  A phenomenological thermodynamic theory of BaxSr(1-x)TiO3 (BST-x) thin films
epitaxially grown on cubic substrates is developed using the Landau-Devonshire
approach. The eighth-order thermodynamic potential for BT single crystal and
modified fourth-order potential for ST single crystal were used as starting
potentials for the end-members of the solid solution with the aim to develop
potential of 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 BST-x (x > 0.2)
solid solutions. For low Ba content we constructed the specific phase diagram
where five phases converge at the multiphase point (T_N2 = 47 K, x = 0.028) and
all transitions are of the second order. The "concentration-misfit strain"
phase diagrams for 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.
