  Using Landau-Ginsburg-Devonshire approach and available experimental results
we reconstruct the thermodynamic potential of the layered ferroelectric
CuInP$_2$S$_6$ (CIPS), which is expected to be applicable a wide range of
temperatures and applied pressures. The analysis of temperature dependences of
the dielectric permittivity and lattice constants for different applied
pressures unexpectedly reveals the critically important role of the nonlinear
electrostriction in this material. With the nonlinear electrostriction included
we calculated temperature and pressure phase diagrams and spontaneous
polarization of bulk CIPS. Using the coefficients of the reconstructed
four-well thermodynamic potential, we study the strain-induced phase
transitions in thin epitaxial CIPS films, as well as the stress-induced phase
transitions in CIPS nanoparticles, which shape varies from prolate needles to
oblate disks. We reveal the strong influence of the mismatch strain, elastic
stress and shape anisotropy on the polar properties and phase diagrams of
nanoscale CIPS. Also, we derived analytical expressions, which allow the
elastic control of the nanoscale CIPS polar properties. Hence obtained results
can be of particular interest for the strain-engineering of nanoscale layered
nanoferroelectrics.
