TITLE:
Conditions for Singularity of Twist Grain Boundaries between Arbitrary 2-D Lattices
AUTHORS:
David Romeu, Jose L. Aragón, Gerardo Aragón-González, Marco A. Rodríguez-Andrade, Alfredo Gómez
KEYWORDS:
Grain Boundaries; Crystallography of Interfaces; Coincidence Site Lattice
JOURNAL NAME:
Crystal Structure Theory and Applications,
Vol.1 No.3,
December
27,
2012
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.