What is a Crystal ?


Michel, Louis



Abstract : An historical survey of our knowledge of crystal structure and of the mathematical problem of paving space with one or a few types of stones show that a crystal has not necessarily a translation lattice. The recently discovered crystals of alloys Al with 14% Mn have an ecosahedral symetry (incompatible qith translation lattice). Their electron micrographs show a structure similar to a Penrose tiling. It seems that long range order characterizing crystals can be obtained from projection of a thin slab of genuine crystal in higher dimension so that crystal physical properties can be described by quasi-periodic functions (as generalizing periodic ones) or may be almost periodic functions.




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MICHEL, “What is a Crystal ?,” Archives de l'IHES, consulté le 22 juin 2024, https://omeka.ihes.fr/document/P_85_68.pdf.