Structural evolution and mechanism of strain glass transition in Ti48.7Ni51.3 shape memory alloy studied by anomalous small-angle X-ray scattering

The in-situ anomalous small-angle X-ray scattering (ASAXS) technique was used to investigate the strain glass transition (SGT) in as-quenched Ti48.7Ni51.3 shape memory alloy during a thermal cycle of 30 °C to the SGT temperature Tg (−50 °C) and then to 30 °C again. The Ni atoms play a critical role as point defects in the SGT mechanism and are very difficult to characterize using conventional tools. ASAXS identified the distribution of Ni atoms in nanodomains, which have a disk-like core–shell configuration with a Ni-rich shell and a highly Ni-rich core. Moreover, the morphological evolution, growth and shrinkage of the highly Ni-rich core domains during the thermal cycle through Tg are demonstrated. The enhancement and reversible behavior of the local lamellar ordering arrangement of nanodomains during the SGT process at Tg are revealed. The structural evolution and local ordering arrangement of nanodomains can play a role in hindering martensitic transformation. The ASAXS results provide new knowledge about the SGT beyond that from current simulation works. However, this corresponding structure of the nanodomains was destroyed when the specimen was heated to 250 °C.


Results
temperature-dependent ASAXS measurement of the as-quenched ti 48.7 ni 51.3 SMA. Figure 1 (a)(a'), (b)(b'), (c)(c') and (d)(d') show the results of the temperature-dependent 2D ASAXS patterns of the as-quenched Ti 48.7 Ni 51.3 SMA measured using 8000 eV and 8226 eV at 30 °C, −50 °C (at T g ), 30 °C (end of cycle) and 250 °C (aging), respectively. The radial streaks in the 2D ASAXS patterns shown in Fig. 1 provide direct evidence of the plate-/disk-like morphology of the nanodomains 17,28,[35][36][37][38] . The corresponding 1D ASAXS profiles are shown in Fig. 2. In that figure, the power-law scattering behavior (I(Q) ∝ Q −2 ) in the middle Q range (0.02-0.06 Å −1 ) of the ASAXS profiles also reveals direct evidence that the nanodomains are plate-/disk-like in shape 26 . The power-law scattering behavior of the exponent of −4 in the low Q range (0.003-0.009 Å −1 ) is contributed by the very large particles (surface scattering), which are beyond the scope of this study 26 . Also in Fig. 2, one can find that the 1D ASAXS profiles measured at different energies for the same temperature have similar profile shapes, except for some small peaks (i.e., structure peaks) only appearing in the ASAXS profiles measured at 8000 eV. Unlike the 1D ASAXS profiles without the structure peaks measured at 8226 eV (near the absorption edge of Ni), the structure peaks in the profiles measured at 8000 eV were apparently induced by Ni atoms in the nanodomains and thus provide evidence of Ni-rich nanodomains. These small structure peaks in the 8000 eV profiles could not be measured by the in-house SAXS instrument because its incident X-ray intensity was much lower than that of synchrotron X-ray radiation. On the other hand, Fig. 2 also indicates that two ASAXS profiles measured at two different energies substantially demonstrated a slight discrepancy between them, suggesting that the nanodomains were comprised of two components, (1) a Ni-rich component and (2) a highly Ni-rich component, in contrast to the Ti-Ni matrix. The present study further characterized the nanodomains to have a two-component structure by two approaches as follows.

