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

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DOI: 10.4236/csta.2012.13010    3,997 Downloads   7,119 Views  

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

D. Romeu, J. Aragón, G. Aragón-González, M. Rodríguez-Andrade and A. Gómez, "Conditions for Singularity of Twist Grain Boundaries between Arbitrary 2-D Lattices," Crystal Structure Theory and Applications, Vol. 1 No. 3, 2012, pp. 52-56. doi: 10.4236/csta.2012.13010.

References

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