  In present work we calculated the three components of polarization in
phenomenological theory framework by consideration of three Euler-Lagrange
equations, which include mismatch effect and influence of misfit dislocations,
surface tension and depolarization field. These equations were solved with the
help of variational method proposed by us earlier. This approach lead to the
free energy in the form of algebraic equation of different powers of
polarization components with the coefficients dependent on film thickness,
mismatch effect, temperature and other parameters. Several new terms
proportional to misfit strain appeared in the free energy expression: built-in
electric field normal to the surface originated from piezoelectricity in
vicinity of surface even in the cubic symmetry of bulk ferroelectrics,
renormalization of bulk transition temperature via electrostriction, odd powers
of normal to the surface component of polarization. The obtained free energy
made it possible to calculate all properties of the film by conventional
procedure of minimization. It was shown that in both cases self-polarized phase
does exist in definite regions of aforementioned coordinates, its nature being
mismatch effect. The calculations of pyroelectric coefficient and dielectric
permittivity dependencies on temperature, strain and thickness had shown the
unusual behaviour of these quantities, e.g. existence of pyroelectricity at
thicknesses less than critical one for ferroelectric-paraelectric phase
transition.
