Valence electron rules for compounds with tetrahedral structures and anionic tetrahedron complexes

For compounds with tetrahedral structure or anionic tetrahedron complex two valence electron concentration rules can be formulated which correlate the number of available valence electrons with particular features of the crystal structure. These two rules are known as the tetrahedral structure equation where the total valence electron concentration, VEC, is used as parameter and the generalized 8-N rule where the parameter of interest is the partial valence electron concentration in respect to the anion, VECA. From the tetrahedral structure equation one can calculate the average number of non-bonding orbitals per atom and, in the case of non-cyclic molecular tetrahedral structures, the number of atoms in the molecule. An application of the generalized 8-N rule allows the derivation of the average number of anion - anion bonds per anion or the number of valence electrons which remain with the cation to be used for cation - cation bonds and/or lone electron pairs. These rules have been used not only to predict probable structural features of unknown compounds but also to point out possible errors in composition or structure of known compounds

Calculation of the BO₃ triangle to BO₄ tetrahedron ratio in borates

A bonding model, valid for a limited group of borates, is formulated which allows the ratio of triangularly to tetrahedrally coordinated B atoms to be calculated from the chemical formula. The anion complex, which is formed by covalently bound atoms, has non-directed ionic bonds with the surrounding cations. To complete its electron octet, each O atoms of the complex forms exactly two covalent bonds either with 2 B and/or with 1 B and 1 H atom, depending on the number of OH groups. The B atoms have no preference for either triangular of tetrahedral O coordination. However, a change of a B–O base triangle to an isoelectronic base tetrahedron decreases the number the O atoms which can be used for B–O–H bonds and increases the number of shared O atoms engaged in B–O–B bonds – and vice versa. The ratio of B–O triangles to tetrahedra is adjusted such that O atoms can form the proper number of B–O–B and/or B–O–H bonds. Using the model one can also prove that a borate with OH groups and all its dehydration products (independent whether they are crystallized or a glass) should have the same ratio of three-to four-coordinated B atoms. Under the presupposition that the bonding model is applicable, one can specify a simple mixture of base triangles and/or base tetrahedra with which it should be possible to construct an anion complex. The observed complex is either built up with this simple mixture or with a mixture of base polyhedra derived from the sinple one by cross-substitution which does not change the triangle to tetrahedron ratio. The realization of the bonding model is in principle possible only in a restricted omposition range in which lie one quarter of the known borates. The equation to calculate the triangle to tetrahedron ratio has been tested on all borates within this range. An agreement was found for 85 percent of the 222 investigated crystal structures

Crystal chemical information to be obtained from the bond-number equality concept

Based on the bond-number equality concept an equation is derived for anion complexes of normal valence compounds with triangularly and/or tetrahedrally coordinated central atoms and anions having one, two, three and four bonds to central atoms: %delta = 4 - (n/m') x [2 - %A[1] + %A[3] + 2 x %A[4]]. %Delta is the ratio of the number of central atoms with triangular anion coordination to the sum of all central atoms in the anion complex. n/m' is the ratio of the number of all A anions to the number of all central atoms C' in the anion complex. %A[1] is the ratio of the number of anions with one bond to a central atom to the sum of all anions in the anion complex. %A[3] and %A[4] are defined accordingly. The equation can be used to formulate the possible crystal chemical formulae, which are characterized by partitions of central atoms and anions according to their bond numbers. Nitridosilicates and selected oxoborates are treated as examples of applications of the equation

From Hume-Rothery's 8-<i>N</i> rule to valence electron rules for Zintl phases and their extensions

The 8-N rule by Hume-Rothery (1931) for structures of main group elements relates the number of covalent atom bonds with the group number, i.e. the number of valence electrons. The atoms, by forming shared two-electron bonds, complete their octets. Hume-Rothery's idea was subsequently applied to rationalize anion-anion bonds in ionic compounds. A generalized 8-N rule which considers both anion-anion and cation-cation bonds was published in 1964/65. It can be used with iono-covalent and also strongly polar intermetallic compounds, the latter referred to as Zintl phases. Structural features are interpreted in terms of an underlying ionic bonding scheme where electropositive elements transfer valence electrons to electronegative elements which complete their octets, if necessary by forming homonuclear bonds. The generalized 8-N rule has recently been combined with other valence rules to derive for ionocovalent compounds possible base polyhedra, small building units, with which can be constructed neutral and anionic polyhedron complexes

Fritz H. Laves – 100 years young

This year Fritz Laves, professor for crystallography and petrography and head of the Mineralogical Department at the University and the Eidgenössische Technische Hochschule in Zurich from 1954 to 1976, an accomplished leading scientist and outstanding pioneer in crystal chemistry, would be 100 years old