The three dimensional periodic nature of crystalline structures was so strongly anchored in the mind of scientists that the numerous indications that seemed to question this model had serious difficulties to acquire a status of validity. The discovery of aperiodic crystals, a generic term including modulated, composite and quasicrystal structures, started in the seventies of last century with the discovery of incommensurately modulated structures with the presence of satellite reflections surrounding the main reflections in the diffraction patterns. The need to use additional integers to index such diffractograms was soon adopted and theoretical considerations showed that any crystal structure requiring more than three integers to index its diffraction pattern could be described as a periodic object in a higher dimensional space, i.e. superspace, with dimension equal to the number of required integers. The structure observed in physical space is thus a three-dimensional intersection of the structure described as periodic in superspace. Once the symmetry properties of aperiodic crystals were established, the superspace theory was soon adopted in order to describe numerous examples of incommensurate crystal structures from natural and synthetic organic and inorganic compounds even to proteins. Aperiodic crystals exhibit thus perfect atomic structures with long-range order, but without any three-dimensional translational symmetry. The discovery of modulated structures was soon followed by the discovery of composite structures consisting of structural entities with partly independent translations and finally by the discovery of quasicrystals. In recent years, the use of CCD and imaging plate systems considerably improved the sensitivity of data collection for aperiodic structures and in particular modulated structures and, therefore, there was a need for further improvement of the methods. Today, several computer programs are able to solve and refine incommensurately modulated structures using the superspace approach. In nature, it is uncommon to find minerals having strong and sharp incommensurate satellites that could be used for a higher dimensional refinement. Here we describe several cases of aperiodic minerals (natrite, calaverite, melilite, fresnoite, pearceite-polybasite, cylindrite) including the first example of a natural and stable quasicrystalline structure (icosahedrite) which definitely settles any doubt, which could remain on the long-term stability of quasicrystals.

Aperiod Mineral Structures / Bindi, Luca; Chapuis, Gervais. - ELETTRONICO. - (2017), pp. 213-254.

Aperiod Mineral Structures

BINDI, LUCA;
2017

Abstract

The three dimensional periodic nature of crystalline structures was so strongly anchored in the mind of scientists that the numerous indications that seemed to question this model had serious difficulties to acquire a status of validity. The discovery of aperiodic crystals, a generic term including modulated, composite and quasicrystal structures, started in the seventies of last century with the discovery of incommensurately modulated structures with the presence of satellite reflections surrounding the main reflections in the diffraction patterns. The need to use additional integers to index such diffractograms was soon adopted and theoretical considerations showed that any crystal structure requiring more than three integers to index its diffraction pattern could be described as a periodic object in a higher dimensional space, i.e. superspace, with dimension equal to the number of required integers. The structure observed in physical space is thus a three-dimensional intersection of the structure described as periodic in superspace. Once the symmetry properties of aperiodic crystals were established, the superspace theory was soon adopted in order to describe numerous examples of incommensurate crystal structures from natural and synthetic organic and inorganic compounds even to proteins. Aperiodic crystals exhibit thus perfect atomic structures with long-range order, but without any three-dimensional translational symmetry. The discovery of modulated structures was soon followed by the discovery of composite structures consisting of structural entities with partly independent translations and finally by the discovery of quasicrystals. In recent years, the use of CCD and imaging plate systems considerably improved the sensitivity of data collection for aperiodic structures and in particular modulated structures and, therefore, there was a need for further improvement of the methods. Today, several computer programs are able to solve and refine incommensurately modulated structures using the superspace approach. In nature, it is uncommon to find minerals having strong and sharp incommensurate satellites that could be used for a higher dimensional refinement. Here we describe several cases of aperiodic minerals (natrite, calaverite, melilite, fresnoite, pearceite-polybasite, cylindrite) including the first example of a natural and stable quasicrystalline structure (icosahedrite) which definitely settles any doubt, which could remain on the long-term stability of quasicrystals.
2017
97809030595
Aperiodic Mineral Structures
213
254
Bindi, Luca; Chapuis, Gervais
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1094441
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