I.D. Brown

Empirical bond-strength–bond-length curves for oxides

Bond-strength-bond-length relationships for bonds between oxygen and H+, Li+, Be2+, B3+, Na+, Mg2+, Al3+, Si4+, P5+, S6+, K+, Ca2+, Sc3+, Ti4+, V5+, Cr6+, Mn2+, Fe3+, Fe2+, Co2+, Cu2+, Zn2+, Ga3+, Ge4+ and As5+ 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/R0)-N where s = bond strength, R = bond length and R0 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, R0 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+, Cu2+ and V5+). 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.

Chemical and Steric Constraints in Inorganic Solids

The structures observed for many inorganic solids are the result of a compromise between the conflicting requirements of chemical bonding and threedimensional geometry. The ideal chemical structure and bond geometry can be predicted using the bondvalence model which is developed in some detail. The constraints imposed on this geometry when the ideal structure is mapped into three-dimensional space require, in many cases, that ideal bond lengths be strained. Particularly in compounds containing bonds of intermediate strength (e.g. the oxides and halides of di- and trivalent cations), the relaxation of this strain can result in non-stoichiometry, stabilization of unusual oxidation states, distortion of bonding environments and lowering of symmetry. The resulting rich crystal chemistry is often associated with important physical properties such as ferroelectricity and superconductivity. Examples are given which show that these properties can, at least in some cases, be derived directly from the chemical formula by considering the problems of generating a structure that conforms to both the chemical and the spatial constraints.

VALENCE : a program for calculating bond valences

The DOS program VALENCE is designed to calculate bond valences from bond lengths and vice versa. It can also calculate bond-valence sums and average bond lengths, and can determine bond-valence parameters from the bonding environments of different cations.

Predicting bond lengths in inorganic crystals

Bond lengths in inorganic crystals can be predicted by solving a model based on a network of chemical bonds. The results agree with observed bond lengths to within a few hundredths of an hngstrrm for most bonds except for those to alkali metals. An earlier method of predicting bond lengths [Baur (1970), Trans. Amer. Cryst. Assoc. 6, 129-155] gives predictions of comparable overall accuracy but the difference in the approaches leads to significant differences in the predictions for individual bonds. The two methods each have their own strengths and should be considered as complementary. The model has possible extensions to amorphous materials and suggests, for example, that the lone pair of valence electrons is not responsible for the distorted environments found in TeCI 4 and T e I 4 in the solid state. 1305

Recent developments in the bond valence model of inorganic bonding

The valences of bonds can be predicted from the bonding network using (by analogy with electrical networks) Kirchhoff-like equations which lead to the definition of a new atomic property, the Valence Potential. The computer algorithm used in this prediction indicates that the electrons on any ion tend to be shared equally between all the bonds and that, despite appearances to the contrary, the rules of bonding around cations and anions are identical. These rules are the basis of a number of structure prediction and modelling techniques which make use of the correlation between bond valence and bond length. A three parameter equation is proposed to describe this relation for those bonds (e.g. H-O, Na-O, Tl-O) which occur with a wide range of lengths and for which, therefore, the usual two parameter equations are not adequate.

A Real-Space Computer-Based Symmetry Algebra

A computer-based symmetry algebra is described which permits the reconstruction of an infinite bond network from the asymmetric connectivity without an a priori knowledge of atomic coordinates. The algebra requires not only an algorithmic ordering of the Wyckoff groups but the designation of one site in each Wyckoff group as a special-position representative (SPR) site. The algebra is designed to be used for analysing the bonding network of compounds appearing in the Inorganic Crystal Structure Database.

CIF: the computer language of crystallography

The Crystallographic Information File (CIF) was adopted in 1990 by the International Union of Crystallography as a file structure for the archiving and distribution of crystallographic information. The CIF standard is now well established and is in regular use for reporting crystal structure determinations to Acta Crystallographica and other journals. The structure of CIF is flexible and extensible and is compatible with other evolving standards. It is well suited to relational and object-oriented models, and is being adopted by the crystallographic databases. This paper reviews the development of CIF and describes its salient features. Future extension of the standard to include implementation of methods will allow CIF to exploit the potential of advanced information-handling software.

Thermal Expansion of Chemical Bonds

Using the bond-valence model, a relationship is developed between the thermal expansion of a chemical bond, its amplitude of thermal vibration and its force constant. An empirical expression found between bond valence and the force constants derived from vibrational spectroscopy allows all of these quantities to be predicted from either the expected or the observed bond valence. The thermal expansion predicted by these relations is in excellent agreement with the average expansion observed around cations in inorganic solids, but individual bonds are found to expand more or less than this depending on strains and constraints within the structure. Comparison between the theoretical and observed amplitudes of thermal vibration gives a quantitative measure of correlation between the thermal motions of atoms that form the bond. The theory also shows how the parameters used in calculating bond valences from bond lengths should be corrected for temperature.

Hydrogen bonding in perchloric acid hydrates

A bond-valence analysis of five perchloric acid hydrates shows that normal hydrogen bonds account for only about one half of the bonding of the perchlorate ion. Each H atom also forms an average of four additional weak interactions (H ⋯ O acceptor ~ 2.3 to 3.1 A; O-H ⋯ O ~ 80 to 120°) which account for the rest of the bonding. A distinction can be made between the normal and the very weak hydrogen bonds in the lower hydrates but this distinction is less clear in the higher hydrates where the distribution of H ⋯ O bond strengths tends to form a continuum.

Specification of the Crystallographic Information File format, version 2.0

Version 2.0 of the CIF format incorporates novel features implemented in STAR 2.0. Among these are an expanded character repertoire, new and more flexible forms for quoted data values, and new compound data types. The CIF 2.0 format is compared with both CIF 1.1 and STAR 2.0, and a formal syntax specification is provided.