First-order phase transitions in ferroelectric films

We discuss a version of the Landau–Devonshire model for films undergoing a first-order phase transition. The spatial variation P(z) of the order parameter is described by an Euler–Lagrange equation with associated boundary condition. We define a general numerical scheme for finding P(z) and evaluating the resulting thermodynamic functions. Results are presented for the thickness, temperature and boundary-condition dependence of P(z), the free energy and entropy and the superheating, supercooling and thermodynamic critical temperatures.