Molecular Dynamics Simulations of Cascades in Nuclear Graphite
H. J. Christie, D. L. Roach, D. K. RossThe University of Salford, UK
I. Suarez-Martinez, M. Robinson, N. Marks Curtin University, Perth, Western Australia
A. McKenna, M. Heggie Surrey University, UK
• Motivation
• Background
• Methodology
• Results:• Graphite
• Carbon Materials
• Conclusions and Further Work
Outline
• 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
• 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.
Methodology
Swift Heavy Ions Cascades Defects
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
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 sp2 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
MethodologyThe Environment Dependent Interaction Potential
• Developed for Pure Carbon Systems (Marks, 2000)
• Interactions vary according to the environment
• Accurate description of bond-making and breaking
U U2 ( rij ,Zi) U3 (rij ,rik ,,Zi)
MethodologyThe Ziegler-Biersack-Littmarck Potential
• Universally employed in ion implantation simulations
• Screened Coulomb potential
• High accuracy at small bond lengths
)(1
4 0
2
21 rr
ezzVzbl
Thermostats
Fixed atoms
PKA region
Thermostats
Methodology
Methodology
Thomson Problem
• Randomise initial direction of PKA
• Eliminate Human Bias
• Substantial number of results
• Produces 1400 cascades
Methodology
Left: 20 directionsToday: 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
Results – 250eV Cascade
Results – 1000eV Cascade
Results – 1000eV Cascade
Results
Single interlayer Interstitial
Bi-pentagon I2 grafted intralayer bridge
Grafted Interstitial
α-β I2 interlayer bridge
Stone-Wales
β-β I2 bent interlayer bridge
Latham, JP 20, 395220 (2008)
Latham, JP 20, 395220 (2008)
Latham, JP 20, 395220 (2008)
El-Barbary, et al, PRB 68, 144107 (2003)
Telling & Heggie, Phil Mag. 87, 4797 (2007)
Telling & Heggie, Phil Mag. 87, 4797 (2007)
Latham, JP 20, 395220 (2008)
Vacancy
Latham, JP 20, 395220 (2008)
Split Interstitial
Results
Results: Diamond
Ef = 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 atomsPKA energy 1KeV
Results: Diamond
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
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.
Results: High Density Amorphous Carbon
ResultsLow Den-Amor-Carbon High Den-Amor-Carbon Graphite
Graphite is Directionally Dependent
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
Further Work
• Further analysis of material after cascade
• High energy cascades for graphite (several MeV)
• Complete Thomson directions
• Comparison of different materials
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.