## Date of Award

8-2022

## Document Type

Dissertation

## Degree Name

Doctor of Philosophy (PhD)

## Department

Environmental Engineering and Earth Science

## Committee Chair/Advisor

Lindsay Shuller-Nickles

## Committee Member

Rachel Getman

## Committee Member

Brian Powell

## Committee Member

Ezra Cates

## Abstract

Quantum-mechanical calculations using density functional theory with the generalized gradient approximation were employed to investigate the effects dopants have on the uranium dioxide (UO_{2}) structure. Uraninite is a common U^{4+} mineral in the Earth's crust and an important material used to produce energy and medical isotopes. Though the incorporation mechanism remains unclear, divalent cations are known to incorporate into the uranium dioxide system. Three charge-balancing mechanisms were evaluated to achieve a net neutral system, including the substitution of (1) a divalent cation for a tetravalent uranium atom and oxygen atom; (2) two divalent cations for a tetravalent uranium atom; and (3) a divalent cation for a tetravalent uranium atom and associated oxidation of two additional tetravalent uranium atoms. Multiple incorporation scenarios were considered for each charge-balancing mechanism to determine the lowest energy case. Driven by current literature, these calculations were implemented using collinear spin with the PBE exchange-correlation functional and the inclusion of the Hubbard U term[1] (U = 4.5 eV and J = 0.50 eV) as implemented by the Dudarev method. For the energetically favorable incorporation mechanisms, Sr^{2+} incorporation is favored over Mg^{2+}, Ca^{2+}, and Ba^{2+} incorporation by 0.11 eV to 0.97 eV. The coupled substitution of two divalent cations for one uranium cation is unfavorable. The mechanism where the substitution of a divalent cation for a U^{4+} atom is accompanied by the oxidation of two U^{4+} to U^{5+} atoms (*e.g.*, ∆E_{incorp} (Sr^{2+}) = -3.63 eV) is the most favorable incorporation mechanism compared to the other mechanisms investigated in this dissertation.

To further understand how the spin on the U-atoms influence the structural, energetic, and magnetic properties, collinear (*i.e.*, antiferromagnetic (AFM) 1**k** ordering) and noncollinear (*i.e.*, AFM 3**k** ordering) spin are investigated on various bulk UO_{2} system with and without the inclusions of a dopant (*i.e.*, Sr^{2+} and Zr^{4+}). AFM 1**k** ordering confines the spin on the U-atoms to the ±z-direction (*i.e.*, spin-up and spin-down), while AFM 3**k** ordering allows the spins to be anywhere in space (*e.g.*, (x, y, z) position). Experimental measurements have determined that UO_{2} exhibits AFM 3**k** spin ordering, but most of the theoretical calculations in the literature use the approximated 1**k** order scheme. The Liechtenstein approach is implemented where the inclusion of the Hubbard U terms, U and J, were 3.35 eV and 0.00 eV, respectively. Both the PBE and PBEsol exchange-correlation functionals were used. A systematic workflow was established to minimize errors that could arise from starting each calculation from the experimental lattice parameters. Defect-free and defect calculations of bulk UO_{2} using noncollinear spin with the PBEsol functional produced the best structural (*e.g.*, lattice constants), electronic (*e.g.*, band gap energy), and magnetic (*e.g.*, magnetization vectors) properties compared to the other theoretical setups. The density of state and projected magnetization vectors for bulk uranium dioxide were compared to the available computational data.

Understanding the interaction between the water - UO_{2} surface can explain the corrosion behavior of the uranium dioxide lattice. Dopant inclusion in the low-index (*i.e.*, (100), (110), and (111)) UO_{2} surfaces were explored with and without water adsorption using noncollinear spin. To accommodate a complex dopant scheme (e.g., Sr-dopant with two U^{5+} atoms) and lower the dopant concertation, a 2x2 surface area is used. Due to having a larger surface area and resource limitations, the surface thickness is four layers which correspond to 8 formula units per layer for the (100) and (110) surfaces and 16 formula units for the O-An-O units in the (111) surface. Generally, the anhydrous UO_{2} surface follows the surface stability trend where γ_{(111)} < γ_{(110)} < γ_{(100)}. However, in the presence of water, the surface stability trend changes such that the (100) UO_{2} surface becomes the most stable. Including a dopant (*e.g.*, Sr^{2+} and Zr^{4+}) into the low-index surfaces had little influence on the energetics. Still, there is an impact on the magnetic and structural properties locally around the dopant site. The hydration energies[2] and surface energies[3] were compared with available computational data.

Lastly, multiple spin configurations were evaluated to determine the influence of the two unpaired 5*f* electrons of U^{4+} on the energetics of bulk coffinite, as well as the (100), (110), (011), and (211) coffinite (USiO_{4}) surfaces. Coffinite is one of few naturally-occurring U^{4+} uraninite (UO_{2}) alteration products, making coffinite formation and dissolution key factors for risk assessment of potentially contaminated sites. The spin configuration has no impact on the total energy for bulk coffinite or the (211) coffinite surface, where the largest energy difference between spin configurations is ΔE = 0.016 eV and ΔE = 0.032 eV, respectively. Whether the spin was favorable is dictated by how the surface is terminated, with the same spin (*i.e.,* up/up or down/down) or has symmetric ordering perpendicular to the surface. Overall, the surface energy trend for coffinite is γ_{(100)} < γ_{(110)} < γ_{(011)M} < γ_{(211)} < γ_{(011)Si}. Interestingly, the uranium-terminated γ_{(011)} is less thanγ_{(211)} but greater thanγ_{(211)} when terminated with silicates. The surface energies (γ) of the isostructural silicate minerals, namely thorite (ThSiO_{4}) and zircon (ZSiO_{4}), were also calculated to compare the equilibrium morphologies of USiO_{4}, ThSiO_{4}, and ZrSiO_{4}, which were simulated using the Wulff construction method. Equilibrium crystal structures[4] constructed using the metal-terminated (011) surface for this work exhibit similar features to the coffinite, thorite, and stetindite (CeSiO_{4}) crystals synthesized in the lab that are dominated by the {100} tetragonal prism and {011} tetragonal bipyramid. Bader charge analysis, the density of state, charge density, and electron localization function plots for bulk coffinite, thorite, and zircon were compared to the available computational and experimental data.

[1] Density functional theory alone cannot describe the insulating character of the ground state for correlated materials, such as uranium dioxide. By including a correctional term, called the Hubbard U term, to the Hamiltonian (Ref. Chapter 3) of the strongly correlated electronic states, such as the *f*-orbitals in uranium, the system correctly becomes an insulator.

[2] Hydration energy is the energy gained by adsorbing water on a bare surface.

[3] The surface energy is a measure of excess energy at the surface compared to the bulk crystal and is used to ascertain surface reactivity or, conversely, surface stability.

[4] Using the Wulff method, the calculated surface energies are used to create the equilibrium shape of a crystal, showing the favorability of certain crystal planes over others. These crystal shapes are called equilibrium crystal structures and can be compared to available SEM and TEM images in the literature.

## Recommended Citation

Hoover, Megan, "Quantum-Mechanical Evaluation of Defects in Uranium-Bearing Materials" (2022). *All Dissertations*. 3146.

https://open.clemson.edu/all_dissertations/3146

## Author ORCID Identifier

0000-0001-5963-0128

#### Included in

Computational Engineering Commons, Condensed Matter Physics Commons, Other Materials Science and Engineering Commons