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The Applications of Clifford Algebras to Crystallography Using Mathematica

In: Clifford Algebras with Numeric and Symbolic Computations

Author

Listed:
  • A. Gómez

    (Universidad Nacional Autónoma de México, Instituto de Física)

  • J. L. Aragón

    (Universidad Nacional Autónoma de México, Instituto de Física)

  • O. Caballero

    (Universidad Nacional Autónoma de México, Instituto de Física)

  • F. Dávila

    (Escuela Superior de Física y Matemáticas-I.P.N., Departamento de Matematicas)

Abstract

The discovery of materials such as incommensurate structures and quasicrystals makes necessary to extend crystallography to more than three dimensions. In this work, we explore the use of Clifford algebras to describe n-dimensional lattices. This point of view allows to phrase the geometrical crystallography in a concise language valid in any dimension. Applications to the problems of faceting and phason degrees of freedom in quasicrystals are presented and solved using a Mathematica package which is also presented in the work.

Suggested Citation

  • A. Gómez & J. L. Aragón & O. Caballero & F. Dávila, 1996. "The Applications of Clifford Algebras to Crystallography Using Mathematica," Springer Books, in: Rafał Abłamowicz & Josep M. Parra & Pertti Lounesto (ed.), Clifford Algebras with Numeric and Symbolic Computations, pages 251-266, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-8157-4_17
    DOI: 10.1007/978-1-4615-8157-4_17
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