Mechanism for the Sidewise Motion of 180° Domain Walls in Barium Titanate

Abstract

An important unanswered question concerning the sidewise motion of 180\ifmmode^\circ\else\textdegree\fi{} domain walls in single crystal BaTi${\mathrm{O}}_{3}$ is the mechanism by which the boundaries move. This paper considers two possible models. One model assumes that the wall motion results from the repeated nucleation of steps along existing parent 180\ifmmode^\circ\else\textdegree\fi{} domain walls and that the nucleation rate is the controlling factor in the propagation of the wall. The second model investigated involves paired screw dislocations of opposite sense which propagate the wall in a manner analogous to certain types of crystal growth.Many features of the experimental data are consistent with the nucleation model. The nucleated steps are assumed to be triangular slabs along the wall and about one lattice constant thick. For a field of 300 v ${\mathrm{cm}}^{\ensuremath{-}1}$, the critical nucleus is calculated to be 7\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ cm wide (along the electroded crystal surface) and 16\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ cm high (along the ferroelectric axis). For limited ranges of field, the model gives a wall velocity dependence on field of $v\ensuremath{\propto}\mathrm{exp}(\ensuremath{-}\frac{\ensuremath{\delta}}{E})$, which agrees with experiment. The magnitude of the calculated activation field $\ensuremath{\delta}$ agrees with experiment if the energy of the additional wall consequent on a nucleation is set equal to 0.4 ergs ${\mathrm{cm}}^{\ensuremath{-}2}$. The calculated temperature dependence of $\ensuremath{\delta}$ is through ${{P}_{s}}^{3}{T}^{\ensuremath{-}1}{{\ensuremath{\epsilon}}_{a}}^{\ensuremath{-}\frac{1}{2}}$ and is in fair quantitative agreement with experiment. The approximately square domains observed in the low field region are consistent with the model, and the change in shape of the domains observed at higher fields can likewise be explained if slightly different wall energies are assumed for the edges of the nucleated steps on the two different types of 180\ifmmode^\circ\else\textdegree\fi{} domain walls.The screw dislocation model does not predict a wall velocity $v\ensuremath{\propto}\mathrm{exp}(\ensuremath{-}\frac{\ensuremath{\delta}}{E})$ in a straightforward way. It is only with certain unrealistic restrictions on the dislocation density or the wall mobility that this model will give the correct form of $v$. However, it is suggested that this mechanism may contribute to the wall motion with fields of a few thousand volts per centimeter or higher.