1.2 Classification of batteries...2

The measured displacement of the L3 centroid and the normalized intensities of the white line are plotted in (b) and (c), respectively.85 4.6 Calculation of the VASP partial density of states of Fe 3d per formula unit. A 14% increase in unoccupied states from LiFePO4 to FePO4 is predicted..86 4.7 VASP calculation of the partial density of O 2p states per formula unit.

Introduction

Classification of batteries

The theoretical potential of a cell

If the process takes place under isothermal and isobaric conditions, and the system is isolated from its environment with no volumetric work, then the electrical work should be equal to the change in the Gibbs free energy of the cell. For simplicity, we use νi as the universal symbol for the coefficient of the ith reactants in the reaction equation.

The Gibbs’ phase rule and voltage profile

The Gibbs phase rule states that the ratio between the number of degrees of freedom f, the number of separate phases p and the number of independent components c in a closed system at equilibrium is given by z. If we keep temperature and pressure constant (which is usually assumed for battery reactions), the degrees of freedom are reduced to.

Li-ion batteries

Cathodes for Li-ion batteries

The material can insert and remove a large amount of lithium to maximize battery capacity. To ensure good cell life, the material must have good tolerance to structural changes during the reversible lithium insertion and extraction process.

Fig. 1.3 The layered structure of LiMO 2 . The unit cell is outlined by the wire frame

Anodes for Li-ion batteries

This process represents the interaction between the fast electrons and the Coulomb potential of an atomic nucleus. In inelastic scattering, part of the kinetic energy of the incident electron is transferred to the electrons or atoms in the sample.

The theory of inelastic electron scattering

The Born approximation
The inelastic scattering cross-section
The Bethe surface
The dipole selection rule

The final expression for the double differential cross section for inelastic electron scattering in solids is. The first integral on the right-hand side vanishes due to the orthogonality of the atomic wave functions.

Fig. 2.1 Illustration of the wave vectors and particle positions for electronic scattering from an atom

Electron energy loss spectrometry (EELS)

Instrumentation

For TEM-based EELS, high-energy electrons are focused onto a thin sample and the transmitted primary electrons are collected by the EELS spectrometer mounted at the bottom of the TEM column. Electrons with a velocity v enter the magnetic field B produced by the pair of magnets and move along a circular path due to the Lorentz force F =−ev×B. QX and QY are quadrupole magnetic lenses to correct the first-order aberration of the sector magnets.

Fig. 2.5 A schematic diagram showing the electron trajectories and energy dispersion in a 90˚ magnetic sector spectrometer

Features of an EELS spectrum

The transferred energy causes collective, resonant oscillations of the valence electrons known as "plasmons". The plasmon peak position is a function of valence electron density in the material. They represent a convolution between the density of states (DOS) of the valence and conduction bands. This is known as the "chemical shift." The intensity of the fringe is proportional to the number of atoms in the material, so the intensity can be used to measure composition.

Fig. 2.8 The O K-edge in Fe 2 O 3 showing the ample fine features in the ELNES region due to solid state effects

Spectrum processing for quantitative analysis

Extracting the single scattering distribution

The recorded data is the sum of all multiple distribution distributions convolved with an instrument broadening function r(ΔE) [7]. Using an inverse Fourier transform on Eq. 2.40), the single scattering distribution s1(ΔE) can be recovered. The single scattering distribution of the high loss region is given by applying inverse Fourier transform to the following equation.

Background subtraction

The simpler "Fourier ratio method" is used only to remove the influence of low-loss processes from the high-loss region. A is not important since it is the amplitude and can be chosen arbitrarily to match the experimental data. Electron Energy Loss Transmission Spectrometry in Materials Science and the EELS Atlas; WILEY-VCH: Hoboken, 2004.

Fig. 2.9 (a) The power-law background model (dashed line) used to remove the background under Si L-edge (solid line)

Introduction

A clear shift of the Ni K-edge was observed in X-ray absorption near-edge spectra (XANES). First, during delithiation, only small changes in the intensities and positions of the white lines at the Ni L2,3 edges are measured. Here we report results from a new computational effort to assess the effects of the Ni2+ to Ni4+ transition on the white lines at the Ni L edges that we measured in a new experimental effort using electron energy loss spectrometry.

