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Table 4738 lists examples of CSL (coincident site lattice) translation vectors and angles of
misorientation (θ) at Σ11 <110> FCC tilt grain and twin boundaries. Figure 4738 shows the Σ11 CSL produced by rotation of two (black and white) FCC crystals. The density of the coincident sites is 1/11 so that it is a Σ11 boundary. The CSL translation vectors in the (110) plane are and , where the Miller indices are given relative to the black lattice and . An arbitrary Σ11 [110] tilt grain boundary (GB) can be obtained by aligning the GB plane parallel to a chosen CSL plane in the [110] direction and discarding white sites on one side and black sites on the other side of the plane. The choice of these CSL planes as boundary planes produces two wellknown symmetrical tilt GBs: Σ11 [110] and Σ11 [110], respectively.
Figure 4738. Σ11 lattice misorientation
viewed along the [110] direction [1].
Table 4738. Examples of CSL (coincident site lattice) translation vectors and angles of
misorientation (θ) at Σ11 <110> FCC tilt grain and twin boundaries.
CSL translation vectors 
Angle of misorientation (θ) 



50.48°



/ 
50.48°



[1] J. A. Brown and Y. Mishin, Dissociation and faceting of asymmetrical tilt grain boundaries: Molecular dynamics
simulations of copper, Phys. Rev. B 76, 134118 (2007). 