Phasenübergänge in Kristallen

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We consider the elasticity of cristalline solids whose free energy density depends on the local concentration of chemical substances in such a way that according to the concentration of these substances different geometrical configurations (phases) of the crystal are preferred. The local concentration of the chemical substances is changed by diffusion. The time scales for the diffusion and the elastic relaxation are different. In the models we consider the surface energy of the hypersurfaces separating regions of different phase is taken into account. We plan to enhance the understanding of the interplay of surface energy and elastic energy by investigating the continuum limit of discrete models. For these aims, we plan to adapt and extent methods from analysis (implicit time discretization, weak convergence, G-Limit, functions of bounded variation) and from geometric measure theory Revolution of varifolds according to Brakke/Soner).