Experimental

The experimental spectra were consistent with results reported by others, but the atomic multiplet calculations showed that shifts at the Ni L edges were too small to be associated with the formation of Ni4+. The EELS spectra were acquired with a Philips EM420 transmission electron microscope operated at 100 kV with a Gatan 666 parallel EELS spectrometer. The spectra were acquired in image mode (diffraction coupling) with a typical analysis area of 104 nm2.

Fig. 3.1 Indexed X-ray powder diffraction patterns from samples of different states of lithiation (a) Li x Ni 0.5 Mn 0.5 O 2 (with Si as an internal standard) and (b) Li x Ni 1/3 Mn 1/3 Co 1/3 O 2 .

Computational

The shapes of the L2,3 transition metal edges are significantly altered by atomic multiplet effects because there is significant overlap of the radial wave functions for the 2p hole and the holes in the partially filled 3D band. The initial and final states are specified as a sum of terms in the LS coupling scheme. The strengths of the various transitions are calculated from the relevant matrix elements of the Hamiltonian.

Results

EELS

The changes in intensity show no obvious trend, indicating no obvious trend in the valence of the Ni atom after delithiation. A plot of normalized K-edge pre-dot intensities versus Li concentration is shown in Fig. Spectra were normalized to the main peak (532–543 eV) to show pre-peak intensity.

Fig. 3.2 Mn L 2,3 white lines from (a) Li x Ni 0.5 Mn 0.5 O 2 and (b) Li x Ni 1/3 Mn 1/3 Co 1/3 O 2 with different x values

Electronic structure calculations

For both Ni and Mn atoms, there is a small increase in charge density with delithiation. A very small increase in charge density at Ni and Mn atoms was found after delithiation, corresponding to less than 0.1 electron. The intensity from 0 to 4 eV above the Fermi level (Ef) corresponds to the intensity in the experimental prepeak.

Fig. 3.8 Normalized intensity of pre-peak at O K-edge of Li x CoO 2 , Li x Ni 0.8 Co 0.2 O 2 , and Li x Ni 1/3 Mn 1/3 Co 1/3 O 2 , showing trends with delithiation

Discussion

Nevertheless, a Ni2+ to Ni3+ transition caused by the extraction of a Li+ ion is inconsistent with the 0.07 electron per electron limit. Li+ ion obtained from the change in intensity of the white lines in Fig. This is not exactly quantitative, but it shows that the change in electron density around the O atoms is significant and is able to account for much of the charge compensation around a Li+ ion. Changes in the spin density at Ni atoms during delithiation are not necessarily representative of the change in charge density that gives the change in valence.

Conclusion

Especially since the charge density is not isotropic, it is therefore more difficult to define an exact valence based on charge density plots such as Fig. Nevertheless, even considering small changes in lattice parameter upon delithiation, there is a small decrease in the electron density around Ni atoms when the material is delithiated. Finally, the trends with lithiation in the spin density at Ni atoms are not representative of the trends in charge density.

Introduction

Density functional theory (DFT) calculations show that Fe 3d states dominate the bottom of the conduction bands in both LiFePO4 and FePO4. The shift of the Fe K-edge of up to 4.3 eV during delithiation, observed by in situ X-ray absorption spectroscopy (XAS), has been attributed to oxidation of Fe2+ to Fe3+ [17]. After delithiation, an upward shift of about 2 eV at the Fe L3 peak and a stronger binding character of the Fe 3d and O 2p orbitals were detected.

Experimental

High resolution electron energy loss spectroscopy (EELS) measurements also revealed a shift of Fe white lines and the presence of a new peak at the OK edge after delithiation [19]. Quantification of the near-edge structure at Fe L-edges and the OK-edge shows that the Fe and O atoms play equal roles in charge compensation upon delithiation. We also report features of the lithium distribution at both room temperature and high temperature, showing that the high-temperature disrupted phase of Li0.6FePO4 is preserved at low temperatures.

