Microscopic theory of successive phase transitions in alkali cyanides based on the Hubbard operators

Abstract

Abstract The energy levels and eigen wave functions of cyanide (CN) molecules in eight well potential of cubic symmetry are found to construct a finite representation (A1g + T2g )x(A2g + E g ) of the Hubbard operators. Interaction of the CN molecules with each other and crystal strains are formulated via the Hubbard operators. It is shown that the last interaction results in two phase transitions of a first order: cubic→ rhombohedral → orthorhombic with temperature decreasing. In correspondence with these phases a quadrupolar ordering of the CN molecules and a distortion of the CN potential take place. In the orthorhombic phase the CN potential can have two or four minima with equilibrium orientations of the CN molecules along (110) whereas in the cubic phase they were (111). A further decreasing of the temperature leads to antiferroelectric ordering of the CN molecules in KCN due to the dipole-dipole interactions.