Automatic determination of the morphotropic phase boundary in lead magnesium niobate titanate Pb(Mg_1/3Nb_2/3)_(1-x)Ti_xO₃ within a single crystal using birefringence imaging

A detailed phase diagram of Pb(Mg_1/3Nb_2/3)_(1-x)Ti_xO₃, conventionally abbreviated to PMN-PT, has been constructed around the morphotropic phase boundary from measurements taken from one single crystal possessing a composition gradient. Optical birefringence imaging was employed as a function of temperature to plot retardation and orientation information as a function of temperature and position within the crystal. Electron-probe microanalysis measured the composition across the crystal and this enabled the phase boundaries to be plotted to high precision. Cubic (C), rhombohedral (R), tetragonal (T) and monoclinic (M) phases were observed, with the a C-R-T critical point at a composition x = 0.275 (4) at 394.7 (5) K on heating and at the same composition at 386.5 (5) K on cooling, in close agreement with phase diagrams suggested by published dielectric and diffraction experiments.