Molecular Dynamics Simulations of Cascades in Nuclear Graphite

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

3. Motivation Show how graphite behaves extremely differently to other carbon materials 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. 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 – Nordlundet al., Smith, Yazyevet al. • 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

5. Methodology

6. Swift Heavy Ions Cascades Defects Methodology 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.

7. Molecular Dynamics (MD) - a simulation of the movement of atoms Methodology START • 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 sp2 sheets described using Lennard- • Jones interaction • Environment Dependent Interaction Potential • – atom centred bond order was employed • drawing on an earlier Silicon EDIP method Initialise Positions and Velocities Analyse Data Update Positions and Velocities Calculate Forces on all atoms using Chosen Potential

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

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

10. Methodology Thermostats PKA region Fixed atoms Thermostats

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

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

13. Results – 250eV Cascade

14. Results – 1000eV Cascade

15. Results – 1000eV Cascade

16. Results

17. Split Interstitial Bi-pentagon I2 grafted intralayer bridge Results Latham, JP 20, 395220 (2008) α-β I2 interlayer bridge Latham, JP 20, 395220 (2008) Stone-Wales Latham, JP 20, 395220 (2008) β-β I2 bent interlayer bridge Telling & Heggie, Phil Mag. 87, 4797 (2007) Vacancy Latham, JP 20, 395220 (2008) Single interlayer Interstitial El-Barbary, et al, PRB 68, 144107 (2003) Grafted Interstitial Telling & Heggie, Phil Mag. 87, 4797 (2007) Latham, JP 20, 395220 (2008)

18. Results: Diamond

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

20. Properties: Results: Glassy Carbon • 100% sp2 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 Atoms can travel further without causing collisions because of the large number of vacant spaces. This causes a large number of atoms to be displacedover a greater distance.

21. Results: High Density Amorphous Carbon

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

23. Remarkable Result! Graphite does not behave like any other material Summary • 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.