The phase, whose hexagonal unit cell is shown in panel (a), and the phase, panel (b), behave very differently under applied pressure. The ratio between the oxygen octahedral and cuboctahedra-volumes of the phase decreases with increasing pressure: the crystal is contracting and thus the cations (which fit oxygen octahedra tightly) have to take larger relative volume from the total volume (from the cuboctahedra, which has excess of space for Pb) by tilting oxygen octahedra. The symmetry prohibits this mechanism in the and phases. Density-functional theory computations predict that has an entropy term benefit at elevated temperatures. Two rhombohedral (corresponding to the phase) pseudocubic cells are shown by dotted lines in panel (a). Due to the octahedral tilting, indicated by arrows, the two cells are not equivalent: the tilting corresponds to the symmetry lowering. The primitive cell of the phase is shown by dotted lines in panel (b). Structure figure was prepared by the vesta software.21
(a) X-ray diffraction pattern measured from a Pb(Zr0.54Ti0.46)O3 sample at 303 K and 0 GPa, (b) observed (red) and calculated (green) time-of-flight neutron powder diffraction data and its difference curve between measured and computed curves (purple). The tick marks, from down to up, are from the , , NaCl (pressure standard), and graphite (from the pressure chamber) phases. Insets show the pseudo-cubic 200 reflections, labelled as and ( phase) and ( phase). The lattice parameters were Å, Å, Å and ( phase), and Å and Å ( phase).
Observed (red) and calculated (green) time-of-flight neutron powder diffraction data and its difference curve between measured and computed curves (purple) for a Pb(Zr0.54Ti0.46)O3 sample at 303 K and 3 GPa. The tick marks, from down to up, are from the , , NaCl (pressure standard), and graphite (from the pressure chamber) phases. The inset shows the pseudo-cubic 200-reflection region (compare with Fig. 2).
Rhombohedral weight fraction at ambient conditions and as a function of temperature at approximately 1 and 3 GPa pressures.
Pseudo-cubic lattice parameters of the , , , and phases as a function of temperature at approximately 1 GPa, panels (a) and (b), and 3 GPa pressures, panels (c) and (d). The phase transformed to the phase at around 400 K at 1 GPa pressure, panel (b). At 1.26 GPa pressure at room temperature the angle was . The rhombohedral angle is also given on right-hand side panels and is given with respect to the rhombohedral axes. Due to the thermal pressure, the pressure values of the highest two temperatures (cubic phase) are larger.
Octahedral tilt angles (a), octahedral edge lengths (b), and polyhedral volume fractions of the phase at ambient conditions and as a function of temperature at approximately 1 and 3 GPa pressures.
(a) -cation (Zr or Ti) and oxygen bond lengths in the rhombohedral phase. The difference between and bond lengths increases with increasing pressure. The decrease in difference seen at 1.41 GPa pressure is probably related to the vicinity of the transition to the cubic phase. (b) The distance between the oxygen triangles. In both panels, the 3 GPa data are indicated by dotted lines. The inset shows the displacement of the cations under pressure. At ambient pressures, the is closer to the larger triangle and displaces towards smaller triangle under pressure.
Recovery run collected on a Pb(Zr0.54Ti0.46)O3 sample at 303 K and 0 GPa. Observed intensity is given by a red line and calculated intensity by a green line. The purple line gives the difference curve between measured and computed curves. The tick marks, from down to up, are from the , (due to the lower statistics of the recovery data constraints were introduced to the phase so that true symmetry used in the refinements was ), NaCl, and graphite phases. The rhombohedral phase fraction was .
The asymmetric unit of the phase as defined in Ref. 23.
Statistical figures-of-merit numbers as given by gsas program. The and parameters are defined in the gsas manual.31 Reference to figures in which the refinement results were used is given. The results for different data sets are not always directly comparable as the data quality depends on the experimental conditions. For instance, at higher pressures the background contribution increases.
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