Most technologically useful materials arise as
polycrystalline microstructures, composed of a myriad of small crystallites,
grains, separated by interfaces, grain boundaries. The energetics and connectivity of the
network of boundaries are implicated in many properties across all scales of
use, for example, functional properties, like conductivity in microprocessor
wires, and lifetime properties, like fracture toughness in structures. Engineering a microstructure to achieve a
desired set of performance characteristics is a major focus in materials
science. In [1], a framework for
modeling critical events in microstructure evolution was proposed and applied
to a simplified one-dimensional system.
By regarding a system of grain boundaries as a collection of interacting
particles, one can then utilize the machinery of statistical mechanics, in
particular, Boltzmann kinetics. The
results obtained were found to compare favorably with numerical simulations as well
as experimental data in both the distributions of grain boundary lengths and
orientations.
In my research, I have utilized an analogous
approach to extend prior work to a more realistic two-dimensional model. The extension to two dimensions is
non-trivial in that topological reconfigurations (critical events) such as
neighbor switching, absent in one dimension, must now be treated. The resulting model is a partial
integro-differential equation describing the evolution of the distribution of
misorientations in a two-dimensional grain boundary network, a distribution
which is of great importance to materials scientists and engineers. Currently, I am exploring numerical methods
of solution including the method of finite differences and Direct Simulation
Monte Carlo. The plausibility of the
derived model will require numerical validation by means of comparison with
results gathered from numerical simulations and experimental data. Next summer I am applying for an NSF funded
REU out of Harvard’s Materials Science and Engineering Center and I believe
that having participated in the EXTREEMS-QED program and having done research
in the field of materials science will greatly increase my chances of being
selected. The work I am doing is also
topical in that in 2011, under the Obama administration, the Materials Genome
Initiative was launched, a multi-agency initiative designed to create a new era
of policy, resources, and infrastructure that support U.S. institutions in the
effort to discover, manufacture, and deploy advanced materials twice as fast,
at a fraction of the cost.
Bibliography
[1] Barmak, K., et al. "A new
perspective on texture evolution." International
Journal on Numerical Analysis and Modeling 5 (2008): 93-108.
