Degenerate structure of transformation twins and estimation of dislocation density in martensite crystals

In the dynamic theory of martensitic transformations, the wave mechanism of controlling martensite crystal growth is determined by the superposition of wave beams of quasi-longitudinal (or longitudinal) waves carrying the “tensile–compression” deformation in the orthogonal directions. The wave beam formation is considered to be a result of the formation of excited (vibrational) states. The existence of transformation twins is interpreted as a result of a matched propagation with respect to long-wave ($l$ waves) and short-wave ($s$ waves) shifts. The matching condition is analyzed for the $\gamma$–$\alpha$ martensitic transformation in iron-base alloys. It is shown for the first time that the transition to a degenerate twin structure with the allowance for the medium discreteness enables one to estimate the dislocation density in crystals with habit $\{557\}$, which agrees with that observed experimentally.