Momentum distribution of the uniform electron gas: improved parametrization and exact limits of the cumulant expansion

The momentum distribution of the unpolarized uniform electron gas in its Fermi-liquid regime, n(k,r_s), with the momenta k measured in units of the Fermi wave number k_F and with the density parameter r_s, is constructed with the help of the convex Kulik function G(x). It is assumed that $n(0,r_s), n(1^\pm, r_s)$, the on-top pair density g(0,r_s) and the kinetic energy t(r_s) are known (respectively, from effective-potential calculations, from the solution of the Overhauser model, and from Quantum Monte Carlo calculations via the virial theorem). Information from the high- and the low-density limit, corresponding to the random-phase approximation and to the Wigner crystal limit, is used. The result is an accurate parametrization of n(k,r_s), which fulfills most of the known exact constraints. It is in agreement with the effective-potential calculation of Takada and Yasuhara [1991 {\it Phys. Rev.} B {\bf 44} 7879], is compatible with Quantum Monte Carlo data, and is valid in the density range $r_s \lesssim 12$. The corresponding cumulant expansions of the pair density and of the static structure factor are discussed, and some exact limits are derived

Screened exchange corrections to the random phase approximation from many-body perturbation theory

The random phase approximation (RPA) systematically overestimates the magnitude of the correlation energy and generally underestimates cohesive energies. This originates in part from the complete lack of exchange terms, which would otherwise cancel Pauli exclusion principle violating (EPV) contributions. The uncanceled EPV contributions also manifest themselves in form of an unphysical negative pair density of spin-parallel electrons close to electron-electron coalescence. We follow considerations of many-body perturbation theory to propose an exchange correction that corrects the largest set of EPV contributions while having the lowest possible computational complexity. The proposed method exchanges adjacent particle/hole pairs in the RPA diagrams, considerably improving the pair density of spin-parallel electrons close to coalescence in the uniform electron gas (UEG). The accuracy of the correlation energy is comparable to other variants of Second Order Screened Exchange (SOSEX) corrections although it is slightly more accurate for the spin-polarized UEG. Its computational complexity scales as $\mathcal O(N^5)$ or $\mathcal O(N^4)$ in orbital space or real space, respectively. Its memory requirement scales as $\mathcal O(N^2)$

Editors’ Choice—4D Neutron and X-ray Tomography Studies of High Energy Density Primary Batteries: Part I. Dynamic Studies of LiSOCl2 during Discharge

The understanding of dynamic processes in Li-metal batteries is an important consideration to enable the full capacity of cells to be utilised. These processes, however, are generally not directly observable using X-ray techniques due to the low attenuation of Li; and are challenging to visualise using neutron imaging due to the low temporal resolution of the technique. In this work, complementary X-ray and neutron imaging are combined to track the dynamics of Li within a primary Li/SOCl2 cell. The temporal challenges posed by neutron imaging are overcome using the golden ratio imaging method which enables the identification of Li diffusion in operando. This combination of techniques has enabled an improved understanding of the processes which limit rate performance in Li/SOCl2 cells and may be applied beyond this chemistry to other Li-metal cells

Hellmann-Feynman theorem and fluctuation-correlation analysis of the Calogero-Sutherland model

Exploiting the results of the exact solution for the ground state of the one-dimensional spinless quantum gas of Fermions and impenetrable Bosons with the mu/x_{ij}^2 particle-particle interaction, the Hellmann-Feynman theorem yields mutually compensating divergences of both the kinetic and the interaction energy in the limiting case mu to -1/4. These divergences result from the peculiar behavior of both the momentum distribution (for large momenta) and the pair density (for small inter-particle separation). The available analytical pair densities for mu=-1/4, 0, and 2 allow to analyze particle-number fluctuations. They are suppressed by repulsive interaction (mu>0), enhanced by attraction (mu<0), and may therefore measure the kind and strength of correlation. Other recently proposed purely quantum-kinematical measures of the correlation strength arise from the small-separation behavior of the pair density or - for Fermions - from the non-idempotency of the momentum distribution and its large-momenta behavior. They are compared with each other and with reference-free, short-range correlation-measuring ratios of the kinetic and potential energies.Comment: 30 pages, 9 figures, revised version, short version appeared as PRB 62, 15279-15282 (2000

Multi-Dimensional Characterization of Battery Materials

Demand for low carbon energy storage has highlighted the importance of imaging techniques for the characterization of electrode microstructures to determine key parameters associated with battery manufacture, operation, degradation, and failure both for next generation lithium and other novel battery systems. Here, recent progress and literature highlights from magnetic resonance, neutron, X-ray, focused ion beam, scanning and transmission electron microscopy are summarized. Two major trends are identified: First, the use of multi-modal microscopy in a correlative fashion, providing contrast modes spanning length- and time-scales, and second, the application of machine learning to guide data collection and analysis, recognizing the role of these tools in evaluating large data streams from increasingly sophisticated imaging experiments

Neutron imaging of lithium batteries

Advanced batteries are critical to achieving net zero and are proposed within decarbonization strategies for transport and grid-scale applications, alongside their ubiquitous application in consumer devices. Immense progress has been made in lithium battery technology in recent years, but significant challenges remain and new development strategies are required to improve performance, fully exploit power density capacities, utilize sustainable resources, and lower production costs. Suitable characterization techniques are crucial for understanding, inter alia, three-dimensional (3D) diffusion processes and formation of passivation layers or dendrites, which can lead to drastic capacity reduction and potentially to hazardous short circuiting. Studies of such phenomena typically utilize 2D or 3D imaging techniques, providing locally resolved information. 3D X-ray imaging is a widely used standard method, while time-lapse (4D) tomography is increasingly required for understanding the processes and transformations in an operational battery. Neutron imaging overcomes some of the limitations of X-ray tomography for battery studies. Notably, the high visibility of neutrons for light-Z elements, in particular hydrogen and lithium, enables the direct observation of lithium diffusion, electrolyte consumption, and gas formation in lithium batteries. Neutron imaging as a non-destructive analytical tool has been steadily growing in many disciplines as a result of improvements to neutron detectors and imaging facilities, providing increasingly higher spatial and temporal resolutions. Further, ongoing developments in diffraction imaging for mapping the structural and microstructural properties of battery components make the use of neutrons increasingly attractive. Here, we provide an overview of neutron imaging techniques, generally outlining advances and limitations for studies on batteries and reviewing imaging studies of lithium batteries. We conclude with an outlook on development methods in the field and discuss their potential and significance for future battery research