L. Bellaiche et D. Vanderbilt, Virtual crystal approximation revisited: Application to dielectric and piezoelectric properties of perovskites, PHYS REV B, 61(12), 2000, pp. 7877-7882
We present an approach to the implementation of the virtual crystal approxi
mation (VCA) for the study of properties of solid solutions in the context
of density-functional methods. Our approach can easily be applied to any ty
pe of pseudopotential, and also has the advantage that it can be used to ob
tain estimates of the atomic forces that would arise if the real atoms were
present, thus giving insight into the expected displacements in the real a
lloy. We have applied this VCA technique within the Vanderbilt ultrasoft-ps
eudopotential scheme to predict dielectric and piezoelectric properties of
the Pb(Zr0.5Ti0.5)O-3 solid solution in its paraelectric and ferroelectric
phases, respectively. Comparison with calculations performed on ordered all
oy supercells and with data on parents compounds demonstrates the adequacy
of using the VCA for this perovskite solid solution. In particular, the VCA
approach reproduces the anomalous Born effective charges and the large val
ue of the piezoelectric coefficients.