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 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 $465 K, and the third is continuous from the tetragonal to the cubic Pm3m space group (No. 221) at $700 K. The obtained phase-transition sequence is R3c ! Amm2 ! P4mm ! Pm3m. 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 À , 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.