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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

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