Multiscale modelling of H and He in W or: 18 years of atomistic simulations of W K. Nordlund, J. Polvi, K. O. E. Henriksson, K. Heinola, T. Ahlgren, A. E. Sand, A. Lasa, C. Björkas, E. Safi, F. Djurabekova Department of Physics and Helsinki Institute of Physics University of Helsinki, Finland
Nuclear The materials ion beam simulation Particle physics groups materials in Helsinki Nanostructures Prof. Kai Nordlund Principal investigator Doc. Antti Kuronen Principal investigator Doc. Krister Henriksson Nuclear Materials Doc. Jani Kotakoski Nanostructures (TU Wien, Austria) Doc. Flyura Djurabekova Principal investigator Dr Carolina Björkas Fusion reactor mat'ls Dr Jussi Polvi Fusion reactor mat ls M Sc Andrea Sand Fusion reactor mat ls M Sc Mohammad Ullah Irradiation of GaN M Sc Harriet Åhlgren Graphene Dr Stefan Parviainen Particle physics mat'ls Dr Ville Jansson Particle physics mat'ls Dr Zhenxing Wang Particle physics mat'ls M Sc Laura Bukonte Fusion reactor mat ls M Sc Andrey Ilinov Nanomechanics M Sc Wei Ren Carbon nanostructures M Sc Fredric Granberg Dislocations M Sc Morten Nagel Nuclear materials M Sc Kostya Avchachov Irradiation of metals M Sc Aleksi Leino Nanostructures in silica M Sc Avaz Ruzibaev Particle physics mat ls M Sc Junlei Zhao Nanoclusters M Sc Yi-Nan Liu Fusion reactor mat ls M Sc Elnaz Safi Fusion reactor mat ls M Sc Alvaro Lopez Surface ripples M Sc Shuo Zhang Fusion reactor mat ls Mr Jesper Byggmästar Nanowires M Sc Anders Korsbäck Particle physics mat ls (CERN) M. Sc. Ekaterina Baibuz Particle physics mat'ls M Sc Mihkel Veske Particle physics mat'ls M Sc Simon Vigonski Particle physics mat'ls
Contents Background: overview of plasma-wall interaction physics and chemistry Quick overview of plasma-wall relevant simulation methods: DFT, MD, BCA, KMC Results: 1. Very first atomistic simulations of W from 1996 2. Difference in H vs. He bubble formation 3. Multiscale modelling of D trapping in W 4. Mechanism of W fuzz formation Conclusions Kai Nordlund, Department of Physics, University of Helsinki 3
Plasma-wall interactions in fusion reactors energies of impinging ions D+T fusion reaction in ITER and future fusion power plants will produce lots of 14.4 MeV neutrons and 3.5 MeV alphas H, D, T, He + plasma impurities Atom erosion The alphas & other ions & neutrals leaking from the plasma bombard the main wall He energy ~ 1 MeV Others ~ 10 kev 1 MeV Flux high Divertor is bombarded by D, T and He leaking from the plasma Energies ~ 1 ev 100 ev Flux very high, ~ 10 20 ions/cm 2 s Divertor [Thanks to Dr. Taina Kurki-Suonio for useful discussions on this issue] Kai Nordlund, Department of Physics, University of Helsinki 4
The rich materials science of plasma-wall interactions in fusion reactors Just for a single ion all of the below may result Crater Sputtered atom Adatom Amorphization Vacancy Interstitial Interstitial-like dislocation loop 3D extended defects Vacancy-like dislocation loop Implanted ion Kai Nordlund, Department of Physics, University of Helsinki 5
Plasma-wall interactions and materials science Crater Plasma Sputterring Adatom Plasma-wall interactions community Amorphization Interstitial-like dislocation loop Vacancy Vacancy-like dislocation loop Interstitial 3D extended defects Implanted ion Materials science community Kai Nordlund, Department of Physics, University of Helsinki 6
Plasma-wall interactions and materials science coming together Crater Amorphization Interstitial-like dislocation loop Plasma Tritium migration and desorption Vacancy Vacancy-like dislocation loop Interstitial 3D extended defects Implanted ion Sputterring Adatom Plasma-wall interactions community Now coming together Materials science community Kai Nordlund, Department of Physics, University of Helsinki 7
The rich materials science of plasma-wall interactions: high fluences In addition, for multiple ions i.e. prolonged irradiation many more things can happen, for instance: Spontaneous roughening/ripple formation [T. K. Chini, F. Okuyama, M. Tanemura, and K. Nordlund, Phys. Rev. B 67, 205403 (2003); Norris et al, Nature communications 2, 276 (2011)] Precipitate/nanocluster, bubble, void or blister formation inside solid [Bubbles e.g: K. O. E. Henriksson, K. Nordlund, J. Keinonen, D, Physica Scripta T108, 95 (2004); Nanocrystals e.g. 75S. Dhara, Crit. Rev. Solid State Mater. Sci. 32, 1 [2007)] Kai Nordlund, Department of Physics, University of Helsinki 8