Structural characterization of core-shell disk domains in the as-quenched sample by ASAXS
Model fitting of ASAXS intensities measured at two X-ray energies. The first proposed method of model fitting is called approach I here. The X-ray scattering amplitude (or length) of an atom, f(E), can be expressed by  www.nature.com/scientificreports www.nature.com/scientificreports/ where Z is the atomic number and f(E) is a complex number. The anomalous dispersion correction terms f′ and f ″ are significant only near the absorption edge. The real part, Z + f′, is related to the coherent scattering. The imaginary part, f ″, is related to the absorption. The real and imaginary parts of the scattering length of Ni and Ti atoms as a function of incident X-ray energy E are shown in Fig. 3. Thereafter, the scattering length density of each phase, including the matrix and the Ni-rich and highly Ni-rich components in the nanodomains, can be obtained by dividing the average scattering length by the average atomic volume within the phase 27 : where X i is the fraction of the atom i and Ω is the average atomic volume. The difference (or contrast) between the component phase and the matrix phase is given by 27 where C i p and C i m are the concentrations of element i in the component p and the matrix m, respectively. Ω can be assumed to be identical in the component phase and matrix. Therefore, the ASAXS profile measured at 8226 eV can be modelled by 4 2 where A is a constant describing the smooth surface of a large particle, Δρ denotes the scattering length density contrast between the nanodomains and the matrix, and P(Q) is the form factor of the nanodomains. S(Q) is the structure factor describing the interaction between the nanodomains and signifying a kind of ordered arrangement of nanodomains. S(Q) exhibits the form of several discrete small peaks whose amplitude of intensity is strongly affected by the incident X-ray energy or scattering contrast here. The form factor of the polydispersed disk-like nanodomains with a radius R and a Schulz distribution of thickness t can be given by [39][40][41][42] : where η and V p are the volume fraction and the particle volume, respectively, and j 0 and j 1 are the zero-order Bessel function and the first-order Bessel function, respectively. The integral over α averages the form factor over all possible orientations of the disks with respect to Q. f(t) is the normalized Schulz distribution of the thickness, in which the polydispersity of the thickness is related to σ /t avg , where σ is the variance of the Schulz distribution and t avg is the mean thickness. Generally, S(Q) can be approximately 1.0 within the region outside the discrete peak. In the present study, the intensities of discrete small peaks of the structure factor S(Q) are much weaker than the form factor, so the model fitting of ASAXS profiles using Eq. (5) can ignore the discrete contribution of small structure peaks (let S(Q) = 1 for the full profile), unlike the continuous profile. The ASAXS profiles measured at different energies for all temperatures can be fitted well with Eq. (5), as shown by the solid curves in Fig. 2. The structure parameters determined by approach I are listed in Table 1. The determined polydispersity parameter is less than 0.05, showing the monodispersed system. There are certain uncertainties in model fitting. According to Table 1, the determined thicknesses of the nanodomains for different energies are almost the same for each temperature. However, the values of the determined radii at 8000 eV for 30 °C, −50 °C and 30 °C again are larger than those determined at 8226 eV by a factor of ~2 nm. Therefore, based on this ASAXS analysis www.nature.com/scientificreports www.nature.com/scientificreports/ result, we can propose that the structure model of a nanodomain is a core-shell disk. The disk-like core-shell nanodomain is comprised of a highly Ni-rich disk as the core and a Ni-rich shell around it, as shown in Fig. 4. The shell thickness (the difference in radii of the inner disk and outer disk) for each temperature is ~2 nm. This thickness can be explained by the fact that the 8000 eV beam can "see" the morphology of the full core-shell disk, while the 8226 eV beam can only "see" the morphology of the core (highly Ni-rich domain). The difference between the determined structures is the shell (Ni-rich domain). Further explanation of this model fitting method is provided as follows. The form factor of the nanodomains, Eq. (5), can be alternatively expressed by the following equation.
where ∆ρ c 2 and P Q ( ) c are the scattering contrast and the associated form factor of the core domain, respectively; ∆ρ s 2 and P Q ( ) s are the scattering contrast and the associated form factor of the shell domain, respectively. As illustrated in Fig. 3, when the incident 8000 eV energy is switched to 8226 eV energy, f Ni can be reduced by 4% and approach the value of f Ti . Meanwhile, the f ″ Ni and f Ti (including f ′ Ti and f ″ Ti ) values remain unchanged. The Ni concentrations, C Ni and X Ni , in the core domain are much higher than that in the shell domain. According to Eqs. (2) and (3), the scattering length density of the shell phase is much lower than that of the core phase. Therefore, ∆ρ s 2 of Eq. (6) can be very small and be relatively neglected compared to the ρ Δ c 2 value, providing the explanation of why the incident 8226 eV energy only "sees" the core part.

