## 2 Materials and Methods
The 41-12 alloy had significant etching difficulties after some thermomechanical treatments. Therefore, electron backscattered diffraction (EBSD) was chosen for the analysis of grain structures with grain sizes larger than 1 \(\upmu\)m, while transmission electron microscopy was chosen for grain structures smaller than 1 \(\upmu\)m.  
To determine the phase state before and after all TMT routes and the crystallographic limit of recovery strain (\(\varepsilon_{r}\)max), \(X\)-ray diffraction analysis (XRD) was carried out at RT using 8 mm \(\times\) 10 mm specimens and a DRON-4 diffractometer (Russia) with CuK\({}_{\alpha}\) radiation in the 30-90 deg 20 range. Specimens were mechanically ground down with P1200 abrasive paper and chemically etched in a 1 HF:3 HNO3:6H2O solution to remove the oxidized and mechanically damaged layer. The lattice parameter \(a_{\beta}\) of the BCC \(\beta\)-phase was calculated using Nelson-Riley extrapolation. To determine the \(\varepsilon_{r}\)max, specimens were additionally cold-rolled with a true strain of \(e\) = 0.3 to induce and stabilize the orthorhombic \(\alpha^{\prime\prime}\)-phase. The maximum \(\beta\)+\(\alpha^{\prime\prime}\) martensitic transformation lattice strain, i.e., the maximum crystallographic recovery strain limit, \(\varepsilon_{r}\)max, was calculated from (020)\(\alpha^{\prime\prime}\) and \(\{110\}_{\beta}\) peak positions following the methodology of [19], as follows:  
\[\varepsilon_{r}^{max}\ =\ \frac{b_{\alpha^{\prime\prime}}-\sqrt{2}a_{\beta}}{ \sqrt{2}a_{\beta}}, \tag{1}\]  
The EBSD study was performed on 10 mm \(\times\) 10 mm specimens using the FEI Scios DualBeam system (Thermo Fisher Scientific, Waltham, MA, USA). For EBSD mapping, the beam voltage and current were equal to 30 kV and 3.2 nA. The orientation maps were calculated using TSL OIM data collection software V.8 and then processed by TSL Oim Analysis software 7.2.1. Specimens were mechanically ground down with P4000 abrasive paper, polished with 0.5 \(\upmu\)m SiO\({}_{2}\) suspension, and etched with [PERSON]'s solution. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**CR Degree** & **Deformation Value** & **PDA** & **TMT Designation** \\ \hline \multirow{2}{*}{Moderate} & \(e\) = 0.3 & 600 \({}^{\circ}\)C, 30 min & 0.3 + 600 (30) \\  & 800 \({}^{\circ}\)C, 30 min & 0.3 + 800 (30) \\ \hline \multirow{2}{*}{Intermediate} & \(e\) = 1.5 & 600 \({}^{\circ}\)C, 30 min & 1.5 + 600 (30) \\  & 800 \({}^{\circ}\)C, 30 min & 1.5 + 800 (30) \\ \hline \multirow{3}{*}{Severe} & \multirow{3}{*}{\(e\) = 3.0} & 550 \({}^{\circ}\)C, 5 min & 3.0 + 550 (5) \\  & 600 \({}^{\circ}\)C, 5 min & 3.0 + 600 (5) \\ \cline{1-1}  & 600 \({}^{\circ}\)C, 30 min & 3.0 + 600 (30) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Processing routes for the studied alloys. Figure 1: Microstructures of 22-6 (**a**), 18-15 (**b**), and 41-12 (**c**) alloys after hot rolling and homogenization annealing. TEM was performed using a JEM-2100 transmission electron microscope (JEOL, Tokyo, Japan) at 200 kV. Specimens of 5 mm \(\times\) 5 mm size were chemically etched in 1 HF:3 HNO3:6H\({}_{2}\)O solution down to 0.1 mm and then thinned on a PIPS II Gatan ion-thinning device (Gatan, Pleasanton, CA, USA). Based on the images obtained by EBSD and TEM, the true average grain size \(\overline{D}\), of the \(\beta\)-phase was measured by the random linear intercept method using at least 100 grains for calculation [36]. Since high-angle (\(\geq\)15\({}^{\circ}\)) boundaries were used in this method, some deformed areas of the initial grains with some possible internal substructures or high dislocation densities were also involved in the calculations.