Point-charge electrostatics in disordered alloys

Abstract

A simple analytic model of point-ion electrostatics has been previously proposed (R. Magri, S. -H. Wei, and A. Zunger, Phys. Rev. B 42, 11388 (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 (1) i 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 qi vs. N (1) i , particularly for fcc alloys, (ii) the magnitudes of total electrostatic energies in random alloys, (iii) the relationships between constant-occupation-averaged charges qi and Coulomb shifts Vi (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 qi and the constant-charge-averaged Coulomb shift V 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 qi vs Vi 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.

Lattice charge models and core level shifts in disordered alloys

“…The MLCM has been shown to reproduce the values of Q i and V i obtained from order-N calculations to a high degree of accuracy -when the model is appropriately parameterized 21 . However, the MLCM has been criticized for the fact that it has too many free parameters 14,23 .…”

“…41. There have also been many investigations into how E M varies with composition in binary random alloys 20,21,42,43 . However, as far as the authors are aware there have been no such studies for ternary random alloys.…”

“…However, despite the shortcomings of the LCM, it certainly performs far better than might be expected from its simplicity. With this in mind, several generalizations of the LCM have been proposed 21,22 . The most successful of these is the multi-shell linear charge model (MLCM) 21,22 , in which each pair of unlike sites separated by R β transfer an amount of charge 2λ β , with the convention that the A site loses 2λ β while the B site gains 2λ β .…”

“…With this in mind, several generalizations of the LCM have been proposed 21,22 . The most successful of these is the multi-shell linear charge model (MLCM) 21,22 , in which each pair of unlike sites separated by R β transfer an amount of charge 2λ β , with the convention that the A site loses 2λ β while the B site gains 2λ β . Assuming that no charge transfer occurs between pairs of sites separated by more than R βmax , then the free parameters in the model become λ 1 , λ 2 , .…”

Charge Distributions in Metallic Alloys: A Charge Excess Functional Theory Approach

“…[5,6] belong. For this purpose I have evaluated the charge distributions in 40 Cu 0.50 Zn 0.50 bcc random alloy samples, each containing 432 atoms.…”