where ∆θ is the angular deviation threshold, θ 0 = 15 • a constant corresponding to the low-to highangle GB threshold and Σ is the reciprocal density of coincidence lattice points (i.e. the coincident site lattice number). The Brandon criterion predicts that the amount of distortion that the GB can accommodate (e.g. via introduction of GB dislocations) before losing coincidence should decrease with Σ because the density of coincident sites decreases with Σ. In contrast, Figure shows that correlation lengths generally increase with Σ. That is to say that in general there is a trend of GB energies being correlated over longer length scales with increasing Σ. This seems reasonable since the deepest cusps in the GB energy landscape (corresponding to small correlation lengths) tend to correspond to the lowest-Σ GBs. This suggests that while strict coincidence may indeed be lost over smaller crystallographic deviations with increasing Σ, GB energies seem to be relatively insensitive to this loss of coincidence and instead seem to be increasingly correlated over larger length scales. This may explain why previous researchers found Sigma to be a poor predictor of GB energy .