Physical mechanisms in the phase transitions of sodium superoxide

We consider the various physical mechanisms that contribute to the ground-state energy (Eg) of the ordered pyrite (OP) and the marcasit\'e (M) phases of NaO₂. We find that the ionic and molecular-crystal contributions to Eg (Madelung potential, O₂^--Na⁺ and O₂^--O₂^- repulsion, Van der Waals and quadrupole-quadrupole interaction between O₂^- molecules) favor the OP structure by an energy of 2204 K per O₂^- molecule. Contributions to Eg arising from splitting of the orbital degeneracy of the O₂^- ion, quadrupole---electric-field gradient interaction, and antiferromagnetic exchange coupling between O₂^- spins favor the M structure by 2468 K per O₂^- 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 $T=0$ 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 O₂^--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 kln1.62 whereas the experimental value is kln2.35. The possible sources of discrepancy between theory and experiment are discussed.