Figure 1.
(a) A single grain boundary consists of an infinite row of helicoidal dislocations along the x-axis, separated by spacing ℓd. This rotates planar layers at z =−∞ through an angle α at z =+∞. (b) The bulk TGB phase results from combining an infinite row of these grain boundaries periodically along the z-axis, separated by ℓb. Each grain boundary rotates the layer normals through angle α, thus the grain boundaries themselves must be rotated with respect to one another along the z-axis. (c) The director field n = cos(σ(z))ex + sin(σ(z))ey also rotates in accordance with the layers. It is close to constant within each grain and jumps through angle α across each grain boundary. The width of this jump is given by the penetration depth λ.