GEOMETRICAL DERIVATION OF SIMPLE LAYER-TYPE STRUCTURES

GEOMETRICAL DERIVATION OF SIMPLE LAYER-TYPE STRUCTURES 

From a geometrical point of view, a crystal structure may be considered as composed of coordination polyhedra. In inorganic compounds one usually discusses the cation coordination, i.e. the polyhedra formed around the cations by the bonded neighbors which are anions in normal valence compounds, but also include cations in polycationic compounds. The number of vertices of these polyhedra, the coordination number, depends largely on the cation-to-anion radius ratio. It is quite obvious that a minimum coordination number is necessary for the formation of a layer structure. With a coordination number 2, only chains or finite molecules are possible. A high coordination number, on the other hand, will lead to a three-dimensional or framework structure. 

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GEOMETRICAL DERIVATION OF SIMPLE LAYER-TYPE STRUCTURES 9... 

The distinction between these three types of boundaries will become clearer once we deal with examples. In the following sections the mathematical tools will be derived that are necessary to describe transport across these boundaries. They will then be applied to real environmental boundaries. We will also distinguish between different geometrical shapes of the boundary. Flat boundaries are easier to describe mathematically than spherical boundaries. The latter will be used to describe the exchange between suspended particles or droplets, and the surrounding fluid (algal cells in water, fog droplets in air, etc.). Furthermore, boundaries can be simple (one layer ) or have a multiple structure. 

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