BECCA BARBERA

Age 16 | Hamilton, ON

4th place Chemistry for Life Award at the International Science & Engineering Fair of the American Chemical Society | Association for Women Geoscientists Award at the Bay Area Science & Engineering Fair | Earth & Environmental Sciences Award | Harrison Family Chemistry Award | Michael G. DeGroote Institute for Infectious Disease Research Award | Metallurgy and Petroleum Award at the Canadian Institute of Mining

Edited by Cameron Macdonald

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The purpose of this experiment was to determine the diffusion coefficient of Pu³⁺ through MX-80 clay, alongside the interference of the SR-270-PW brine solution of sedimentary rock formations. This study has many valuable applications and provides nuclear waste management organizations with specific data regarding location and storage methods, which will both ensure public protection and support clean-energy production. Using Materials Studio, a molecular dynamic simulation program, a montmorillonite (MMT) unit cell was constructed, then optimized using Dmol3 module’s GGA-PBE functional. A Pu³⁺ ion was optimized following the same process. To mimic the 6.0 M Na-Ca-Cl brine solution (SR-270-PW), the appropriate ions were inserted into the water layer, and the structure was reoptimized. Production simulations were conducted using the Forcite module, NVT ensemble, and Nosé thermostat at 298 K, with convergence having occurred after 14 simulations. The mean squared displacement (MSD) of each individual simulation was calculated, then an average MSD of all the simulations was determined, followed by a linear regression analysis. Using the Einstein relation, D=〈|r(t)-r(0)|〉/ 2nt, the diffusion coefficient of Pu³⁺, was calculated to be 1.31 ± 0.29 x10^-11 m²/s. This value indicates that, in the rare case that Pu³⁺ ions do escape the engineered barriers, they will have already decayed into harmless materials before migrating into our geosphere.

INTRODUCTION

Nuclear energy is a fundamental method of energy production world-wide. As the second-largest source of low-carbon power, it has consistently increased in popularity over the past seven years, now sourcing approximately 10% of the world’s electricity (Ritchie, 2020). The Deep Geological Repository (DGR) model is a long-term dry storage plan for used nuclear fuel that is present world-wide, and was chosen by the Canadian government in 2007, as proposed by the Nuclear Waste Management Organization (NWMO). This method involves the use of both natural and engineered barriers, specifically an MX-80 bentonite-clay buffer/sealant surrounding the copper-coated used fuel containers, all of which are further protected by the geosphere. Regardless of all the safety procedures in place, and how prevalent this energy is in society, many people are still fearful of nuclear power and, more specifically, the daunting element that is plutonium. The purpose of this experiment was to determine the diffusion coefficient of Pu³⁺ through MX-80 bentonite clay, alongside the interference of the reference 6.0 M Na-Ca-Cl brine solution (SR-270-PW) proposed by the NWMO regarding sedimentary rock formations. Information regarding the diffusion of radionuclides through the DGR model is crucial in ensuring public and environmental safety, as it tests the engineered barriers efficacy to obstruct the ions from entering our geosphere.

**Figure 1**: Multi-Barrier System – 1) Fuel Pellet, 2) Fuel Element + Bundle, 3) Fuel Container, 4) Bentonite Clay, 5) Geosphere

There are many difficulties and risks associated with the physical experimentation of plutonium, such as safety, availability, and societal influences regarding ionizing radiation and its association with nuclear weapons, all of which have created a significant paucity of migration data. In order to form a hypothesis, data pertaining to chemical analogs, such as americium and neptunium, was used. Since diffusion experiments are very lengthy, as migration occurs over long periods of time, several studies on americium reported diffusion rates of “close to zero” (Allard, 2011). It was hypothesized that the diffusion coefficient of plutonium would be greater than that of americium, as Am³⁺ has an approximate sorption value of 5.75 m³/kg in bentonite clay with pH of 6 (Vilks & Yang, 2018), whereas Pu³⁺ has an approximate value of 3.91 m³/kg (Vilks & Yang, 2018), and higher sorption values are associated with lower diffusion rates. According to a previous experimental study, conducted under reducing conditions and at a pH of 8.5, the Np⁴⁺ diffusion coefficient was determined to be 6x10^-15 m²/s (Nagasaki et al., 1999). The study found that sorption values increased with pH values, up to 8.5, then began to decrease. This suggests that 6x10^-15 m²/s is an underestimate to the diffusion coefficient at a pH of 6. Certainly, there are several other factors, alongside size and sorption values, involved with rates of diffusion; however, as an estimate, the hypothesized Pu³⁺ values would still remain within range of Am³⁺ and Np⁴⁺.

