Partial dark-field microscopy for investigating domain structures of double-layer microsphere film

A lateral dislocation in a double-layer microsphere film is very difficult to identify because the constituent domains have the same two-dimensional crystalline orientation. Orientation-sensitive optical techniques cannot resolve this issue. Here, we demonstrate that partial dark-field (pDF) optical microscopy can be very effective in identifying this type of domain boundary and dislocation of a close-packed microsphere double-layer. Using the hexagonal symmetry of the close-packed microsphere film and the light-focusing property of microspheres, the partially blocked dark-field condenser can provide much higher contrast than other optical microscopy modes can in identifying the laterally dislocated domains. The former can also distinguish domains with different crystalline orientation by rotating the pDF stop. The simplicity of the pDF mode will make it an ideal tool for the structural study of close-packed double-layer microsphere films.

(1) Experimental setup Figure S1. A rotation mount holding a pDF stop is added on a commercial dark-field condenser (Olympus, U-DCD). For the specific crystalline orientation of the domain, we can find a specific rotation angle of the pDF stop showing the maximum or minimum brightness of that domain. We set this angle as 0°, and the other angles are defined as relative values, considering this angle as the reference angle. For the full DF image, the pDF stop can be removed from the light path.

(2) Light sources for the pDF images
We used a 405-nm LED instead of white light from a halogen lamp to obtain most of the images in this manuscript to minimize the possible chromatic aberrations. However, for the case of microspheres larger than 0.75 μm, both a 405-nm LED and a halogen lamp produced a sufficiently good contrast in the pDF images.
In contrast, for the case of 0.5-μm microspheres (Figs. 6d & 6h in the manuscript), a 405-nm LED did not provide sufficient contrast in the pDF mode compared with white light from the halogen lamp. When a film of this size of microspheres was observed using white light, a specific wavelength of visible light (blue light in this case) was dominant in the acquired image.
Therefore, for a small microsphere, the diameter of which is comparable to the wavelength of visible light, either the specific wavelength of light matching the microsphere size or white light should be used to obtain maximum contrast in the pDF image.

(3) Applicability to the double-layer of different sized microspheres
There are many applications in which the microspheres of the upper layer have a different size than the microspheres of the lower layer.
When the diameter (φ A ) of the upper-layer microsphere is smaller than 1 √3 times the diameter (φ B ) of the lower-layer microsphere, every hollow of the lower layer can be occupied by the upper-layer microspheres because there should be no overlap between the upper-layer microspheres on the nearest-neighbor hollows of the lower layer (Fig. S2). In this case, a dislocation such as that described in Fig. 1 of the manuscript cannot exist, and most defects of 4 the film may originate from the 2D crystalline orientation mismatch. Therefore, the pDF method would not be necessary for this case.
When φ A is larger than 1 √3 times φ B , only half of the hollows of the lower layer can be occupied by the upper-layer microspheres, similar to the case of the single-sized microspheres, because of the geometrical constraint between the upper-layer microspheres on the nearestneighbor hollows of the lower layer. In this case, we expect that the pDF method can effectively distinguish the dislocation with a large contrast, similar to the case of the single-sized microspheres. Figure S3 shows a pDF image of a binary film consisting of 2 um Silica beads as the lower layer and 1 um PS beads as the upper layer. Even though we could not fabricate a close-packed double-layer film, this figure clearly shows that the pDF method can alternately illuminate the upper-layer beads depending on their positions.