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Figure 1
The irregular nature of the Σ function is illustrated. In (a), the bicrystal pattern obtained of a Σ5 CSL, which corresponds to a misorientation of [\theta = 36.87^{\circ}], is shown. In (b), a bicrystal pattern with misorientation [\theta = 37.52^{\circ}] is shown. While there is only a slight change in the extent of overlap between the lattices from (a) to (b), the value of Σ changes from 5 to 3133. In fact, for all misorientations where [\tan \theta/2] is irrational, a coincidence site lattice does not exist and [\Sigma = \infty]. The atoms in this illustration are represented using the mollifier [\Phi = \left\{ \exp[1/(1-x^2)], x \in [-1,1], \ 0 \ {\rm else} \right\}] (Runnels, 2017BB6).

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ISSN: 2053-2733
Volume 73| Part 2| March 2017| Pages 85-86
https://doi.org/10.1107/S2053273317003321
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