Formation of breathing pyrochlore lattices: structural, thermodynamic and crystal chemical aspects†
A pyrochlore lattice is a three-dimensional network of corner-sharing tetrahedra. Crystals with a pyrochlore lattice formed from the atoms of a transition metal give rise to a rich variety of condensed phases and novel phenomena caused by geometrical frustration. A type of this structure with different metal–metal distances is known as a breathing pyrochlore lattice. The formation of breathing pyrochlore lattices is accompanied in many cases by clustering and the appearance of exotic ground states, as well as intriguing physical properties. The formation of breathing pyrochlore lattices was investigated on the example of F3m ordered pyrochlores in terms of group-theoretical analysis, Landau thermodynamics and crystal chemistry. In this article, it has been shown that the order parameter described Fdm → F3m phase transition is realized in the displacements of the atoms located at the 16c, 16d, and 48f Wyckoff positions of the initial parent pyrochlore structure, as well as the ordering of atoms located at the 8b and 48f Wyckoff positions (the type of atom ordering is 1 : 1 in each case). For some ordered pyrochlores, we estimate the order parameter magnitude and its contribution to atomic displacements. Two main thermodynamic paths of the phase transitions between initial high-symmetry and low-symmetry phases occurring as a result of both second- and first-order phase transitions in the vicinity tricritical point are possible based on the Landau-type phase diagram. The structural features of F3m ordered pyrochlores are established (breathing pyrochlore lattices, bridges between tetrahedral structural units, breathing six-member rings of tetrahedra, anion-centered clusters in the ordered α-pyrochlores, and cage-structures in the ordered β-pyrochlores). The existence of new classes of pyrochlore-like materials that inherit the structural features of F3m ordered pyrochlores is predicted.