What is a Crystal ?
CRISTAUX
MATHEMATIQUES
PAVAGE
FONCTIONS
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.
MICHEL
P/85/68
IHES
12/1985
A4
8 f.
EN
TEXTE
PREPUBLICATION
P_85_68.pdf
1985