Microstructure equilibration with consideration of elastic and interfacial interactions via quantum annealing with application to the solid electrolyte LLZO

We present a detailed derivation of the elastic energy of a homogeneous, isotropic linear elastic medium consisting of different coherent martensite variants or phases and its mapping to an Ising model, as required for an efficient quantum annealing determination of the equilibrium microstructure. The approach is demonstrated for a sample with a large number of grains with a tetragonal eigenstrain. Furthermore, we illustrate how the elastic effects may lead to the formation of ion conducting channels in the doped solid electrolyte ${\mathrm{Li}}_7{\mathrm{La}}_3{\mathrm{Zr}}_2{\mathrm{O}}_{12}$ (LLZO). Apart from bulk elastic and chemical effect we demonstrate how to include interfacial effects into the quantum annealing approach and emphasize the importance of high precision elastic calculations.