Thermodynamics of phase transitions in Zintl clusters from density functional theory: making and breaking of bonds in Ba3Ge4

Abstract

Density functional theory, in conjunction with the quasi-harmonic approximation, has been used to study the equilibrium between the orthorhombic and tetragonal phases of Ba₃Ge₄. A transition from the high-temperature tetragonal phase containing isolated Ge₄⁶⁻ units to the low-temperature orthorhombic phase, where precisely half of the Ge₄⁶⁻ units are polymerised along one axis, is predicted at 930 K, somewhat higher than the experimental value of 630 K. An analysis of the phonon density of states shows that the lower entropy of the orthorhombic phase is not associated directly with the polymerisation of the Ge₄⁶⁻ units, but rather with the contraction of the unit cell, which raises the frequencies of ion–ion modes involving the relative motions of the Ba²⁺ and Ge₄⁶⁻ units. Calculations also predict that a third, as yet unobserved, p-tetragonal phase, where all of the Ge₄⁶⁻ units are polymerised to form two separate chains running in orthogonal directions, might be accessible at pressures close to 1 GPa.