The lattice dynamical mean field criterion for low energy dislocation structure formation in shape memory alloys

Abstract

The low energy dislocation structure (LEDS) predicted by the lattice-variant shear theory consists of transformation dislocations created by two lattice-variant shears: a primary shear on a system with degenerate stress,sense, and a habit plane shear for which the variants self-accommodate. Two correlations (microscopic and macroscopic), analogous to amplitudon and phason soft mode branches of phenomenological theories, are required in order to maintain the mean field: (i) the high energy dislocation structure (HEDS) at each source (transformation dislocations of one sign) correlates with the opposite-sign HEDS at other sources to cancel their long-range stress fields; (ii) the primary shear at each source periodically alternates its direction on a system with degenerate stress sense. The macroscopic correlation of fluctuating LEDS (domain wall motion) gives rise to critical behavior and diverging physical properties. LEDS motion is characterized by a soliton or sliding mode phason which, when the domains are narrow, modulates the wavevector of the microscopic soft phonon mode and gives rise to an electron-phonon interaction for a possible electronic transition.