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A finite difference informed random walker (FDiRW) solver for strongly inhomogeneous diffusion problems

In nature, many complex multi-physics coupling problems exhibit strong diffusivity inhomogeneity. For instance, in the context of radionuclide absorption by porous wasteform materials within a flowing waste stream, the difference of species’ diffusivity in solid and liquid phases spans by 3~8 orders of magnitude. To solve the diffusion equations with strongly inhomogeneous diffusivity, traditional discretization-based methods, such as the Finite Difference Method (FDM), require infinitesimally small time steps (<10 -10 ) as high spatial resolutions are employed in most microstructure evolution processes, leading to prohibitively high computational costs. Here, this work developed an integrated numerical approach (FDiRW: Finite Difference informed Random Walk) to tackle this challenge. The idea is that utilizing the Random Walk concept, the fast diffusion is modeled as a superposition of point source’s solution for a concentration distribution while FDM is used to obtain the point source’s solution at each node. A mesh-coarsening algorithm is developed to generate an exclusive coarse mesh for FDiRW approach to maximize its efficiency. The effectiveness of the coarse mesh-based FDiRW approach is validated by benchmarking Finite Difference solutions. Numerical results demonstrated that FDiRW achieves a remarkable 1000x computational efficiency improvement over FDM while preserving desired accuracy for a medium-sized model of 192 × 192 × 192 grids. Finally, as models scale up, a floating-point operations (PLOPs) analysis of the FDiRW algorithm reveals that its computational complexity grows quadratically in terms of the number of nodes employed in computation.

36 MATERIALS SCIENCE

M3SF-24LL010302052-Comprehensive Analysis of Radionuclide Interaction with Hydrothermally Altered Repository Materials

This progress report (Level 3 Milestone Number M3SF-24LL010302052) summarizes research conducted at Lawrence Livermore National Laboratory (LLNL) within the Crystalline Work Package Number SF-24LL01030205. The research is focused on actinide and radionuclide sequestration in hydrothermally altered repository materials. In FY24, we completed a rigorous analysis of Se sorption to iron oxide phases using our L-SCIE sorption database. This effort explicitly accounts for surface titration behavior of oxide surfaces that was the subject of a recently published manuscript (Han et al., 2023). With this in mind, our Se sorption analysis now yields a more robust workflow for developing self-consistent surface complexation modeling approaches that can be adapted to specific SCM conceptual and numerical approaches (i.e. non-electrostatic, diffuse layer, triple layer models). In late FY24, we plan to publish the results of our comprehensive surface complexation modeling of Se(IV) and Se(VI) sorption to iron oxide mineral phases and provide a path forward to developing robust radionuclide sorption models for use in performance assessment. In FY24, we also submitted a manuscript summarizing our approach to integrating radionuclide sorption and coprecipitation phenomena and evaluation of radionuclide partitioning values across a range of radionuclides relevant to performance assessment. We demonstrated our approach in detail using Se sorption and coprecipitation with iron oxide minerals as a test case. This manuscript was recently accepted for publication in Applied Geochemistry (Balboni et al., Accepted). We also continued experiments to identify radionuclide interaction with hydrothermally altered crystalline repository and backfill materials. Recent research performed at Los Alamos National Laboratory (LANL) and Sandia National Laboratory (SNL) has provided key insights regarding the hydrothermal alteration behavior of bentonite backfill in the presence of repository materials (steel, concrete, etc.). We are now examining how mineral alteration affects retardation behavior of a suite of radionuclides of interest to repository performance assessment. These experiments also allow us to test the predictive ability of our component additivity approach to surface complexation and ion exchange. Our guiding hypothesis is that a robust surface complexation/ion exchange model and associated database, developed using our L-SCIE approach, can effectively predict changes in radionuclide sorption behavior resulting from the hydrothermal alteration of mineralogy in a repository near field. A short update of results to date is presented below.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA

M3SF-25LL010302052 - Radionuclide Interaction with Hydrothermally Altered Repository Materials

