Theory of the formation of P4132(P4332)-phase spinels

Abstract

A group-theoretical, thermodynamic, and structural study of the formation of P4₁32(P4₃32) spinel modification has been performed. In particular, the occurrence of unique hyper-kagome atomic order is analyzed. The critical order parameter inducing a phase transition is established. It is shown that the calculated structure of the low-symmetry P4₁32(P4₃32) phase is formed as a result of displacements of atoms of all types and due to the cation and anion ordering. The problem of the occurrence of unique hyper-kagome atomic order in the structures of P4₁32(P4₃32) spinel modifications is considered theoretically. It is proven within the Landau theory of phase transitions that the P4₁32(P4₃32) phase can be formed from the high-symmetry Fd3m phase with an ideal spinel structure only as a result of first-order phase transition. Therefore, the formation of hyper-kagome sublattice in the P4₁32(P4₃32) phase is accompanied by a significant transformation of the spinel structure.