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Topic Name: U of M Scientists has Brought Out the Mystery of Quasicrystal Using Computer Simulation
Category: STRUCTURAL
Research persons: Sharon Glotzer
Location: University of Michigan, United States
Details
The method to the madness of quasicrystals has been a mystery
to scientists. Quasicrystals are solids whose atoms aren't arranged in a
repeating pattern, as they are in ordinary crystals. Yet they form intricate
patterns that are technologically useful.
A computer simulation performed by
University of Michigan
scientists has given new insights into how this unique class of solids forms.
Quasicrystals incorporate clusters of atoms as they are, without rearranging
them as regular crystals do, said Sharon Glotzer, a professor in the
Department of
Chemical Engineering at University of Michigan.
Crystals form when liquids freeze into solids. When a normal
crystal grows, a crystallite nucleus develops first. The atoms in the liquid
attach one-by-one to the crystallite, as though following a template. If the
atoms have already formed a cluster on their own, they must rearrange in order
to fit the template. This is how a repeating pattern forms.
In the case of quasicrystals, though, atoms that have already
formed stable shapes away from the crystallite can still bind to it. They don't
have to make adjustments.
"In our simulations of quasicrystals, we observed that the
atoms attach to the crystallite in large groups," said chemical engineering
doctoral student Aaron Keys. "These groups have already formed locally stable
arrangements, and the growing quasicrystal assimilates them with minimal
rearrangement."
Because quasicrystals aren't as regimented as regular
crystals, the solid can reach a "structural compromise," where liquid-like
molecular arrangements are retained in the solid state. This allows
quasicrystals to form more easily than regular crystals.
Quasicrystals are found in certain metal alloys that tend to
resist wear and corrosion, and are used in non-stick coatings, for example. They
also have high tensile strength, meaning high forces are required to stretch
them to their breaking point.
"Learning how they grow will help us figure out to how
engineer quasicrystalline structures from new building blocks, which could lead
to a slew of new materials," Glotzer said.
Glotzer and Keys are authors of a paper on the research, "How
do quasicrystals grow"," published in Physical Review Letters. Their paper is
featured in an article in the current edition of the journal Nature.
Glotzer is also a professor in the departments of
Materials Science
and Engineering,
Macromolecular
Science and Engineering, and Physics.
Note for Quasicrystals
Quasicrystals are structural forms that are both ordered and nonperiodic. The
term and the concept were introduced originally to denote a specific arrangement
observed in solids which can be said to be in a state intermediary between
crystal and glass. Producing Bragg diffraction, they share a defining property
with crystals, but differ from them by lacking a simple repeating structure.
Mathematical artefacts, known as aperiodic tiling, were invented in the early
1960s, but some twenty years later physical experiments gave conclusive evidence
of their material existence. Within the field of crystallography and solid state
physics the discovery has produced a paradigm shift which is indeed a minor
scientific revolution. It was realized that quasicrystals had been investigated
and observed earlier but until then the prevailing views about atomic structure
of matter lead to their being explained away.
An ordering is nonperiodic if it lacks translational symmetry, which means that
a shifted copy will never match exactly with its original. The ability to
diffract comes from the existence of an indefinitely large number of elements
with a regular spacing, a property loosely described as long-range order.
Experimentally the aperiodicity is revealed in the unusual symmetry of the
diffraction pattern. The first officially reported case of what came to be known
as quasicrystals was made by Dan Shechtman and coworkers in 1984. Between a
mathematical model of a quasicrystal, such as the Penrose tiling, and the
corresponding physical systems, the distinction is taken to be evident and
usually does not have to be emphasized.
The intuitive considerations obtained from simple model aperiodic tilings are
formally expressed in the concepts of Meyer and Delone sets. The mathematical
counterpart of physical diffraction is the Fourier transform and the qualitative
description of a diffraction picture as 'clear cut' or 'sharp' means that
singularities are present in the Fourier spectrum. There are different methods
to construct model quasicrystals. These are the same methods that produce
aperiodic tilings with the additional constraint for the diffractive property.
