Conjugation of crystal structures in alloys with martensitic transformations: the possibility of constructing a habitus plane by methods of differential geometry

The phase transformation austenite-martensite can be considered as a homogeneous deformation, as a result of which a sphere of unit radius turns into an ellipsoid of deformation. A method for determining the position of the habitus plane based on the analysis of the curvature of the spatial curve of the intersection of the sphere and the deformation ellipsoid is proposed. The algorithm includes finding the coordinates of the point of minimum curvature by numerical methods, determining the position of the straightening plane at the specified point, and the coordinates of the center of curvature. The vector "center of curvature – the point of minimum curvature" defines the normal to the habitus plane. Comparison of the calculated values of the invariant plane indices with the experimental ones showed satisfactory agreement for a number of alloys. It is possible that the deviation of the calculated data from the experimental data for some alloys is due to the need to take into account the deviation from the orientation relationship in the process of martensite transformation.