Some stereochemical criteria concerning the structural stability of A2BX4compounds of typeβ-K2SO4

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Abstract
In A2BX4 structures which are isostructural to β-K2SO4 (with A being a monoatomic cation) there are two crystallographically independent cations surrounded by 11 and 9 X-atoms. The 11-coordinated cation is less firmly bound and the arrangement of its five closest neighbours is irregular. One of these contacts is approximately parallel to the pseudohexagonal axis of the structure and is often shorter than the sum of the corresponding ionic radii. A survey of available structural data indicates that the low-temperature structural instability of a good number of these compounds is related to the coordination of this 11-coordinated cation and especially to the bonding strength of this short bond, which is often the shortest cation-anion contact in the structure. Typically, the relative contribution of this contact to the bond-valence sum of the 11-coordinated cation is larger in the compounds which undergo phase transitions at lower temperatures. The presence of this short contact is correlated with the ratio of the lattice parameters a/b (Pnma-setting). In general, the Pnma phase is unstable at low temperatures in those compounds where this ratio is smaller. On the other hand, the value of a/b can be related to the ratio of the effective sizes of cations and BX4 tetrahedra, so that typical low-temperature instabilities of the β-K2SO4 structure occur for smaller values of the ratio between cation radius and the sum of the ionic radii of atoms A and X. In most cases, the resulting phase transitions stabilize modulated structures (frequently incommensurate), with slight distortions with respect to the β-K2SO4 structure. However, when the bond valence sum of the eleven-coordinated cation is extremely low, more drastic (first-order) structural changes are observed (e.g. phase transitions into the Sr2GeS4 structure type). In addition, the survey indicates, especially in complex oxides, that low-temperature phase transitions are more probable in those structures with looser packing. Considering the criteria proposed, a set of compounds is indicated where low-temperature phase transitions are plausible.

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