Anisotropic “X-ray diffraction” dimensions of ellipsoid-shaped crystallites of cathode powders LiFePO$_4$

A. V. Bobyl'^a, I. A. Kasatkin^b, O. I. Kon'kov^a, M. P. Faradzheva<sup>ac

a</sup> Ioffe Institute, St. Petersburg, Russia
^b Saint Petersburg State University, St. Petersburg, Russia
^c Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia

Abstract: The relationship between the anisotropic dimensions of powder crystallites obtained by X-ray diffraction $(D_{i\mathrm{XRD}})$, and their linear dimensions $(L_i)$ has been investigated by numerical calculations. The following analytical expression is found for the orthorhombic lattice of ellipsoidal LiFePO$_4$ crystallites with their lognormal size distribution: $D_{i\mathrm{XRD}}$ = (3/4+0.38 $W_i^2$)$\bar{L_i}$, where $\bar{L_i}$ and $W_i$ – the mean value of the size and the variance of this distribution along the $i$-th crystallographic axis. The use of the obtained expression allows increasing the accuracy of complementary X-ray and electron-microscopic measurements for the purpose of experimental determination of parameters of projections of the function of (marginal) distributions on axes and correlation coefficients between them.

Keywords: LiFePO$_4$, marginal size distribution, lognormal distribution.

UDC: 06.5; 15.2

Received: 03.05.2023
Revised: 28.09.2023
Accepted: 29.09.2023

DOI: 10.61011/PJTF.2024.01.56916.19615

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