Point-charge electrostatics in disordered alloys

Lattice charge models and core level shifts in disordered alloys

Differences in core level binding energies between atoms belonging to the same chemical species can be related to differences in their intra- and extra-atomic charge distributions, and differences in how their core holes are screened. With this in mind, we consider the charge-excess functional model (CEFM) for net atomic charges in alloys (Bruno et al 2003 Phys. Rev. Lett. 91 166401). We begin by deriving the CEFM energy function in order to elucidate the approximations which underpin this model. We thereafter consider the particular case of the CEFM in which the strengths of the 'local interactions' within all atoms are the same. We show that for binary alloys the ground state charges of this model can be expressed in terms of charge transfer between all pairs of unlike atoms analogously to the linear charge model (Magri et al 1990 Phys. Rev. B 42 11388). Hence, the model considered is a generalization of the linear charge model for alloys containing more than two chemical species. We then determine the model's unknown 'geometric factors' over a wide range of parameter space. These quantities are linked to the nature of charge screening in the model, and we illustrate that the screening becomes increasingly universal as the strength of the local interactions is increased. We then use the model to derive analytical expressions for various physical quantities, including the Madelung energy and the disorder broadening in the core level binding energies. These expressions are applied to ternary random alloys, for which it is shown that the Madelung energy and magnitude of disorder broadening are maximized at the composition at which the two species with the largest 'electronegativity difference' are equal, while the remaining species have a vanishing concentration. This result is somewhat counterintuitive with regards to the disorder broadening since it does not correspond to the composition with the highest entropy. Finally, the model is applied to CuPd and CuZn random alloys. The model is used to deduce the effective radii associated with valence electron charge transfer for Cu, Pd and Zn in these systems for use in the 'ESCA potential model' of x-ray photoelectron spectroscopy. The effective radii are found to be R1/3, where R1 is the nearest neighbor distance, with only small variations between chemical elements and between different systems. The model provides a framework for rationalizing the disorder broadenings in these systems: they can be understood in terms of an interplay between the broadening in the Madelung potentials and the broadening in the intra-atomic electrostatic potentials.