Phase-homogeneous LiFePO4 powders have been synthesized. The content of impurity crystalline phases was less than 0.1%, according to synchrotron diffractometry (SXRD) data. Anisotropic crystallite sizes L¯Vhkl were determined by XRD. A low resistance covering layer of mechanically strong ferric-graphite-graphene composite with impregnated ferric (Fe3+) particles < 10 nm in size increases the cycleability compared to industrial cathodes. In accordance with the corrosion model, the destruction of the Fe3+-containing protective layer of crystallites predominates at the first stage, and at the second stage Fe escapes into the electrolyte and to the anode. The crystallite size decreases due to amorphization that starts from the surface. The rate capability, Q(t), has been studied as a function of L¯Vhkl, of the correlation coefficients rik between crystallite sizes, of the Li diffusion coefficient, D, and of the electrical relaxation time, τel. For the test cathode with a thickness of 8 μm, the values of D = 0.12 nm2/s, τel = 8 s were obtained. To predict the dependence Q(t), it is theoretically studied in ranges closest to experimental values: D = 0.5 ÷ 0.03 nm2/s, τel = 8/1 s, average sizes along [010] L¯1 =90/30 nm, averaged r¯ = 0/1.
Radon-Nikodym approach to relaxation dynamics, where probability density is built first and then used to calculate observable dynamic characteristic is developed and applied to relaxation type signals study. In contrast with L 2 norm approaches, such as Fourier or least squares, this new approach does not use a norm, the problem is reduced to finding the spectrum of an operator (virtual Hamiltonian), which is built in a way that eigenvalues represent the dynamic characteristic of interest and eigenvectors represent probability density. The problems of interpolation (numerical estimation of Radon-Nikodym derivatives is developed) and obtaining the distribution of relaxation rates from sampled timeserie are considered. Application of the theory is demonstrated on a number of model and experimentally measured timeserie signals of degradation and relaxation processes. Software product, implementing the theory is developed.
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