MATERIALS

This experiment was conducted on Biovia Materials Studio 2017, on a version 10 Windows operating system. Optimization runs were performed using Dmol³ Calculation Tools, and performance simulations were conducted using Forcite Calculation and Analysis Tools. CLAYFF Force fields were assigned to each atom, and the SR-270-PW brine solution was implemented using Adsorption Locator Tools.

METHOD

The MX-80 clay was modeled using a phyllosilicate sheet structure, with all Al³⁺ ions in opposition to Lowenstein’s rule having been substituted with Mg²⁺. The unit cell was then geometry optimized, using the DMol³ module of Materials Studio, which produced final lattice parameter outputs of a = 5.18 Å, b = 8.99 Å, c = 9.60 Å; α = γ = β = 90°, with a molecular formula of [Al₃Mg][Si₈]O₂₀(OH)₄. Proper charges were then assigned to each ion, based on the CLAYFF force field data - a general force field that has proven appropriate for the simulation of hydrated and multicomponent mineral systems (Cygan et al., 2004). A Pu³⁺ ion was optimized following the same process, to be implemented later on. The probable ionization of plutonium is dependent both on oxidation-reduction potential (Eh) and the activity of hydrogen ions (pH). At an Eh value of -200 mV, with a pH level of 6, which is the anticipated environment in sedimentary ground water (Vilks & Yang, 2018), Pu(III) is the oxidation state expected, with a Pu³⁺ ionization.

Following optimization, the model was replicated to create a 1x2x1 supercell, which was used in the simulations. Next, the super cell parameters were extended, to allow for the inclusion of water molecules into the structure. In relation to previous studies, the C lattice parameter was extended to 18.8 Å, the associated length for a 3-water-layer (3WL) model (Holmboe et al., 2011). Using Adsorption Locator Tools, in Materials Studio, 30 molecules of H₂O and 2 Na⁺ ions were inserted into the cell. The water molecules inserted were modelled using the Single Point Charge (SPC) water model. Two Na⁺ ions were included (one per unit cell) in order to create an electroneutral environment, as MMT is negatively charged due to isomorphic substitution. The adsorption calculation was performed using the CLAYFF force field, the Ewald Summation method for electrostatic potential, and Van der Waals’ atom-based forces. The cell was then re-optimized, with a, b, α, and γ held constant, and c and β able to vary, thereby allowing for a more natural configuration of molecules. The new cell dimensions were 5.16 x 17.92 x 18.35 Å, α = γ = 90 ̊, β = 92.45 ̊.

In order to run the simulation at ground-temperature, three preliminary dynamic simulations had to be performed - the first at 100 K, the second at 200 K, and lastly at 298 K. Using Materials Studio’s Forcite module, the task was performed with the NPT ensemble - an isothermal-isobaric composite where the amount of substance (N), pressure (P) and temperature (T) are conserved. It was run at 1.0x10^-4 GPa (standard atmospheric pressure), with a timestep of 0.5 fs and a total simulation time of 500 ps. Furthermore, the Berendsen barostat, CLAYFF force field, Ewald electrostatics and Van der Waals’ atom-based forces were appointed. Next, using Adsorption Tool calculations, the 6.0 M brine solution, found within a sedimentary DGR, was added to the model. Based off the accepted ratios of 166.092 g/L NaCl and 154.745 g/L CaCl₂⋅2 H2O (Walker, 2018), where 1 molecule represents 1 mole, 2 Na⁺, 3 Cl^-, and 1 Ca²⁺ ions, along with 1 H₂O molecule, were added. The interlayer model was now complete, and ready to run the simulations. Each dynamics simulation was executed using the Forcite module, NVT ensemble and Nosé thermostat, for a duration of 1 ns. Each simulation was performed at a now steady 298 K, which is why the Nosé thermostat was chosen. Convergence was considered to have taken place when five consecutive simulation runs had a percent deviation less than 5%, which occurred after a total of 14 simulations were completed. The mean squared displacement (MSD) of each individual simulation was calculated, then an average MSD of all the simulations was determined. A linear regression was performed on the average MSD, which was used to determine the diffusion coefficient.

RESULTS

As the R ² value was 0.9818, there is large positive linear association, meaning that the points are close to the linear trend line, indicating that the fit is appropriate. The equation of this line was y = 0.0052x. Using the Einstein relation, D=〈|r(t)-r(0)|〉/ 2nt, where r(t) – r(0) represents the MSD, n is equal to the dimensionality of the system, and t represents time, the diffusion coefficient of Pu ³⁺, in the specified conditions, was calculated to be 1.31 x10^-11 m²/s. Using the following formula, CI=x ̅±z (s/√n), where x ̅ represents the sample mean, z represents the confidence level value, s equates to the sample standard deviation and n represents the sample size, the confidence interval, at a 95% confidence level, was determined to be 0.29 x10^-11 m² /s. Therefore, the final diffusion value was calculated to be 1.31 ± 0.29 x10 ^-11 m ² /s.

