Temperature-strain phase diagram for BaTiO3 thin films

The shifts of ferroelectric phase transition temperatures and domain stabilities of $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ thin films as a function of strain and temperature were studied using phase-field simulations. A new Landau-Devonshire thermodynamic potential based on an eighth-order polynomial was employed for describing the bulk free energy of $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ single crystals, which allows the exploration of domain stability in the full range of experimentally accessible compressive and tensile strains. Based on the simulation results, a phase diagram was constructed, which displays the stability of various ferroelectric phases and domain structures as a function of temperature and strain.