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'Ground states' are the lowest energy states of
matter. They are created in real life by taking a liquid and
slowly cooling it until you reach absolute zero temperature. The
resulting arrangement of molecules or particles is a 'ground
state,' which often is an ordered crystal structure. This image
shows a snapshot of a liquid before the cooling process.
'Ground states' are the lowest energy states of
matter. They are created in real life by taking a liquid and
slowly cooling it until you reach absolute zero temperature. The
resulting arrangement of molecules or particles is a 'ground
state,' which often is an ordered crystal structure. This image
shows an ordered ground state (called the face-centered cubic
lattice), which is the end result of the slow cooling process.
Images: Courtesy of Torquato Labs
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"We believe our 'duality relations' will be a
useful theoretical tool to understand how individual particles come
together to form a crystal," said Salvatore Torquato, a professor of
chemistry who co-wrote the paper with senior chemist Frank Stillinger.
"If we can tune the interactions among particles that form a crystal,
we might be able to create materials that respond to light or
mechanical stress in novel ways."
A material that maintains its exact size and shape through extremes in
temperature, for example, might be valuable in the manufacture of
orbiting space telescopes, whose mirrors need to retain their shape as
they pass from sunlight into the Earth's shadow.
A crystal is the state of matter that is easiest to analyze because
its frozen molecules are motionless and often regularly organized. A
crystal's properties - its ability to bend light, for example -
generally reveal valuable information about how its constituent
molecules will behave at higher temperatures, such as when they become
a liquid.
The challenge is that many complex materials can crystallize into a
multitude of different structures. When a substance is cooled to
nearly absolute zero, and it can take on an enormously large number of
possible "ground states" -- the term for the molecular arrangement
with the lowest possible energy. Scientists seek to determine the true
ground state because it provides a fundamental understanding of matter
in the solid state and its possible uses. However, determining which
molecular pattern is the true ground state requires mathematical proof
that is hard to come by.
"We resort to approximations," said Christos Likos, a professor of
theoretical physics at the University of Dusseldorf in Germany. "They
help us produce meaningful results sometimes, but we need to have a
lighthouse occasionally to show us we're on the right path. Such
lighthouses are rare in this business, but Sal and Frank have found
one."
Torquato and Stillinger's findings explore particles' behavior as they
attract and repel each other over varying distances. By analyzing this
behavior, the scientists were able to conceive a precise mathematical
correspondence - called duality relations - between possible
arrangements of particles. The work will enable the researchers to
draw important conclusions about how particles at very low
temperatures interact over great distances, a situation that is very
difficult to treat theoretically.
"Once ground states can be determined and controlled with certainty,
scientists might create materials with properties virtually unknown in
nature," Torquato said.
The Department of Energy funded the team's research, which appears in
the Jan. 16 edition of the journal Physical Review Letters:
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