## Radiation Damage

When atoms in a metal are set into motion through impacts by high energy neutrons or ions the electrons in the metal become excited. These electronic excitations exert a drag on the motion of atoms in the metal, which in the past has been approximated in molecular dynamics simulations by a classical friction force.

By applying Ehrenfest dynamics to a simple s-band tight binding model of Cu to large-scale simulations of radiation damage, the accuracy of the standard approach in classical molecular dynamics was tested for capturing the effect of electronic excitations through a linear damping term in the classical equations of motion. Our model was the simplest conceivable that had the essential ingredients of (a) an explicit quantum mechanical treatment of the electrons, coupled to the motion of the ions, which allowed the electrons to occupy excited states, (b) an explicit treatment of the classical equations of motion of the ions, with forces determined by the evolving electronic structure through Ehrenfest dynamics, (c) computational simplicity to enable us to simulate up to 30,000 metallic atoms fully dynamically. We showed that viscous damping is an excellent model for the average energy transfer rate from hot ions to cold electrons, but that it does not reproduce the direction of the damping force and hence it does not capture its true effect on the ionic dynamics. We showed that electrons acquired a thermal distribution of excited energies, which supports models in which the ions and electrons have two different temperatures. We also produced simple models of transition metals, which capture the densities of states in the vicinity of the Fermi energy for large-scale simulations of radiation damage in which electrons are treated explicitly. We also showed that the additional force on ions caused by excited electrons is not simply anti-parallel to the ion motion, as widely assumed in these classical MD simulations, and that its direction depends on the local atomic environment.

Collision sequences are inherently relatively low energy processes in metals, and therefore the energy loss is primarily through ionic processes rather than electronic excitation. However, we showed that the transfer of energy to electrons was maximized along close-packed directions, where focused collision sequences were formed as opposed to the more diffuse cascades formed along higher index directions.

We carried out simulations of channelling and discovered a remarkable resonance in the electronic charge on the channelling atom, accompanied by a peak in the electronic stopping power. Our work shows that earlier theoretical treatments of electronic excitations using dielectric function theory have missed the crucial physics that the crystal structure exerts a periodic potential in time as the ion travels along the channel, and this periodic potential is responsible for the resonances we observed.

“A simple model of atomic interactions in noble metals based explicitly on electronic structure”, A P Sutton, T N Todorov, M J Cawkwell and J Hoekstra, Phil. Mag. A 81, 1833-1848 (2001)

“A simple model for large-scale simulations of fcc metals with explicit treatment of electrons”, D R Mason, W M C Foulkes and A P Sutton, Phil. Mag. Letts., 90, 51-60 (2010).

“Electronic damping of atomic dynamics in irradiation damage of metals”, D R Mason, J Le Page, C P Race, W M C Foulkes, M W Finnis and A P Sutton. J. Phys.: Condens. Matter, 19 436209 (2007).

“Electronic excitations and their effect on the interionic forces in simulations of radiation damage in metals”, C P Race, D R Mason and A P Sutton, J.Phys.: Condens. Matter 21, 115702 (2009)

“An improved model of interatomic forces for large simulations of metals containing excited electrons”, C P Race, D R Mason and A P Sutton, New Journal of Physics 12 093049 (17pp), doi:10.1088/1367-2630/12/9/093049, (2010). Selected for inclusion in IOP Select on the basis of impact, novelty and significance.

“A new directional model for the electronic frictional forces in molecular dynamics simulations of radiation damage in metals”, C P Race, D R Mason and A P Sutton, J. Nucl. Mats., 425, 33-40 (2012) doi:10.1088/1367-2630/14/7/073009

“The treatment of electronic excitations in atomistic models of radiation damage in metals”, C P Race, D R Mason, M W Finnis, W M C Foulkes, A P Horsfield and A P Sutton. Reports on Progress in Physics 73 116501 (2010).

“Quantum mechanical simulations of electronic stopping in metals”, **D.R. Mason, C.P. Race, W.M.C. Foulkes****, M.W. Finnis, A.P. Horsfield ^{ }and A.P. Sutton, **Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 269, 1640-1645 (2011): doi:10.1016/j.nimb.2010.11.052

“Resonant charging and stopping power of slow channeling atoms in a crystalline metal”, D R Mason, C P Race, M H F Foo, A P Horsfield, W M C Foulkes and A P Sutton, New Journal of Physics, 14, 073009 (2012). DOI:10.1088/1367-2630/14/7/073009

“Quantum-classical simulations of slow heavy channelling ions in metals”, C P Race, D R Mason, M H F Foo, W M C Foulkes, A P Horsfield and A P Sutton, J. Phys.: Condens. Matter 25 (2013) 125501, doi:10.1088/0953-8984/25/12/125501, http://iopscience.iop.org/0953-8984/25/12/125501/

## Dislocation Dynamics

Kinks

A major challenge in the simulation of dislocation motion by a kink mechanism using molecular dynamics (MD) is that to see any dislocation motion unrealistically large stresses often have to be applied. In this we developed a new representation of a dislocation that allowed us to simulate its motion at realistic stresses.

