Physical mechanisms in the phase transitions of sodium superoxide

We consider the various physical mechanisms that contribute to the ground-state energy ($E_g$) of the ordered pyrite (OP) and the marcasité ($M$) phases of Na${\mathrm{O}}_2$. We find that the ionic and molecular-crystal contributions to $E_g$ (Madelung potential, ${\mathrm{O}}_2^{-}$-${\mathrm{Na}}^{+}$ and ${\mathrm{O}}_2^{-}$-${\mathrm{O}}_2^{-}$ repulsion, Van der Waals and quadrupole-quadrupole interaction between ${\mathrm{O}}_2^{-}$ molecules) favor the OP structure by an energy of 2204 K per ${\mathrm{O}}_2^{-}$ molecule. Contributions to $E_g$ arising from splitting of the orbital degeneracy of the ${\mathrm{O}}_2^{-}$ ion, quadrupole—electric-field gradient interaction, and antiferromagnetic exchange coupling between ${\mathrm{O}}_2^{-}$ spins favor the $M$ structure by 2468 K per ${\mathrm{O}}_2^{-}$ molecule. An estimate of the librational zero-point energies in both phases suggests that the energies of the two phases are very close to each other. Within the present accuracies of our calculation we cannot definitely conclude that $M$ structure has lower energy at $T=0\mathrm{}$ as seen experimentally. However the molecular orientations obtained in each phase from energy minimization agree well with the experiment. The first-order phase transition from OP to disordered pyrite (DOP) has been studied in a molecular-field approximation. The results are in reasonable agreement with experiment. We find that ${\mathrm{O}}_2^{-}$-${\mathrm{Na}}^{+}$ repulsion plays an important role in the observed orientational order-disorder transition. The theoretical value of the order-disorder transition temperature is calculated to be 300 K compared to 223 K obtained experimentally. The discontinuity in the entropy at the transition is calculated to be $k\ln 1.62$ whereas the experimental value is $k\ln 2.35$. The possible sources of discrepancy between theory and experiment are discussed.