The effective ionic radii of Shannon & Prewitt [Acta Cryst. (1969), B25, 925-945] are revised to include more unusual oxidation states and coordinations. Revisions are based on new structural data, empirical bond strength-bond length relationships, and plots of (1) radii vs volume, (2) radii vs coordination number, and (3) radii vs oxidation state. Factors which affect radii additivity are polyhedral distortion, partial occupancy of cation sites, covalence, and metallic character. Mean NbS+-O and Mo6+-O octahedral distances are linearly dependent on distortion. A decrease in cation occupancy increases mean Li+-O, Na+-O, and Ag+-O distances in a predictable manner. Covalence strongly shortens Fe2+-X, Co2+-X, Ni2+-X, Mn2+-X, Cu+-X, Ag+-X, and M-H-bonds as the electronegativity of X or M decreases. Smaller effects are seen for Zn2+-X, Cd2+-X, In3+-X, pb2+-X, and TI+-X. Bonds with delocalized electrons and therefore metallic character, e.g. Sm-S, V-S, and Re-O, are significantly shorter than similar bonds with localized electrons.

KAREN GRAM JENSEN AND BODIL JERSLEV 925 structure is viewed along the b axis. This projection illustrates very clearly that the external shape of a crystal -in this case the prominence of {10T} -is a function of the packing of the molecules in the crystal lattice.We are indebted to Professor R. W. Asmussen, Chemical Laboratory B, Technical University of Denmark for his kind interest and support during the final stages of this research.

A set of 61 ion polarizabilities has been derived from the dielectric constants of 129 oxides and 25 fluorides using a least squares refinement technique in conjunction with the Clausius–Mosotti equation. These polarizabilities can be used to estimate mean dielectric constants of ‘‘well-behaved’’ compounds. They should be particularly useful in calculation of mean dielectric constants of compounds whose dielectric constants have not been determined. They can also be used as a framework for distinguishing unusual dielectric behavior from normal dielectric behavior where deviations can frequently be attributed to piezo- or ferroelectricity, conductivity (ionic or electronic), ‘‘rattling’’ or ‘‘compressed’’ cations with correspondingly high or low polarizabilities, or the presence of dipolar impurities. Deviations observed from calculated dielectric constants can be used to search for unusual physical behavior.

Bond-strength-bond-length relationships for bonds between oxygen and H +, Li +, Be 2+, B a+, Na +, Mg2+, AI3+, Sia+, ps+, $6+, K +, Ca2+, Sc3+, Ti4+, Vs+, Cr6+, Mn2+, Fea+, Fe2+, C02+, Cu2+, Zn2+, Ga 3+, Ge 4+ and As s+ have been derived by requiring that the sums of the bond strengths around the cations be equal to their valence in 417 crystals whose structures have been accurately determined. The relationship is of the form s = (R/Ro)-N where s = bond strength, R = bond length and Ro and N are fitted constants. It is further shown that all ions with an isoelectronic core can be fitted by a single pair of parameters, Ro and N, that are independent of the ionic character of the bond and the coordination number of the cation. The resulting bond strengths have the property that they are directly related to the covalent character of the bond and that their sum around each atom is, on average, within about 5% of its valence. The bond-strength-bond-length curves are particularly useful in accounting for bonding in cases where the coordination is very distorted (e.g. Na +, Cu 2+ and Vs+). They can also be used to predict the positions of hydrogen atoms, to analyze for different oxidation states and site occupancies, to calculate ionic radii and to provide an indication of the correctness of crystal structure determinations.