Lattice Parameters and Electronic Bandgap of Orthorhombic Potassium Sodium Niobate K$$_{0.5}$$Na$$_{0.5}$$NbO$$_{3}$$ from Density-Functional Theory

We perform a theoretical analysis of the structural and electronic properties of sodium potassium niobate K $$_{1-x}$$ Na $$_{x}$$ NbO $$_{3}$$ in the orthorhombic room-temperature phase, based on density-functional theory in combination with the supercell approach. Our results for $$x=0$$ and $$x=0.5$$ 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 $$_{0.5}$$ Na $$_{0.5}$$ NbO $$_{3}$$ compared to both end members of the solid solution. Furthermore, we find that the electronic bandgap varies very little between $$x=0$$ and $$x=0.5$$ , reflecting the small changes in the lattice parameters.