A theoretical physicist at the National
Institute of Standards and Technology (NIST) has developed a method for
calculating the motions and forces of thousands of atoms simultaneously over
a wider range of time scales than previously possible. The method overcomes
a longstanding timing gap in modeling nanometer-scale materials and many other
physical, chemical and biological systems at atomic and molecular levels.
Colorized simulation of what happens to 1100 carbon atoms in a ‘flat’ sheet of graphene about 20 microseconds after the central atom is moved slightly upwards. Darker violet colors indicate atoms that have dropped below their original position, whereas the lighter green colors show where atoms have risen. Credit: V.K. Tewary/NIST
The new mathematical technique* can significantly improve modeling of atomic-scale
processes that unfold over time, such as vibrations in a crystal. Conventional
molecular dynamics (MD) techniques can accurately model processes that occur
in increments measured in picoseconds to femtoseconds (trillionths to quadrillionths
of a second). Other techniques can be used over longer periods to model bulk
materials but not at the molecular level. The new NIST technique can access
these longer time scales—in the critical range from nanoseconds to microseconds
(billionths to millionths of a second)—at the molecular level. Scientists
can now measure and understand what happens at key points in time that were
not previously accessible, and throughout the full spectrum of time scales of
interest in MD, says developer Vinod Tewary.
Modeling of material properties and physical processes is a valuable aid and
supplement to theoretical and experimental studies, in part because experiments
are very difficult at the nanoscale. MD calculations are usually based on the
physics of individual atoms or molecules. This traditional approach is limited
not only by time scale, but also by system size. It cannot be extended to processes
involving thousands of atoms or more because today’s computers—even
supercomputers—cannot handle the billions of time steps required, Tewary
says. By contrast, his new method incorporates a “Green’s function,”
a mathematical approach that can calculate the condition of a very large system
over flexible time scales in a single step. Thus, it overcomes the system size
problem as well as the timing gap.
Tewary illustrated the new technique on two problems. He showed how a pulse
propagating through a string of atoms, initiated by moving the middle atom,
could be modeled for just a few femtoseconds with conventional MD, whereas the
NIST method works for several microseconds. Tewary also calculated how ripples
propagate in 1,100 carbon atoms in a sheet of graphene over periods up to about
45 microseconds, a problem that could not be solved previously. Normally thought
of as a static flat sheet, the atoms in graphene actually must undulate somehow
to remain stable, and the new technique shows how these ripples propagate. (See
accompanying image and movie). Consisting entirely of carbon atoms, graphene
is a recently discovered honeycomb crystal material that may be an outstanding
conductor for wires and other components in nanoscale electronics.
The new NIST technique is expected to enable modeling of many other processes
that occur at time scales of nano- to microseconds, such as formation and growth
of defects, conduction of heat, diffusion and radiation damage in materials.
The technique could improve results in many different fields, from modeling
of new nanotechnologies in the design stage to simulating the radiation damage
from a “dirty bomb” over time.
NIST researchers plan to write a software program encoding the new technique
to make it available to other users.
* V.K. Tewary. Extending time scale in molecular dynamics simulations: propagation
of ripples in graphene. Physical Review B, Vol. 80, No. 16.. Published online
Oct. 22, 2009.
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