Materials Theory

An efficient and accurate approach for calculating exact exchange and other two-electron integrals has been developed for periodic electronic structure methods. Traditional approaches used for integrating over the Brillouin zone in band structure calculations, e.g. trapezoidal or Monkhorst-Pack, are not accurate enough for two-electron integrals. This is because their integrands contain multiple singularities over the double integration of the Brillouin zone, which with simple integration methods lead to very inaccurate results. A common approach to this problem has been to replace the Coulomb interaction with a screened Coulomb interaction that removes singularities from the integrands in the two-electron integrals, albeit at the inelegance of having to introduce a screening factor which must precomputed or guessed. Instead of introducing screened Coulomb interactions in an ad hoc way, the method developed in this work derives an effective screened potential using a Filon-like integration approach that is based only on the lattice parameters. This approach overcomes the limitations of traditionally defined screened Coulomb interactions for calculating two-electron integrals, and makes chemistry many-body calculations tractable in periodic boundary conditions. This method has been applied to several systems for which conventional DFT methods do not work well, including the reaction pathways for the addition of H2 to phenol and Au$_{20}^{-}$ nanoparticle, and the electron transfer of a charge trapped state in the Fe(II) containing mica, annite.

Cellular patterns formed by self-organization of dislocations are a most conspicuous feature of dislocation microstructure evolution during plastic deformation. To elucidate the physical mechanisms underlying dislocation cell structure formation, we use a minimal model for the evolution of dislocation densities under load. By considering only two slip systems in a plane strain setting, we arrive at a model which is amenable to analytical stability analysis and numerical simulation. We use this model to establish analytical stability criteria for cell structures to emerge, to investigate the dynamics of the patterning process and establish the mechanism of pattern wavelength selection. This analysis demonstrates an intimate relationship between hardening and cell structure formation, which appears as an almost inevitable corollary to dislocation dominated strain hardening. Specific mechanisms such as cross slip, by contrast, turn out to be incidental to the formation of cellular patterns.

Coarse-grained descriptions of dislocation motion in crystalline metals inherently represent a loss of information regarding dislocation-dislocation interactions. In the present work, we consider a coarse-graining framework capable of re-capturing these interactions by means of the dislocation-dislocation correlation functions. The framework depends on a convolution length to define slip-system-specific dislocation densities. Following a statistical definition of this coarse-graining process, we define a spatial correlation function which will allow the arrangement of the discrete line system at two points—and thus the strength of their interactions at short range—to be recaptured into a mean field description of dislocation dynamics. Through a statistical homogeneity argument, we present a method of evaluating this correlation function from discrete dislocation dynamics simulations. Finally, results of this evaluation are shown in the form of the correlation of dislocation densities on the same slip-system. These correlation functions are seen to depend weakly on plastic strain, and in turn, the dislocation density, but are seen to depend strongly on the convolution length. Implications of these correlation functions in regard to continuum dislocation dynamics as well as future directions of investigation are also discussed.

An electrochemical cell contains three open thermodynamic systems that, in dynamic equilibrium, equalize their electrochemical potentials with that of their surrounding by forming an electric-double-layer-capacitor at the interface of the electrolyte with each of the two electrodes. Since the electrode/electrolyte interfaces are heterojunctions, the electrochemical potentials or Fermi levels of the two materials that contact the electrolyte at the two electrodes determine the voltage of a cell. The voltage is the sum of the voltages of the two interfacial electric-double-layer capacitors at the two electrode/electrolyte interfaces. A theoretical analysis of the thermodynamics that gives a quantitative prediction of the observed voltages in an asymmetric cell with an S8 relay at the positive electrode is provided. In addition, new discharge data and an X-ray photoelectron spectroscopy analysis of the lithium plated on the positive electrode of a discharged cell is presented. Ab initio, DFT methods were used to calculate the band structure and surface-state energies of the crystalline S8 solid sulfur relay. The theoretical exposition of the thermodynamics of the operative driving force of the chemical reactions in an electrochemical cell demonstrate that our initial experimental data and conclusions are valid. Other reported observations of lithium plating on the positive electrode, observations that were neither exploited nor their origins specified, are also cited.