We have employed a combination of powder neutron diffraction and single-crystal synchrotron X-ray diffraction to characterize the pressure-induced phase transitions that occur in the perovskite-type relaxor ferroelectric PbSc0.5Ta0.5O3 (PST) and Pb0.78Ba0.22Sc0.5Ta0.5O3 (PST-Ba). At ambient pressure the symmetry of the average structure for both compounds is Fm\bar{3}m as a result of partial ordering of the Sc and Ta cations on the octahedral sites. At pressures above the phase transition both the neutron and X-ray diffraction patterns exhibit an increase in the intensities of h,k,l = all odd reflections and no appearance of additional Bragg reflections. Synchrotron single-crystal X-ray diffraction data show that the intensity of hhh peaks, h = 2n + 1, does not change with pressure. This indicates that the structural distortion arising from the phase transition has a glide-plane pseudo-symmetry along the 〈111〉 cubic directions. Rietveld refinement to the neutron powder data shows that the high-pressure phase has either R\bar{3}c or R\bar{3} symmetry, depending on whether the presence of 1:1 octahedral cation ordering is neglected or taken into account, and comprises octahedral tilts of the type a
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a
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a
− that continuously evolve with pressure. The cubic-to-rhombohedral transition is also marked by a large increase in the anisotropy of the displacement ellipsoids of the Pb cations, indicating larger displacements of Pb cations along the rhombohedral threefold axis rather than within the perpendicular plane. For PST the anisotropy of the Pb displacement parameters decreases at approximately 3 GPa above the phase-transition pressure. For both PST and PST-Ba the average magnitudes of Pb-cation displacements expressed in terms of isotropic displacement ellipsoids gradually decrease over the entire pressure range from ambient to 7.35 GPa.