Isolated kinks on thermally fluctuating ½<111> screw, <100> edge, and ½<111> edge dislocations in bcc iron were simulated under zero stress conditions using molecular dynamics. Kinks were seen to perform stochastic motion in a potential landscape that depended on the dislocation character and geometry, and their motion provided fresh insight into the coupling of dislocations to a heat bath. The kink formation energy, migration barrier, and friction parameter were deduced from the simulations. A discrete Frenkel-Kontorova-Langevin model was able to reproduce the coarse-grained data from MD at ∼10^{−}^{7} of the computational cost, without assuming an a priori temperature dependence beyond the fluctuation-dissipation theorem. Analytical results revealed that discreteness effects play an essential role in thermally activated dislocation glide, revealing the existence of a crucial intermediate length scale between molecular and dislocation dynamics. The model was used to investigate dislocation motion under the vanishingly small stress levels found in the evolution of dislocation microstructures in irradiated materials.

“Theory and simulation of the diffusion of kinks on dislocations in bcc metals”, T D Swinburne, S L Dudarev, S P Fitzgerald, M R Gilbert and A P Sutton, Phys. Rev. B 87, 064108 (2013). http://link.aps.org/doi/10.1103/PhysRevB.87.064108

Dislocation dynamics under shock loading

Under shock loading conditions dislocations can move at speeds approaching the shear wave speed. Under these circumstances it is essential to treat the time-dependence of the elastic fields explicitly, otherwise nonsensical results may be generated, such as the activation of dislocation sources ahead of the shock front. This work builds on earlier work of Markenscoff to construct the essential ingredients of an elastodynamic treatment, as opposed to treatments based on elastostatics, of the dynamics for straight edge dislocations under shock loading conditions.

“A dynamic discrete dislocation plasticity method for the simulation of plastic relaxation under shock loading”, B Gurrutxaga-Lerma, D S Balint, D Dini, D E Eakins, A P Sutton, Proc. R. Soc. A 469, 20130141 (2013). http://dx.doi.org/10.1098/rspa.2013.0141

## Grain Boundary Structure

** **Phase field models

Phase-field models have been applied in recent years to grain boundaries in single-component systems. The models are based on the minimization of a free energy functional, which is constructed phenomenologically rather than being derived from first principles. In single-component systems, the free energy is a functional of a “phase field,” which is an order parameter often referred to as the crystallinity in the context of grain boundaries, but with no precise definition as to what that term means physically. In this research we derived the phase-field model by Allen and Cahn from classical density functional theory first for crystal-liquid interfaces and then for grain boundaries. The derivation provided a clear physical interpretation of the phase field, and it shed light on the parameters and the underlying approximations and limitations of the theory. The research also suggested how phase-field models may be improved systematically.

“Phase field model of interfaces in single-component systems derived from classical density functional theory”, G Pruessner and A P Sutton, Phys. Rev. B 77, 054101 (2008).

Grain boundaries in strontium titanate

The configurational phase space of grain boundaries in multi-component systems is astronomically larger than in single component systems. In this work we developed a genetic algorithm to explore this space for grain boundaries in strontium titanate using an empirical potential. The structures were refined with density functional theory and their thermodynamic stability was assessed at different chemical potentials.

“Interatomic potentials for strontium titanate: an assessment of their transferability and comparison with density functional theory”, N A Benedek, A L-S Chua, C Elsaesser, A P Sutton and M W Finnis, Phys. Rev. B 78 064110 (2008).

“A genetic algorithm for predicting the structures of interfaces in multicomponent systems”, A L-S Chua, N A Benedek, L Chen, M W Finnis and A P Sutton, Nature Materials 9, 418-422 (2010) http://dx.doi.org/10.1038/NMAT2712. There was a news and views article by W Craig Carter in Nature Materials 9, 383-384 (2010).

“The structure of grain boundaries in strontium titanate: theory, simulation and electron microscopy”, Sebastian von Alfthan, Nicole A Benedek, Lin Chen, Alvin Chua, David Cockayne, Karleen J Dudeck, Christian Elsaesser, Michael W Finnis, Christoph T Koch, Behnaz Rahmati, Manfred Ruehle, Shao-Ju Shih, and Adrian P Sutton, Annu. Rev. Mater. Res. 40, 557–99 (2010).

## Polymers

In this research we addressed the problem of imposing rigid constraints between connected sites in a dynamic computer simulation. For two important cases, the linear and ring topologies, each site is connected to at most two nearest neighbors. The constraint matrix is then invertible in order n operations. We showed that, this being the case, a computational method based on a matrix inversion of the linearized constraint equations (MILC SHAKE) can be orders of magnitude faster than the simple SHAKE or RATTLE methods.

MILC SHAKE was then used to develop a new model for polymers which we called REVLD (Rigid, Excluded Volume, Langevin Dynamics). REVLD is similar to the coarse-grained, bead spring model for linear chains except that the inter-bead distance is rigidly constrained instead of using an inter-bead potential to encapsulate the connectivity. Static and dynamic results showed that REVLD accurately reproduces the single-chain behavior of real polymers known from experiment, theory, and published data from existing models. Additionally, a time step can be used that is at least comparable to simulations using a FENE potential without introducing any computational overhead for accessing longer time scale modes.

