Local field effects at Li K edges in electron energy-loss spectra of Li,Li2Oand LiF

Abstract

Local field effects (LFEs) in low-losses of electron energy-loss spectra of Li, ${\mathrm{Li}}_{2}\mathrm{O}$, and LiF were calculated using the density functional theory under the generalized gradient approximation. By including the lithium $1s$ semicore state in the pseudopotentials, the amplitude of LFE was assessed all the way up to the Li K edge (from $0\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}80\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$). They are found to be much larger for semicore levels ($2s$ of oxygen, $2s$ of fluorine, and $1s$ of lithium) than for the valence electron energy-loss region. LFEs at the Li K edge are studied in detail. In particular, for $q=0$ they are shown to increase with the inhomogeneities of the compounds (from Li to LiF). The influence of the magnitude and the direction of $\mathbf{q}$ is also presented. Both parameters have negligible effect in the case of Li metal but changes are quite substantial for ${\mathrm{Li}}_{2}\mathrm{O}$ and LiF. This is in agreement with the isotropy and the delocalization of the metallic bonding as compared to the ionic one. LFEs at the Li K edge are, however, whatever the compound, much smaller than those observed at transition metal ${\mathrm{M}}_{2,3}$ edges situated at similar energy positions. This result can be accounted for by considering the wave functions associated with the initial and final states involved in both edges. For lithium battery materials, most often presenting a transition metal edge close to the Li K edge, these findings imply significant consequences with respect to the interpretation of their electron energy-loss spectroscopy spectra. In particular, LFE can be expected to be stronger in positive electrodes than in negative ones.