Rate Capability of LiFePO4 Cathodes and the Shape Engineering of Their Anisotropic Crystallites

Abstract

For cuboid and ellipsoid crystallites of LiFePO 4 powders, by X-ray diffraction (XRD) and microscopic (TEM) studies, it is possible to determine the anisotropic parameters of the crystallite size distribution functions. These parameters were used to describe the cathode rate capability within the model of averaging the diffusion coefficient D over the length of the crystallite columns along the [010] direction. A LiFePO 4 powder was chosen for testing the developed model, consisting of big cuboid and small ellipsoid crystallites (close to them). When analyzing the parts of big and small rate сapabilities, the fitting values D = 2.1 and 0.3 nm 2 /s were obtained for cuboids and ellipsoids, respectively. When analyzing the results of cyclic voltammetry using the Randles-Sevcik equation and the total area of projections of electrode crystallites on their (010) plane, slightly different values were obtained, D = 0.9 ± 0.15 and 0.5 ± 0.15 nm 2 /s, respectively. We believe that these inconsistencies can be considered quite acceptable, since both methods of determining D have obvious sources of error. However, the developed method has a clearly lower systematic error due to the ability to actually take into account the shape and statistics of crystallites, and it is also useful for improving the accuracy of the Randles-Sevcik equation. It has also been demonstrated that the shape engineering of crystallites, among other tasks, can increase the cathode capacity by 15% by increasing their size correlation coefficients.

Using the BWA (Bertaut-Warren-Averbach) Method to Optimize Crystalline Powders Such as LiFePO4

“…Equation ( 2) is a special case of (3) with the ratio of powers: 1 = 2 = 2/g. The moduli signs are omitted in Equation (2), since the shapes of LiFePO 4 crystallites can be described even with only g < 30 [14,27] and their 0-th genus topology [28], i.e., excluding torus-type shapes.…”

“…In particular, knowing the mass of the cathode powder, its density and the statistics of the size distribution of crystallites, with Equations ( 7) and (8), it is possible to determine the inner surface of the cathode and use it to improve the accuracy of determining the diffusion coefficient using the Randles-Sevcik equation [14], as well as for quantitative calculations of the rate of electrochemical reactions using the Butler-Volmer equation [27]. In this case, the shape of crystallites must be preliminarily determined by analyzing TEM and SEM images of crystallites either visually or using software processing methods [29][30][31][32].…”

“…Based on TEM and SEM studies [2,7,10,11], various size distribution functions: lognormal, normal, gamma, and Poisson are normally used, more precisely, their one-dimensional projections onto some linear dimension. The first two of them can be used in their three-dimensional versions with pairwise correlations between sizes along the coordinate axes [12][13][14], while for the last two, such a possibility is not "transparent and easily accessible" [15][16][17]. In some exceptional cases, analytical approximations of distributions with a large dispersion of sizes may be useful [11].…”

“…It was noted above that only the lognormal [13,14] and normal [12] distributions can be used to describe anisotropic particles, taking into account their pairwise covariances between the sizes. For the remaining two, they can also be adjusted to lognormal and normal with smaller errors compared to those arising when covariances are not taken into account.…”

“…In [49], marginal size distributions of crystallites in LiFePO 4 powders were determined along all three crystallographic axes, and in [14], the parameters of the 3-dimensional lognormal function f LM L were determined:…”