIEW 6 of 10 was found in 10Al upon heating and the residual strain remained. It is considered that the residual strain could be ascribed to slip deformation, which originates from dislocation motions, and arises along with SIMT during loading. The RT superelasticity of 10Al was practiced for the very first time in this study. Judging from the results, σy of 10Al is surmised to be both a critical stress for slip deformation and σSIMT. In short, σy of all specimens was accompanied with SIMT during loading in this study. For further analysis of superelasticity of the 10Al, the cyclic loading-unloading tensile test was performed. Specimens were subjected to 1.5% stain in the first cycle followed by repeated 0.5% strain per cycle until they fractured. The stress-strain curves via the cyclic loading-unloading tensile test are shown in Figure 4a. The overall shape recovery strain (εsr), transformation strain of superelasticity (εse), and residual plastic strain (εp) of each cycle, which were evaluated from Figure 4a, are plotted as a function of applied strain in Figure 4b. It was found that εsr and εse increased linearly up to an applied strain of 6% before decreasing. The maximum εse was 2.4% at an applied strain of 6%, and the maximum εsr reached 4.8%. The obtained εse in this 10Al surpassed that of 2.3% εse of the greatly investigated Ti-26Nb (mol%) alloy [32]. It is expected that further manipulation of the alloy composition and/or heat-treatment could develop highly practical SMAs with promoted superelastic strain. Our research group is still working on the development of other related alloys, and improvements of the β-Ti-based SMAs will be published in future. Given that 0Al and 5Al performed SME while 10Al exhibited superelasticity, reverse MT start temperatures (As) are deduced to be lower than the heating temperature of 500 K and RT of around 300 K, respectively. This suggests that As was reduced by more than 200 K via 10% Al addition. The reduced amount in this study agreed well with that 25-40 K/mol% Al claimed in literature [12,33,34].
Firstly, from transformation stress and temperature points of view, generally, the σβ-α″ of SMAs follows Clausius-Clapeyron equation and increases linearly with temperature difference between MT and operation temperatures. Assuming that forward MT temperature also decreases with Al in the similar manner of reverse MT temperature, the lowest σβ-α″ would appear in 0Al and increase with Al. However, composition dependence of σβ-α″ in this study did not show such a trend. Secondly, from a phase equilibrium point of view, while taking As as phase equilibrium temperature of β phase and α″ phase, stable phase at RT for 0Al and 5Al should be the α″ phase. Despite the speculation, apparent phases were β + ωath. Therefore, finally, it is rational to consider that β phase was Given that 0Al and 5Al performed SME while 10Al exhibited superelasticity, reverse MT start temperatures (A s ) are deduced to be lower than the heating temperature of 500 K and RT of around 300 K, respectively. This suggests that A s was reduced by more than 200 K via 10% Al addition. The reduced amount in this study agreed well with that 25-40 K/mol% Al claimed in literature [12,33,34].
Firstly, from transformation stress and temperature points of view, generally, the σ β-α" of SMAs follows Clausius-Clapeyron equation and increases linearly with temperature difference between MT and operation temperatures. Assuming that forward MT temperature also decreases with Al in the similar manner of reverse MT temperature, the lowest σ β-α" would appear in 0Al and increase with Al. However, composition dependence of σ β-α" in this study did not show such a trend. Secondly, from a phase equilibrium point of view, while taking A s as phase equilibrium temperature of β phase and α" phase, stable phase at RT for 0Al and 5Al should be the α" phase. Despite the speculation, apparent phases were β + ω ath . Therefore, finally, it is rational to consider that β phase was "quenched-in" by formations of the ω ath phase. According to the inferences, it is necessary to take the suppression of SIMT by the ω ath phase into account. It is expected that suppression of phase transformation increases with the ω ath phase amount resulting in high σ SIMT .
A small amount of the ω ath phase (i.e., small I ω /I β ) but high ρ N was found in 5Al, whose σ β-α" at 510 MPa was 170 MPa higher than 340 MPa of 0Al, indicating that suppression of SIMT greatly depends on ρ N . Not surprisingly, 10Al possessing both a small amount and low ρ N of the ω ath phase performed superelasticity. This could be attributed to the least suppressed SIMT leading to a limited increment of σ β-α" . It was concluded that to achieve RT superelasticity, it is crucial to suppress both the amount and ρ N of the ω ath phase. Based on our results, keeping ρ N below a threshold is especially an effective strategy. Therefore, introducing additive elements which sufficiently suppress the ω ath phase could be practicable; moreover, as mentioned previously, A s , which is less affected by ω ath phase than M s , is also a critical factor.
