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Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods). Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numerical complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange) part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. This technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Order within disorder: The atomic structure of ion-beam sputtered amorphous tantala (a-Ta{sub 2}O{sub 5})

Amorphous tantala (a-Ta{sub 2}O{sub 5}) is a technologically important material often used in high-performance coatings. Understanding this material at the atomic level provides a way to further improve performance. This work details extended X-ray absorption fine structure measurements of a-Ta{sub 2}O{sub 5} coatings, where high-quality experimental data and theoretical fits have allowed a detailed interpretation of the nearest-neighbor distributions. It was found that the tantalum atom is surrounded by four shells of atoms in sequence; oxygen, tantalum, oxygen, and tantalum. A discussion is also included on how these models can be interpreted within the context of published crystalline Ta{sub 2}O{sub 5} and other a-T{sub 2}O{sub 5} studies.

36 MATERIALS SCIENCE↗

Insight into the Atomic Structure of High-Voltage Spinel LiNi 0.5 Mn 1.5 O 4 Cathode Material in the First Cycle

Application of high-voltage spinel LiNi 0.5 Mn 1.5 O 4 cathode material is the closest and the most realistic approach to meeting the midterm goal of lithium-ion batteries for electric vehicles (EVs) and plug-in hybrid electric vehicles (HEVs). However, this application has been hampered by long-standing issues, such as capacity degradation and poor first-cycle Coulombic efficiency of LiNi 0.5 Mn 1.5 O 4 cathode material. Although it is well-known that the structure of LiNi 0.5 Mn 1.5 O 4 into which Li ions are reversibly intercalated plays a critical role in the above issues, performance degradation related to structural changes, particularly in the first cycle, are not fully understood. Here, we report detailed investigations of local atomic-level and average structure of LiNi 0.5 Mn 1.5 O 4 during first cycle (3.5–4.9 V) at room temperature. We observed two types of local atomic-level migration of transition metals (TM) ions in the cathode of a well-prepared LiNi 0.5 Mn 1.5 O 4 //Li half-cell during first charge via an aberration-corrected scanning transmission electron microscopy (STEM). Surface regions (~2 nm) of the cycled LiNi 0.5 Mn 1.5 O 4 particles show migration of TM ions into tetrahedral Li sites to form a Mn 3 O 4 -like structure. However, subsurface regions of the cycled particles exhibit migration of TM ions into empty octahedral sites to form a rocksalt-like structure. The migration of these TM ions are closely related to dissolution of Ni/Mn ions and building-up of charge transfer impedance, which contribute significantly to the capacity degradation and the poor first-cycle Coulombic efficiency of spinel LiNi 0.5 Mn 1.5 O 4 cathode material. Accordingly, we provide suggestions of effective stabilization of LiNi 0.5 Mn 1.5 O 4 structure to obtain better electrochemical performance.

25 ENERGY STORAGE↗

Confinement of quasi-atomic structures in Ti 2 N and Ti 3 N 2 MXene electrides

Metal carbides, nitrides, or carbonitrides of early transition metals, better known as MXenes, possess notable structural, electrical, and magnetic properties. Analyzing electronic structures by calculating structural stability, band structure, density of states, Bader charge transfer, and work functions utilizing first principle calculations, we revealed that titanium nitride MXenes, namely Ti 2 N and Ti 3 N 2 , have excess anionic electrons in their lattice voids, making them MXene electrides. Bulk Ti 3 N 2 has competing antiferromagnetic (AFM) and ferromagnetic (FM) configurations with slightly more stable AFM configuration, while the Ti 2 N MXene is nonmagnetic. Although Ti 3 N 2 favors AFM configuration with hexagonal crystal systems having 6/ mmm point group symmetry, Ti 3 N 2 does not support altermagnetism. The monolayer of the Ti 3 N 2 MXene is a ferromagnetic electride. These unique properties of having non-nuclear interstitial anionic electrons in the electronic structure of titanium nitride MXene have not yet been reported in the literature. Density functional theory calculations show TiN is neither an electride, MXene, or magnetic.

