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

Na0.5K0.5NbO3 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 Na0.5K0.5NbO3 in the temperature range from 2 to 875K shows the presence of three phase transitions. The first one, at approximate to 135K, is discontinuous from the rhombohedral R3c (No. 161) space group to the room-temperature orthorhombic Amm2 (No. 38) space group; the second is discontinuous from the orthorhombic to the tetragonal P4mm space group (No. 99) at approximate to 465K, and the third is continuous from the tetragonal to the cubic space group (No. 221) at approximate to 700K. The obtained phase-transition sequence is R3cAmm2 P4mmPmm. 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, 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.