“Efficient constraint dynamics using MILC SHAKE”, A G Bailey, C P Lowe and A P Sutton, J. Comp. Phys., 227, 8949-8959 (2008)

“REVLD: A coarse grained model for polymers”, A G Bailey, C P Lowe and A P Sutton, Comp. Phys. Commun. 180, 594-599 (2009).

## Current Research Projects (July 2013)

** **Dynamic discrete dislocation plasticity (D3P) (with B Gurrutxaga-Lerma, D Balint, D Dini, D Eakins)

Dislocation mobilities in metals (with T Swinburne and S Dudarev)

Delayed hydride cracking in zirconium (with J Majevadia, D Balint, M Wenman and R Nazarov (MPIE))

Wear and failure of polycrystalline diamond composites (with M Tajabadi Ebrahimi, D Dini, D Balint and Element 6)

Polymer membranes for nanofiltration (with R Broadbent, J Spencer and A Mostofi)

Multi-scale molecular modelling of fluid flow through membranes (with J Muscatello, A Mostofi, E Muller and BP-ICAM)

Mechanical properties of ultra high molecular weight polyethylene (with A Hammad and L Iannucci)

Elastomer seals in hostile environments (with M Khawaja, A Mostofi and Baker Hughes)

## What I think about in the shower

I have been developing a metric for the 5D geometrical parameter space of grain boundaries. I have formulated a solution involving a direct product of two metric spaces and I am testing it on some examples.

I am also fascinated by the concept of stress at the atomic scale, and its relation to the continuum concept of stress. For example the usual virial expression for stress in an atomic assembly does not satisfy the equation of mechanical equilibrium in a continuum.

## Collaborators

Professor Peter Haynes of Materials and Physics, and Dr David Rugg of Rolls-Royce plc., Imperial College London, This is a TSM-CDT PhD project on the fundamentals of cold dwell fatigue in titanium, for which the student is Adam Ready., 2013

Dr Dini Mechanical Engineering, Dr D Balint Mechanical Engineering, and Dr Serdar Ozbayraktar of Element 6, Imperial College London, Supervision of TSM-CDT PhD project on failure of diamond composites for which the students is Mahdieh Tajabadi Ebrahimi., 2013

Dr David Curry, Technology Fellow at Baker Hughes, Imperial College London, PhD projects in the TSM-CDT on permeation of gases through elastomer seals for which the students are Mohammed Khawaja and Nicola Molinari., 2013

Professor Lorenzo Iannucci of Aeronautical Engineering, Imperial College London, This is a TSM-CDT PhD project on modelling the mechanical properties of ultra high molecular weight polyethylene, for which the PhD student is Ali Hammad, 2012

Professor Sergei Dudarev, Culham Centre for Fusion Energy, Supervision of TSM-CDT PhD project on dislocation mobilities in bcc metals, undertaken by Thomas D J Swinburne, 2022 - 2014

Dr Daniel Balint Mechanical Engineering; Dr Daniele Dini Mechanical Engineering; Dr Daniel Eakins Physics, Imperial College London, Supervision of TSM-CDT PhD project on elastodynamic treatment of dislocation dynamics, for which the student is Benat Gurrutxaga Lerma, 2011

Professor Joerg Neugebauer; Dr Roman Nazarov, Max Planck Institute for steel research, Calculation of elastic dipole tensor for hydrogen in zirconium using density functional theory. Part of the TSM-CDT PhD project of Jassel Majevadia., 2010

Dr Mark Wenman of Materials, Dr Daniel Balint of Mechanical Engineering, Imperial College London, Suprvisions of TSM-CDT PhD project on delayed hydride cracking in zirconium, 2010

Dr A Mostofi of Materials and Physics, Dr J Spencer of Materials and Physics, Professor A Livingston of Chemical Engineering, Imperial College London, Supervision of TSM-CDT PhD project on modelling os polymer membranes for nanofiltration, for which the student is Richard Boradbent., 2010

Dr C P Lowe, Van ’t Hoff Institute for Molecular Sciences, Universiteit van Amsterdam, Coarse grained modelling of polymers, 2006 - 2009

Dr T N Todorov, Queen's University Belfast; Professor Matthew Foulkes, Physics at Imperial College; Professor Mike Finnis Materials and Physics at , Imperial College; Dr Andrew Horsfield, Materials at Imperial College; Dr Daniel Mason, Physics at Imperial College; Mr Chris Race, Physics at Imperial College, Imperial College London and Queen's University Belfast, Electronic excitations during radiation damage of metals, 2005 - 2010

Professor David Cockayne, FRS, Oxford University, Modelling the structure and properties of intergranular films in strontium oxide, 2005 - 2009

## Research Staff

Benedek,N

Chua,A

Muscatello,J

Pruessner,G

## Research Student Supervision

Le Page,J, The transfer of energy between electrons and ions in solids

Race,CP, The modelling of radiation damage in metals using Ehrenfest dynamics