Cryolite, cubic structure

The ideahzed cubic cryolite-structure is characterized by the following positions of the space group xa3m (No. 225), (z = 4) ... 

The occupation of lattice sites differing widely in size and coordination, by equally sized A-ions, is the reason, why the ideal cryolite structure appears strained and therefore tends to distort. This distortion, as Bode and Foss (44) described in detail, results in various rotations of the MeFe-octahedra, whereby the fluoride ions always move away from the edges of the unit cell and thus enlarge the space available for the octahedrally coordinated A-ion. In addition a further distortion may shift the atoms from the originally face-centered arrangement, so that structures of lower S3unmetry may be observed. But the cubic cryolite-type is still to be seen as the basic form of these distorted modifications, which appear at lower temperatures only and become cubic if the temperature is raised (J52). 

In this cubic cryolite structure, investigated by Bode and Foss 44), the MeFe-octahedra again are oriented in such a way, that the fluoride ions lie somewhat off the cell edges. This fact explains that the observed lattice constants are always considerably smaller than the radii sum 2rMe + 2rA + 4rp, which accounts for a linear array of ions only. 

A special feature is presented by the structures of the cryolite family, in which two different C.N.s, 6 and 12 resp., are offered to the same A-ions. This C.N. of 6, unfavourable to potassium and the larger alkali ions, is the reason why compounds of this kind often show either distortion from cubic symmetry or a deficit of alkali ions, especially if prepared from aqueous solution (77). According to the general formula Aa- MeFe- XH2O 1) some fluorine can be substituted by water in the crystal lattice. 

This account of these structures has been based on the mode of packing of the c.p. layers. For the alternative description in terms of the way in which the octahedral BX groups are joined together by sharing X atoms, see Chapter 5. The structures based on cubic closest-packing are normally illustrated and described in terms of the cubic unit cell. We noted earlier that the cryolite structure is a superstructure of perovskite the relation between the perovskite, cryolite, and K2PtQg structures is described in Chapter 10 (p. 388). 

From the structural standpoint it is preferable to write the formulae of compounds of the cryolite family in the form A2(B B")Xg rather than A3BX6 because in this structure one-third of the A atoms in the formula A3BX6 are, like the B atoms, in octahedral holes in a cubic close-packed A2X6 (AX3) assembly the other two-thirds, corresponding to the ions in the K2PtCl6 structure, are surrounded by twelve equidistant X ions. Accordingly the cryolite structure is very closely related also to the perovskite structure. In Fig. 10.7 the A and X atoms are... 

---