**Figure 4:** Simulation Results - Graph

**Figure 5:** Average Mean Squared Displacement and Linear Regression Analysis

DISCUSSION

This studied determined the diffusion coefficient of Pu³⁺, in the specified conditions, to be 1.31 ± 0.29 x10^-11 m²/s, which is crucial in discerning the extent to which these radioisotopes may spread through the ground, should they escape the engineered barriers in place. There is approximately 0.12 kg of plutonium per fuel bundle (Jackson, 2003). Since plutonium-239 has a half-life of roughly 24 100 years, these results indicate that, in the case that any plutonium escapes from its container, it will only travel through approximately 12.96 m of MX-80 clay, before having completely decayed into harmless materials. Each individually used fuel container is encased in a highly compacted clay buffer, which is separated from neighbouring boxes by bentonite clay spacer blocks. Within the chamber, any open spaces are then filled with bentonite clay. Furthermore, a 6-10 metre-thick highly compacted clay seal will be used at the entrance of each placement room (NWMO, 2015). This implies that the plutonium within the radioactive waste will be unable to advance the clay protection and enter the geosphere. Deep geological repositories are prepared to last up to 1 000 000 years (more than double plutonium’s expected life-span), which denotes that even in cases where plutonium may be active for a several years longer, it would remain contained, and would not pose any risk to the environment or nearby populations. This is in accordance with the expected results, as other radioactive elements, such as uranium, reporting higher diffusion coefficients and longer half-lives, are also being accounted for by the deep geological repository model. These results dismiss the stigma surrounding plutonium within spent nuclear fuel, by disproving the common belief that its radioactive properties will emit ionizing radiation onto the nearby populace, while also polluting our earth and water systems.

CONCLUSION

In conclusion, the diffusion coefficient of the Pu³⁺ ion through a 3-water layer compacted MMT clay barrier, influenced by SR-270-PW 6.0 M brine solution, was determined to be 1.31 ± 0.29 x10^-11 m²/s, which supports the hypothesized range. This study has many valuable applications and provides the NWMO, alongside several other dedicated organizations world-wide, with specific data to be considered upon when deciding on the DGR host location and storage methods, alongside performance and safety assessments. Information on radionuclide migration gives confidence to both scientists and the public alike, regarding the benefits and security of nuclear energy, through sufficient containment of radioactive waste. As previously mentioned, nuclear energy accounts for roughly 10% of the world’s electricity production. If taken to higher proportions, significant improvements to the global environmental energy crisis are to be anticipated, as nuclear power is considered both clean and sustainable.

ACKNOWLEDGEMENTS

I would firstly like to thank the Canadian Science Fair Journal for giving me this opportunity, as well as all my wonderful science teachers at Cathedral High School who encouraged me to pursue this project. I would also like to thank Dr. Shinya Nagasaki and his team, who had greatly inspired me during my co-op last fall. Above all, I am very thankful to my family, who were exceptionally supportive, and equally share my excitement for science!

REFERENCES

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Cygan, R. T., Liang, J.-J., & Kalinichev, A. G. (2004). Molecular Models of Hydroxide, Oxyhydroxide, and Clay Phases and the Development of a General Force Field. The Journal of Physical Chemistry B, 108(4), 1255–1266. https://doi.org/10.1021/jp0363287

Ensuring Safety: Multiple-Barrier System. Nuclear Waste Management Organization. (2015). https://www.nwmo.ca/~/media/Site/Files/PDFs/2015/11/16/20/36/Secure_Accessible_MultipleBarrier_Backgrounder_EN.ashx?la=en.

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Torstenfelt, B., Andersson, K., Kipatsi, H., Allard, B., & Olofsson, U. (1981). Diffusion Measurements in Compacted Bentonite. MRS Proceedings, 6, 295–302. https://doi.org/10.1557/proc-6-295

Vilks, P., & Yang, T. (2018, August). Sorption of Selected Radionuclides on Sedimentary Rocks in Saline Conditions – Updated Sorption Values. Nuclear Waste Management Organization. https://www.nwmo.ca/~/media/Site/Reports/2018/10/29/18/49/NWMOTR201803.ashx?la=en.

Walker, A. (2018). Sorption Study of Se(-II) onto Illite, Bentonite, and Shale Under High Ionic Strength Conditions. MacSphere. http://hdl.handle.net/11375/24082.

Diffusion Mechanism of Pu3+ in Sedimentary Repository Conditions: First Principle Molecular Dynamics Study