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Order and disorder in AlCuCo quasicrystal ; an electron diffraction study

Traditional definition of crystal was based on a concept of ordered unit cell in real space, by anticipating its infinite repetition on three-dimensional lattice[3]. However, crystal ordering can be driven and arranged by additional spatial parameters ; it can be incommensurately modulated and perfectly ordered on long range scale with no strict periodicity on three-dim lattice. Such type of order is prominently revealed in reciprocal space, so that the contemporary definition of crystal refers to: “... an essentially discrete diffraction diagram”[4]. Aperiodic crystals, as well as their diffraction patterns have to be analysed in terms of higher-dimensional crystallography, i.e. by using more then 3 lattice parameters in an expanded space with 3+d dimensions[4]. Quasiperiodicity in real three-dim space reveals strict periodicity in expanded higher-dim space, so that one can consider two general categories of crystals: periodic (PC) and quasiperiodic (QC). Structural disorder in direct space of PC is revealed in reciprocal space (diffraction diagram) by additional intensity in between the basic spots of reciprocal lattice. The same holds for QC, as shown in electron diffraction patterns of Al.63Cu.24Co.13, in Fig.1. Mesh of sharp discrete spots with 10-fold symmetry in Fig.1(a), have to be assigned by 4+1 indexes ; the corresponding in-plane decagonal structure is based on the 4-dim pentagonal lattice. The out of plane periodic structure is revealed in Fig.1c&d, by lines of spots indicating double and quadruple layer stacking with lattice parameter 0.42 nm and 0.84 nm. Diffuse intensity in Fig.1b discloses disorder within the double layer structural unit with first-neighbour correlation q*≈ 4 nm-1. Higher or lower compositional in-plane order was locally observed by variable intensity of spots in Fig.2a&b, so that an indexing on primitive or centred pentagonal lattice cell can be used.

crystal structure; quasicrystals; electron diffraction

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