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Figure 6
Curvature contrasts at the D- and G-twin boundaries. (a), (b) Averaged Gaussian curvatures, 〈K〉, and the corresponding relative variances, ΔK2/〈K〉2, plotted against c/a for the rPD and H surface families. The rPD family is obtained by rhombohedrally deforming the D surface. The surfaces in (a) are scaled such that the volume per fundamental patch (equivalent to the primitive unit-cell volume, [{a^2}c\sqrt 3 /2]) is 2. The two (i.e. upper and lower) curves for each family correspond to two distinct minimal surfaces existing for given unit-cell dimensions. As c/a is decreased, the upper branch approaches the catenoid limit argued by Traizet (Traizet, 2008BB49). In (b), five sampling data of the relative variance of the distance function, d, for the H-surface family (Schröder-Turk et al., 2006BB41) are plotted as black squares with an interpolating dashed curve. (c), (d) The same quantities as shown in (a) and (b) but plotted against a/c and b/c for the oDb family. The surfaces in (c) are scaled such that the volume per fundamental patch (equivalent to the primitive unit-cell volume, abc/2) is 2. The position of the reference unit cell [Fig. 5[link](c), centre] is indicated with a green star, whereas the position of the cubic D surface is indicated with a yellow diamond. For the G surface, 〈K〉 is slightly (∼1.2%) above the surface in favour of a deformation along the dotted green arrow, whereas ΔK2/〈K〉2 is beneath the surface by ∼20%, coinciding with that of the D surface (yellow diamond) in favour of a deformation along the solid green arrow. (e) Colour maps showing the distributions of the Gaussian curvatures along the D, H, G and oDb surfaces with undistorted unit-cell dimensions, showing enhanced curvature contrasts for the H and oDb surfaces.

IUCrJ
Volume 7| Part 2| March 2020| Pages 228-237
ISSN: 2052-2525
https://doi.org/10.1107/S2052252519017287