  In the computation of the material properties of random alloys, the method of
"special quasirandom structures" attempts to approximate the properties of the
alloy on a finite volume with higher accuracy by replicating certain statistics
of the random atomic lattice in the finite volume as accurately as possible. In
the present work, we provide a rigorous justification for a variant of this
method in the framework of the Thomas-Fermi-von Weizs\"acker (TFW) model. Our
approach is based on a recent analysis of a related variance reduction method
in stochastic homogenization of linear elliptic PDEs and the locality
properties of the TFW model. Concerning the latter, we extend an exponential
locality result by Nazar and Ortner to include point charges, a result that may
be of independent interest.
