A. P. Sutton and V. Vitek, “On the Structure of Tilt Grain Boundaries in Cubic Metals II: Asymmetrical Tilt Boundaries,” Philosophical Transactions of the Royal Society, Vol. 309, No. 1506, 1983, pp. 37-54. doi:10.1098/rsta.1983.0021

has been cited by the following article:

• 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.