A Model for Grain Boundary Thermodynamics

Systematic microstructure design requires reliable thermodynamic descriptions of each and all microstructure elements. While such descriptions are well established for most bulk phases, thermodynamic assessment of crystal defects is challenged because of their individualistic nature. In this paper, a model is devised for assessing grain boundary thermodynamics based on available bulk thermodynamic data. We propose a continuous relative atomic density field and its spatial gradients to describe the grain boundary region with reference to the defect-free, homogeneous bulk and derive the grain boundary Gibbs free energy functional. Grain boundary segregation isotherm and phase diagram are computed for a regular binary solid solution, qualitatively discussed for the Pt-Au system. The relationships between the grain boundary's atomic density, excess free volume, and misorientation angle are discussed. Combining the current density-based model with available bulk thermodynamic databases capacitates constructing databases, phase diagrams, and segregation isotherms for grain boundaries, opening possibilities for studying and designing heterogeneous microstructures.