Symmetry, stability, and diffraction properties of icosahedral crystals

Conference · Mon Dec 31 23:00:00 EST 1984

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
• Country of Publication: United States
• Language: English

Related Subjects

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