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Crystalline variational methods.

Jean E Taylor1

  • 1Mathematics Department, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854, USA. taylor@math.rutgers.edu

Proceedings of the National Academy of Sciences of the United States of America
|November 13, 2002
PubMed
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Crystalline surface free energy functions, where equilibrium crystal shapes are polyhedra, allow for mathematical and physical investigations. Geometric calculus of variations provides methods to study these crystalline surface energy properties.

Area of Science:

  • Materials Science
  • Mathematical Physics
  • Surface Science

Background:

  • Surface free energy dictates equilibrium crystal shape.
  • The Wulff shape represents the equilibrium crystal shape.
  • Standard area functional assumes uniform surface free energy.

Purpose of the Study:

  • Define and investigate crystalline surface free energy functions.
  • Extend questions from uniform surface energy to crystalline cases.
  • Explore mathematical and physical implications of crystalline surface energy.

Main Methods:

  • Definition of crystalline surface free energy.
  • Analysis of Wulff shapes as polyhedra.
  • Application of geometric calculus of variations.

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Main Results:

  • Crystalline surface free energy functions generalize the area functional.
  • Mathematical and physical questions are applicable to crystalline surface energies.
  • Geometric calculus of variations offers tools for analysis.

Conclusions:

  • Crystalline surface energy is a rich area for study.
  • The Wulff shape provides a geometric constraint for surface energy.
  • Methods from geometric calculus are effective for these investigations.