Symmetry, stability, and diffraction properties of icosahedral crystals

Conference · Tue Jan 01 00:00:00 EST 1985

OSTI ID:5140920

Bak, P

In a remarkable experiment on an Mn-Al alloy, Shechtman et al. observed a diffraction spectrum with icosahedral symmetry. This is inconsistent with discrete translational invariance since the symmetry includes a five-fold axis. In this paper, it is shown that the crystallography and diffraction pattern can be described by a six-dimensional space group. The crystal structure in 3d is obtained as a cut along a 3d hyperplane in a regular 6d crystal. Displacements of the 6d crystal along 6 orthogonal directions define 6 continuous symmetries for the icosahedral crystal, three of which are phase symmetries describing internal rearrangements of the atoms.

• Research Organization: Brookhaven National Lab., Upton, NY (USA)
• DOE Contract Number: AC02-76CH00016
• OSTI ID: 5140920
• Report Number(s): BNL-37043; CONF-850871-19; ON: DE86001196
• Resource Relation: Conference: International conference on neutron scattering, Santa Fe, NM, USA, 19 Aug 1985; Other Information: Portions of this document are illegible in microfiche products
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
CRYSTALS
CRYSTAL STRUCTURE
CRYSTALLOGRAPHY
DIFFRACTION
SPACE GROUPS
STABILITY
SYMMETRY
COHERENT SCATTERING
SCATTERING
656000* - Condensed Matter Physics