## 3 Results and Discussion
### Crystallographic Limit of Recovery Strain  
It was previously reported in [46] that grain refinement down to a nanometer-scaled grain size and the development of a dislocation substructure in the parent B2-phase in Ti-Ni SMAs significantly reduce the crystallographic limit of recovery strain (\(\epsilon_{r}{}^{max}\)). Thus, it was of interest to compare the effect of grain size on the crystallographic limit of recovery strain of the studied Ti-Nb-Zr alloys, particularly as this effect had not yet been studied in nickel-free Ti-based SMAs. All alloys after TMT were selected for the study and grain structures were graded into three ranges: coarse-grained after 1.5 + 800 (30); fine-grained after 1.5 + 600 (30); and ultrafine-grained structure after 3.0 + 600 (5) and 3.0 + 550 (5). Specimens of these alloys which contained predominant parent \(\beta\)-phases after TMT were subjected to additional CR with \(e\) = 0.3 to produce a stress-induced \(\alpha^{\prime\prime}\)-martensite that was thermally stabilized by cold plastic deformation. The corresponding fragments of the X-ray diffractograms are shown in Figure 9.  
Since there are not enough \(\alpha^{\prime\prime}\)-phase lines with well-measured positions to use a conventional least-squares method to calculate the lattice parameters and consequently the crystallographic limit of recovery strain with a representative accuracy, a direct calculation is used based on the \((020)_{\alpha^{\prime\prime}}\) and \(\{110\}_{\beta}\) peak positions, as in [19]. All alloys after TMT at 3.0 + 550 (5) (Figure 9-l) had their smallest average true grain size (\(\overline{D}\)); however, after additional CR, the 18-15 alloy (Figure 9k) did not form enough \(\alpha^{\prime\prime}\)-phases with clearly visible \((020)_{\alpha^{\prime\prime}}\) X-ray lines to calculate the crystallographic limit of the recovery strain (\(\epsilon_{r}{}^{max}\)), the more so, it was overlapped by a stronger \((100)_{\alpha}\) line. Therefore, the 3.0 + 600 (5) route was chosen to calculate the crystallographic resource of recovery strain in the ultrafine-grained structure of the \(\beta\)-phase (Figure 9g-i).  
Based on the \((020)_{n^{\prime\prime}}\) and \(\{110\}_{\beta}\) peak positions, the interplanar distances of d\({}_{020a}\)\" and d\({}_{110\beta}\) and the crystallographic limit of recovery strain (\(\epsilon_{r}{}^{max}\)) were calculated for the studied Ti-Nb-Zr alloys (Table 3).  
The 41-12 alloy in the coarse-grained state exhibits the highest crystallographic limit of recovery strain of \(\epsilon_{r}{}^{max}\)\(\approx\) 6%. This value is considered high for nickel-free SMAs. The transition from high- to low-Zr and low- to high-Nb alloys leads to a pronounced decrease in the \(\epsilon_{r}{}^{max}\) value to \(\approx\)5% for the 18-15 alloy and to \(\approx\)3% for the 22-6 alloy. These results correlate well with the literature data [19; 24; 25]. Decreases in grain size and the transition to the ultrafine-grained structure of the \(\beta\)-phase do not affect the crystallographic limit of recovery strain (Figure 10). The trend of a decreasing crystallographic limit of recovery strain with grain refinement is well known in Ti-Ni SMAs [46]. However, this has been reported for grain sizes close to 100 nm (0.1 \(\upmu\)m) and below. In contrast, in the current study, all alloys had larger minimum average grain sizes: 0.15 \(\pm\) 0.01 \(\upmu\)m for 22-6, 0.68 \(\pm\) 0.04 \(\upmu\)m for 18-15, and 0.38 \(\pm\) 0.03 \(\upmu\)m for the 41-12 alloy. Therefore, in future research, the impact of grain size dependence on the crystallographic limit of recovery strain in Ti-Zr-Nb SMAs needs to be confidently verified.  
Figure 9: X-ray diffractograms of 22-6 (**a**,**d**,**g**,**i**), 18-15 (**b**,**e**,**h**,**k**), and 41-12 (**c**,**f**,**i**,**i**) alloys subjected to stabilizing cold rolling after 1.5 + 600 (30) (**a**–**c**), 1.5 + 800 (30) (**d**–**f**), 3.0 + 550 (5) (**j**–**l**), and 3.0 + 600 (5) (**g**–**i**).