Multiscale Statistics & Crystals
Magnesium Oxide (MgO) is a ceramic with molecular units distributed in space in an
essentially cubic arrangement. As with many materials, the energy
corresponding to a given plane within this cubic arrangement depends on the
normal vector to that plane. For example, a point (x,y,z) on the
surface, the z axis represents the energy and (x,y)
represents a particular choice of the normal vector to a given plane within the
crystal. Purely experimental determination of the energy corresponding to
a wide variety of planes is tedious. Consequently, accurate
representations are rare.
One way to circumvent this problem is to experimentally collect (via automation)
vast amounts of geometric data from specimens and then employ such data in
physically based equations wherein the data acts as coefficients, and the
corresponding surface energy as unknowns. This typically leads to
thousands of simultaneous and overdetermined linear equations. Through
intelligent multiscale sorting into urns and averaging of these
equations, accurate representations of the surface energy can be developed.
The images at left depict computed representations of the surface energy of the
MgO at two consecutive levels of urn refinement.
This work was completed in 2000 as part of a larger effort called the Mesoscale
Interface Mapping Project (MIMP), an NSF funded research center at
Carnegie Mellon University.
Darren E. Mason in the Albion College Department of Mathematics and Computer
Science is an affiliated faculty member of this project. For more information
about this work and other exciting interdisciplinary projects in materials
science, check out the MIMP
web page as well as
Dr. Mason's web
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