Anion packing density: a universal quantity for both dense and porous crystalline inorganic phases

To compare densities of inorganic high-pressure phases their molal volumes or specific gravities are usually employed, whereas for zeolites and other microporous materials the so-called framework density, FD, is applied. The definition of FD, which refers only to phases with three-dimensional tetrahedron frameworks, is extended to a 'generalized framework density' d(f), which is independent of the dimensionality of the framework and the coordination number(s) of the framework cations. In this paper the anion packing density, d(ap), is introduced as a new quantity which is not only applicable to any inorganic phase but, in contrast to FD and d(f), also allows quantitative comparisons to be made for crystalline inorganic phases of any kind. The anion packing density can readily be calculated if the volume and content of the unit cell and the radii of the anions of a phase are known. From d(ap) values calculated for high-pressure silica polymorphs studied under very high pressure, it is concluded that Shannon-Prewitt effective ionic radii do not sufficiently take into account the compressibility of the anions.