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Computer Modelling of Thoria: Determining the Suitability of Thoria for a Next Generation Nuclear Fuel. Dr Paul Martin, Dr David Cooke, Prof. Bob Cywinski (Hudds) and Prof. S.C. Parker (Bath). Universities Nuclear Technology Forum University of Huddersfield 11 th - 13 th April 2011

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Contents Why Thoria ? Background and the Thoria Fuel Cycle Computational methods and results - Potential model validation - Modelling the of bulk material & Calculations of thermo-physical properties: 1. Internal structure - MD 2. Thermal expansion - MD 3. Defect Chemistry – Static modelling 4. Oxide ion diffusion - MD 5. Heat Capacity – MD 6. Uranium clustering at surfaces and bulk - LD Conclusions

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Why Study Thoria ? Background and the Thoria Fuel Cycle

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Thorium is four times more plentiful than uranium in the earth's crust All of the thorium dug from the ground can be usefully burnt ThO 2 produces little Plutonium ∴ doesn’t contribute to proliferation When used in an energy amplifier Thorium produces far less nuclear waste The process can ‘eat’ spent waste from conventional reactors Experts propose a new future for low carbon energy production : Nuclear power from Thoria Professor Bob Cywinski (right) with Nobel Laureate Professor Carlo Rubbia, former Director of CERN

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Thorium Cycle Spallation Stop neutron bombardment = cycle stops Absorbs neutron to become Th 233 Electron loss Energy released By Nuclear fission and Neutrons freed to continue process Further Decay Thorium is not fissile

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Computational methods and Results

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2 main methods: QM v MM Molecular MechanicsQuantum Mechanics Water on CaO {100} surface Force dominated by electrostatic interactions, but include repulsion, van der Waals and polarisability Can study larger systems But needs reliable potential parameters Very Accurate But very slow Shell model calculations

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Potentials and Static Simulations Model Validation – 3 parameter sets used to optimise geometry of bulk Thoria. Values from atomistic calcs ALL fall in range produced by DFT and experimental (which vary widely). (eg) Latt. Param. Within 0.03 Å of expt. determined structure. Lewis B & Balducci : shell model parameters. Lewis A: rigid ion – Use for subsequent MD – computationally less expensive Cell Parameter a / Å Elastic constants /GPa C 11 C 12 C 44 Moduli Bulk Shear Youngs /GPa /GPa /GPa Lewis A Lewis B Balducci 5.61 5.62 5.59 43191.7 86.4 43091.7 72.9 435 92.3 86.3 205 114 399 204 103 398 207 114 403 Terki (DFT) Shein (DFT) Shein (Expt.) 5.59 5.62 5.59 355106 54 315 73.1 75.7 339 71.0 77.0 193 82 215 193 94.5 244 175-290 82-106 215-261

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Molecular Dynamic (Bulk) Simulations Timestep = 0.001 ps Simulation time = 10 6 steps 1 ns NB. If use shell model, timestep = 0.0001 ps Ensemble : nst constant temperature, stress. Number of atoms (allow shape change) Pure cell : 500 Th 1000 O U Doped Cells : 1.0 % 2.0 % 5.0 % 10.0 % Using Lewis A potential (Rigid Ion) – less expensive Similar dopant levels to those found in fuel rods of ThO 2 based reactor – then more extreme levels

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Full Radial Distribution Function Analysis ThO 2 Supports no phase change over the full range of temperatures. Temps : 1500K – 3600K U levels: 1% U - 10 % U

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Thermal Expansion ThO 2 has favourable thermophysical properties because of the higher thermal conductivity and lower co-efficient of thermal expansion compared to UO 2 [5] - Better fuel performance [6] Rao et al. Thermal expansion and XPS of U-Thoria Solid Solutions. Journ. Nuc. Mat. 281 (2000) [NB] Exptl. Experimental Work involves much higher % doping and lower temperatures.

