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Relative phase stability and lattice dynamics of NaNbO$_3$ from first-principles calculations

We report total energy calculations for different crystal structures of NaNbO$_3$ over a range of unit cell volumes using the all-electron full-potential (L)APW method. We employed both the local-density approximation (LDA) and the Wu-Cohen form of the generalized gradient approximation (GGA-WC) to test the accuracy of these functionals for the description of the complex structural behavior of NaNbO$_3$. We found that LDA not only underestimates the equilibrium volume of the system but also predicts an incorrect ground state for this oxide. The GGA-WC functional, on the other hand, significantly improves the equilibrium volume and provides relative phase stability in better agreement with experiments. We then use the GGA-WC functional for the calculation of the phonon dispersion curves of cubic NaNbO$_3$ to identify the presence of structural instabilities in the whole Brillouin zone. Finally, we report comparative calculations of structural instabilities as a function of volume in NaNbO$_3$ and KNbO$_3$ to provide insights for the understanding of the structural behavior of K$_{1-x}$Na$_x$NbO$_3$ solid solutions.