This progress report (Level 3 Milestone Number M3SF-25LL010302052) summarizes research conducted at Lawrence Livermore National Laboratory (LLNL) within the Crystalline Host Rock Properties & Processes - LLNL Number SF-25LL01030205. Observed changes in radionuclide sorption after bentonite/clay heating have implications for radionuclide diffusive transport through engineered barriers and must be considered when designing waste disposal repositories. Recent research performed at Los Alamos National Laboratory (LANL) has provided key insights regarding the hydrothermal alteration behavior of bentonite backfill in the presence of repository materials (steel, concrete, etc.). We are examining how this mineral alteration affects retardation behavior of a suite of radionuclides of interest to repository performance assessment. Sorption experiments and data analysis for 233 U were initiated in FY24 following earlier experiments performed on 243 Am, 90 Sr, 137 Cs. In FY25, we completed the 233 U study and initiated and completed a study of 237 Np sorption. Below, we summarize the results and potential impacts of hydrothermal alteration on radionuclide retardation and assess the importance of this process to radionuclide migration from a GHRDC. We also use statistical tools (i.e. PCA) to help us determine the major drivers in affecting changes in measured Kd values induced by hydrothermal alteration. These experiments also allow us to test the predictive ability of our component additivity approach to surface complexation and ion exchange. Our guiding hypothesis is that a robust surface complexation/ion exchange model and associated database can effectively predict changes in radionuclide sorption behavior resulting from the hydrothermal alteration of mineralogy in a repository near field. In November 2024 the paper “Selenium interaction with iron minerals: Quantitative comparison of sorption and coprecipitation impacts on mobility” was published in Applied Geochemistry. A short update of results to date is presented below. In FY25, we also actively supported the DITUSC project, which is part of the EURADII initiative, as associate partners. We are executing the Migration2025 conference and support associated the NEA-TDB and Thermochimie workshops that will provide critical international engagements and develop consensus and synergy in thermodynamics as it relates to supporting the US nuclear waste repository program.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W

Uptake and Binding of At‐211 Into K‐ and Cs‐Derivatives of Alpha‐Zirconium Phosphate Nanoplatelets for Use as a Targeted Alpha Therapy Delivery Platform

The ion exchange behavior of K- and Cs-derivatives of α-zirconium phosphate, A-ZrP, with the targeted alpha therapy (TAT) radionuclide 211 At, as At + and AtO + , has been investigated. The K-ZrP shows strong affinity for both At+ and AtO + , ≥99% uptake. The affinity to Cs-ZrP was less pronounced, 87%–94% uptake, favoring At + . The binding strength was tested against several leaching solutions, including carbonate, phosphate buffered saline (PBS), 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (HEPES) buffers, and ethylenediaminetetraacetic acid (EDTA) solutions at various concentrations (0.1–10 mM). K-ZrP retained 211 At in all buffer and EDTA solutions up to 1 mM (<0.5% leaching). The Cs-ZrP showed no leaching of At + , while AtO + leached (1%–3%) in the carbonate and HEPES buffers, along with all of the EDTA solutions, with complete retention only in the PBS buffer. In all cases, when the EDTA concentration reached 10 mM, 211 At leaching was observed. Once incorporated into the ZrP nanoplatelets, significant shielding of the α-particles was observed, not only attenuating the intensity of the emission but also reducing the energy of the α-particles themselves exiting the nanoplatelets. These properties provide the basis for K-ZrP, and to a lesser extent, Cs-ZrP to be further considered as potentially promising candidates for a delivery mechanism of 211 At for application in TAT.

astatine-211

Actinium purification from elemental components of stainless steel and aluminum

Radioisotopes of actinium are valuable because of their potential use in the medical industry. Actinium-225 shows promise for treating disease—like cancer—via targeted alpha therapy (TAT), and the longer-lived actinium-227 is the parent of two radionuclides with potential application in TAT radiopharmaceuticals, thorium-227 and radium-223. Continuing progress in the development of these medical applications requires robust and diverse methods for extracting and purifying actinium from a wide range of matrices. Further, to define the strengths and limitations of separation methods commonly employed in actinium processing, we characterized the performance of ion exchange and extraction chromatographic steps for removing contaminants found in stainless steel (chromium, iron, nickel, and silicon) and aluminum from actinium-227. While AG-MP1 anion exchange resin with HCl (aq) successfully removed iron, cation exchanger AG 50W-X8 removed most other contaminants. The most persistent contaminant was aluminum, which was removed using a DGA Normal extraction resin. These results are presented within the context of applying that methodology toward actinium purification strategies.

36 MATERIALS SCIENCE

Uptake and binding of La 3+ and Cr 3+ ions by alkali metal substituted alpha-zirconium phosphate

