Editors’ choice—4D neutron and X-ray tomography studies of high energy density primary batteries: Part II. multi-modal microscopy of LiSOCl2 cells

The ability to track electrode degradation, both spatially and temporally, is fundamental to understand performance loss during operation of lithium batteries. X-ray computed tomography can be used to follow structural and morphological changes in electrodes; however, the direct detection of electrochemical processes related to metallic lithium is difficult due to the low sensitivity to the element. In this work, 4-dimensional neutron computed tomography, which shows high contrast for lithium, is used to directly quantify the lithium diffusion process in spirally wound Li/SOCl$_{2}$ primary cells. The neutron dataset enables the quantification of the lithium transport from the anode and the accumulation inside the SOCl$_{2}$ cathode to be locally resolved. Complementarity between the collected neutron and X-ray computed tomographies is shown and by applying both methods in concert we have observed lithium diffusion blocking by the LiCl protection layer and identified all cell components which are difficult to distinguish using one of the methods alone

A Geometric Formulation of Quantum Stress Fields

We present a derivation of the stress field for an interacting quantum system within the framework of local density functional theory. The formulation is geometric in nature and exploits the relationship between the strain tensor field and Riemannian metric tensor field. Within this formulation, we demonstrate that the stress field is unique up to a single ambiguous parameter. The ambiguity is due to the non-unique dependence of the kinetic energy on the metric tensor. To illustrate this formalism, we compute the pressure field for two phases of solid molecular hydrogen. Furthermore, we demonstrate that qualitative results obtained by interpreting the hydrogen pressure field are not influenced by the presence of the kinetic ambiguity.Comment: 22 pages, 2 figures. Submitted to Physical Review B. This paper supersedes cond-mat/000627

Electronic resonance states in metallic nanowires during the breaking process simulated with the ultimate jellium model

We investigate the elongation and breaking process of metallic nanowires using the ultimate jellium model in self-consistent density-functional calculations of the electron structure. In this model the positive background charge deforms to follow the electron density and the energy minimization determines the shape of the system. However, we restrict the shape of the wires by assuming rotational invariance about the wire axis. First we study the stability of infinite wires and show that the quantum mechanical shell-structure stabilizes the uniform cylindrical geometry at given magic radii. Next, we focus on finite nanowires supported by leads modeled by freezing the shape of a uniform wire outside the constriction volume. We calculate the conductance during the elongation process using the adiabatic approximation and the WKB transmission formula. We also observe the correlated oscillations of the elongation force. In different stages of the elongation process two kinds of electronic structures appear: one with extended states throughout the wire and one with an atom-cluster like unit in the constriction and with well localized states. We discuss the origin of these structures.Comment: 11 pages, 8 figure

Extended Hartree-Fock method based on pair density functional theory

A practical electronic structure method in which a two-body functional is the fundamental variable is constructed. The basic formalism of our method is equivalent to Hartree-Fock density matrix functional theory [M. Levy in {\it Density Matrices and Density Functionals}, Ed. R. Erdahl and V. H. Smith Jr., D. Reidel, (1987)]. The implementation of the method consists of solving Hartree-Fock equations and using the resulting orbitals to calculate two-body corrections to account for correlation. The correction terms are constructed so that the energy of the system in the absence of external potentials can be made to correspond to approximate expressions for the energy of the homogeneous electron gas. In this work the approximate expressions we use are based on the high-density limit of the homogeneous electron gas. Self-interaction is excluded from the two-body functional itself. It is shown that our pair density based functional does not suffer from the divergence present in many density functionals when homogeneous scaling is applied. Calculations based on our pair density functional lead to quantitative results for the correlation energies of atomic test cases.Comment: to appear in Physical Review

Entanglement Measures for Single- and Multi-Reference Correlation Effects

Electron correlation effects are essential for an accurate ab initio description of molecules. A quantitative a priori knowledge of the single- or multi-reference nature of electronic structures as well as of the dominant contributions to the correlation energy can facilitate the decision regarding the optimum quantum chemical method of choice. We propose concepts from quantum information theory as orbital entanglement measures that allow us to evaluate the single- and multi-reference character of any molecular structure in a given orbital basis set. By studying these measures we can detect possible artifacts of small active spaces.Comment: 14 pages, 4 figure

