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Quasicrystals @ Jewel Info 4 U
By:Ritika
Quasi crystals stand as a
special case of in-commensurate
crystal phase. Quasi crystals are
present in a space group having more
than three dimensions. For instance,
structures like dihedral and
icosahedral structures are
categories belonging to this type.
Even the two-dimensional Penrose
patterns could be matched with
symmetry structure of quasi
crystals.
Applying the concept of
crystallography to quasicrystals is
an interesting topic and is based on
the fact that any d-dimensional
non-crystallographic point group
possesses dimensional
representations that are compatible
with periodicity. The periodic
structures could be grouped and
calculated in various
crystallographic methods like space
groups, Bravais lattices and point
groups. Quasi crystals are available
in various inter metallic alloy
systems. Quasicrystals are generally
defined as periodic lattices.
Higher Dimensional Space
 Because of the periodicity loss,
quasicrystals could not be defined
in 3D-space in a method as we
normally do for normal crystal
structures. In other words, for
normal crystal structures due to the
three-dimensional translational
periodicity of crystal structure, we
assign Miller indices which are
integer values for recording the
reflections. Factors like friction,
adhesion, corrosion and wear
resistance could be determined and
studied well in surface or
interfacial regions. However, these
could not give an in-depth study
about structure of crystal. In case
of quasi crystals, for marking the
above integer indices, it needs at
least five linearly independent
vectors. That is polygonal
quasicrystals would at least require
five indices and icosahedral
quasicrystals would require six
indices. So quasiperiodic structures
are defined as a period one in a
higher dimensional space
Types of Quasicrystals:
* quasiperiodic in Two Dimensions:
This is also referred to as
polygonal or dihedral quasicrystals.
It has sub elements namely
octagonal, decagonal and
dodecagonal. This has one periodic
direction which lies perpendicular
to the quasiperodic layers.
* quasiperiodic in Three Dimensions:
This type has no periodic direction
and icosahedral quasicrystals fall
under this type.
* new type: Icosahedral
quasicrystals with broken symmetry
fall in this category.
Tiling in Quasicrystals:
Before the finding of quasicrystals,
the method by which a plane was
covered was using two different
types of tiles which reflected a
non-periodic fashion. In 1984,
quasicrystals were introduced and
also it was found that there exists
a similarity among 3D-Penrose
pattern and icosahedral
quasicrystal. For instance, if one
wants to record the diffraction
pattern of Al-Mn quasicrystal this
could be done by placing the atoms
on the vertices of a 3D-Penrose
pattern. These results in producing
a Fourier Transform that details
about the diffraction pattern of Al-Mn
quasicrystal. Thus quasicrystal acts
as a framework and when filled with
atoms in correct fashion would
result in producing quasicrystal
structures.
Symmetry and Diffraction Pattern
in Quasicrystals
The diffraction pattern in
quasicrystal determines the symmetry
which helps in finding the type of
the quasicrystal. Symmetry is
expressed by the set of rotations
that leave the directions of the
facets unchanged. For instance, the
icosahedral quasicrystal results in
a Laue pattern when an x-ray beam is
used along one of the five-fold
axes. The complete atomic structure
solution of an icosahedral
quasicrystalline material was
reported recently by Japanese
researchers. To determine clearly
about how the atoms are arranged and
positioned in a quasicrystal, we can
use the Patterson function that
epitomizes all the information about
the inter-atomic vectors contained
in the diffraction pattern.
Methods Used for Determining the
Structure of Quasicrystals:
There are two methods which are sued
for determining and solving the
structure of quasicrystals. They
are:
* 3D method
* nD structure analysis
* 3D method: In 3D method, the input
obtained from HRTEM images, well
known and defined structures are
used combined, which results in
producing a realistic structure
model.
* nD structure analysis: In nD
structure analysis method, the
structure is modeled based on the
elements present in nD unit cells.
This is in contrast with the 3D
method as this is a quantitative
analysis method. Here least-squares
method is used for finding and
calculating the diffraction patterns
and also for remodeling the same.
Thus, this method makes use of
various mathematical methods and
tools just as used in a conventional
crystal with the only difference in
this method being extended to the nD
space.
Quasicrystals have structures that
are neither crystalline nor
amorphous. However, they are
intermediate structures with
associated diffraction patterns.
They are characterized by elements
and attributes like length of
adjacent lattice vectors, five-fold
orientation symmetries and absence
of translation symmetries. Thus,
besides the crystalline and
amorphous solids, the quasicrystals
are a new type of space filling
interesting forms of matter. Thus,
the structure of quasicrystals which
are not generally distributed
periodically in a physical space
that is, they are not periodic in 3D
space are defined well in a higher
dimensional space using a
crystallographic approach.
Quasicrystals with a hierarchical
structure exhibit a self-similarity
in the radial part of their
direction.
The x-ray holography and
quasicrystals are associated
resulting in two unique experimental
considerations. This showed that for
the first time x-ray holography can
be tested on a non crystalline
solid. Also in addition, this proved
that atomic positions in
quasicrystals can be observed in
direct space and in 3D with no
prerequisite atomic model and no
necessity for a sophisticated
extension of the classical
crystallography to a six-dimensional
space. This gives structural
information in direct space without
presuming a prerequisite model.
For instance, icosahedral CdYb
quasicrystal has been solved using
X-ray diffraction data collected on
the D2AM beam line. This model was
further refined by using data in six
dimensional analysis which included
in it phase reconstruction
procedure. The model also leads to a
description of the hierarchical
packing of the clusters. The
clusters are packed together to form
a 'cluster of clusters'. This
cluster of clusters in turn forms a
larger cluster. The inflation
property continues at infinity and
is used to explain the
quasicrystal's physical properties.
This method thus paves the way for
further investigation into the
stability and physical properties of
quasicrystals. Nowadays, the growth
technique of quasicrystals is
perfected to a level that large
ideal quasicrystals could be
produced. These will contribute
significantly to the understanding
of the quasicrystals.
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