Analytical Treatment of the Isotropic and Tetragonal Lattice Green Functions for the Face-centered Cubic, Body-centered Cubic and Simple Cubic Lattices
B.A. Mamedov

doi:10.3970/cmc.2014.043.087
Source CMC: Computers, Materials & Continua, Vol. 43, No. 2, pp. 87-95, 2014
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Keywords Isotropic lattice Green functions, tetragonal lattice Green functions, face-centered cubic lattice, body-centered cubic lattice, simple cubic lattice.
Abstract In this paper, we propose an efficient method to calculate the isotropic and tetragonal lattice Green functions for the face-centered cubic (FCC), bodycentered cubic (BCC) and simple cubic (SC) lattices. The method is based on binomial expansion theorems, which provide us with analytical formulae through basic integrals. The resulting series present better convergence rates. Several acceleration techniques are combined to further improve the efficiency of the established formulas. The obtained results for the lattice Green functions are in good agreement with the known numerical calculation results.
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