Self-consistent Overhauser model for the pair distribution function of an electron gas in dimensionalities D=3 and D=2

We present self-consistent calculations of the spin-averaged pair distribution function $g(r)$ for a homogeneous electron gas in the paramagnetic state in both three and two dimensions, based on an extension of a model that was originally proposed by A. W. Overhauser [Can. J. Phys. {\bf 73}, 683 (1995)] and further evaluated by P. Gori-Giorgi and J. P. Perdew [Phys. Rev. B {\bf 64}, 155102 (2001)]. The model involves the solution of a two-electron scattering problem via an effective Coulombic potential, that we determine within a self-consistent Hartree approximation. We find numerical results for $g(r)$ that are in excellent agreement with Quantum Monte Carlo data at low and intermediate coupling strength $r_s$, extending up to $r_s\approx 10$ in dimensionality D=3. However, the Hartree approximation does not properly account for the emergence of a first-neighbor peak at stronger coupling, such as at $r_s=5$ in D=2, and has limited accuracy in regard to the spin-resolved components $g_{\uparrow\uparrow}(r)$ and $g_{\uparrow\downarrow}(r)$. We also report calculations of the electron-electron s-wave scattering length, to test an analytical expression proposed by Overhauser in D=3 and to present new results in D=2 at moderate coupling strength. Finally, we indicate how this approach can be extended to evaluate the pair distribution functions in inhomogeneous electron systems and hence to obtain improved exchange-correlation energy functionals.Comment: 14 pages, 7 figuers, to apear in Physical Review

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

High speed 4D neutron computed tomography for quantifying water dynamics in polymer electrolyte fuel cells

In recent years, low temperature polymer electrolyte fuel cells have become an increasingly important pillar in a zero carbon strategy for curbing climate change, with their potential to power multiscale stationary and mobile applications. The performance improvement is a particular focus of research and engineering roadmaps, with water management being one of the major areas of interest for development. Appropriate characterisation tools for mapping the evolution, motion and removal of water are of high importance to tackle shortcomings. This article demonstrates the development of a 4D high speed neutron imaging technique, which enables a quantitative analysis of the local water evolution. 4D visualisation allows the time resolved studies of droplet formation in the flow fields and water quantification in various cell parts. Performance parameters for water management are identified that offer a method of cell classification, which will, in turn, support computer modelling and the engineering of next generation flow field design

4D imaging of lithium batteries using correlative neutron and X ray tomography with a virtual unrolling technique

The temporally and spatially resolved tracking of lithium intercalation and electrode degradation processes are crucial for detecting and understanding performance losses during the operation of lithium batteries. Here, high throughput X ray computed tomography has enabled the identification of mechanical degradation processes in a commercial Li MnO2 primary battery and the indirect tracking of lithium diffusion; furthermore, complementary neutron computed tomography has identified the direct lithium diffusion process and the electrode wetting by the electrolyte. Virtual electrode unrolling techniques provide a deeper view inside the electrode layers and are used to detect minor fluctuations which are difficult to observe using conventional three dimensional rendering tools. Moreover, the unrolling provides a platform for correlating multi modal image data which is expected to find wider application in battery science and engineering to study diverse effects e.g. electrode degradation or lithium diffusion blocking during battery cyclin

Density-functional theory of elastically deformed finite metallic system: work function and surface stress

The effect of external strain on surface properties of simple metals is considered within the modified stabilized jellium model. The equations for the stabilization energy of the deformed Wigner-Seitz cells are derived as a function of the bulk electron density and the given deformation. The results for surface stress and work function of aluminium calculated within the self-consistent Kohn-Sham method are also given. The problem of anisotropy of the work function of finite system is discussed. A clear explanation of independent experiments on stress-induced contact potential difference at metal surfaces is presented.Comment: 15 pages, 1 figur