Domain walls in ferroelectrics

Spontaneous unit‐cell deformation accompanies spontaneous polarization in perovskite ferroelectrics, thereby making it energetically favorable for domain walls to form on particular planes that satisfy mechanical compatibility. Historically, domain walls are found analytically, solving for walls with compatible strains within the wall plane. However, analytical solutions do not give any information about relative energetics of nonideal domain walls. Here, the orientation of the most favorable domain walls and the relative energetics of nonideal domain walls are predicted by calculating strain mismatch and charge discontinuity over all possible domain wall orientations. This is done for common ferroelectric phase symmetries of tetragonal, rhombohedral, orthorhombic, and monoclinic type. In tetragonal and rhombohedral symmetry, the domain walls are independent of any external stimulus as long as the symmetry is maintained. In orthorhombic and monoclinic symmetry, the orientation of certain mechanically permissible domain walls changes with temperature and/or electric field as the unit cell distorts, while others do not. Additionally, in monoclinic systems, domain wall planes are shown to exist that are not perfectly permissible but are very close to permissible, thus, these walls were not found by prior analytical methods. The visualization of strain compatibility of all the domain walls makes it easy to see precisely on which planes domain walls are expected or not expected and how the domain walls change their orientation under the effect of external stimulus. Such an analysis can also be used to investigate the relative and changing energetics of nonideal domain walls in systems under thermal, compositional, electrical, and mechanical stimuli.