The modified transverse Ising model considering double-peak probability distribution functions is constructed and applied to investigate the thermodynamic properties of compositionally graded Ba1xSrxTiO3 thin films. Spatial nonuniformity in compositional concentration is exhibited to give rise to nonuniformity in polarization with corresponding spatial variation. It is found that the magnitude and the sign of the polarization gradients are dependent on the compositional gradient. We also find that the origin of polarization offset is strongly related to not only the compositional gradient but also the temperature. In addition, the compositional gradient plays an important role in the pyroelectric coefficient of the graded film versus temperature, where one or two broad and smooth pyroelectric peaks occur except for a sharp peak at the Curie temperature.

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