Spatial correlations in quasi-crystalline structures

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Abstract
A quasi-crystal is generated from a given, higher-dimensional, parent periodic lattice. Translations of this lattice within a unit cell generate all non-identical states of the same, uniquely defined, physical quasi-crystal. An ensemble-averaging procedure over these states is utilised to obtain the pair distribution and coordination numbers of the quasi-crystal. Results of specific calculations are given for the primitive icosahedral quasi-crystal. A scheme is given for the construction of general decorated quasi-lattices and their corresponding singlet and pair distributions. Implications for icosahedral quasi-crystals and their packing densities are discussed.

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