The rich materials science of plasma-wall interactions: high fluences Phase changes, e.g. amorphization: Amorphous layer Highly defective layer Spontaneous porousness formation, fuzz - Highly fusion-relevant now, He -> W does it [http://vlt.ornl.gov/research/201 10119_highlight_doerner.pdf] Kai Nordlund, Department of Physics, University of Helsinki 9
Consequences of plasma-wall interactions for fusion How are all these relevant for fusion? Implantation => T stays in walls (retention) => VERY BAD Sputtering => erosion => BAD Sputter heavy impurities into edge plasma => cooling => GOOD Sputter heavy impurities into main plasma => cooling => BAD Sputtered molecules can migrate => redeposition => BAD Damage the material => worse heat conduction => BAD Damage the material => material becomes brittle, may crack=> BAD Produce gas bubbles => blisters => flaking => dust => BAD So it is very problematic from many points of view, and improved understanding is needed to understand and avoid harmful effects! Kai Nordlund, Department of Physics, University of Helsinki 10
Irradiation effects: What is needed to model all this: the multiscale modelling framework Sequential and concurrent multiscale modelling m Finite Element Modelling mm Rate equations Length μm BCA Discrete dislocation dynamics nm DFT Classical Molecular dynamics Kinetic Monte Carlo ps ns μs ms s hours years Time Kai Nordlund, Department of Physics, University of Helsinki 11
Methods DFT = Density functional theory Density functional theory (DFT) is the de facto workhorse of the so-called ab initio methods of computational chemistry and materials physics ab initio: the system is described quantum-mechanically bottom-up, (ideally) non-empirically DFT can be understood as a way to solve an approximation of the true Schrödinger equation Cf. classical simulations: the interaction between atoms is described by a potential function fitted to external data Really heavy computationally: scales as O(N 3 ) where N is the number of nuclei + electrons in the system => System sizes <~100 atoms Kai Nordlund, Department of Physics, University of Helsinki 12
Methods MD = Molecular dynamics MD is solving Newton s (or Lagrange or Hamilton) equations of motion to find the motion of a group of atoms Iterative technique over fs time step, limited in time to ~ ns Forces can be obtained classically or from DFT If classical, scales as O(N) => system sizes ~ millions atoms Normally in equilibrium, but special techniques to handle irradiation effects developed Adaptive time step, repulsive potentials; electronic stopping, etc Interatomic potential development crucial: cf. side talk by J. Polvi Kai Nordlund, Department of Physics, University of Helsinki 13
Methods BCA = Binary collision approximation The original way to treat ion irradiation effects on a computer Developed by Mark Robinson, ~1955 - Channeling was predicted by BCA before it was experimentally found! In BCA the collisions of an incoming ion are treated as a sequence of independent collisions, where the ion motion is obtained by solving the classical scattering integral Straight path between collisions Kai Nordlund, Department of Physics, University of Helsinki 14
Methods KMC = Kinetic Monte Carlo The long-time-scale damage relaxation phase after the collisional stage of irradiation can take microseconds, seconds, days or years This time scale is clearly inaccessible to MD Kinetic Monte Carlo (KMC) is able to handle all this Needs as input all rates and reactions in the system: diffusion rate, incoming ion rate, defect recombination reactions, Time moved forwards using -log RAND(0,1)/R where R is sum of all rates in the system => when fast rates vanish, simulation time speeds up by itself (big advantage to MD) Kai Nordlund, Department of Physics, University of Helsinki 15
Contents revisited Background: overview of plasma-wall interaction physics and chemistry Quick overview of plasma-wall relevant simulation methods: DFT, MD, BCA, KMC Results: 1. Very first atomistic simulations of W from 1996 2. Difference in H vs. He bubble formation 3. Multiscale modelling of D trapping in W 4. Mechanism of W fuzz formation Conclusions Kai Nordlund, Department of Physics, University of Helsinki 16
