Fig. 1. Anisotropic strain in (011)-oriented PMN-PT.

(A) Cartesian coordinates x, y, and z are defined to be the crystal [100],$\left[01\overline{1}\right]$, and [011] directions, respectively. Polarization directions in (011)-oriented PMN-PT unit cell, grouped into rhombohedral in-plane (R_IP; orange), rhombohedral up (R_UP; blue), and orthorhombic up (O_UP; purple). Rhombohedral down (R_DOWN) and orthorhombic down (O_DOWN) are not shown but are, respectively, R_UP and O_UP mirrored about the xy plane. The in-plane cut through the unit cell (shaded gray area) is rectangular with sides of length $a\sqrt{2}$by a, where a is the lattice parameter. (B) Electrostrictive deformations (not to scale) of the unit cell for the cubic (zero FE polarization), R_IP, R_UP, and O_UP polarization groups. The down deformations are identical to up. In-plane projections of polarization vectors are shown for R_IP (light orange) and R_UP (light blue). (C) Plots of linear electrostriction strains ε_xx and ε_yy and the anisotropic strain ε_xx − ε_yy for R_IP, R_UP, and O_UP polarization groups. Numerical values are in table S1.