Capillary effects on curved solid–liquid interfaces: An overview

This overview begins with observations of capillary-mediated effects on crystal-melt interfaces in microgravity and attempts to interpret them using the LeChâtelier–Braun effect and Kelvin's equation—both local equilibrium requirements applicable at curved interfaces. Numerical studies of interfacial kinetics followed, using Greens function distributions that simulated evolving sharp solid–liquid interfaces undergoing pattern formation. Those methods exposed a need for more incisive steady-state techniques. Grain boundary grooves were used as constrained, stationary, microstructures. Their steady-state profiles derive from variational calculus and were analyzed for their imputed Gibbs–Thomson thermopotentials for comparative thermodynamic studies. Variational profiles, however, have unrealistic zero-thickness transitions between phases, and thus lack fluxes of energy or solute that occur on real interfaces. The exact formulation of variational profiles, however, advantageously supports field-theoretic calculations of their first-order formation free energy, thermodynamic stability, capillary-mediated chemical potentials, interfacial gradients and scalar divergences. These linked fields all depend on an interface's curvature distribution, i.e., its geometry, but others, for example tangential fluxes of energy and solute, also depend on interface thickness and structure, i.e., thermodynamics. We comparatively analyzed capillary-mediated fields up to 4th-order, including the surface Laplacian of a profile's chemical potential. This Laplacian is proportional to scaled divergences of fluxes that appear on counterpart real or simulated microstructures with congruent shapes. Divergent energy fluxes manifest as cooling distributions, which cause depression of the thermochemical potential measured along diffuse-interfaces simulated with phase-field. Cooling distributions are visualized to explain qualitative and quantitative features of a microstructure's steady-state thermal maps. Evidence is included of how thickness and shape of crystal-melt interfaces co-determine whether, and to what extent, interfacial transport occurs. Understanding the origin and actions of interfacial capillary fields might offer improved control of microstructure at mesoscopic levels, accessible with these deterministic fields through physical and chemical means.