By Ted Janssen, Gervais Chapuis, Marc de Boissieu
Until eventually the Seventies all fabrics studied consisted of periodic arrays of unit cells, or have been amorphous. within the final a long time a brand new type of reliable country topic, referred to as aperiodic crystals, has been stumbled on. it's a lengthy variety ordered constitution, yet with no lattice periodicity. it truly is present in a variety of fabrics: natural and anorganic compounds, minerals (including a considerable element of the earths crust), and steel alloys, lower than quite a few pressures and temperatures. due to the loss of periodicity the standard options for the learn of constitution and actual homes now not paintings, and new concepts must be built. This publication bargains with the characterisation of the constitution, the constitution decision and the examine of the actual homes, specifically dynamical and digital houses of aperiodic crystals. The therapy relies on an outline in an area with extra dimensions than 3, the so-called superspace. this permits us to generalise the traditional crystallography and to appear another way on the dynamics. the 3 major sessions of aperiodic crystals, modulated stages, incommensurate composites and quasicrystals are handled from a unified standpoint, which stresses similarities of some of the structures. The ebook assumes as a prerequisite an information of the elemental concepts of crystallography and the speculation of condensed subject, and covers the literature on the leading edge of the sector.
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Additional info for Aperiodic crystals: from modulated phases to quasicrystals
The system consisting of the monolayer and the top layer of the substrate forms an incommensurate composite. 5 Quasicrystals The discovery of an alloy with icosahedral symmetry in 1982 meant a further breakthrough for aperiodic crystals. In rapidly quenched AIMn a diffraction pattern was observed with fairly narrow peaks at positions where the six basis vectors point to the six pairs of parallel facets of a dodecahedron. The intensity distribution had the symmetry of an icosahedron, a point group not allowing lattice periodicity in three-dimensional space.
The spots display, of course, the eight-fold symmetry, but they do not belong to a two-dimensional reciprocal lattice. On the contrary, the spots are all over the place, although their intensities are in most cases very low. The position of every spot, however, may be reached by a linear combination of four basis vectors, indicated in the figure. Now consider the sixteen points with coordinates 0 or 1. They form a regular pattern which is the projection of a four-dimensional cube on the two-dimensional plane.
When an intermetallic liquid cools down above the melting temperature such clusters are often present. In terms of close packing, an atom may be surrounded by at most twelve atoms of the same kind. This gives a dodecahedral surrounding. Such a structure may not be continued in a periodic way with the same symmetry. However, in quasicrystals the structure becomes quasiperiodic and in the structure one may distinguish clusters with (broken) dodecahedral or icosahedral symmetry. These clusters in general overlap.