1. Predicting the Effect of Fission Products in UO 2 Kaajal H. Desai a, David Parfitt a, Scott L. Owens b, Robin W. Grimes a a Department of Materials, Imperial College, Prince Consort Road, London, UK b Nexia Solutions, Hinton House, Risley, Warrington, Chesire UK Imperial College OF SCIENCE, TECHNOLOGY AND MEDICINE Presentation at the VERCORS meeting

2. Aim: demonstrate what atomic scale computer simulation can provide, that is useful for developing a better understanding of the behaviour of nuclear fuels (particularly as they relate to fission product behaviour). What can simulations do for you? Correlate experimental data with existing physical models (fill in the gaps and work out what’s missing). Generate data for known physical processes (point the way to better hunting grounds for experimental work). Develop new physical models that underpin phenomena (work out what science actually matters).

3. First – Correlate experimental data with physical models Use fission product inventories to investigate fuel swelling. Lattice swelling/contraction due to accommodation of soluble fission products as a function of fission product concentration. Affect on mechanical properties – elastic constants and bulk moduli as a function of fission product concentration.

4. First – Correlate experimental data with physical models The Physical process is well established. No new “science” is being suggested. Checking existing data and correlating it. Hence: fillng in the gaps and working out what’s missing.

5. Swelling Calculation Defect volume, V D, is calculated by: K T (Å 3 eV -1 ) is the isothermal compressibility, V 0 (Å 3 ) initial unit cell volume f (eV) the internal defect formation energy calculated within the Mott-Littleton approximation Mechanical constants are calculated using: Bulk Modulus

6. Range of Fission Products (FP) Different solution sites – U and O substitution, interstitial octahedral site, cluster sites Fuel Stoichiometry  Zr 4+, Ce 4+ - sites:,  Sr 2+ - sites : Isolated Clustered Isolated Clustered or  Y 3+, La 3+, Pr 3+, Nd 3+, Sm 3+, Eu 3+, Gd 3+, Dy 3+ sites: Isolated Clustered or Isolated Clustered Model Considerations

7. Results I: Zr accommodation

8. Results II: Ce accommodation

9. FP Accommodation: Sr Number of ways Sr can be accommodated in lattice UO 2 - substitution on U site is energetically favoured Charge compensated in 2 ways V O ·· Oxygen vacancy formation U U · Uranium oxidation, U 5+ formation Similarly for the trivalent, Y and lanthanide fission products

10. Results III: Sr accommodation

11. Results IV: La accommodation

12. Results V: Pr accommodation

13. Results VI: Nd accommodation

14. Results VII: Sm accommodation

15. Results VIII: Eu accommodation

16. Results IX: Gd accommodation

17. Results X: Dy accommodation

18. Results XI: Predicted Change in Bulk Modulus due to Sr

19. Results XIII: Predicted Change in Bulk Modulus due to Zr and Ce

20. Summary A specific burnup yields a specific fission product inventory. This work aims to provide data from which it is possible to determine a change of lattice parameter or change in mechanical property of the UO 2 lattice as a consequence of the dissolved fraction of those fission products.  For example, Sr 2+ --> Increased lattice parameter Zr 4+ --> Decreased lattice parameter

21. Second – Generate data for known physical processes The aim is to help to direct experimental work. The physical process is well established, but the significance to fuels not necessarily realised. Appropriate experimental data does not yet exist. Classic example: compositional changes due to segregation.

22. Aim of Segregation Study Computer simulation is used to investigate the accommodation and segregation of fission products to the (111), (110) and (100) surfaces of UO 2  Fission products considered: Ce 4+, Zr 4+, Ba 2+, Sr 2+, Kr 0 and Xe 0  Ba 2+ and Sr 2+ are charge compensated by a single oxygen vacancy  Kr 0 and Xe 0 are compensated by two oxygen vacancies Important results concern:  Segregation dependence on the surface type  Defect cluster orientation with respect to a given surface  Anion termination configuration for dipolar surfaces This work provides information regarding the anisotropic release of fission products. see Stanek et al. Mat. Res. Symp. Proc. 654 (2001) AA 3.32.

23. Methodology Computational codes CASCADE and MARVIN are used. A defect (isolated or clustered) is introduced to a characteristic lattice and moved stepwise through the bulk. The total energy of Region 1 is calculated for each step and the energies are compared with respect to when the cluster is furthest from the surface (i.e. in the bulk).

24. Divalent ClusterConfigurations: (111) The nearest neighbour {(Ba/Sr U )’’:(V O ).. } configuration is preferred. There are four unique nearest neighbour cluster configurations with respect to the (111) surface, shown below. Each of these configurations must be modelled.

