Boundary Motion In Polyhedral Space-filling Networks
Author(s)
M. E. Glicksman
Abstract
Boundary motion in polyhedral
space-filling networks
M. E. Glicksman
Materials Science & Engineering Department, Rensselaer Polytechnic
Institute, Troy, New York 12180-3590, USA
Abstract
Kinetics, topology, and geometrical combinatorics are combined to impose spacefilling
requirements on network structures comprised of polycrystalline grains,
foam bubbles, or biological cells. The theory developed here centers on representing
network cells as uniform N-hedra, with face curvatures that satisfy Young-
Laplace thermodynamic equilibria at contact faces and triple lines. The analysis
yields analytic kinetic relations that predict the volumetric growth rates for irregular
polyhedral cells comprising a 3-dimensional network microstructure. These
results extend to three dimensions the von Neumann-Mullins law, which provides
the well-known kinetic relation that is valid for tessellations in two dimensions.
The 3-d kinetic laws derived here may prove useful for constructing more accurate
models of grain
Keywords
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