Lecture 15b Two Dimensional Objects

# Lecture 15b Two Dimensional Objects - Beyond Continuum...

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Beyond Continuum Before I talk about grain boundaries and other types of interfaces, some general comments about how we deal with energies/properties. The standard approach is to consider how a property scales as a function of the size of the system (R). In a generic sense one can write: P(R) = AR 3 + BR 2 + CR + D A => Bulk behavior B => Surface/Interface term, or at least what scales as a surface term C => Edge/Line term D => Limit for atomic behavior The bulk properties of a material only depend upon “A”; but we have additional terms. Examples If P(R) is a free energy B = surface free energy (for a surface); interfacial free energy, grain boundary free energy or stacking fault free energy. Normally use γ C = dislocation free energy D = point defect free energy P(R) is an entropy – similar Other things as well. For instance dE/de (e a strain) is the stress in the bulk. Similarly we can discuss can write d γ /de as an interfacial/surface stress term, or a line stress term for a dislocation.

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Lecture 15b Two Dimensional Objects - Beyond Continuum...

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