Nonlinear elasticity theory of dislocation formation and composition change in binary alloys in three dimensions

We present a Ginzburg–Landau theory of dislocation dynamics in binary alloys in which the elastic energy is a periodic function of the anisotropic strain components. The composition is twofold coupled to the elastic field via the lattice misfit and via the composition dependence of the elastic moduli (elastic inhomogeneity). We numerically solve the dynamic equations for the lattice displacement and the composition to describe various dislocation processes in three dimensions. On stretching in one-phase states, dislocations proliferate to form a tangle. They tend to be created near pre-existing dislocations. On stretching in two-phase states, dislocations appear in the interface region and glide into the soft region. They are detached from the interface to expand as closed loops, where hard precipitates are acting as dislocation mills. We also follow phase separation around screw dislocations.