Browning, Jim | Search NASA

DOE OSTI2021

A multi-dimensional Child–Langmuir law for any diode geometry

While prior theoretical studies of multi-dimensional space-charge limited current (SCLC) assumed emission from a small patch on infinite electrodes, none have considered emission from an entire finite electrode. In this paper, we apply variational calculus (VC) and conformal mapping, which have previously been used to derive analytic solutions for SCLC density (SCLCD) for nonplanar one-dimensional geometries, to obtain mathematical relationships for any multi-dimensional macroscopic diode with finite cathode and anode. We first derive a universal mathematical relationship between space-charge limited potential and vacuum potential for any diode and apply this technique to determine SCLCD for an eccentric spherical diode. We then apply VC and the Schwartz–Christoffel transformation to derive an exact equation for SCLCD in a general two-dimensional planar geometry with emission from a finite emitter. Particle-in-cell simulations using VSim agreed within 4%–13% for a range of ratios of emitter width to gap distance using the thinnest electrodes practical for the memory constraints of our hardware, with the difference partially attributed to the theory's assumption of infinitesimally thin electrodes. After generalizing this approach to determine SCLCD for any orthogonal diode as a function of only the vacuum capacitance and vacuum potential, we derive an analytical formulation of the three-dimensional Child–Langmuir law for finite parallel rectangular and disk geometries. These results demonstrate the utility for calculating SCLCD for any diode geometry using vacuum capacitance and vacuum potential, which are readily obtainable for many diode geometries, to guide experiment and simulation development.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Solid Electrolyte Interphase Architecture Determined through In Situ Neutron Scattering

We demonstrate through a combination of in operando solvent exchange and depth-sensitive neutron reflectometry that the solid electrolyte interphase (SEI) formed after the initial lithiation of a silicon anode, using a standard LiPF6 ethylene carbonate/ethyl methyl carbonate electrolyte, is chemically homogeneous across the liquid-solid interface. The data show the SEI is accessible to solvent/salt exchange throughout the layer indicating the poorly bound nature of the SEI components. Further, the data indicates that P-F species, from the decomposition of the LiPF6 salt, are highly mobile and removed from the SEI with solvent exchange. Critically, the SEI layer is structurally homogenous, in contrast to the reports in the literature of an inorganic/organic bilayer, which is important to our understanding of SEI formation and chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