1. Surface effects in W First simulations of radiation effects in W In 1996-1997, we simulated effects of W self-irradiation of W to compare with the experimental vacancy distribution maps measured by field ion microscopy from the Seidman group 20, 30 kev W -> W Good agreement obtained in vacancy cluster distribution provided surface effects taken into account! Showed surface dominate defect production even at 30 kev! [Zhong, Nordlund, Ghaly, Averback, Phys. Rev. B 58 (1998) 2361] Kai Nordlund, Department of Physics, University of Helsinki 17
2. Bubble formation and blistering in W: Difference of H and He bubble formation in W Depth of blisters vastly different. H: at micrometer depths He: close to projected range (<100 Å) Why is this? We considered many possibilities: Damage different: no, since also non-damaging irr. produces bubbles!! Difference in diffusivity: no, about the same Thermal gradients: no Different kinds of W samples in experiments: no But how about differences in trapping behaviour? Kai Nordlund, University of Helsinki 18
2. Bubble formation and blistering in W: H vs. He self-trapping: energetics results MD energetics of H-H or He-He pair: Most important features confirmed by DFT H-H He-He 4 ev non-binding 1 ev binding < 0.2 evbinding Almost no binding for H-H, but strong (1 ev) binding for He-He! Explains why H and He bubble formation depths so different! [K. O. E. Henriksson, K. Nordlund, A. Krasheninnikov, and J. Keinonen, Appl. Phys. Lett. 87, 163113 (2005)] Kai Nordlund, University of Helsinki 19
2. Bubble formation and blistering in W: He bubble depths We also used Kinetic Monte Carlo (KMC) simulations of He migration in W to check whether He bubble depths obtained with self-trapping are the same as in experiments Results: T(K) Our KMC Expt. Reference 300 100 Å 62 Å Nicholson and Walls 1978 2370 2200 Å 0 5000 Å Chernikov and Zakharov 1989 Reasonable agreement! [K. O. E. Henriksson, K. Nordlund, A. Krasheninnikov, and J. Keinonen, Appl. Phys. Lett. 87, 163113 (2005); K. O. E. Henriksson, K. Nordlund, A. Krasheninnikov, and J. Keinonen, Fusion Science & Technology 50, 43 (2006)] Kai Nordlund, University of Helsinki 20
2. Bubble formation and blistering in W: Animation of KMC bubble formation He bubble formation: mobile atoms red, immobile He in clusters orange, large clusters green or blue [K. O. E. Henriksson, K. Nordlund, A. Krasheninnikov, and J. Keinonen, Fusion Science & Technology 50, 43 (2006)] Kai Nordlund, University of Helsinki 21
2. Bubble formation and blistering in W: Near-surface blistering of W by He MD simulation of 100 ev He -> W Resembles W fuzz. Published before fuzz was observed! More on this later [K. O. E. Henriksson, K. Nordlund, and J. Keinonen, Nucl. Instr. Meth. Phys. Res. B. 244, 377 (2005)] Kai Nordlund, University of Helsinki 22
3. Physics of H and He effects in W Traps for T in W divertors Neutrons induce damage also in the W divertor This damage may bind T coming from the fusion plasma Retained T limits the usage lifetime of ITER (700 g limit) Hence it is important to know the nature of the damage in W, how much T it can retain, and how it can be taken out To this end, we are doing multiscale modelling of the damage and T binding in W Kai Nordlund, University of Helsinki 23
3. Physics of H and He effects in W DFT, BCA, MD + Rate equations multiscale modelling of H in W diffusion source term trapping detrapping energetics from DFT sink strength and reaction radii from MD source term from BCA, MD, experiments, etc Kai Nordlund, University of Helsinki 24
3. Physics of H and He effects in W Rate equations: comparison with experiments Rate Equation results: Same input parameters as in the experiments: 5, 15, 30 kev/d and 5.8 10 16 D/cm 2 D implantation 30 mins @ RT, annealing 24 hrs Excellent agreement with the experiments Experimental: Ahlgren, Heinola, et al., Nucl. Instr. Meth. B, 249, (2006) Heinola, Ahlgren, et al.,phys. Scripta, T128 (2007) Theory: Ahlgren, Heinola, et al. J. Nucl. Mater. 427 (2012) 152 Kai Nordlund, University of Helsinki 25 25
3. Physics of H and He effects in W Rate equations: determination of D locations The rate equations allow determining where the D is Most D in hydrogen 5 kev D in W in mono-vacancies (V 1 ) at all implantation energies Ahlgren, Heinola, et al. J. Nucl. Mater. 427 (2012) 152 Kai Nordlund, University of Helsinki 26
