Coherency Strain Energy in any Crystal System: Applications to in Situ Observations of Cigm in Calcite

Abstract

AbstractIn situ observations of CIGM in CaCO3 bicrystals with a SrCO3 solute source were made. The change in boundary orientation and migration rate were compared with solute concentration. The liquid film model for coherency strain Induced migration was generalized to any non-cubic system and applied to CaCO3-SrCO3. The coherent layer was modeled as a thin film on an infinite half-space. The strain energy was found from solution of the Hooke's law expressions transformed to the appropriate coordinate system. For triclinic or monoclinic films the strain tensor was found by an eigenvector decomposition of the transformation matrix that defined the lattice parameter change with composition. High anisotropy of Vegard's law constants for CaCO3-SrCO3 caused (111) to have the lowest coherency strain per unit solute. Surfaces perpendicular to (111) in coherent equilibria were predicted to have half the solute concentration and three times the migration driving force of those perpendicular to (111). However, no correlation between solute concentration and boundary orientation was observed. Ambiguous and contradictory evidence for a relationship between solute concentration, boundary orientation, and migration rate was found. The self-stress state of a grain boundary in a solute diffusion field may be better modelled as hydrostatic rather than plane stress. Hydrostatic compression may interact with the boundary excess volume and cause a PV driving force for migration. Predictions based on coherent equilibrium at a surface have not been tested for that geometry in calcite; they should be tested before they are applied to grain boundaries.