Titlebook: Beyond Quasicrystals; Les Houches, March 7 Fran?oise Axel,Denis Gratias Conference proceedings 1995 Springer-Verlag Berlin Heidelberg 1995

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The pentacrystalsntacrystal is any quasicrystal whose points can be written, relative to some basis {..,..., ..} of a real .-dimensional Euclidean space ?., with coefficients in ?[.], the quadratic extension of the rational number field ?. In these lecture notes all quasicrystals are pentacrystals even if they do.no

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From Quasiperiodic to More Complex Systemsmer case the diffraction peaks are infinitely sharp for a perfect infinite crystal, in the latter there are no sharp peaks. The presence of some disorder does not eliminate sharp Bragg peaks as long as long-range order is preserved. Moreover, the sharp Bragg peaks lie on a lattice, the reciprocal la

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Matching Rules and Quasiperiodicity: the Octagonal Tilingsthe main problems about quasicrystals is to understand the simple possibility of a non periodic long range order, since no two atoms have exactly the same environment up to infinity. One possible solution to this problem is to consider that the order stems from privileged local configurations and is

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