A bond-valence approach to the structure, chemistry and paragenesis of hydroxy-hydrated oxysalt minerals. I. Theory

The crystal structure of a mineral may be divided into two parts: (1) the structural unit, an array of high-bond-valence polyhedra that is usually anionic in character, and (2) the interstitial complex, an array of large low-valence cations, simple anions and (H2O) groups that is usually cationic in character. Interstitial complexes link the structural units with weak cation-anion and hydrogen bonds into a continuous structure, and the breakdown of a structure is usually controlled by the strengths of the weak bonds that link the structural units together. The interstitial complex is (usually) a complex cation, and can be characterized by its Lewis acidity, a measure of the electrophilic character of the complex. The structural unit is (usually) a complex oxyanion, and can be characterized by its Lewis basicity. The interaction between the structural unit and the interstitial complex can be examined using. the valence-matching principle from bond-valence theory. If one examines a series of structures with the same structural unit it is evident that the average coordination of the O atoms of the structural unit varies slightly from one structure to another, producing a range of Lewis basicity for this specific structural unit. In this way, a specific structural unit can be stable over a range of Lewis basicity (i.e., over a specific pH range). The formula of an interstitial complex may be written in the following way: {M-[m] (+)(a) M-[n] (2+)(b) M-[l] (3+)(e) (H2O)(d) (H2O)(e) (OH)(f) (H2O)(g) } ((a+2b+3c-f)+), where [n], [m] and [l] are coordination numbers, a, b and c are the numbers of monovalent, divalent and trivalent cations, d is the number of transformer (H2O) groups, e is the number of (H2O) groups bonded to two interstitial cations or one interstitial cation and one hydrogen bond, f is the number of interstitial (OH) groups, and g is the number of (H2O) groups not bonded to any cation. The number of transformer (H2O) groups strongly affects the Lewis acidity of the interstitial complex, and the variation in Lewis acidity of a generalized interstitial complex can be graphically represented as a function of the number of transformer (H2O) groups. Where the Lewis acidity of a generalized interstitial complex overlaps the range of Lewis basicity of a specific structural unit, the valence-matching principle is satisfied and a stable structural arrangement is possible. A range of borate minerals is examined from this perspective. These ideas show that there are considerable restrictions on the details of the interstitial complexes in even the most complicated of the borates. The impetus at present is to understand what controls the composition of complex oxysalt minerals, and the present approach takes some steps toward this goal.