The problem of determining elastic constants of thin ferroelectric films
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A method of determining the constants of the linear equations of the piezoelectric effect dependent on the external conditions is proposed for thin ferroelectric films on the basis of the Landau potential of the phenomenological theory of phase transitions. By the example of single-crystalline barium—titanate thin films, the behavior of material constants is investigated in dependence on the value of the misfit strain. The investigation of material equations is implemented on the basis of the Landau potential of the eighth degree at room temperature. The substantial difference in the elastic, electric, and piezoelectric properties of a thin film from those of a bulk material is shown; the anomalous behavior of constants on the phase boundaries and the extremal behavior inside the r-phase is revealed.
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