  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 [E. Bruno et al., Phys. Rev. Lett. 91,
166401 (2003)]. 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 strength 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 [R.
Magri et al., Phys. Rev. B 42, 11388 (1990)]. 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 having a vanishing concentration. This result is somewhat
counterintuitive with regards to the disorder broadening since it does not...
