POINT-CHARGE ELECTROSTATICS IN DISORDERED ALLOYS

A simple analytic model of point-ion electrostatics has been previousl y 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 a n ordered or random alloy depends linearly on the number N-i((1)) of u nlike neighbors in its first coordination shell. Point charges extract ed from recent large supercell (256-432 atom) local density approximat ion (LDA) calculations of Cu1-xZnx random alloys now enable an assessm ent 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 electros tatic energies in random alloys, (iii) the relationships between const ant-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 ra ndom 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, How ever, for bcc alloys the fluctuations predicted by the model in the q( i) vs V-i relation exceed those found in the LDA supercell calculation s. We find that (a) the fluctuations present in the model have a vanis hing contribution to the electrostatic energy. (b) Generalizing the mo del to include a dependence of the charge on the atoms in the first th ree (two) shells in bcc (fee) - rather than the first shell only - rem oves the fluctuations, in complete agreement with the LDA data. We als o demonstrate an efficient way to extract charge transfer parameters o f the generalized model from LDA calculations on small unit cells.