Аннотация:The effect of epitaxial strain on the phonon spectra, crystal structure,
spontaneous polarization, dielectric, piezoelectric, and elastic properties
of (001)-oriented ferroelectric (BaTiO$_3$)$_m$/(SrTiO$_3$)$_n$
superlattices ($m = n = {}$1--4) was studied using the first-principles
density-functional theory. The ground state of free-standing superlattices
is the monoclinic $Cm$ polar phase. Under the in-plane biaxial compressive
strain, it transforms to tetragonal $P4mm$ polar phase, and under the in-plane
biaxial tensile strain, it transforms to orthorhombic $Amm2$ polar phase.
When changing the in-plane lattice parameter, a softening of several optical
and acoustic modes appears at the boundaries between the polar phases,
and corresponding components of dielectric, piezoelectric, and elastic tensors
diverge critically. The comparison of the mixing enthalpy of disordered
Ba$_{0.5}$Sr$_{0.5}$TiO$_3$ solid solution modeled using two special
quasirandom structures SQS-4 with the mixing enthalpy of the superlattices
reveals a tendency of the BaTiO$_3$--SrTiO$_3$ system to short-range ordering
and shows that these superlattices are thermodynamically quite stable.