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Using the BWA (Bertaut-Warren-Averbach) Method to Optimize Crystalline Powders Such as LiFePO 4

Author

Listed:
  • Aleksandr Bobyl

    (Ioffe Institute, Politekhnicheskaya Str. 26, St. Petersburg 194021, Russia)

  • Oleg Konkov

    (Ioffe Institute, Politekhnicheskaya Str. 26, St. Petersburg 194021, Russia)

  • Mislimat Faradzheva

    (Ioffe Institute, Politekhnicheskaya Str. 26, St. Petersburg 194021, Russia)

  • Igor Kasatkin

    (Research Park, St. Petersburg State University, XRD Research Center, Universitetskaya nab. 7-9, St. Petersburg 199034, Russia)

Abstract

The average sizes L ¯ i , and their dispersion W i along the i -th axis, of crystallites in powders are used to determine X-ray diffraction sizes, D i X R D , averaged over crystallite columns within the BWA method. Numerical calculations have been carried out for an orthorhombic lattice of crystallites, such as LiFePO 4 , NMC, having a Lamé’s g -type superellipsoid shape. For lognormal distributions, the analytical expression for the normalized coefficient K n has been found: K n = D i X R D / L ¯ i = K g , 0 + K g W 2 , where K g , 0 is a constant at W→0, K g is a constant depending on the g -type shape. The dependences of D i X R D are also calculated for normal distribution. A fairly simple equation can be obtained as a result of analytical transformations in the framework of experimentally validated approximations. However, a simpler way is to carry out numerical computer calculations with subsequent approximation of the calculated curves. Using the obtained analytical expressions to control technologies from nuclear fuel to cathode materials will improve the efficiency of flexible energy network, especially storage in autonomous and standby power plants.

Suggested Citation

  • Aleksandr Bobyl & Oleg Konkov & Mislimat Faradzheva & Igor Kasatkin, 2023. "Using the BWA (Bertaut-Warren-Averbach) Method to Optimize Crystalline Powders Such as LiFePO 4," Mathematics, MDPI, vol. 11(18), pages 1-12, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3963-:d:1242328
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    References listed on IDEAS

    as
    1. Karlis, Dimitris, 2005. "EM Algorithm for Mixed Poisson and Other Discrete Distributions," ASTIN Bulletin, Cambridge University Press, vol. 35(1), pages 3-24, May.
    2. Dmitry Agafonov & Aleksandr Bobyl & Aleksandr Kamzin & Alexey Nashchekin & Evgeniy Ershenko & Arseniy Ushakov & Igor Kasatkin & Vladimir Levitskii & Mikhail Trenikhin & Evgeniy Terukov, 2023. "Phase-Homogeneous LiFePO 4 Powders with Crystallites Protected by Ferric-Graphite-Graphene Composite," Energies, MDPI, vol. 16(3), pages 1-28, February.
    3. Vasily Rud & Doulbay Melebaev & Viktor Krasnoshchekov & Ilya Ilyin & Eugeny Terukov & Maksim Diuldin & Alexey Andreev & Maral Shamuhammedowa & Vadim Davydov, 2023. "Photosensitivity of Nanostructured Schottky Barriers Based on GaP for Solar Energy Applications," Energies, MDPI, vol. 16(5), pages 1-15, February.
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