Direct calculation of lattice Green function with arbitrary interactions for general crystals
arXiv:1202.5585 · doi:10.1103/PhysRevE.85.066706
Abstract
Efficient computation of lattice defect geometries such as point defects, dislocations, disconnections, grain boundaries, interfaces and free surfaces requires accurate coupling of displacements near the defect to the long-range elastic strain. Flexible boundary condition methods embedded a defect in infinite harmonic bulk through the lattice Green function. We demonstrate an efficient and accurate calculation of the lattice Green function from the force-constant matrix for general crystals with an arbitrary basis by extending a method for Bravais lattices. New terms appear due to the presence of optical modes and the possible loss of inversion symmetry. By separately treating poles and discontinuities in reciprocal space, numerical accuracy is controlled at all distances. We compute the lattice Green function for a two-dimensional model with broken symmetry to elucidate the role of different coupling terms. The algorithm is generally applicable in two and three dimensions, to crystals with arbitrary number of atoms in the unit cell, symmetry, and interactions.
18 pages, 7 figures
References in corpus (4)
- Cu/Ag EAM Potential Optimized for Heteroepitaxial Diffusion from ab initio Data
- Lattice Green function for extended defect calculations: Computation and error estimation with long-range forces
- Convergence rate for numerical computation of the lattice Green's function
- Lattice Green's function for crystals containing a planar interface
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