Research ArticlePHOTONICS

Domain morphology, boundaries, and topological defects in biophotonic gyroid nanostructures of butterfly wing scales

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Science Advances  10 Jun 2016:
Vol. 2, no. 6, e1600149
DOI: 10.1126/sciadv.1600149
  • Fig. 1 Experimental description.

    (A) An image of the T. imperialis (Kaiser-i-Hind) butterfly (43). (B) A schematic of the experiment. X-ray radiation (1.8-keV photon energy) is generated by the undulator source and spatially filtered by a 5-μm pinhole. The sample is positioned behind the pinhole, and the detector records coherently scattered radiation. A semitransparent beam stop mounted on a metallic wire was used. (C) An optical micrograph of a single wing scale. (D and E) Typical diffraction patterns recorded from different sample areas with x-rays incident normal to the scale. Insets to (D) and (E) show the intensity in the vicinity of the (110) Bragg peaks. Scale bars, 5 cm (A), 50 μm (C), and 0.05 nm−1 (D and E).

  • Fig. 2 A representation of the whole scale oriented similarly to Fig. 1C.

    (A) The angle α between the x axis and a {110} peak (see Fig. 1D) as a function of the position across the scale. An average over all six angles (modulo 60°) is shown. (B) The angle β between the z axis (out of plane of the image) and vector n111 normal to the determined hexagonal set of peaks. (C) The angle γ between the x axis and the projection of n111 onto the xy plane. (D) The thickness of the crystallites determined from the x-ray diffraction data recorded by rocking the scale through the beam. Scale bar, 10 μm; the region for the ptychographic scan is indicated by the black square and the histograms of the angles are shown on the right of the color bars. In (B) to (D), Gaussian fits to the histograms are also shown with centers (RMS widths) of 14° ± 1° (5° ± 1°) (B), 91° ± 1° (20° ± 1°) (C), and 3.0 ± 0.1 μm (0.7 ± 0.1 μm) (D). Angles are positive for clockwise rotation.

  • Fig. 3 Result from ptychographic reconstruction.

    (A) An image of the scale indicated by a black rectangle in Fig. 2 (absorption or reconstructed amplitudes). The color corresponds to the crystal orientation modulo 60° (see color wheel), and edge dislocations are indicated. (B) Zoomed-in image of the region indicated by the white square in (A). The solid line highlights the domain boundary accommodated by edge dislocations between the red (average angle, 52° ± 2°) and the dark red (average angle, 57° ± 3°) domains. (C) Bragg filtered image of (B) obtained by placing a mask in the Fourier transform (35). (D) Squared modulus of a Fourier transform of the sample transmission function (B) multiplied by a Gaussian mask (0.5-μm wide) centered in the lowest indicated dislocation in (B). (E) Reconstructed phases. Average along the vertical is shown together with the color bar on the bottom. Scale bars, 2 μm (A to C and E).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/6/e1600149/DC1

    fig. S1. Orientation determination procedure for one grain.

    fig. S2. Orientation determination procedure for multiple grains.

    fig. S3. Description of angles used in the microdiffraction analysis.

    fig. S4. Distribution of grain orientations.

    fig. S5. A sketch describing the procedure determining the width of the crystal.

    fig. S6. Amplitude (absorption) and phase of the ptychographic reconstruction.

    fig. S7. Robustness of the ptychographic reconstruction.

  • Supplementary Materials

    This PDF file includes:

    • fig. S1. Orientation determination procedure for one grain.
    • fig. S2. Orientation determination procedure for multiple grains.
    • fig. S3. Description of angles used in the microdiffraction analysis.
    • fig. S4. Distribution of grain orientations.
    • fig. S5. A sketch describing the procedure determining the width of the crystal.
    • fig. S6. Amplitude (absorption) and phase of the ptychographic reconstruction.
    • fig. S7. Robustness of the ptychographic reconstruction.

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