Phenomenological theory of phase transitions in epitaxial Ba x Sr1− x TiO3 thin films on (111)-oriented cubic substrates

A phenomenological thermodynamic theory of BaxSr1−xTiO3 (BST-x) thin films epitaxially grown on (111)-oriented cubic substrates is developed using the Landau-Devonshire approach. The group-theoretical analysis of the low-symmetry phases was performed taking into account two order parameters: the polarization related to ionic shifts in polar zone-center F1u mode and the out-of-phase rotation of TiO6 octahedra corresponding to the R25 zone-boundary mode in the parent cubic phase Pm3¯m. The eight-order thermodynamic potential for BST-x solid solutions was developed and analyzed. We constructed the “concentration-misfit strain” phase diagram for BST-x thin films at room temperature and found that polar rhombohedral R3m phase with the polarization normal to the substrate is stable for x > 0.72 and negative misfit strains, while ferroelectric monoclinic C2 and Cm phases with in-plane polarization are stable for much smaller x and positive or slightly negative misfit strains. We constructed the “temperature-misfit strain” phase diagrams for several concentrations (x = 1, 0.8, 0.6, 0.4, and 0.2). Systematic changes of the phase transition lines between the paraelectric and ferroelectric phases are discussed. The phase diagrams are useful for practical applications in thin-film engineering.