Model fitting of difference between ASAXS intensities measured at two X-ray energies
The present study also adopted another approach, approach II, for cross-checking the above proposed approach I. Because the different incident energies can change the atomic scattering length f, Eq. (6) can be expanded into the following equations: where I Q E ( , ) 1 and I Q E ( , ) 2 are the ASAXS scattering profiles at E 1 (8000 eV) and E 2 (8226 eV), respectively. .. and P Q ( ) i are the scattering length density contrast and form factor of the domain i at the incident energy j, respectively. The subscripts H-Ni and Ni denote highly Ni-rich and Ni-rich, respectively. The atomic fraction of Ni in the Ni-rich shell can be regarded as only slightly higher than that of the matrix compared to the highly Ni-rich domains. The scattering contrasts of the Ni-rich domains for both energies may be approximately the same relative to those of highly Ni-rich domains. The scattering contrasts of highly Ni-rich domains for both energies are also significantly different. Therefore, the difference between the ASAXS profiles measured at E 1 (8000 eV) and E 2 (8226 eV) can be expressed as According to Eq. (9), the difference between the ASAXS profiles measured at E 1 and E 2 can be considered to be mainly contributed only by highly Ni-rich domains or by net scattering of the highly Ni-rich domains. This concept, exhibited in Eq. (9), has frequently been adopted in ASAXS analysis and is described in the literature [23][24][25] . Approach II adopts the core-shell form factor model 26 to directly fit the difference between the ASAXS profiles measured at 8000 eV and 8226 eV shown in Fig. 5, which is fitted well. The structure parameters determined by approach II are listed in Table 2.
Pair distance distribution function (PDDF) or DDF is a model-independent method to check the results obtained from the above model-fitting methods. The DDF, P(r), describing the real space of nanodomains can be directly calculated from the inverse Fourier transformation of the SAXS or ASAXS data according to The P(r) functions corresponding to the SAXS profiles measured at 8000 eV for 30 °C, −50 °C and 30 °C again are shown in Fig. 6(a). The P(r) functions corresponding to the ASAXS profiles measured at 8226 eV for 30 °C, −50 °C and 30 °C again are shown in Fig. 6(b). The comparison of P(r) functions measured at two energies for 30 °C, −50 °C and 30 °C again are shown in Fig. 6(c-e), respectively. The typical curve of P(r) for a disk-like particle shows two characteristics: (1) The maximum r position corresponds to the diameter of this particle, and (2) the peak position of P(r) is close to but less than the radius of this particle 43 . According to Fig. 6(a,b), for either 8000 eV or 8226 eV, the maximum r positions (domain diameter) of P(r) for 30 °C, −50 °C and 30 °C again are located at ~ 60 nm, 65 nm and ~60 nm, respectively, being roughly consistent with the model-fitting result of approach I in Table 1. The variation trend of domain size with temperature is the same for all used methods. The area-averaged peak (roughly close to the domain radius) of P(r) for 30 °C, −50 °C and 30 °C again are located at ~ 28 nm, 30 nm and ~28 nm, respectively, also showing the same relative trend. According to Fig. 6(c-e), the area-weighted peak position of 8000 eV is higher than that of 8226 eV for each temperature, showing the evidence of core-shell structure.
