Improvement of Coarse-Grained Particle Method for Materials: Finite-Temperature and Inhomogeneity Effects

The coarse-grained particle (CGP) method has been proposed to coarse-grain a crystalline system of atoms to meso-scale. In the method, virtual particles are distributed in the system, and the inter-particle interaction is calculated through the constrained statistical ensemble average of the atomic Hamiltonian at a given temperature. For simplicity, however, the harmonic approximation has been used for the inter-atomic interaction and hence anharmonicity at finite temperatures has been ignored. We improve the former CGP method to incorporate the anharmonicity of atomic system at finite temperatures into the inter-particle interaction. Also the divide-and-conquer strategy is applied to calculate the inter-particle interaction locally for an inhomogeneous system. Demonstrative simulation runs show that the improved CGP method describes properly both anharmonicity at finite temperatures and difference in local stiffness due to the point defect.