Graph-theoretic construction of periodic bond chains

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Abstract
A programmable graph-theoretic method has been developed to determine, on the basis of the strong bonds, all the periodic bond chains as well as their directions for any crystal type. The chains are constructed irrespective of whether they satisfy the usually imposed conditions of stoichiometry, and sometimes in addition, zero dipole moment perpendicular to the chain direction. Thus the task of finding periodic bond chains in a given structure is ultimately reduced to rejecting those constructed chains which violate the above conditions. The present paper, I, considers the general case of crystals with covalent, ionic or mixed type bonding. The special case of ionic crystals is treated in the following paper, II, (Strom, 1980), and illustrated by an application on trirutile.

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