Mode-crystallography analysis of the crystal structures and the low- and high-temperature phase transitions in Na0.5K0.5NbO3

Abstract

Na0.5K0.5NbO3has been synthesized by the conventional solid-state reaction process. The crystal structures and phase transitions, at low and high temperature, determined from the Rietveld refinements of X-ray and neutron powder diffraction data are reported. The structure evolution of Na0.5K0.5NbO3in the temperature range from 2 to 875 K shows the presence of three phase transitions. The first one, at ∼135 K, is discontinuous from the rhombohedralR3c(No. 161) space group to the room-temperature orthorhombicAmm2 (No. 38) space group; the second is discontinuous from the orthorhombic to the tetragonalP4mmspace group (No. 99) at ∼465 K, and the third is continuous from the tetragonal to the cubic Pm\overline{3}m space group (No. 221) at ∼700 K. The obtained phase-transition sequence isR3c→Amm2 →P4mm→Pm\overline{3}m. No previous studies at low temperature have been carried out on the material with composition Na0.5K0.5NbO3. In the course of the determination of the three experimentally found phases, a novel method of refinement is presented. This is a step forward in the use of the symmetry-adapted modes as degrees of freedom in the refinement process: the parameterization of a direction in the internal space of the, in this case, sole irreducible representation, GM4−, responsible for the symmetry breaking from the parent cubic space group to the polar distorted low-symmetry phases. Eventually, this procedure enables the calculation of the spontaneous polarization.