  The ideal intrinsic barriers to domain switching in c-phase PbTiO_3 (PTO),
PbZrO_3 (PZO), and PbZr_{1-x}Ti_xO_3 (PZT) are investigated via
first-principles computational methods. The effects of epitaxial strain on the
atomic structure, ferroelectric response, barrier to coherent domain reversal,
domain-wall energy, and barrier to domain-wall translation are studied. It is
found that PTO has a larger polarization, but smaller energy barrier to domain
reversal, than PZO. Consequentially the idealized coercive field is over two
times smaller in PTO than PZO. The Ti--O bond length is more sensitive to
strain than the other bonds in the crystals. This results in the polarization
and domain-wall energy in PTO having greater sensitivity to strain than in PZO.
Two ordered phases of PZT are considered, the rock-salt structure and a (100)
PTO/PZO superlattice. In these simple structures we find that the ferroelectric
properties do not obey Vergard's law, but instead can be approximated as an
average over individual 5-atom unit cells.