Structural transition and ordering behavior revealed by the in-situ ASAXS structure factor under the thermal cycle. The morphological characterization and evolution of the core-shell nanodomains during the thermal cycle are revealed by the form factor analysis of ASAXS profiles in the previous sections. This morphological evolution should be closely related to the movement of Ni atoms governed by temperature change. This behavior of Ni atomic movement into/out of the nanodomain core can be independently evidenced by the change in height of the structure peaks (also called the structure factor) within the ASAXS profiles shown in Fig. 2. Basically, the structure factor results from the interaction between domains or the spatial arrangement of   26,42 . These relatively weak structure peaks are marked in detail by the arrows shown in Fig. 7 and do not appear in the SAXS profiles measured by the in-house X-ray instrument 17 . This difference can be attributed to the high resolution and high intensity of synchrotron X-ray radiation. The small structure peaks caused by the spatial arrangement of the concentrated Ni-rich domains are easily self-attenuated in the bulk sample, leading to difficulty in detection. These structure peaks are also detected in the form of bright spots in the radial streaks of the 2D ASAXS patterns, as marked in Fig. 1(e) (e'). The relative positions of these structure peaks of the as-quenched TiNi sample reveal the relationship of integer times. The n th order peak follows the first order peak with a rough position ratio of 1: 2: 3: 4: … : n. For example, from Fig. 7, the position of the first order peak for group A is 0.007 Å −1 , that of the second order peak is 0.014 Å −1 , and so on. This relationship agrees with the prediction of the structure factor of concentrated lamellar stacks with periodic distance 44,45 . According to the general concept of the ordered lamellar structure, the average distance between lamellae (or plates) D can be approximated by D = 2π/Q 1 . Here, the Q 1 value is the peak position of the first-order peak. Therefore, it can be proposed that the several plate-like nanodomains construct an ordered arrangement with equal spacing (like the structure of lamellar stacks).

Discussion
The ASAXS profiles shown in Fig. 2 could be fitted by two possible form-factor models. One is the disk form factor to depict the whole disk of the nanodomain, comprising the shell and core components, at 8000 eV and only the core component at 8226 eV, followed by constructing the real morphology with a Ni-rich shell and highly Ni-rich core, denoted by approach I. The other is the form factor of the core-shell disk model 26,42,46 with two scattering contrast values directly fitting the profile resulting from the difference between the ASAXS profiles at 8000 eV and at 8226 eV, denoted by approach II. Both single disk and core-shell form factors can fit well the continuous scattering profiles under ignorance of S(Q), as shown in Figs. 2 and 5. The corresponding structure parameters determined by approach I and approach II, shown in Tables 1 and 2, respectively, are close to each other. The core radius R c and thickness t c of core-disk nanodomains determined by approach II grew from R c = 29.2 nm and t c = 2.6 nm at 30 °C to be 32.0 nm and 4.0 nm, respectively, when the irradiated sample was cooled down to −50 °C (at T g ). Moreover, the R c and t c of core-disk nanodomains shrank to 29.6 nm and 3.0 nm, respectively, when the irradiated sample was subsequently heated to 30 °C. The shell thickness under the thermal cycle (30 °C → −50 °C → 30 °C end) remained at about 2 nm. The fitted radius (~26 nm) of nanodomains in our previous SAXS result 17 was less than that (~ 30 nm) of this synchrotron ASAXS analysis. The discrepancy is attributed to the Q min of the Q range in this ASAXS study having a much lower value and accounts for the greater power-law scattering intensity than that of the SAXS data of the previous SAXS measurement. If the fitted ASAXS data had been limited to a short Q range and had no power-law model fitting, we would have had the same fitting result as the previous result. In this study, we found that the morphological change (growth) of the highly Ni-rich domain www.nature.com/scientificreports www.nature.com/scientificreports/ (core part) occurs when the sample is cooled from 30 °C towards T g . This morphological change is reversible in the sample heated back to 30 °C. Notably, the structural evolution and then the reversible behavior of the highly Ni-rich disk nanodomains exhibited in as-quenched Ti 48.7 Ni 51.3 SMA during this thermal cycle of 30 °C → −50 °C (~ T g ) → 30 °C (end) are evidenced in this ASAXS study for the first time. This behavior has never been mentioned in the existing theory, in which the strain-glass transition is proposed to arise from the growth of the strain field in the matrix based on the assumption of a uniformly unchanged distribution of Ni point defects 2,4,8 .
