Conditions for Singularity of Twist Grain Boundaries between Arbitrary 2-D Lattices

David Romeu, Jose L. Aragón, Gerardo Aragón-González, Marco A. Rodríguez-Andrade, Alfredo Gómez

Departamento de Matemáticas, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos, México City, México.
Departamento de Materia Condensada, Instituto de Física, Universidad Nacional Autónoma de México, México City, México.
Departamento de Nanotecnología, Centro de Física Aplicada y Tecnología Avanzada, Universidad Nacional Autónoma de México, México City, México.
Programa de Desarrollo Profesional en Automatización, Universidad Autónoma Metropolitana, México City, México.

DOI: 10.4236/csta.2012.13010                

Abstract

We have shown that the expression =2tan^-1/ derived by Ranganathan to calculate the angles at which there exists a CSL for rotational interfaces in the cubic system can also be applied to general (oblique) two-dimensional lattices provided that the quantities ² and /cos() are rational numbers, with =|b|/|a| and is the angle between the basis vectors a and b. In contrast with Ranganathan’s results, N; given by N=tan²() needs no longer be an integer. Specifically, vectors a and b must have the form a=(1,0); b=(r,tan) where r is an arbitrary rational number. We have also shown that the interfacial classification of cubic twist interfaces based on the recurrence properties of the O-lattice remains valid for arbitrary two-dimensional interfaces provided the above requirements on the lattice are met.

Keywords

Grain Boundaries; Crystallography of Interfaces; Coincidence Site Lattice

Conflicts of Interest

The authors declare no conflicts of interest.

References

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