Thus for a Substitution tiling the eigenvalues of the substitution matrix should
be Pisot numbers. The aperiodic structures obtained by the cut and project
method are made diffractive by chosing a suitable orientation for the
construction. This is indeed a geometric approach which has also a great appeal
for physicists.
Real world systems are finite and imperfect, so the distinction between
quasicrystals and other structures is an always open question. Since the
original discovery of Shechtman hundreds of quasicrystals have been reported and
confirmed. Such structures are found most often in aluminium alloys (Al-Ni-Co,
Al-Pd-Mn, Al-Cu-Fe), but other compositions are also possible (Ti-Zr-Ni,
Zn-Mg-Ho, Cd-Yb). Different mechanisms have been proposed to explain the
generation of quasicrystals and are still discussed. The physical properties of
quasicrytals are still studied and new results are currently obtained. Since
2004 different research groups have reported evidence for quasicrystal ordering
in liquids and polymers. Such occurrences have come to be known as 'liquid' or,
more generally, 'soft' quasicrystals.
Note for Crystal Structure
In mineralogy and crystallography, a crystal structure is a unique arrangement
of atoms in a crystal. A crystal structure is composed of a motif, a set of
atoms arranged in a particular way, and a lattice. Motifs are located upon the
points of a lattice, which is an array of points repeating periodically in three
dimensions. The points can be thought of as forming identical tiny boxes, called
unit cells, that fill the space of the lattice. The lengths of the edges of a
unit cell and the angles between them are called the lattice parameters. The
symmetry properties of the crystal are embodied in its space group. A crystal's
structure and symmetry play a role in determining many of its properties, such
as cleavage, electronic band structure, and optical properties.
The crystal structure of a material or the arrangement of atoms a crystal can be
described in terms of its unit cell. The unit cell is a tiny box containing one
or more motifs, a spatial arrangement of atoms. The units cells stacked in
three-dimensional space describes the bulk arrangement of atoms of the crystal.
The unit cell is given by its lattice parameters, the length of the cell edges
and the angles between them, while the positions of the atoms inside the unit
cell are described by the set of atomic positions (xi,yi,zi) measured from a
lattice point.
The defining property of a crystal is its inherent symmetry, by which we mean
that under certain operations the crystal remains unchanged. For example,
rotating the crystal 180 degrees about a certain axis may result in an atomic
configuration which is identical to the original configuration. The crystal is
then said to have a twofold rotational symmetry about this axis. In addition to
rotational symmetries like this, a crystal may have symmetries in the form of
mirror planes and translational symmetries, and also the so-called compound
symmetries which are a combination of translation and rotation/mirror
symmetries. A full classification of a crystal is achieved when all of these
inherent symmetries of the crystal are identified.
Note for Crystallite
A crystallite is a domain of solid-state matter that has the same structure as a
single crystal. Metallurgists often refer to crystallites as "grains".
Solid objects that are large enough to see and handle are rarely composed of a
single crystal, except for a few cases (gems, silicon single crystals for the
electronics industry, certain types of fiber, and single crystals of a
nickel-based superalloy for turbojet engines). Most materials are
polycrystalline; they are made of a large number of single crystals —
crystallites — held together by thin layers of amorphous solid. The crystallite
size can vary from a few nanometers to several millimeters.
If the individual crystallites are oriented randomly (that is, if they lack
texture), a large enough volume of polycrystalline material will be
approximately isotropic. This property helps the simplifying assumptions of
continuum mechanics to apply to real-world solids. However, most manufactured
materials have some alignment to their crystallites, which must be taken into
account for accurate predictions of their behavior and characteristics.
Material fractures can be intergranular fracture or a transgranular fracture.
There is an ambiguity with powder grains: a powder grain can be made of several
crystallites. Thus, the (powder) "grain size" found by laser granulometry can be
different from the "grain size" (or, rather, crystallite size) found by X-ray
diffraction (e.g. Scherrer method), by optical microscopy under polarised light,
or by scanning electron microscopy (backscattered electrons).
Coarse grained rocks are formed very slowly, while fine grained rocks are formed
quickly, on geological time scales. If a rock forms very quickly, such as the
solidification of lava ejected from a volcano, there may be no crystals at all.
This is how obsidian forms.
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