Phase-field simulations of partial melts in geological materials

A diffuse interface description based on a multi-phase-field model for geological grain microstructures is introduced, especially useful in the treatment of partially molten structures. Each grain as well as different phases are represented by individual non-conserved order parameters, the phase fields φαφα, which are defined on the complete simulation domain. The derivation of the model from a Ginzburg–Landau type free energy density functional is briefly shown and all occurring energy contributions are discussed. Also, the nondimensionalisation necessary to relate the simulation to real experiments and a brief overview of the numerical methods used in the simulations is given. To illustrate the applicability of the method to large grain systems a simulation of normal grain growth was carried out. The results on the dynamics of the process are in close agreement with theory. The extension of the phase-field model to incorporate phases with conserved volume is described next. This capacity is exploited for the liquid phase in a partially molten structure, where melt and a solid mineral phase are in equilibrium. Simulations with isolated melt inclusions within a grain structure in 2D and 3D are presented, resulting in the formation of the correct dihedral angles corresponding to the solid/solid and solid/liquid interface energies γSSγSS and γSLγSL. The case of complete wetting of the grain boundaries, if γSL/γSS<0.5γSL/γSS<0.5 is shown. Taking the structure of an analogue experiment as initial data, a simulation of a grain structure with a melt fraction of 3.6% and a dihedral angle of 10∘10∘ were performed using the phase-field model. The comparison with a sharp interface front-tracking model for this case results in a highly comparable microstructure evolution.