The conversion of alpha-zirconium phosphate, Zr(HPO 4 ) 2 ·H 2 O, to the K-, Rb-, and Cs-phases and the subsequent ion exchange behavior of these alkali metal phases, A-ZrP, with La 3+ and Cr 3+ have been investigated. The conversion to the A-ZrP phases was achieved by reaction with metal chloride, metal hydroxide solution, and confirmed through various techniques, including X-ray powder diffraction, thermogravimetry analysis, IR spectroscopy, scanning and transmission electron microscopy, and X-ray photoelectron spectroscopy. The effect of material hydration, which increased the interlayer distance, was also examined. The ion exchange behavior of the A-ZrP showed strong affinity for both La 3+ , a representative for trivalent lanthanide metals, and Cr 3+ , a representative for the trivalent transition metals, with a rapid, near quantitative removal of the M 3+ ions at a pH of 3 when the ion concentration was ≤25% of the ion exchange capacity of the materials. Additionally, the ion affinity was shown to be pH and concentration-dependent, decreasing with a decrease in pH or an increase in ion concentration. Lastly, the binding strength of La- and Cr-loaded ZrP materials was examined through a series of leaching experiments in a carbonate buffer, phosphate buffer, HEPES buffer, and a series of EDTA solutions at various concentrations. No observable leaching occurred in the carbonate buffer, phosphate buffer, HEPES buffer, or when the EDTA concentration was below 0.1 mM. These results highlight the potential for the A-ZrP materials to provide a platform for trivalent transition metal and trivalent lanthanide radionuclide capture for various applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

The corrosion behavior of borosilicate glass in the presence of cementitious waste forms

Borosilicate glasses are widely used for radioactive waste disposal due to their ability to incorporate a variety of contaminants and radionuclides while exhibiting high durability in various disposal scenarios. This research evaluated the dissolution of borosilicate glass using both single-pass-flow-through (ASTM C1662-18) and product consistency test (ASTM C1285-21) methods with different solutions, including a cementitious-contacted water (called grout-contacted, GC, from this point) and solutions with varying levels of dissolved cementitious species such as Si, Ca, Al. Here, the results indicated that the presence of Ca plays a crucial role in suppressing glass corrosion, as evidenced by the slower normalized dissolution rates, which were one order of magnitude lower for boron and two orders of magnitude lower for rhenium, observed in both Ca-amended and GC solutions compared to the pH 12 buffer solution. This effect is attributed to the formation of a dense, low-porosity, and strongly bonded calcium silicate hydrate (CSH) layer on the glass surface, which implies that a glass corrosion process is influenced by ion exchange involving alkali ions Na + , K + , Ca 2+ , and hydrogen-containing species. A small number of glass particles treated in the GC solution showed minor corrosion pits in the form of shallow craters with an average diameter of approximately 500 μm. This observation is correlated with a significant reduction, 2000 to 3000 times lower, in the cumulative volume of glass pores, indicating that smaller pore voids were “sealed” in the presence of Ca 2+ ions, likely attributed to the formation of CSH precipitation or other corrosion products such as calcium carbonate saturated from the grout solution. These findings suggest that the presence of dissolved Ca in the GC solution can slow down the dissolution of borosilicate glass, contrary to the expected trend of higher dissolution rates resulting from exposure to high alkaline and thus higher pH solutions.

36 MATERIALS SCIENCE

The production and separation of 161 Tb with high specific activity at the University of Utah

Targeted radiotherapy (TRT) is an increasingly prominent area of research in nuclear medicine, particularly in the context of treating cancerous tumors. One radionuclide of considerable interest for TRT is terbium-161 (t 1/2 = 6.95 days), which undergoes beta emission and shares similar decay properties as 177 Lu (FDA-approved as LUTATHERA® and PLUVICTO®). Besides beta emission, 161 Tb also emits a significant number of conversion and Auger electrons further enhancing its therapeutic potential. Terbium-161 can be produced using nuclear reactors through an indirect neutron capture reaction, $^{160}_{64}$Gd(n,γ) $^{161}_{64}$Gd → (3.7 min, β – ) $^{161}_{65}$Tb, from 160 Gd targets. However, a key challenge in utilizing 161 Tb for TRT lies in effectively separating target and product materials to attain high specific activity for radiolabeling. Here, we detail the production of no-carrier added 161 Tb using low flux research reactors (mean thermal (< 0.625 eV) neutron flux: 1.356 ×10 12 n • cm –2 • s –1 ) like the University of Utah TRIGA Reactor, using enriched 160 Gd 2 O 3 targets (1.5 ± 0.3 µCi of 161 Tb per mg of 160 Gd target per hour of irradiation). We also developed a separation technique based on cation exchange and extraction chromatography, suitable for mCi level irradiations with targets exceeding 200 milligrams. In a simulated full-scale irradiation, 161 Tb was successfully isolated from large mass targets using cation exchange (AG 50W-X8, with 2-hydroxyisobutyric acid at 70 mM, pH 4.75) and extraction chromatography (LN Resin, 0.5 – 0.75 M HNO 3 ) methods. Here, this resulted in high apparent molar activities of [ 161 Tb]Tb-DOTA (113 ± 3 MBq/nmol), demonstrating high purity 161 Tb relevant for potential future preclinical applications.

161Tb