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.

1046SHORT COMMUNICATIONS parallel to the (110) plane in the structures. Nevertheless, structural control by electron concentration of necessity involves some geometrical feature, since it results from the action of planes of energy discontinuity in reciprocal space. The one constant geometrical feature common to all of these 40 tetragonal structures is the fl-Sn like pseudo-cell of T metal atoms with c/nal/2 ~-0.577 = 1/1/3 (the value for equilateral triangles in the nets of T atoms), so it would seem that structural stability must result from the achievement of some constant electron concentration within this psuedo-cell. This conclusion is entirely consistent with the observed fact that (at least for V~ >7) the controlling feature is a constant electron concentration per T atom or per fl-Sn like pseudo-cell, and not as in all other recognized cases of 'electron' phases, a controlling electron concentration per atom in the structure. Whether the 14 electrons per T atom represent 10 in inner filled energy bands and 4 in outer bands as in p-Sn itself, is an interesting speculation that magnetic measurements might solve. Corrections resulting from an r 3 vs. a 3 replot of earlier data are presented for the ionic radii of rock salt, C rare earth, and fluorite oxides.The non-equivalence of r 3 vs. a 3 and r vs. a plots for isotypic series of compounds was recently pointed out by *Contribution No. 1646. tPresent address:

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Transformation of three commercial anatase powders resulted in sigmoid curves of transformation vs. time, which were interpreted in terms of a nucleation‐growth process. Analysis of these curves by several rate laws led to activation energies for nucleation of 109, 136, and 148 kcal/mole and for growth of 100, 115, and 190 kcal/mole, respectively. The rate of transformation and activation energy are governed by the nature and amount of impurities which determine the defect structure of the TiO2, i.e. the concentration of oxygen vacancies or interstitials. It is suggested that, in general, oxygen vacancies accelerate and the interstitials inhibit the transformation. CuO additions and hydrogen atmospheres accelerated the transformation by the introduction of oxygen vacancies and/or by reduction to a second TinO2n−1 Magnéli phase which could act as a nucleating agent. The transformation is retarded in vacuum; this retardation is attributed to the introduction of titanium interstitials.

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