Nonempirical calculation of the Pb(${\mathrm{Sc}}_{0.5}$${\mathrm{Ta}}_{0.5}$)${\mathrm{O}}_3$-${\mathrm{PbTiO}}_3$ quasibinary phase diagram

The nonempirical potential induced breathing (PIB) method has been used to calculate structural parameters and total energies for ${\mathrm{PbTiO}}_3$ (PT), ten different ordered structures with stoichiometry Pb(${\mathrm{Sc}}_{0.5}$ ${\mathrm{Ta}}_{0.5}$)${\mathrm{O}}_3$ (PST), and 104 different structures with stoichiometries between PST and PT. The PIB results for intermediate stoichiometries predict two ordered ground-state phases at X(${\mathrm{PbTiO}}_3$)=1/4 and X=1/2. The differences in total energies were used as a basis for fitting a set of effective cluster interactions, and the resulting Hamiltonian was used as input for a cluster-variation method (CVM) phase diagram calculation. The CVM calculation predicts a third ordered phase at X≊1/4. This phase is not a ground state, but it is predicted to be stable at higher temperatures than either of the ground-state phases and, therefore, to be more likely to be found experimentally.