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