Microstrain in tetragonal lead-zirconate-titanate: The effect of pressure on the ionic displacements

Piezoelectric materials respond to external stimuli by adjusting atomic positions. In solid-solutions, the changes occurring in atomic scale are very complex since the short- and long-range order are different. Standard methods used in diffraction data analysis fail to model the short-range order accurately. Pressure-induced cation displacements in ferroelectric Pb(Zr_0.45Ti_0.55)O₃ perovskite oxide are modeled by starting from a short-range order. We show that the model gives the average structure correctly and properly describes the local structure. The origin of the microstrain in lead zirconate titanate is the spatially varying Zr and Ti concentration and atomic distances, which is taken into account in the simulation. High-pressure neutron powder diffraction and simulation techniques are applied for the determination of atomic positions and bond-valences as a function of pressure. Under hydrostatic pressure, the material loses its piezoelectric properties far before the transition to the cubic phase takes place. The total cation valence +6 is preserved up to 3.31 GPa by compensating the increasing B-cation valence by decreasing Pb-displacement from the high-symmetry position. At 3.31 GPa, Pb-displacement is zero and the material is no more ferroelectric. This is also the pressure at which the Pb-valence is minimized. The average structure is still tetragonal. The model for microstrain predicts that the transition occurs over a finite pressure range: Pb-displacements are spatially varying and follow the distribution of Zr and Ti ions.