As mentioned above, the model constructed from the combination of the ASAXS profiles measured at 8000 eV and 8226 eV, and that constructed directly from the difference in ASAXS profiles measured with different energies, can both substantially reflect the characteristics of the highly Ni-rich part. According to Fig. 7(a), the structure peaks revealing the lamellar stacks and the spatially ordered arrangement with equal spacing in the as-quenched sample could be divided into three groups, denoted by A, B, and C. The spots in the streaks of the 2D ASAXS patterns show that they originate from differently-oriented grains. The Q 1 values of groups A, B and C are 0.007 Å −1 , 0.009 Å −1 and 0.01 Å −1 , respectively. The corresponding spacing D for groups A, B and C (D = 2π/Q 1 ) can be determined to be 897 Å, 698 Å and 628 Å, respectively. As shown in Fig. 7, each group has several structure peaks, e.g., A1, A2, …, demonstrating the characteristic of the highly ordered packing of the nanodomains. The observed first-order peaks (in logarithm scale) are not sharp because they are located in the high background contributed by the form factor. The spatially ordered lamellar arrangement of nanodomains may be formed during the quenching process and could be closely related to the critical Ni composition. More interestingly, when the temperature is cooled to T g , as shown in Fig. 7(b), the intensities of the first-and second-order structure peaks of each group largely increase and become sharp in shape, which can be attributed in theory to the increase in the scattering length density contrast Δρ of the core domain as well as the number of the ordered lamellae. The increase in Δρ of the core domain may be caused by the short-range movement of Ni atoms into the core domain, which is consistent with the morphological growth of the core domain at T g (determined by the form factor in the previous sections). This local action may enhance the number of the "seen" (by contrast) nanodomains in the ordering arrangement based on the assumption that the total number of nanodomains during the thermal cycle is not changed. This kind of local Ni movement and ordering arrangement of nanodomains occurs quickly in the in-situ ASAXS measurement during the thermal cycle. Therefore, the kinetics of Ni movement and the core-domain growth at T g are fast. It can be speculated that the driving force of structural transition is not classical thermal diffusion. The driving force may be the free energy and could be similar to that of the formation of the spinodal decomposition, which has the characteristic of fast movement from a low concentration to a high concentration 47,48 . The mechanistic origin and the driving force are still not known and need to be further investigated. www.nature.com/scientificreports www.nature.com/scientificreports/ When the temperature returns from −50 °C (~T g ) to 30 °C, except for in group B, the structure peaks of the other groups become weak in intensity and less in number (Fig. 7(c)), showing the phenomenon that Ni atoms move out of the nanodomains and the number of the "seen" (by contrast) nanodomains in the ordered arrangement decreases. The structural evolution of the strain glass transition appears be possibly reversible with heating to 30 °C, but the material cannot return to its original state. The thermal effect on nanodomains at a higher temperature of 250 °C causes almost all of the structure factor peaks to disappear (Fig. 7(d)), signifying that a large number of Ni atoms move out from the nanodomains and thus cause the loss of ordering arrangement or lamellar stacks. The large amount of Ni atoms thermally diffusing in the matrix could serve as the source of the precipitation at high temperature, according to the classical mechanism of nucleation and growth. The form factor analysis in the previous sections consistently shows that the nanodomain rapidly grows in radius and thickness, as shown in Table 1. The precipitation of Ti 48.7 Ni 51.3 SMA at the annealing temperature of 250 °C was quantitatively reported in our previous study 17 . From this study, one can find that, for as-quenched Ti 48.7 Ni 51.3 SMA, the structural evolution mechanism (ordering array of nanodomains) between 30 °C and −50 °C (T g ) is entirely different from the precipitation mechanism exhibited at 250 °C.

