Symmetry-adapted order parameters and free energies for solids undergoing order-disorder phase transitions

Abstract

Order-disorder phase transitions are common in a wide range of materials and are exploited in many technological applications. A key challenge in developing predictive mesoscale models for these materials lies in constructing rigorous first-principles based thermodynamic descriptions. In this study, the authors develop a general formalism to generate order parameters for any crystal structure and alloy ordering. Furthermore, they describe a thermodynamic and statistical mechanics framework to determine the free energy as a function of order parameters. The methods described here are broadly applicable to any multicomponent crystalline solid and provide the first step in generating truly $a\phantom{\rule{0}{0ex}}b\phantom{\rule{0.333em}{0ex}}i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ multiscale models.