First-principles study of $({\mathrm{BiScO}}_3{)}_{1-x}-({\mathrm{PbTiO}}_3{)}_x$ piezoelectric alloys

We report a first-principles study of a class of $({\mathrm{BiScO}}_3{)}_{1-x}-({\mathrm{PbTiO}}_3{)}_x$ (BS-PT) alloys recently proposed by Eitel et al. as promising materials for piezoelectric actuator applications. We show that (i) BS-PT displays very large structural distortions and polarizations at the morphotropic phase boundary (MPB) (we obtain a $c/a$ of $\sim 1.05–1.08$ and $P_{\mathrm{tet}}\approx 0.9\mathrm{C}/{\mathrm{m}}^2);$ (ii) the ferroelectric and piezoelectric properties of BS-PT are dominated by the onset of hybridization between $\mathrm{B}\mathrm{i}/\mathrm{P}\mathrm{b}-6p$ and $\mathrm{O}-2p$ orbitals, a mechanism that is enhanced upon substitution of Pb by Bi; and (iii) the piezoelectric responses of BS-PT and $\mathrm{Pb}\left({\mathrm{Zr}}_{1-x}{\mathrm{Ti}}_x\right){\mathrm{O}}_3$ (PZT) at the MPB are comparable, at least as far as the computed values of the piezoelectric coefficient $d_{15}$ are concerned. While our results are generally consistent with experiment, they also suggest that certain intrinsic properties of BS-PT may be even better than has been indicated by experiments to date. We also discuss results for PZT that demonstrate the prominent role played by Pb displacements in its piezoelectric properties.