Symbolic Formulation for Defect Solids

The inability of orthodox chemical formulation to accommodate defect solids has been appreciated for some 

The simplest method possible involves distinction between sites and entities and provision of a sign denoting the way in which one operates on the other. Their interaction gives rise to a symbol describing the various types of defect. We shall now write down the symbols required and their definitions. (In choosing as a symbol for the lattice site, we have attempted to avoid conflict with current use.) 

We must now construct a symbol representing the situation wherein a number n of entities A is distributed over m locations B in such a way that only one of A can be in one location B at any instant. This is expressed concisely by the symbol (.4 Implicit in this symbol is the fact that (m-n) B locations are unoccupied by A% and thus (m-n) vacancy defects of some type are present. It is possible that the A s will be distributed over the B locations at a time (where is a small integral number, usually not greater than 2) this would be expressed by the symbol (qA i BJ. 

The situation will also arise where we wish to write a symbol for r entities C distributed over n v4 s, which are in turn distributed over m B s. This is done by writing (C, A 5J. For r C s and n A s distributed at random over m B s write (C A jBj. If two different types of defect occur in association in the one crystal, then we express this fact by writing ( 4 

We are now in a position to apply this symbolism to specific defects, a few examples of which are listed below. 

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