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Coefficient of Thermal Expansion of Uranium/Thoria Solid Solutions as a Function of Temperature. Uranium does not effect low thermal expansion fractional change in size per degree change in temperature at a constant pressure Lit. Value for average linear thermal expansion coefficients = 9.04 x 10 -6 K -1 [7] Journ. Nuc. Mat. 288, 1, 2001, 83-85. 10 % U – Extreme Levels 1%, 2%, 0% U – Normal operational levels

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Plot of Average Coefficient of Linear Expansion against % Uranium content over temp. range (1500 – 3220 K) Exptl. Lit. Value= Average lattice thermal expansion coefficient (293 to 1473 K) of pure thoria = 9.58 × 10 −6 K -1 [8] (Ceramics. Int. 31, 6, 2005, 769-772.) 1.02.010.0 0.0 1.0 5.0 10.0 % Uranium

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Statics: Defect Chemistry 1.Because of high energy fission products and initial neutron bombardment, fuel rods contain vacancies and interstitials. 2.We Calculate energy required to form vacancies, interstitials and to substitute U 4+ into the crystal lattice Super Cell /eV (periodic boundary conditions) Mott-Littleton /eV (2 region approach) O 2- Vacancy Th 4+ Vacancy O 2- Interstitial Th 4+ Interstitial U 4+ Interstitial U 4+ on Th 4+ site 13.97 81.34 -7.79 -56.80 -59.41 -1.59 14.43 81.01 -7.81 -57.43 -59.98 -1.59 Schottky Trio ThO 2 Anion Frenkel Cation Frenkel 3.01 3.08 12.27 3.21 3.31 11.79 Calcs predict substitution of U 4+ onto Th 4+ site costs only -1.59 eV, suggesting that doping the crystal with U will not adversely affect the stability of bulk Thoria.

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Oxide Ion Diffusivity – Activation Free Energy of Migration Predictions [NB] Th ion – diffusion so small, the errors involved would be bigger than the value Both pure ThO 2 and U doped ThO 2 E act = approx 360-380 kJ. Mol -1 = approx 3.6 – 3.9 eV Therefore, little or no diffusion ~0.5 eV ~0.7 eV Our calculated values agree with experiment

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Heat Capacity (C p ) – compares well with Th doped LiF C p = (dH/dT) p Slope = 40.942 kJ/mol/K = 40942 J/mol/K = 0.3100 kJ/g/K = 310.031 J/Kg/K Pure ThO 2 Th doped LiF 400 – 700 J/Kg/K Temperature (K)

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Effect of Lattice Uranium, Defects and Interstitials on Heat Capacity Uranium alone - little change Uranium + Oxygen Interstitials -density increase Uranium + oxygen defects -Less dense High energy fission products and initial neutron bombardment means fuel rods contain vacancies and interstitials.

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Conclusions We use atomistic simulation to help determine suitability of thoria as a next generation nuclear fuel –Involves similar dopant levels to those found in fuel rod, and higher levels too –Full range of temperatures from ambient to the extreme working conditions The 3 ThO 2 potentials give very similar optimal bulk geometries – so we use rigid-ion Lewis A model – computationally less demanding ThO 2 has favourable thermophysical properties – low coefficient of thermal expansion, (1500 – 3200 K). Uranium doping at levels found in fuel rods and well above this level, does increase expansivity, but not greatly. Doping at the levels found in fuel rods does not effect stability of Bulk ThO 2, over the temperature range under test. Very Low Ion Diffusivity. Even for Oxide ion E act (diffusion) = approx. 3 - 4 eV Our work does point towards thoria being a suitable next generation fuel Future work includes effect of defects and other dopants and effect of neutron bombardment at the {111} surface to calculate recoil energies for ThO 2

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Acknowledgements 1. The Science and Technology Facilities Council for funding 2. National Grid Service (NGS) for computing resource. 3.CCP 5 for travel/collaboration grant between Huddersfield and Bath. 4.Many thanks go to the following for useful discussions/collaborations regarding science, lattice and molecular dynamics simulations or NGS use: Prof. Bob Cywinski Dr D.J. Cooke Dr. P. Martin Prof. S.C. Parker Tom Shapley Dr. Marco Molinari Jennifer Crabtree Mofuti Mehlape University of Bath:

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References 1.Lewis G., Catlow C. Journal Physics C – Solid State Physics 18, 1149, (1985). 2.Balducci et al. Chemistry of Materials 12, 677, (2000). 3.Terki et al. Computational Materials Science 33, 44, (2005). 4.Shein et al. J. Nucl. Mater., 361, No. 1, 69-77 (2007). 5.Thorium Fuel Cycle. Potential Benefits and Challenges. I.A.E.A.-tec-doc-1450 May 2005. 6.Rao et al. Thermal expansion and XPS of U-Thoria Solid Solutions. Journ. Nuc. Mat. 281 (2000) 7.Journ. Nuc. Mat. 288, 1, 2001, 83-85. 8.Ceramics. Int. 31, 6, 2005, 769-772

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