Ab initio study of elastic properties of Pb(Ti,Zr)O3

We studied the elastic constant tensor for Pb(T0.5Zr0.5)O-3, in the rhombohedral and tetragonal phases. Young's modulus in the rhombohedral phase is very anisotropic. It has two narrow and large peaks along and perpendicular to polarization direction and is small in all intermediate directions. Tetragonal PZT is soft along the polarization direction and stiff in perpendicular directions. Both rhombohedral and tetragonal PZT have small c(44) elastic coefficients and large s(44) compliances; it is soft with respect to shear perpendicular to the polarization directions in each structure. We find a very small energy difference between relaxed tetragonal and rhombohedral PZT. The softness of PZT with respect to polarization rotation is partly responsible for its high electromechanical coupling.