Gradient-stress on polarization in Ba1-xSrxTiO3 films

A group of position-thickness-dependent stresses are used to modified Landau-Devonshire theory to investigate the second-order phase transition in Ba1−x Sr x TiO3 films. The result shows that the short-range interaction between the unit cells of the film and the substrate induces the phase transition dispersion and the rise of the transition temperature in the films. The dependence of the effective dielectric constant on the temperature and the average spontaneous polarization on the film thickness are computed, which qualitatively agree with the experiments.