Inhomogeneous microscopic shear strains in a complex crystal lattice subjected to large macroscopic strains (exact solutions)

Abstract

Nonlinear theory of microscopic and macroscopic strains is developed for the case of large inhomogeneous relative displacements of two sublattices making up a complex crystal lattice; in this case, in addition to an acoustic mode, a pseudooptical, strongly nonlinear mode is excited. The equation of relative motion of the sublattices can be solved exactly for the specific case of a centrosymmetric crystal. The corresponding equilibrium equation is the sine-Helmholtz equation and has a doubly periodic solution. This solution describes fragmentation of the lattice, more specifically, the appearance of a domain superstructure with large periods, whose building blocks contain oppositely sensed rotons separated by topological defects that are opposite in sign. Purely elastic microscopic strains are followed by elastoplastic ones. Both types of strain arise as a result of bifurcation, which causes a change from the initially homogeneous strain field to an inhomogeneous one. The domain sizes take on optimal values when the external homogeneous macroscopic strains reach a certain threshold magnitude.