Structural chemistry of A₂MX₄ compounds (X = O, F) with isolated tetrahedral anions: search for the densest structure types

The packing density of various structures is important not only for understanding and the prediction of high-pressure phase transitions, but also because of its reported correlation with thermodynamic stability. Plotting the cube root of formula volume against the cation radii (R) for nine morphotropic series with isolated tetrahedral anions, A₂MO₄ (M = Si, Ge, S, Se, Cr, Mn, Mo, W) and A₂BeF₄, permits the comparison of packing densities for 13 structure types (about 80 individual compounds and several solid solutions) stable at (or near) ambient temperature. The spinel type is the densest. The next densest types are those of K₂MoO₄, Tl₂CrO₄, β-Ca₂SiO₄, β-K₂SO₄, Ag₂CrO₄ and Sr₂GeO₄. In three series (M = Ge, Mo, W) the densest type comes with somewhat intermediate values of R, and not the largest, in contrast to the classical homology rule. Another contradiction with traditional views is that some of the densest phases have abnormally low overall binding energies. The correlation between packing density and coordination number (CN) is better when CN of A counts entire MX₄ groups rather than individual X atoms; many, but not all, A₂MX₄ structures have binary A₂M analogues (of course, A and M are not necessarily the same in these structure types). The most frequent arrangement of A around M is of the Ni₂In type: a (distorted) pentacapped trigonal prism.