Lattice parameters and electronic bandgap of orthorhombic potassium sodium niobate K $$_{0.5}$$ 0.5 Na $$_{0.5}$$ 0.5 NbO $$_{3}$$ 3 from density-functional theory

We perform a theoretical analysis of the structural and electronic properties of sodium potassium niobate K $$_{1-x}$$ 1 - x Na $$_{x}$$ x NbO $$_{3}$$ 3 in the orthorhombic room-temperature phase, based on density-functional theory in combination with the supercell approach. Our results for $$x=0$$ x = 0 and $$x=0.5$$ x = 0.5 are in very good agreement with experimental measurements and establish that the lattice parameters decrease linearly with increasing Na contents, disproving earlier theoretical studies based on the virtual-crystal approximation that claimed a highly nonlinear behavior with a significant structural distortion and volume reduction in K $$_{0.5}$$ 0.5 Na $$_{0.5}$$ 0.5 NbO $$_{3}$$ 3 compared to both end members of the solid solution. Furthermore, we find that the electronic bandgap varies very little between $$x=0$$ x = 0 and $$x=0.5$$ x = 0.5 , reflecting the small changes in the lattice parameters. Graphic abstract