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

Both theoretical relations and observed structure data imply the following relationships: for a series of multi-cation isostructural compounds such as A (sub m) B (sub n) . . . Xp, the unit-cell volume V and the radius r (sub A) for a cation A are related, when the anion and other cations are fixed as follows: V = (p + qr (sub A) ) (r (sub x) + r (sub A) ) (super 3) (p, q = const.). A simplified relation for binary isostructural compounds is: V = k(r (sub x) + r (sub A) ) (super 3) (k = const.). An approximation based on the above equations results in a linear relationship between V and r (super 3) (sub A) . Another approximation gives rise to a linear correlation between V and r (sub A) .