  Ternary cubic perovskite compounds of the form A_(1/3)A'_(1/3)A''_(1/3)BO_3
and AB_(1/3)B'_(1/3)B''_(1/3)O_3, in which the differentiated cations form an
alternating series of monolayers, are studied using first-principles methods.
Such compounds are representative of a possible new class of materials in which
ferroelectricity is perturbed by compositional breaking of inversion symmetry.
For isovalent substitution on either sublattice, the ferroelectric double-well
potential is found to persist, but becomes sufficiently asymmetric that
minority domains may no longer survive. The strength of the symmetry breaking
is enormously stronger for heterovalent substitution, so that the double-well
behavior is completely destroyed. Possible means of tuning between these
behaviors may allow for the optimization of resulting materials properties.
