Mode-crystallography analysis of the crystal structures and the low- and high-temperature phase transitions in Na_0.5K_0.5NbO₃

Abstract

Na 0.5 K 0.5 NbO 3 has 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 Na 0.5 K 0.5 NbO 3 in 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 rhombohedral R 3 c (No. 161) space group to the room-temperature orthorhombic Amm 2 (No. 38) space group; the second is discontinuous from the orthorhombic to the tetragonal P 4 mm space 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 is R 3 c → Amm 2 → P 4 mm → Pm \overline{3} m . No previous studies at low temperature have been carried out on the material with composition Na 0.5 K 0.5 NbO 3 . 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, GM 4 − , 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.