Discovery of Quasicrystals; Icosahedral Phase
The existence of quasicrystals in an icosahedral phase
was first conjectured and investigated
as a candiate
for the blue phase in liquid crystals
H. Kleinert and K. Maki,
Lattice Textures in Cholesteric Liquid Crystals
Fortschr. Phys. 29, 1 (1981). See p. 242 and 243.
A phase with these properties was discovered experimentally
three years later by Shechtman at al. in 1984:
D. Shechtman at al.,
Phys. Rev. Lett. 53, 1951 (1984)
a rapid solidification of the alloy Al86Mn14.
For more details on this system
click on this link!
See also the citations of Kleinert and Maki in the review article on Liquid Crystals
A picture of the square of the icosahedral order parameter in Eq. (4,22)
of above Kleinert and Maki paper
can easily be
plotted with the help of this short Mathematica Pragram:
k[n_]:=2 Pi *n/nfold
By changing the number nfold, the program draws a picture of the density
of other two-dimensional
quasicrystal symmetries, for instance a picture of
the nfold=7 heptagonal order parameter:
And see the mathematical history
Note added in 2011:
Shechtman's experimental discovery just earned him the Nobel Prize 2011 for a
``Paradigm Shift in Crystallography".
Chemists had a hard time believing in the existence
of a five-fold symmetric crystal structure discussed in our 1981
paper with Maki.