Incommensurate structures

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Abstract
Incommensurate structures occur in a very wide range of crystalline materials and illustrate a number of interesting aspects of the physics of atomic interaction in the context of crystal structure and bonding. Formal theories that deal with the origin of these phases are reviewed and shown to have a great deal in common. Several important examples of incommensurate structures in simple compounds are described and these include the minerals quartz and nepheline. Nepheline, which has not been analysed previously shows an interaction between oxygen displacements associated with the loss of a triad axis, a three-state Potts model, and potassium- vacancy ordering. The important role of incommensurate structures in mineral solid solutions is discussed and illustrated with reference to the plagioclase feldspar solid solution.

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