Amorphous structure and corrugated space I. Theory

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Abstract
The structure of amorphous materials can usefully be described in terms of disclinations (i.e. rotation dislocations). The disclinations are associated with the curvature of the space. Consequently amorphous structures can be described as a tiling of a randomly corrugated hypersurface. This paper demonstrates for two-dimensional systems a set of sum rules relating the number of polygons of n edges in a domain to the valence of the atoms and to the average curvature on the domain. Approximations are proposed for a generalization to three dimensions.

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