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

Aleksandr Bobyl (), Oleg Konkov, Mislimat Faradzheva and Igor Kasatkin
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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

Mathematics, 2023, vol. 11, issue 18, 1-12

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.

Keywords: crystallites in powders; Lamé’s shape; X-ray sizes; Bertaut–Warren–Averbach; normal distributions; lognormal distribution; energy storage; energy optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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