Weining Man
Princeton University
Geometry and Symmetry in Experimental Condensed Matter Physics
and Material Science
Photonic Quasicrystals & Random Ellipsoid Packings
Friday, February 22, 2008, 4:00 p.m.
Refreshments at 3:45 p.m.
ABSTRACT
Geometry and symmetry play an important role in the design
of new materials.
In particular this talk investigates photonic quasicrystals
and ellipsoid packings, problems in which the geometry
of the building blocks and the structural symmetry
determine the physical properties. Photonic
quasicrystals are constructed from dielectric
material arranged in a quasiperiodic pattern
whose rotational symmetry is forbidden for
periodic crystals. Because quasicrystals have
higher point group symmetry than ordinary crystals,
they can have more uniform bandgaps. Since calculating
the band structure of 3D photonic quasicrystals is
fundamentally challenging, and to date beyond the
range of computation in a reasonable time, we decided
to answer the question experimentally. We constructed
the world's first and largest (in terms of the
number of units) 3D icosahedral Photonic quasicrystal
(composed of polymer) using stereolithography. With our
novel method to make polar plots of its microwave transmission
vs. frequency and incident angle, we obtained the first-ever
visualization of the Brillouin zone of a quasicrystal.
Before our experimental work it was not at all clear that
Brillouin zones existed or had physical meaning in
quasicryatals. We proved that the nearly spherical
Brillouin zones of 3D icosahedral quasicrystals make them
one of the most promising candidates for complete
photonic bandgaps found to date. For ellipsoidal
granular material packing, we designed and performed
different experiments, including MRI scans, to extrapolate
the bulk density of an infinitely large random system, using
a limited number of particles. We found in both experiments
and simulations that ellipsoids can pack randomly more
densely than spheres because of their extra degree of
freedom associated with their rotational axes. Surprisingly
the packing fraction has a cusp-like minimum for spheres and
increases sharply with aspect ratios different from unity.
A major fundamental question remains as to whether any shape
particle can produce an amorphous packing of higher density
than its crystalline packing. It will be enlightening to
find the correlations between this ratio of amorphous and
crystal packings and features of the equilibrium phase
diagrams for various particle shapes.