  In this article, we motivate the detailed comparison of the physical
properties of individual configurations of a ferroelectric solid solution as a
means toward developing first principles models for these systems. We compare
energies, dielectric constants epsilon_infinity, mode effective charges of
local polar distortions, and the zero temperature piezoelectric behavior of
several ordered Pb_3GeTe_4 supercells. Cluster expansions of these properties
show the importance of second-neighbor effects, which can be related to
symmetry-preserving relaxation and its effect on the symmetry breaking polar
instabilities.