Anionic electrons↗

Local atomic structure of Pd and Ag in the SiC containment layer of TRISO fuel particles fissioned to 20% burn-up

The structure and speciation of fission products within the SiC barrier layer of tristructural-isotropic (TRISO) fuel particles irradiated to 19.6% fissions per initial metal atom (FIMA) burnup in the Advanced Test Reactor (ATR) at Idaho National Laboratory (INL) was investigated. As-irradiated fuel particles, as well as those subjected to simulated accident scenarios, were examined. The TRISO particles were characterized using synchrotron X-ray absorption fine-structure spectroscopy (XAFS) at the Materials Research Collaborative Access Team (MRCAT) beamline at the Advanced Photon Source. The TRISO particles were produced at Oak Ridge National Laboratory under the Advanced Gas Reactor Fuel Development and Qualification Program and sent to the ATR for irradiation. XAFS measurements on the palladium and silver K-edges were collected using the MRCAT undulator beamline. Analysis of the Pd edge indicated the formation of palladium silicides of the form Pd x Si (2 ≤ x ≤ 3). In contrast, Ag was found to be metallic within the SiC shell safety tested to 1700 °C. To the best of our knowledge, this is the first result demonstrating metallic bonding of silver from fissioned samples. Knowledge of these reaction pathways will allow for better simulations of radionuclide transport in the various coating layers of TRISO fuels for next generation nuclear reactors. In conclusion, they may also suggest different ways to modify TRISO particles to improve their fuel performance and to mitigate potential fission product release under both normal operation and accident conditions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Elucidating the Atomic Structures of the Gel Layer Formed during Aluminoborosilicate Glass Dissolution: An Integrated Experimental and Simulation Study

The altered glasses produced during aqueous dissolution of silicate and borosilicate glasses are among the most complex structures to understand at the atomic level due to their amorphous nature, random porosity and various levels of hydration. In this study, we gained insights of the complex atomic structures of altered aluminoborosilicate glasses by combining a range of experimental and computational approaches. The altered glasses were prepared by dissolution of three glasses with varying level of alumina in acid for 7 days. A comprehensive set of experimental [elemental analysis, high-energy X-ray diffraction, 29 Si and 27 Al solid-state nuclear magnetic resonance (NMR), and O 1s X-ray photoelectron spectroscopy (XPS)] and modeling (molecular dynamics (MD) simulations using non-reactive and reactive force fields) were used to study the atomic structures of these altered glasses. Elemental analysis showed that most of the B in the pristine glasses was leached into the solution and was not contained in the altered glass. The 29 Si and 27 Al solid-state NMR spectra revealed that the altered glasses have more polymerized silicate network as compared to those in the pristine glasses due to the reformation of linkages among Si and Al oxygen polyhedral in the altered glasses. The bridging and non-bridging (or hydroxyl O) atoms in the altered glasses were also quantified from their O 1s XPS spectra. Atomic structure models of the altered glasses were constructed by using MD simulations using the reactive force field based on the compositional information obtained from experiments. Various pore structures were generated using the charge-scaling (CS) method by using different initial densities and CS temperatures; the best CS parameters of each alternated glass were then determined by comparing with the experimental structure factors obtained from high energy X-ray diffraction. Pore and the atomic structures and vibrational properties around these pore surfaces were analyzed. Furthermore, these results from this comprehensive study thus provides a realistic insight into the pore morphology, atomic structure, and vibrational properties of altered glasses.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Influence of the plasma environment on atomic structure using an ion-sphere model

Plasma environment effects on atomic structure are analyzed using various atomic structure codes. To monitor the effect of high free-electron density or low temperatures, Fermi-Dirac and Maxwell-Boltzmann statistics are compared. After a discussion of the implementation of the Fermi-Dirac approach within the ion-sphere model, several applications are considered. In order to check the consistency of the modifications brought here to extant codes, calculations have been performed using the Los Alamos Cowan Atomic Structure (cats) code in its Hartree-Fock or Hartree-Fock-Slater form and the parametric potential Flexible Atomic Code (fac). The ground-state energy shifts due to the plasma effects for the six most ionized aluminum ions have been calculated using the fac and cats codes and fairly agree. For the intercombination resonance line in Fe 22+ , the plasma effect within the uniform electron gas model results in a positive shift that agrees with the MCDF value of B. Saha et al .

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