Phenomenological theory of phase transitions in epitaxialBaxSr1−xTiO3thin films

A phenomenological thermodynamic theory of ${\text{Ba}}_x{\text{Sr}}_{1-x}{\text{TiO}}_3$ $\left(\text{BST-}x\right)$ thin films epitaxially grown on cubic substrates is developed using the Landau-Devonshire approach. The eighth-order thermodynamic potential for ${\text{BaTiO}}_3$ (BT) single crystal and modified fourth-order potential for ${\text{SrTiO}}_3$ single crystal were used as starting potentials for the end members of the solid solution with the aim to develop potential of $\text{BST-}x$ solid solution valid at high temperatures. Several coefficients of these potentials for BT were changed to obtain reasonable agreement between theory and experimental phase diagram for $\text{BST-}x$ $\left(x>0.2\right)$ solid solutions. For low Ba content we constructed the specific phase diagram where five phases converge at the multiphase point ($T_{N2}=48\text{K}$, $x=0.029$) and all transitions are of the second order. The “concentration-misfit strain” phase diagrams for $\text{BST-}x$ thin films at room temperature and “temperature-misfit strain” phase diagrams for particular concentrations are constructed and discussed. Near $T_{N2}$ coupling between polarization and structural order parameter in the epitaxial film is modified considerably and large number of new phases not present in the bulk materials appear on the phase diagram.