We present an incisive spectroscopic technique for directly probing redox orbitals based on bulk electron momentum density measurements via high-resolution x-ray Compton scattering. Application of our method to spinel Li_{x}Mn_{2}O_{4}, a lithium ion battery cathode material, is discussed. The orbital involved in the lithium insertion and extraction process is shown to mainly be the oxygen 2p orbital. Moreover, the manganese 3d states are shown to experience spatial delocalization involving 0.16±0.05 electrons per Mn site during the battery operation. Our analysis provides a clear understanding of the fundamental redox process involved in the working of a lithium ion battery.

Non-destructive determination of lithium distribution in a working battery is key for addressing both efficiency and safety issues. Although various techniques have been developed to map the lithium distribution in electrodes, these methods are mostly applicable to test cells. Here we propose the use of high-energy x-ray Compton scattering spectroscopy to measure the local lithium concentration in closed electrochemical cells. A combination of experimental measurements and parallel firstprinciples computations is used to show that the shape parameter S of the Compton profile is linearly proportional to lithium concentration and thus provides a viable descriptor for this important quantity. The merits and applicability of our method are demonstrated with illustrative examples of Li x Mn 2 O 4 cathodes and a working commercial lithium coin battery CR2032. d d dp p J dp p J S 10 10

Electrification of heavy-duty transport and aviation requires a paradigm shift in electrode 1 materials and anionic redox represents one possible approach to meeting these demanding targets. However, questions on the validity of the O 2− /O − oxygen redox paradigm remain open and alternative explanations for the origin of the anionic capacity have been proposed because electronic orbitals associated with redox reactions cannot be measured by standard experiments. Here, by using high energy x-ray Compton measurements along with firstprinciples modeling, we show how the electronic orbital that lies at the heart of the reversible and stable anionic redox activity can be imaged and visualized and its character and symmetry can be determined. Differential changes in the Compton profile with Li concentration are shown to be sensitive to the phase of the electronic wave function and carry signatures of electrostatic and covalent bonding effects. Our study not only provides a picture of the workings of a lithium-rich battery at the atomic scale but also suggests pathways for improving existing cathodes and designing new ones.

Orbital ordering below 30 K was previously observed in the ferromagnetic Y T iO3 compound both by polarized neutron diffraction (PND) and X-ray magnetic diffraction (XMD). In this paper we report a new procedure for the joint refinement of a unique spin density model based on both PND and XMD data. The distribution of the unpaired 3d-electron of titanium is clearly seen on the magnetization density reconstructed by the Maximum of Entropy Method from the PND data collection at 5 K. The T i 3+ 3d orbital populations obtained by joint model refinement are discussed in terms of the orbital ordering scheme. Small but significant magnetic moments on apical oxygen O1 and yttrium atoms are found. The agreement between experimental and theoretical spin densities obtained using density functional theory is discussed.