en
Mn-Al alloys
range positional ordering
ordering
197-205
basic facts
consideration
1991
electron diffraction patterns
peak
factor G
striking experiments
https://scigraph.springernature.com/explorer/license/
crystals
https://doi.org/10.1007/978-1-4757-1402-9_17
chapters
fact
reflection symmetry
et al
false
invariance
Icosahedral Incommensurate Crystals
physics
translational symmetry
translational invariance
view
Bravais lattice
1991-01-01
matter physics
diffraction spots
al
structure
Shechtman et al
axis
spots
diffraction patterns
lattice
2022-01-01T19:25
point group
positional ordering
symmetry axis
overall icosahedral symmetry
experiments
group
patterns
One of the basic facts of condensed matter physics is that the symmetry of 3d crystals can be described in terms of space groups composed of Bravais lattices of 3d translational symmetries and point groups of rotation and reflection symmetries. Only 2-fold, 3-fold, 4-fold and 6-fold rotation symmetries are allowed. In a striking experiment on an Mn-Al alloy, however, Shechtman et al.1 have observed an electron diffraction pattern with a 5-fold symmetry axis, and an overall icosahedral symmetry (Fig. 1). How can this be possible? The diffraction spots are quite sharp, so there is long range positional ordering, but there can not be translational invariance in view of the considerations above. The spectrum has a “scaling” structure: if the pattern is magnified by a factor G (the golden mean) the positions of peaks remain fixed.
position
incommensurate crystals
terms
space group
positions of peaks
icosahedral symmetry
symmetry
spectra
Icosahedral Incommensurate Crystals
rotation symmetry
long range positional ordering
chapter
alloy
rotation
Pynn
Roger
Scaling Phenomena in Disordered Systems
978-1-4757-1404-3
978-1-4757-1402-9
Pure Mathematics
Springer Nature
doi
10.1007/978-1-4757-1402-9_17
Per
Bak
Arne
Skjeltorp
Mathematical Sciences
Physics Department, Brookhaven National Laboratory, 11973, Upton, New York, USA
Physics Department, Brookhaven National Laboratory, 11973, Upton, New York, USA
dimensions_id
pub.1029934199
Springer Nature - SN SciGraph project