  In alloys exhibiting substitutional disorder, the variety of atomic
environments manifests itself as a `disorder broadening' in their core level
binding energy spectra. Disorder broadening can be measured experimentally, and
in principle can be used to deduce information about specific atomic
environments within a sample. However, progress in this endeavor is hampered by
the lack of a model for this phenomenon which can treat complex systems. In
this work we describe such a model. The model is used to elucidate the
relationship between charge transfer, atomic environment, and disorder
broadening in complex systems, with a focus on the problem of characterizing
the interface quality of CuNi multilayers. We also validate the model against
the results of ab initio electronic structure calculations. Several
counterintuitive aspects of the disorder broadening phenomenon are uncovered,
an understanding of which is essential for the correct interpretation of
experimental results. For instance, it is shown that systems with inhomogeneous
concentration profiles can exhibit disorder broadenings significantly larger
than random alloys. Furthermore in some systems a `disorder narrowing' is even
possible.
