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. 2019 Sep 26;10:4383. doi: 10.1038/s41467-019-12185-7

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© The Author(s) 2019

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 4 — Crystal orientations of a thin section within a human outer enamel rod showing c-axis misorientation by 23°, 27°, and >18°. a HR-TEM micrograph taken from a 130 nm × 130 nm × 100 nm volume within an outer enamel rod, with crystals elongated in plane from top to bottom in (a) (termed vertical hereafter). b Fast Fourier transform (FFT) analysis of the entire image in (a), showing that two of the crystals within this entire volume have their c-axes mis-oriented by 27°. e, f FFT power spectra extracted from (c) and (d) in (a), which include crystals with their (100) planes almost parallel and vertical. In e and f red circles and arrows identify (002) spacings and c-axis directions, respectively; blue circles and blue arrows identify (100) spacings and directions of a-axes, respectively. The (e) FFT indicates the presence of a single crystal of carbonated apatite with its c-axis oriented 5° clockwise from the vertical and its a-axis at 90° from the c-axis as expected for apatite. The (f) FFT indicates the presence of two overlapping crystals, f₁ and f₂. The a-axis of crystal f₁ is horizontal (blue circle). No (001) lattice fringes were detected for f₁, thus its c-axis is out of the image plane in (a). The c-axis of crystal f₂ is oriented at 18° counterclockwise from the vertical (red circle). No (100) lattice fringes were detected for f₂, thus its a-axis is out of the image plane in (a). Crystal f₂ is oriented with its c-axis 18° counterclockwise from the vertical, thus the angle between the c-axes of crystals f₁ and f₂ is at least 18°, but it could be as large as 90°. The c-axes of crystals e and f₂ are 18° + 5° = 23° apart. Since enamel crystals are on average 26 nm × 63 nm in cross-section¹⁸, the 30-nm wide crystals at the center of the image in (a) must be oriented nearly edge-on. Since this section is 100 nm thick, all three crystals identified in the FFTs are either in close proximity to or directly abutting one another. Thus, the c-axes of crystals in close proximity are 23°, 27° and somewhere between 18° and 90° apart. Supplementary Fig. 5 shows where the tooth sample was FIBed to extract this thin section