conclusions
Synchrotron in-situ ASAXS study provides new mechanistic and structural knowledge about the strain glass transition exhibited in as-quenched Ti 48.7 Ni 51.3 SMA. Past simulations and phenomenological models proposed that the induced SRO strain in the glass state was due to the statically-disordered strain domains in the bulk material, based on the assumption that randomly-distributed Ni point defects were fixed in position during strain glass transition. Our ASAXS study provides evidence that Ni point defects concentrate in well-defined nanodomains, with a disk-like core-shell structure consisting of a highly Ni-rich core and a Ni-rich shell in as-quenched Ti 48.7 Ni 51.3 SMA. In addition, at 30 °C, these disk-like nanodomains are locally ordered with a spatially lamellar arrangement. When the temperature decreases to T g , some Ni point defects in the matrix move a short distance into the nanodomains to enlarge the size of the highly Ni-rich core and enhance the ordered structure of the local lamellar arrangement with increased numbers. When the temperature rises back to 30 °C, the morphological evolution of the highly Ni-rich core domains with temperature reveals reversible growth and shrinkage. At 250 °C, the nanodomains grow but lose the corresponding lamellar structure, and precipitation occurs. For as-quenched Ti 48.7 Ni 51.3 SMA, the phase separation mechanism in the range of 30 °C to −50 °C (T g ) is entirely different from the precipitation mechanism exhibited at 250 °C. The ASAXS patterns measured with the near Ni adsorption edge energy demonstrate the structure peaks, signifying the local order arrangement between nanodomains and the associated variation with T g during thermal cycle. This new finding can be regarded to be an experimental breakthrough compared to the current SAXS, SANS and microscopic tools. Therefore, the similar hindrance effect on LRO or the formation of SRO at T g proposed by simulation works may be closely related to the enhancement of the local lamellar or ordering array as well as the morphological variation of the nanodomains.

experimental procedures
A Ti 48.7 Ni 51.3 ingot was prepared in a vacuum arc remelter. The raw materials, titanium (99.99 wt.%) and nickel (99.99 wt.%), were melted six times in high-purity argon atmosphere. The ingot was then hot rolled at 900 °C into a plate of ~2 mm thickness. The plate was subsequently solid-solution treated at 900 °C for 1 h, followed by water-quenching. The grain size in as-quenched Ti 48.7 Ni 51.3 specimens is measured by ASTM E112-88 standard to be 80 ± 15 μm. The specimens for the following ASAXS measurements were cut to a size of 10 × 10 × 0.5 mm 3 and ground to a thickness of ~40 μm so that two or more grains would be contained in the thickness direction. The detailed information on the sample preparations and the experiment conditions can be seen in our previous study 17 .
In-situ ASAXS measurements were conducted at the BL23A beamline, National Synchrotron Radiation Research Center, Taiwan, with a high-flux collimated X-ray beam of ~500 μm in diameter. The temperature-dependent ASAXS measurement was performed with two incident energies of 8000 eV and 8226 eV, which are the far and near absorption K-edge energies of Ni, respectively, for each temperature. The measurements were carried out to investigate the evolution of the Ni-rich nanodomains with temperature and the spatial distribution of Ni atoms in the corresponding Ni-rich nanodomains. The ASAXS measurement of the as-quenched Ti 48.7 Ni 51.3 SMA was performed in-situ first at 30 °C, then at the cooled temperature of −50 °C, and finally at the heated temperature of 30 °C again to complete one cyclic test. According to the results of the physical properties and the DMA tests in our previous study 17 , a sample at −50 °C demonstrates the signs of strain glass transition. Moreover, a subsequent ASAXS measurement was performed at 250 °C after the specimen was aged at 250 °C for 20 min. Each 2D ASAXS pattern was collected for a period of 20 min. According to standard procedures of data reduction, calibration, and background correction, each pattern was azimuthally averaged into a 1D ASAXS profile as a function of the scattering vector Q = 4πsin(θ/2)/λ, in which θ is the scattering angle and λ is the X-ray wavelength.