Relationship between the unit-cell volumes and cation radii of isostructural compounds and the additivity of the molecular volumes of carbonates Available to Purchase

Both theoretical relations and observed structure data imply the following relationships: for a series of multi-cation isostructural compounds such as A_mB_n … Xp, the unit-cell volume V and the radius r_A of a cation A are related, when the anion and other cations are fixed, as follows:

V = (p + qr_A)(r_x + r_A)³ (p, q : const.).

A simplified relation for binary isostructural compounds is:

V = k(r_X + r_A)³ (k = const.).

An approximation based on the above equations results in a linear relationship between V and r³_A. Another approximation gives rise to a linear correlation between V and r_A. An application of the latter relationship shows that the effect of two or more cations in a multi-cation carbonate is equivalent to that of one cation whose radius is an average of the two. This implies that the molecular volume of a multi-cation carbonate is equal to the sum of the molecular volumes of the corresponding component simple carbonates. When the coordinations of cations are the same as in the simple carbonates, the additivity relation gives rise to very accurate values. Regardless of the coordinations, the molecular volume may still be obtained by addition of component volumes, though with slightly Iower accuracy.