Computational

To understand possible charge transfers, it is helpful to distribute the total charge among the various atoms in the unit cell. Features in the fine structures of EELS of transition metal compounds can be influenced by both atomic and solid state electronic effects. The shapes of the L2,3 transition metal edges can be significantly altered by atomic multiplets arising from the overlap of the radial wave functions for the 2p hole and holes in the partially filled 3D band.

Results

These features are less obvious in the disordered sample and disappear in the two-phase sample and the heterosite sample. It is broad in fully lithiated LiFePO4 and becomes sharper in samples containing less lithium. It is almost negligible in the triphyllite (LiFePO4) and the disordered sample, but is distinct in the two-phase and fully deliquized samples.

Discussion

Apparently, Fe atoms are not responsible for the overall charge compensation in LiFePO4 during delithiation and lithiation. In the disordered Li0.6FePO4 sample, the increase in the intensity of the white line is about 7%, which corresponds to the removal of 0.22 electrons. The pre-peak is also visible in the VASP calculations of the oxygen p density of states (Figure 4.7).

Conclusion

However, there is controversy about the degree of ionicity and the associated charge transfer in the Mg-Si bond. The presence of some covalent character in the Mg-Si bond was also supported by Auger spectrometry measurement where occupations in Mg 3s and 3p states were detected [15]. In the present work, we investigate the ionicity of the Mg-Si bond in Mg2Si by electron energy loss spectrometry (EELS) and first-principles calculations.

Fig. 5.1 The antifluorite structure of Mg 2 Si unit cell.

Experimental

Computational

In these calculations, Rkmax=7.0 (the product of the smallest MT radius by the largest wave vector used in the plane wave expansion) and lmax=10 (maximum l for partial waves used within MT spheres) were used to determine the size of set the basis for the wave functions. To evaluate possible charge transfer involved in bonding, the total charge associated with each atom was determined by integrating the charge density around the atom. The integration volume was defined by the procedure of Bader [21], where the boundaries of the volume are along contour lines that follow the interatomic peaks of the charge density.

Table 5.1 The equilibrium structures for c-Si, MgO and Mg 2 Si

Results and discussion

A small non-spherical distortion of the outer contours around O is caused by weak O-O covalent bonds. The Si in c-Si has all 14 electrons bound to the nucleus due to pure covalent Si-Si bonds. In MgO, 1.72 of the 2 Mg 3s valence electrons are transferred to O, corresponding to 86% ionicity.

Fig. 5.3 The Mg L 2,3 -edge of MgO and Mg 2 Si, respectively. The spectra were normalized with a window from 80 - 100eV

Conclusion

Electronic structure of CF x

However, due to the diversity of available carbonaceous precursors [4, 5], the crystallographic structure of CFx can vary considerably, and details of bonds in those materials are unknown. The application of CFx as an anode in batteries is currently limited by its low electrical conductivity.

Fig. 6.2 The C K-edge of graphite-based CF and pristine graphite. The spectra are normalized with a 50 eV window 40 eV beyond the σ * peak

Phase distribution in cathode and anode materials

Introduction

Elemental mapping

The corresponding ionization edge in each spectrum is then quantified to construct a two-dimensional lithium distribution, i.e. distribution of delithiated and lithiated phases. In the electron spectroscopic imaging method, an energy-selection slit is used, which allows electrons to be collected only within a certain energy window, e.g. Li K-edges collected by the spectrometer, which can produce a two-dimensional image. If fine enough spatial resolution can be achieved, elemental mapping can even resolve the concentration gradient between the bulk and grain boundaries, which can be critical to the performance of nano-sized materials [8, 9].

Fig. 6.3 (a) TEM bright field image of alumina with additions of barium silicate. (b) Elemental map using Ba M 4,5 -edge shows the high concentration of Ba at grain boundary and triple pocket

Valence electron density analysis

The vertices of the contours of Fe atoms extend to O atoms after delithiation, indicating more covalent Fe-O bonds. The vertices of contours around Fe atoms and the outer contours around O atoms show behavior similar to that in figure. These electron density plots confirm our conclusions drawn from the EELS measurements and the VASP calculations – there is no charge transfer from P atoms during delithiation, and Fe and O atoms both contribute to the charge compensation.