  Using the method of anharmonic lattice statics, we calculate the equilibrium
structure of steps on 180^o ferroelectric domain walls (DW) in PbTiO_3. We
consider three different types of steps: i) Ti-Ti step that joins a Ti-centered
DW to a Ti-centered DW, (ii) Pb-Pb step that joins a Pb-centered DW to a
Pb-centered DW, and (iii) Pb-Ti step that joins a Pb-centered DW to a
Ti-centered DW. We show that atomic distortions due to these steps broaden a DW
but are localized, i.e., they are confined to regions with dimensions of a few
lattice spacings. We see that a step locally thickens the domain wall; the
defective domain wall is two to three times thicker than the perfect domain
wall depending on the step type. We also observe that steps distort the
polarization distribution in a mixed Bloch-N\'{e}el like way; polarization
rotates out of the domain wall plane near the steps. Our calculations show that
Pb-Pb steps have the lowest static energy.
