We present a quantitative analysis of grain morphology of self-organizing hexagonal patterns based on the phase-field crystal model to examine the effect of stochastic noise on grain coarsening. We show that the grain size increases with increasing noise strength, resulting in enhanced hexagonal orientation due to noise up to some critical noise level above which the system becomes disordered.

Summary Method of evaluation of grain size of hexagonally‐packed cylindrical microdomains is presented by taking as an example the data from the polystyrene‐block‐polyethylenebutylene‐block‐polystyrene (SEBS) triblock copolymer film, where the polystyrene cylinders are embedded in the polyethylenebutylene matrix with being oriented perpendicular to the surface of the film. For this purpose, the two‐dimensional small‐angle X‐ray scattering was measured by illuminating X‐ray beam from the side of the film. The procedure is similar to the method how to evaluate the crystallite size of polymer, using the peak width of crystalline reflection in the wide‐angle X‐ray diffraction (WAXD) measurement. While single crystal is used as the standard sample for the case of WAXD because it can be postulated that the crystallite size is infinity in the single crystal, we propose here to use collagen as a standard sample for the SAXS measurement, since collagen forms very regular stacking of texture with 65.3 nm repeating period and the number of the stacking texture is infinitely large. It was confirmed that the grain size evaluated by the SAXS method was in sufficient accord with the result of the transmission electron microscopic observation.

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Intriguing images of dislocation structures were observed by the transmission electron microscopy (TEM) technique for hexagonally packed cylindrical microdomains in a block copolymer (polystyrene-block-polyethylenebutylene-block-polystyrene triblock copolymer) film. The polystyrene (PS) cylinders were embedded in the polyethylenebutylene (PEB) matrix and oriented perpendicular to the surface of the thin section for the TEM observations. In order to understand such strange dislocation structures, we applied an image processing technique using two-dimensional Fourier transform (FT) and inverse Fourier transform (IFT) methods. It was found that these intriguing images were not ascribed to real dislocation structures but were fake ones due to the moiré effect caused by the overlapping of hexagons with a slightly mismatched orientation. Furthermore, grain boundaries in the ultrathin section can be identified by image processing using FT and IFT methods.