On the unit cell volume expansion in homogeneous series of isotypic structures of “ionic” inorganic compounds

Abstract

Abstract Within a “homogeneous” series of (crystal-chemically) isotypic structures one and only one chemical element E of the sum formula is replaced successively by heavier elements of the same group of the periodic table. For corresponding series of “ionic” compounds, a (coarse) “expectation value” ΔV th for the unit cell volume expansion following the replacement of E(i) by E(j) (with i<j=row numbers in the periodic table) can be calculated by using the empirical formula ΔV th=56.5 (zE ΔρE ( i ) E ( j )) – 0.80 (zE ΔρE ( i ) E ( j ))2, where zE is the number of atoms E per unit cell and ΔρE ( i ) E ( j ) is the linear statistical size (= radius) difference for the two elements E(i) and E(j). Two hundred and twenty-eight different series have contributed to the statistical evaluation of this formula. Series for which E are elements of low valence have been excluded a priori from the calculations if the residual atoms of higher valence by themselves form an infinite framework, as it was suspected, that in structures of this kind the “natural” volume expansion caused by the E(i) → E(j) size increase is hampered by the rigidity of this framework. Application of the above formula to structures of this kind clearly supports this suspicion only, if the framework is of dimensionality three. The results derived from all other investigated structures are qualitatively compatible with the “volume increments rule” published in the 1930s. This suggests that they should be applicable also to isotypic series of crystal structures defined in a less restricted manner.