1. Molecular Dynamics Simulations of Cascades in Nuclear Graphite H. J. Christie, D. L. Roach, D. K. Ross The University of Salford, UK I. Suarez-Martinez, M. Robinson, N. Marks Curtin University, Perth, Western Australia A. McKenna, M. Heggie Surrey University, UK

2. Motivation Background Methodology Results: Graphite Carbon Materials Conclusions and Further Work Outline

3. Show how graphite behaves extremely differently to other carbon materials Motivation Create quality simulations using molecular dynamics in graphite Extend the life-span of current nuclear reactors Crucial information for next generation of nuclear reactors Understanding of processes occurring in irradiated graphite

4. Molecular Dynamics (MD) and Monte Carlo have a heritage that extends back to the Manhattan project (1946) Virtually no MD simulations of radiation damage in graphite Background WHY? Difficult to use MD in Carbon based materials due to its hybridized states and anisotropic layers Only in the last ten years or so have suitable MD potentials for Carbon been developed Previous work – Nordlund et al., Smith, Yazyev et al.

5. Methodology

6. Swift Heavy IonsCascadesDefects Primary Knock-On Atom passes straight through transferring energy to the surrounding atoms Primary Knock-On Atom (denoted in blue) passes through the cell colliding with atoms. Displaced atoms can then collide with other atoms in the cell Primary Knock-On Atoms now has a low energy but can still collide with atoms. Displaced atoms can make interstitials. Vacancies are created when an atoms is displaced. Methodology

7. START Calculate Forces on all atoms using Chosen Potential Update Positions and Velocities Initialise Positions and Velocities Analyse Data Many Potentials for Carbon: Tersoff & Brenner (1988) – short-ranged potentials inverts the density relationship between graphite and diamond Adaptive Interaction REBO (2000) – extension of Brenner potential. Long-ranged interactions between sp 2 sheets described using Lennard- Jones interaction Environment Dependent Interaction Potential – atom centred bond order was employed drawing on an earlier Silicon EDIP method Molecular Dynamics (MD) - a simulation of the movement of atoms Methodology

8. The Environment Dependent Interaction Potential Developed for Pure Carbon Systems (Marks, 2000) Interactions vary according to the environment Accurate description of bond-making and breaking

9. Methodology The Ziegler-Biersack-Littmarck Potential Universally employed in ion implantation simulations Screened Coulomb potential High accuracy at small bond lengths

10. Thermostats Fixed atoms PKA region Thermostats Methodology

11. Thomson Problem Randomise initial direction of PKA Eliminate Human Bias Substantial number of results Produces 1400 cascades

12. Methodology Left: 20 directions Today: 10 directions Up to 160, 000 atoms Side length of 105Å Variable time-step Edge thermostat Follows 5ps of motion Uniform sample of the unit sphere

13. Results – 250eV Cascade

14. Results – 1000eV Cascade

16. Results

17. Single interlayer Interstitial Bi-pentagon I 2 grafted intralayer bridge Grafted Interstitial α-β I 2 interlayer bridge Stone-Wales β - β I 2 bent interlayer bridge Latham, JP 20, 395220 (2008) El-Barbary, et al, PRB 68, 144107 (2003) Telling & Heggie, Phil Mag. 87, 4797 (2007) Latham, JP 20, 395220 (2008) Vacancy Latham, JP 20, 395220 (2008) Split Interstitial Results

18. Results: Diamond

19. E f = 7.33 eV Point defect: (100) split interstitial The cascade in diamond produces the (100) split interstitial which has the lowest formation energy ~ 7eV. Mainwood, Solid-state Electronics, 21 1431(1978) 32768 atoms PKA energy 1KeV Results: Diamond

20. Results: Glassy Carbon 100% sp 2 bonded High temperature resistance and high purity Low density and low electrical resistance Very hard material Low thermal resistance to chemical attack and impermeability to gases and liquids Properties: Atoms can travel further without causing collisions because of the large number of vacant spaces. This causes a large number of atoms to be displaced over a greater distance.

21. Results: High Density Amorphous Carbon

22. Results Low Den-Amor-Carbon High Den-Amor-Carbon Graphite Graphite is Directionally Dependent

23. Summary Remarkable Result! Graphite does not behave like any other material Even at high energies – little damage to final cell Directionally dependent – each cascade unique Graphite behaves completely differently to other carbon materials highlighting it’s uniqueness

24. Further Work Further analysis of material after cascade High energy cascades for graphite (several MeV) Complete Thomson directions Comparison of different materials

25. Acknowledgements This work was completed under the auspices of the Fundamentals of Nuclear Graphite Project, funded by the UK Engineering and Physical Science Research Council, Grant EP/I003312. The Authors would like to gratefully acknowledge the financial support of EPSRC during this work.