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Vibrational algorithms for quantitative crystallographic analyses of hydroxyapatite-based biomaterials: I, theoretical foundations

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Abstract

The Raman spectroscopic method has quantitatively been applied to the analysis of local crystallographic orientation in both single-crystal hydroxyapatite and human teeth. Raman selection rules for all the vibrational modes of the hexagonal structure were expanded into explicit functions of Euler angles in space and six Raman tensor elements (RTE). A theoretical treatment has also been put forward according to the orientation distribution function (ODF) formalism, which allows one to resolve the statistical orientation patterns of the nm-sized hydroxyapatite crystallite comprised in the Raman microprobe. Close-form solutions could be obtained for the Euler angles and their statistical distributions resolved with respect to the direction of the average texture axis. Polarized Raman spectra from single-crystalline hydroxyapatite and textured polycrystalline (teeth enamel) samples were compared, and a validation of the proposed Raman method could be obtained through confirming the agreement between RTE values obtained from different samples.

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Authors and Affiliations

  1. Ceramic Physics Laboratory, Kyoto Institute of Technology, Sakyo-ku, Matsugasaki, 606-8126, Kyoto, Japan

    Giuseppe Pezzotti & Marco Boffelli

  2. Department of Molecular Cell Physiology, Graduate School of Medical Science, Kyoto Prefectural University of Medicine, Kamigyo-ku,, Kyoto, 602-8566, Japan

    Giuseppe Pezzotti & Yoshinori Marunaka

  3. Department of Medical Engineering for Treatment of Bone and Joint Disorders, Osaka University, 2-2 Yamadaoka, Suita, Osaka, 565-0854, Japan

    Wenliang Zhu

  4. Department of Dental Medicine, Graduate School of Medical Science, Kyoto Prefectural University of Medicine, Kamigyo-ku, 465 Kajii-cho, Kawaramachi dori, Kyoto, 602-0841, Japan

    Tetsuya Adachi, Hiroaki Ichioka, Toshiro Yamamoto & Narisato Kanamura

  5. Department of Bio-Ionomics, Graduate School of Medical Science, Kyoto Prefectural University of Medicine, Kamigyo-ku, Kyoto, 602-8566, Japan

    Yoshinori Marunaka

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  1. Giuseppe Pezzotti
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  2. Wenliang Zhu
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Correspondence to Giuseppe Pezzotti.

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Pezzotti, G., Zhu, W., Boffelli, M. et al. Vibrational algorithms for quantitative crystallographic analyses of hydroxyapatite-based biomaterials: I, theoretical foundations. Anal Bioanal Chem 407, 3325–3342 (2015). https://doi.org/10.1007/s00216-015-8472-1

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  • DOI: https://doi.org/10.1007/s00216-015-8472-1

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