  In this paper we study the effect of normal and shear strains and oxygen
vacancies on the structure of 180^o ferroelectric domain walls in PbTiO_3. It
is known that oxygen vacancies move to the domain walls and pin them. Hence, we
assume a periodic arrangement of oxygen vacancies on both Pb-centered and
Ti-centered domain walls in PbTiO_3. We use a semi-analytic anharmonic lattice
statics method for obtaining the relaxed configurations using a shell
potential. In agreement with recent ab initio calculations, we observe that a
Pb-centered domain wall with oxygen vacancies is not stable even under strain.
Our semi-analytic calculations for PbTiO_3 show that oxygen vacancies affect
the structure of 180^o domain walls significantly but do not have a
considerable effect on the thickness of domain walls; they broaden the domain
walls by about fifty percent. We also study the effect of normal and shear
strains on both perfect and defective 180^o domain walls. We observe that
normal and shear strains affect the structure but do not change the domain wall
thickness.
