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. 42, 11 388 (1990)] in which the magnitude of the net charge qi on each atom in an ordered or random alloy depends linearly on the number N-i((1)) of unlike neighbors in its first coordination shell. Point charges extracted from recent large supercell (256-432 atom) local density approximation (LDA) calculations of Cu1-xZnx 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 q(i) vs N-i((1)), particularly for fee alloys, (ii) the magnitudes of total electrostatic energies in random alloys, (iii) the relationships between constant-occupation-averaged charges [q(i)] and Coulomb shifts [V-i] (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 q(i) and the constant-charge-averaged Coulomb shift <(V)over bar (i)> (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 q(i) vs V-i 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 (fee) - 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.