Phasenübergänge in Kristallen

我们考虑晶体固体的弹性，其自由能密度取决于局部化学物质的浓度，这样根据这些物质的浓度，晶体的不同几何构型（相）是优选的。化学物质的局部浓度因扩散而改变。扩散和弹性松弛的时间尺度是不同的。在模型中考虑了不同相区分离的超表面的表面能。我们计划通过研究离散模型的连续极限来增强对表面能和弹性能相互作用的理解。为此，我们计划从分析（隐式时间离散化、弱收敛、g极限、有界变分函数）和几何测量理论（根据Brakke/Soner）中改编和扩展方法。

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).