4. W fuzz The W fuzz issue In 2008 Baldwin and Doerner showed with a linear plasma machine that W when irradiated by ~ 100 ev He (typical fusion reactor energy) forms a highly underdense porous layer, a fuzz Could be very harmful in fusion reactors: Enhances electrical arcing Wall properties change [Baldwin, Doerner, Nucl. Fusion 48 (2008) 035001] Kai Nordlund, University of Helsinki 27
4. W fuzz Multiscale modelling of W fuzz growth To examine this we employed 3 different simulation methods: 1. Density Functional Theory (DFT): Quantum mechanical simulations of He in W to formulate He-W interatomic potential [Juslin and Wirth] 2. Classical Molecular Dynamics (MD) to simulate He irradiation of W 3. Kinetic Monte Carlo of the He migration and bubble formation in W μm Length nm DFT Molecular dynamics Kinetic Monte Carlo ps ns μs ms s Kai Nordlund, University of Helsinki 28
4. W fuzz Observations from MD From the MD simulations (2004+ 2013) we discovered the following physical effects: The surface layer thickness grows roughly as ffffffe = ttte Key processes during implantation: Bubble formation Dislocation loop punching from bubbles leading to surface growth Bubble rupture leading to He loss Only about 0.4 of He implanted, rest reflected Reflected He did not modify material significantly [A. Lasa et al, NIM B 303, 156 (2013)] [K. O. E. Henriksson et al, Physica Scripta T108, 95 (2004)] Unfortunately MD flux way too high compared to experiments Kai Nordlund, University of Helsinki 29
4. W fuzz Development of KMC model These observations from MD were used to develop a new Object KMC model Basic objects: mobile He, trapped He, He in bubbles Simulation cell made to have a variable height h(x,y) on a grid New incoming ions x z BULK y W box Periodic boundaries. Kai Nordlund, University of Helsinki 30
4. W fuzz Results: outcome of typical fuzz OKMC simulation: cross-sectional view Note factor of 10 aspect ratio: cell much wider than high! Kai Nordlund, University of Helsinki 31
4. W fuzz Results: outcome of typical fuzz OKMC simulation: 3D bubble view Kai Nordlund, University of Helsinki 32
4. W fuzz W fuzz On very high fluence irradiation, this leads to the formation of the W fuzz Fuzz layer thickness scales as tttt! Good agreement with experiments! (other W grade) [A. Lasa, S. K. Tähtinen and K. Nordlund, EPL 105, 25002 (2014)] Kai Nordlund, University of Helsinki 33
4. W fuzz Whence the tttt dependence? Surface roughnening! We could rule out diffusion as reason to the tttt dependence: process is trap-dominated. Idea: as the surface roughness increases, bubbles can also rupture to the side. This would increase the rupture probability and hence slow down the growth => tttt? To test this, we made a set of simulations without the surface grid (1x1 grid) i.e. not allowing for surface roughness. Result: only the surface that can roughen (10x10 grid) shows the tttt growth => surface roughening explains the tttt dependence! [A. Lasa, S. K. Tähtinen and K. Nordlund, EPL 105, 25002 (2014)] Kai Nordlund, University of Helsinki 34
Conclusions Bubble formation in W by H and He is dramatically different due to different self-trapping behaviour Experiments on D trapping can be reproduced by a multiscale modelling scheme Combining results from DFT+MD+BCA/MD with an analytical set of Rate Equations for realistic length and time scales Model and experiments on 5, 15 and 30 kev/d implantations and with 5.8x10 16 D/cm 2 were shown to be in excellent agreement W fuzz formation mechanism is explained He bubble growth, loop punching leading to surface roughening and enhanced bubble rupture on rough surfaces Kai Nordlund, University of Helsinki 35
Further reading Recent review: K. Nordlund, C. Björkas, T. Ahlgren,, A. Lasa, and A. E. Sand, http://www.acclab.helsinki.fi/~knordlun/pub/nor13bpreprint.pdf Multiscale modelling of plasma-wall interactions in fusion reactor conditions, J. Phys. D: Appl. Phys. 47, 224018 (2014), Invited paper for Special Issue on Fundamentals of plasma-surface interactions. Tutorial lectures on MD, plasma-wall simulation methods and radiation effects (including full course on radiation effects): http://www.acclab.helsinki.fi/~knordlun/ -> Tutorial material Kai Nordlund, University of Helsinki 36