25. The Zr 4+ segregation energy, E S = 0.26eV, the trap energy, E T = 0.35eV, which suggests that Zr 4+ remain trapped just beneath the (111) surface. For Ce 4+, E S = 0.23eV, which suggests that Ce 4+ does not segregate to the (111) surface. (E T - E S ) is negligible, which suggests that the trapping observed with Zr 4+ is not present. Ce 4+ and Zr 4+ (111) Segregation

26. Ba 2+ and Sr 2+ (111) Segregation The segregation energy E S = - 2.71eV for Ba 2+, thus Ba 2+ will segregate to the (111) surface. A similar trend is observed for Sr 2+, where E S = -1.60eV, though the driving force is reduced. In the bulk (  10Å) there is little cluster configuration preference. Near to the surface, there is a dependence on defect cluster configuration.

27. Ce 4+ and Zr 4+ (110) Segregation The Zr 4+ segregation energy, E S = 0.14eV, which suggests that Zr 4+ will not segregate to the (110) surface. The nonlinear change in energy is due to alternating compression and dilation of atomic layers. For Ce 4+ E S = 0.67eV which suggests that Ce 4+ does not segregate to the (110) surface,more strongly than Zr 4+. The trend for Ce 4+ and Zr 4+ not segregating to the (110) surface is similar to the trend observed for the (111).

28. Ba 2+ and Sr 2+ (110) Segregation The Ba 2+, segregation energy, E S = -2.84eV, suggests that Ba 2+ will segregate to the (110) surface. A similar trend is observed for Sr 2+ where E S = -1.67eV; clearly the driving force is reduced. The segregation of Ba 2+ and Sr 2+ is very similar to that observed with the (111); similar segregation energies and cluster dependence nearer to the surface.

29. Conclusions Concerning Segregation Computer simulation calculations suggest that Ce 4+ and Zr 4+ show no tendency to segregate to the (111) or (110) surfaces of UO 2. Zr 4+ demonstrates a tendency to segregate to the (100)A surface, which suggests segregation is a function of surface. Ba 2+ and Sr 2+ display a tendency to segregate to the (111) and (110) surfaces, with cluster configuration becoming important near the surface in both cases. Segregation is not only a function of fission product chemistry and surface, but also cluster configuration with respect to surface and anion termination in the case of Type 3 surfaces. Fission product release will be highly anisotropic.

30. Third – identify new physical processes

31. Aims of the study Develop a robust computational model that can simulate UO 2 and fission gasses. It must replicate:  High temperature behaviour and defect energies  Good core-core repulsion for high energy collisions Apply this model to predict the evolution of bubbles with respect to:  Bubble size  Fission gas pressure  Temperature of material  Recoil energy

32. Transgranular fracture showing internal void, smaller gas bubbles and larger bubbles at grain boundaries Transgranular fracture showing aligned metal particles leading to a grain boundary All micrographs courtesy of Ian Ray ITU

33. Intergranular and Transgranular Fracture

34. Molecular dynamics of radiation enhanced helium re-solution Helium in bubbles can return to the crystal lattice via radiation-enhanced re-solution rather than thermal resolution...But how does this actually work in practice? It is thought that high-energy fission fragments 'knock out' helium atoms from bubbles leading to resolution.

35. What Bubbles? Several different bubble sizes and shapes have been investigated:  Octahedra constructed from (111) surfaces  Infinite pores from (110) surfaces  Spheres  Larger 'infinite' slab surfaces In UO 2 the morphology of the bubbles is roughly spherical but (111) surfaces are observed (which also dominate equilibrium voids).

36. MD Simulation of 5 keV U Recoil Event sequence: Ballistic phase. Thermal spike. Displacement damage interacts with the He bubble disrupting the bubble/lattice interface. Beginning of recovery phase.

37. MD Simulation of 5 keV U Recoil Event sequence: Ballistic phase and thermal spike are not seen. Displaced lattice ions interacts with the He bubble disrupting the bubble/lattice interface. He “leaks” into the damaged (partly disordered) lattice.

38. MD Simulation of 5 keV U Recoil Event sequence: Ballistic phase. Thermal spike. Lattice ions are displaced into the bubble. UO 2 units are relocated across the bubble facilitating the overall movement of the bubble.

44. Why is this exciting? Physics behind this mode of radiation enhanced resolution is fundamentally different to what has been proposed previously. May explain some 'anomalous' terms in bubble migration models. More accurate and confident modelling leads to less conservatism in fuel performance codes.

46. Directions of Further Work Long timescale dynamics of bubble migration. He migration along dislocations. 'Phase diagram' of the bubbles as a function of temperature, He pressure and displacement cascade energy. Examine Xe gas behaviour as well – Xe adopts solid structures in fission gas bubbles. Aim to aid in reducing conservatism.

47. Summary A simple computational model has been used to generate structure (and defect structure) property composition relationships. Correlated experimental data with physical models (filled in some gaps and work out what’s missing). Identified computational variations close to surfaces (pointed the way for experimental investigations). Developed new physical models that underpin phenomena (worked out what bit actually matters). Need to use a range of computational techniques to underpin and generate the defect property relationships. Imperial College OF SCIENCE, TECHNOLOGY AND MEDICINE