Landau–Devonshire thermodynamic potentials for displacive perovskite ferroelectrics from first principles

A general approach for fitting Landau–Devonshire thermodynamic potentials directly from first principles is developed for simple displacive ferroelectric perovskite materials. As the first step, a \(\hbox {PbTiO}_3\) potential is parameterized completely from density functional theory calculations as a test case, under the only assumption that the transition between the non-polar and polar phases is of first order. The utility of this approach is assessed by comparing quantities characterizing the phase transition, dielectric and piezoelectric properties and equibiaxial strain–temperature phase diagrams with the predictions of several thermodynamic potentials parameterized from experimental data. In the second step, a similar parameterization is generated for a fictitious polar perovskite \(\hbox {SnTiO}_{3}\), enabling us to predictively evaluate an approximate ‘equibiaxial strain–temperature–spontaneous polarization’ phase diagram for its thin films.