Periodic Grain Boundary Grooves: Analytic Model, Formation Energies, and Phase-Field Comparison

Analytic profiles for periodic grain boundary grooves (PGBGs) were determined from variational theory. Variational profiles represent stationary solid-liquid profiles with abrupt, zero-thickness, transitions between adjoining phases. Variational PGBGs consequently lack tangential interfacial fluxes, the existence of which requires more realistic (non-zero) interfacial thicknesses that allow energy and solute transport. Variational profiles, however, permit field-theoretic calculations of their scaled formation free energy and thermodynamic stability, capillary-mediated chemical potentials, and their associated vector gradient distributions, all of which depend on a profile’s geometry, not its thickness. Despite the fact that variational profiles are denied interface fluxes, one may, nevertheless, impute shape-dependent interface transport in the form of a profile’s surface Laplacian of its presumptive chemical potential distribution due to capillarity. We compare variational surface Laplacians with residuals of the thermochemical potential measured along counterpart diffuse-interface PGBGs, simulated via phase-field with metrically-proportional profiles. Fundamentally, it is the thickness of a microstructure’s interfaces and its shape that co-determine whether, and to what extent, gradients of the chemical potential excite fluxes that transport energy and/or solute. PGBGs, both variational and simulated, greatly expand the limited universe of solid-liquid microstructures suitable for steady-state thermodynamic analysis. Understanding the origin and action of these capillary-mediated interfacial fields opens a pathway for estimating and, eventually, measuring how solid-liquid interface thickness modifies the transport of energy and solute during solidification and crystal growth, and influences microstructure.