Based on the results, the effect of Al on σ β-α" and σ α"-β are summarized and illustrated in Figure 5 and Table S1. In Figure 5a, σ β-α" deviates from the linear relationship showing an inflection point as the composition goes from high Al (i.e., 10Al) to low Al (i.e., 5Al), which contains high ρ N and an increment of σ β-α" was thus imposed. On the other hand, during unloading, the effect from the ω ath phase, which suppressed reverse SIMT, is limited; therefore, a linear relationship was constructed (Figure 5b). A summary of stress hysteresis (∆σ) based on the superimposing of loading ( Figure 5a) and unloading (Figure 5b) results is illustrated in Figure 5c. Obviously, significant reduction of ∆σ achieved by 10Al, was found at approximately 180 MPa (Figure 3c).
The phase constituents and phase transformations are summarized in Table 1. There are two possible reasons for achieving RT superelasticity via 10 mol% Al addition. First, the transformation temperature of 10Al was lower than 5Al and the stable phase at RT thus turned into β phase. Second, both the amount and ρ N of the ω ath phase were greatly suppressed; accordingly, ∆σ, which was mitigated to about 180 MPa, enabled reverse SIMT at RT. In brief, for obtaining RT superelasticity, an Al amount up to 10 mol% is a crucial prerequisite.
In 5Al, by contrast, despite a small amount of the ω ath phase, ∆σ was deteriorated by high ρ N . Whether superelasticity could be imposed by simply introducing Mo for reducing A s below RT at 5 mol% Al or not, is considered by making the following presumptions. According to the results, it is known that σ β-α" of 5Al is 510 MPa and ∆σ at around 700 MPa is also estimated (Figure 3b). It could also be inferred that, like 10Al, β phase would be stable at RT as A s is 100 K lower than current A s . According to literature concerning metastable β-Ti alloys, the slope of the Clausius-Clapeyron relation (dσ β-α" /dT) is 3-5 MPa/K [35][36][37]. By considering the minimum of 3 MPa/K, it is deduced that transformation temperature of 100 K is reduced while σ β-α" of 300 MPa is increased. Consequently, σ β-α" would be at approximately 810 MPa via Mo introduction.
Generally, the σ y of solution-treated Ti-alloys is less than 600 MPa, while the average critical stress for slip (σ CSS ) of Ti-Mo-Sn-Zr alloys exhibiting RT superelasticity is 634 MPa [9], and Ti-20Zr-12Nb-2Sn alloy was found in a relatively high σ CSS of approximately 800 MPa until very recently [38]. Therefore, MT is not induced in alloys possessing such a high σ β-α" ; instead, only plastic deformation takes place. Specifically, both SME and superelasticity disappear. This thus explains well the vanishing superelasticity by merely regulating MT temperature via Mo addition without taking the ω ath phase into consideration. Additionally, since many Ti-based superelastic alloys performed ∆σ less than 200 MPa [9,17], suppressing ∆σ to less than 200 MPa for revealing superelasticity is required; hence, Al addition up to 10 mol%, which possessed ∆σ of 180 MPa, is a crucial prerequisite.

Conclusions
In summary, size, amount, and ρN of the ωath phase were reduced to such an extent that the Δσ in Ti-Mo-Al alloys was as low as 180 MPa by increasing Al to 10 mol%, which was beyond already studied samples and has not been explored. Meanwhile, RT superelasticity could be realized by lowering its As below RT. Based on equivalent calculations, additions greater than 6 mol% Mo-equivalent and 10 mol% Al-equivalent would perform

Conclusions
In summary, size, amount, and ρ N of the ω ath phase were reduced to such an extent that the ∆σ in Ti-Mo-Al alloys was as low as 180 MPa by increasing Al to 10 mol%, which was beyond already studied samples and has not been explored. Meanwhile, RT superelasticity could be realized by lowering its A s below RT. Based on equivalent calculations, additions greater than 6 mol% Mo-equivalent and 10 mol% Al-equivalent would perform RT superelasticity. The Mo-equivalent corresponds to 8.4 mol% Cr, 5.5 mol% Co, and 3.9 mol% Fe of typical β-stabilizing elements. Via precise composition manipulation, advancing unexplored RT superelastic alloys is foreseen.