Before 1984, scientists thought they had a complete understanding of all the possible ways atoms and molecules can join together to make a solid. This knowledge, established nearly two centuries ago, is codified in a set of principles known as the laws of crystallography, which are essential for understanding and taking advantage of the physical properties of matter, whether it be making steel for a bridge, cleaving the facets of a diamond, or manipulating the electronic properties of silicon for use in integrated circuits. According to these laws, arrangements of atoms in solids are either completely random, as in the case of window glass, or crystalline, as is the case for sugar or table salt. In the case of crystalline materials, the atoms are organized in a symmetrical lattice like the square tiles in a simple bathroom tiling wherein tiles repeat in a periodic pattern (translational symmetry) that also exhibits a discrete rotational symmetry. The two cases are analogous to mosaics in which the tiles are put together either randomly or in an orderly, symmetrical tessellation. A key fact about regular tessellations, known since the ancient Egyptians, is that only certain symmetries can be obtained. The same rules apply to matter. Thus, periodic materials can only exhibit certain rotational symmetries: two-, three-, four-, and sixfold symmetry axes; five-, seven-, eight-, or higher-fold symmetry axes are strictly forbidden. Icosahedral symmetry, which includes six independent fivefold symmetry axes, is super-forbidden.

How impossible crystals came to Earth: A short history / Bindi, L.; Steinhardt, P.. - In: ROCKS AND MINERALS. - ISSN 0035-7529. - STAMPA. - 93:(2018), pp. 50-57. [10.1080/00357529.2018.1383831]

How impossible crystals came to Earth: A short history

L. Bindi
;
2018

Abstract

Before 1984, scientists thought they had a complete understanding of all the possible ways atoms and molecules can join together to make a solid. This knowledge, established nearly two centuries ago, is codified in a set of principles known as the laws of crystallography, which are essential for understanding and taking advantage of the physical properties of matter, whether it be making steel for a bridge, cleaving the facets of a diamond, or manipulating the electronic properties of silicon for use in integrated circuits. According to these laws, arrangements of atoms in solids are either completely random, as in the case of window glass, or crystalline, as is the case for sugar or table salt. In the case of crystalline materials, the atoms are organized in a symmetrical lattice like the square tiles in a simple bathroom tiling wherein tiles repeat in a periodic pattern (translational symmetry) that also exhibits a discrete rotational symmetry. The two cases are analogous to mosaics in which the tiles are put together either randomly or in an orderly, symmetrical tessellation. A key fact about regular tessellations, known since the ancient Egyptians, is that only certain symmetries can be obtained. The same rules apply to matter. Thus, periodic materials can only exhibit certain rotational symmetries: two-, three-, four-, and sixfold symmetry axes; five-, seven-, eight-, or higher-fold symmetry axes are strictly forbidden. Icosahedral symmetry, which includes six independent fivefold symmetry axes, is super-forbidden.
2018
93
50
57
Bindi, L.; Steinhardt, P.
File in questo prodotto:
File Dimensione Formato  
R&M_impossible crystals.pdf

Accesso chiuso

Tipologia: Pdf editoriale (Version of record)
Licenza: Tutti i diritti riservati
Dimensione 8.16 MB
Formato Adobe PDF
8.16 MB Adobe PDF   Richiedi una copia

I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1107157
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 8
  • ???jsp.display-item.citation.isi??? ND
social impact