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.