Using neutron elastic and inelastic scattering and high-energy x-ray diffraction, we present a comparison of 40% Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_{3}$-60% PbTiO$_{3}$ (PMN-60PT) with pure Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_{3}$ (PMN) and PbTiO$_{3}$ (PT). We measure the structural properties of PMN-60PT to be identical to pure PT, however, the lattice dynamics are exactly that previously found in relaxors PMN and PZN. PMN-60PT displays a well-defined macroscopic structural transition from a cubic to tetragonal unit cell at 550 K. The diffuse scattering is shown to be weak indicating that the structural distortion is long-range in PMN-60PT and short-range polar correlations (polar nanoregions) are not present. Even though polar nanoregions are absent, the soft optic mode is short-lived for wavevectors near the zone-centre. Therefore, PMN-60PT displays the same waterfall effect as prototypical relaxors PMN and PZN. We conclude that it is random fields resulting from the intrinsic chemical disorder which is the reason for the broad transverse optic mode observed in PMN and PMN-60PT near the zone centre and not due to the formation of short-ranged polar correlations. Through our comparison of PMN, PMN-60PT, and pure PT, we interpret the dynamic and static properties of the PMN-xPT system in terms of a random field model in which the cubic anisotropy term dominates with increasing doping of PbTiO$_{3}$.
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