Lattice Boltzmann modeling of the coherent solid–solid transition with elastic effects

A mesoscopic lattice Boltzmann model is proposed to investigate the dynamic evolution of solid-state structures during the hexagonal-to-orthorhombic transition, incorporating the micro-elastic theory. The model enables detailed observation of the morphology of both single- and multi-variant systems. The analytically recovered macroscopic governing equation is fully consistent with the kinetic theory, and the interactions between different domains are well characterized. The strategy opens up a vast range of solid-state phase transitions, particularly those involving multi-phase and multi-domain systems. • Opening a new research avenue by extending the kinetic theory into the previously unexplored domain of solid-state phase transitions • By integrating phase field and micro-elastic theories, the LB model can significantly capture the evolution of solid microstructures and the formation of unique patterns • Offering a novel perspective that addresses the complexities of solid-state phase transitions with high accuracy • Making essential strides towards solving critical problems in solid microstructures.