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      Effect of the Nano Crystal Size on the X-ray Diffraction Patterns of Biogenic Hydroxyapatite from Human, Bovine, and Porcine Bones

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          Abstract

          This paper focuses on the study of the effect of the change of the crystal size on the shape and width of the X-ray diffraction patterns for defatted and deproteinized bones as well as incinerated biogenic hydroxyapatite obtained from bovine, porcine, and human bones. Inductively Couple Plasma showed the presence of some ions such as Mg, K, Al, Fe, Zn, and Na for all samples. The nanometric size of the crystals was determined through High Resolution Transmission Electron Microscopy in which ordered crystals were found. The calcination of raw clean bones at 720 °C produced a transition of crystal size from nano to micro due to a coalescence phenomenon, this was accompanied by a decrease of the peak width of the X-ray diffraction patterns due to the decrease of the inelastic scattering contribution from the microcrystals. A simulation of the effect of the crystallite size on the shape and width of the X-ray patterns was done using PDF-4 software which confirmed that raw ordered bone crystals produce broad peaks which so far have been erroneously assigned to polycrystalline hydroxyapatite with low crystalline quality.

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          Modified Scherrer Equation to Estimate More Accurately Nano-Crystallite Size Using XRD

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            The Scherrer equation and the dynamical theory of X-ray diffraction

            The Scherrer equation is a widely used tool to determine the crystallite size of polycrystalline samples. However, it is not clear if one can apply it to large crystallite sizes because its derivation is based on the kinematical theory of X-ray diffraction. For large and perfect crystals, it is more appropriate to use the dynamical theory of X-ray diffraction. Because of the appearance of polycrystalline materials with a high degree of crystalline perfection and large sizes, it is the authors' belief that it is important to establish the crystallite size limit for which the Scherrer equation can be applied. In this work, the diffraction peak profiles are calculated using the dynamical theory of X-ray diffraction for several Bragg reflections and crystallite sizes for Si, LaB 6 and CeO 2 . The full width at half-maximum is then extracted and the crystallite size is computed using the Scherrer equation. It is shown that for crystals with linear absorption coefficients below 2117.3 cm −1 the Scherrer equation is valid for crystallites with sizes up to 600 nm. It is also shown that as the size increases only the peaks at higher 2θ angles give good results, and if one uses peaks with 2θ > 60° the limit for use of the Scherrer equation would go up to 1 µm.
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              Hydroxyapatite: A review of syntheses, structure and applications in heterogeneous catalysis

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                Author and article information

                Contributors
                marioga@fata.unam.mx
                Journal
                Sci Rep
                Sci Rep
                Scientific Reports
                Nature Publishing Group UK (London )
                2045-2322
                11 April 2019
                11 April 2019
                2019
                : 9
                : 5915
                Affiliations
                [1 ]ISNI 0000 0001 2159 0001, GRID grid.9486.3, Posgrado en Ciencia e Ingeniería de Materiales, , Centro de Física Aplicada y Tecnología Avanzada, Universidad Nacional Autónoma de México, Campus Juriquilla, ; 76230 Querétaro, Qro. Mexico
                [2 ]ISNI 0000 0001 2159 0001, GRID grid.9486.3, Licenciatura en Tecnología, , Centro de Física Aplicada y Tecnología Avanzada, Universidad Nacional Autónoma de México, Campus Juriquilla, ; 76230 Querétaro, Qro. Mexico
                [3 ]ISNI 0000 0001 2159 0001, GRID grid.9486.3, Departamento de Nanotecnología, , Centro de Física Aplicada y Tecnología Avanzada, Universidad Nacional Autónoma de México, Campus Juriquilla, ; 76230 Querétaro, Qro. Mexico
                Author information
                http://orcid.org/0000-0002-3009-6635
                http://orcid.org/0000-0003-1413-9065
                Article
                42269
                10.1038/s41598-019-42269-9
                6459976
                30976023
                7662acab-582c-4511-a092-5f0b4a1bfb94
                © 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/.

                History
                : 19 October 2018
                : 21 March 2019
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