Reduction-oxidation (redox) reactions that transfer conduction electrons from the anode to the cathode are the fundamental processes responsible for generating power in Li-ion batteries. Electronic and microstructural features of the cathode material are controlled by the nature of the redox orbitals and how they respond to Li intercalation. Thus, redox orbitals play a key role in performance of the battery and its degradation with cycling. We unravel spectroscopic descriptors that can be used to gain an atomic-scale handle on the redox mechanisms underlying Li-ion batteries. Our focus is on X-ray Compton Scattering and Positron Annihilation spectroscopies and the related computational approaches for the purpose of identifying orbitals involved in electrochemical transformations in the cathode. This review provides insight into the workings of lithium-ion batteries and opens a pathway for rational design of next-generation battery materials.

The structure of nanoparticles has been difficult to determine accurately because the traditional structure methods rely on large monocrystals. Here, we discuss the structure of nanoparticles based on real-space modeling of the pair distribution function obtained by a Fourier transformation of the high-energy X-ray scattering structure factor. In particular, we consider X-ray scattering data taken from colloidal manganese oxide nanoparticles used in Lithium-ion batteries, air-purification, and biomedical systems, which are known to exist in various nanometer-sized polymorphs. Insight is thus obtained into characterizing the structural relaxation of the MnO₆ octahedra, which are the key building blocks of oxide nanoparticles, important in many technologies.

Bismuth has recently attracted interest in connection with Na-ion battery anodes due to its high volumetric capacity. It reacts with Na to form Na ${}_3$ Bi which is a prototypical Dirac semimetal with a nontrivial electronic structure. Density-functional-theory based first-principles calculations are playing a key role in understanding the fascinating electronic structure of Na ${}_3$ Bi and other topological materials. In particular, the strongly-constrained-and-appropriately-normed (SCAN) meta-generalized-gradient-approximation (meta-GGA) has shown significant improvement over the widely used generalized-gradient-approximation (GGA) scheme in capturing energetic, structural, and electronic properties of many classes of materials. Here, we discuss the electronic structure of Na ${}_3$ Bi within the SCAN framework and show that the resulting Fermi velocities and s-band shift around the $\Gamma$ point are in better agreement with experiments than the corresponding GGA predictions. SCAN yields a purely spin-orbit-coupling (SOC) driven Dirac semimetal state in Na ${}_3$ Bi in contrast with the earlier GGA results. Our analysis reveals the presence of a topological phase transition from the Dirac semimetal to a trivial band insulator phase in Na ${}_3$ Bi ${}_x$ Sb ${}_{1-x}$ alloys as the strength of the SOC varies with Sb content, and gives insight into the role of the SOC in modulating conduction properties of Na ${}_3$ Bi.

We discuss the atomic structure of amorphous ferromagnetic FeCoB alloys, which are used widely in spintronics applications. Specifically, we obtain the pair-distribution functions for various atomic pairs based on high-energy x-ray diffraction data taken from an amorphous Co ₂₀ Fe ₆₁ B ₁₉ specimen. We start our reverse Monte Carlo cycles to determine the disordered structure with a two-phase model in which a small amount of cobalt is mixed with Fe ₂₃ B ₆ as a second phase. The structure of the alloy is found to be heterogeneous, where the boron atoms drive disorder through the random occupation of the atomic network. Our analysis also indicates the presence of small cobalt clusters that are embedded in the iron matrix and percolating the latter throughout the structure. This morphology can explain the enhanced spin polarization observed in amorphous magnetic materials.

Decagonal quasiperiodic ordering of Sn thin films on $d$-Al-Ni-Co is shown based on scanning tunneling microscopy (STM), low-energy electron diffraction, and density functional theory (DFT). Interestingly, the decagonal structural correlations are partially retained even up to a large film thickness of 10 nm grown at $165\pm 10\mathrm{K}$. The nucleation centers called “Sn white flowers” identified by STM at submonolayer thickness are recognized as valid patches of the decagonal clathrate structure with low adsorption energies of these motifs. Due to the excellent lattice matching (to within 1%) between columns of Sn dodecahedra in the clathrate structure and pentagonal motifs at the $d$-Al-Ni-Co surface, the interfacial energy favors clathrate over the competing Sn crystalline forms. DFT study of the Sn/Al-Ni-Co composite model shows good mechanical stability, as shown by the work of separation of Sn from Al-Ni-Co slab that is comparable to the clathrate self-separation energy. The relaxed surface terminations of the ${\mathrm{R}}_2{\mathrm{T}}_4$ clathrate approximant are in self-similarity correspondence with the motifs observed in the STM images from monolayer to the thickest Sn film.