  Using first-principles supercell calculations, we have investigated
energetic, structural and dielectric properties of three different A(B'B'')O_3
perovskite alloys: Ba(Zn_{1/3}Nb_{2/3})O_3 (BZN), Pb(Zn_{1/3}Nb_{2/3})O_3
(PZN), and Pb(Zr_{1/3}Ti_{2/3})O_3 (PZT). In the homovalent alloy PZT, the
energetics are found to be mainly driven by atomic relaxations. In the
heterovalent alloys BZN and PZN, however, electrostatic interactions among B'
and B'' atoms are found to be very important. These electrostatic interactions
are responsible for the stabilization of the observed compositional long-range
order in BZN. On the other hand, cell relaxations and the formation of short
Pb--O bonds could lead to a destabilization of the same ordered structure in
PZN. Finally, comparing the dielectric properties of homovalent and
heterovalent alloys, the most dramatic difference arises in connection with the
effective charges of the B' atom. We find that the effective charge of Zr in
PZT is anomalous, while in BZN and PZN the effective charge of Zn is close to
its nominal ionic value.
