Point-charge electrostatics in disordered alloys

A simple analytic model of point-ion electrostatics has been previously proposed [R. Magri, S. -H. Wei, and A. Zunger, Phys. Rev. B 42, 11 388 (1990)] in which the magnitude of the net charge (Formula presented) on each atom in an ordered or random alloy depends linearly on the number (Formula presented) of unlike neighbors in its first coordination shell. Point charges extracted from recent large supercell (256-432 atom) local density approximation (LDA) calculations of (Formula presented)(Formula presented) random alloys now enable an assessment of the physical validity and accuracy of the simple model. We find that this model accurately describes (i) the trends in (Formula presented) vs (Formula presented), particularly for fcc alloys, (ii) the magnitudes of total electrostatic energies in random alloys, (iii) the relationships between constant-occupation-averaged charges 〈(Formula presented)〉 and Coulomb shifts 〈(Formula presented)〉 (i.e., the average over all sites occupied by either A or B atoms) in the random alloy, and (iv) the linear relation between the site charge (Formula presented) and the constant-charge-averaged Coulomb shift (Formula presented) (i.e., the average over all sites with the same charge) for fcc alloys. However, for bcc alloys the fluctuations predicted by the model in the (Formula presented) vs (Formula presented) relation exceed those found in the LDA supercell calculations. We find that (a) the fluctuations present in the model have a vanishing contribution to the electrostatic energy. (b) Generalizing the model to include a dependence of the charge on the atoms in the first three (two) shells in bcc (fcc) — rather than the first shell only — removes the fluctuations, in complete agreement with the LDA data. We also demonstrate an efficient way to extract charge transfer parameters of the generalized model from LDA calculations on small unit cells.