A critical review of the use of classical interatomic potentials for sputtering and sticking calculations

Transcription

1 CMS A critical review of the use of classical interatomic potentials for sputtering and sticking calculations Kai Nordlund Department of Physics and Helsinki Institute of Physics University of Helsinki, Finland

2 Contents 0. Levels of molecular dynamics 1. Brief review of interatomic potential philosophies 2. MD Sputtering and sticking calculations in nonfusion materials 3. MD Sputtering calculations in fusion materials - With some recent results 4. Conclusions Kai Nordlund, Department of Physics, University of Helsinki 2

3 Simulation team members Prof. Kai Nordlund Principal investigator Doc. Antti Kuronen Senior scientist Doc. Arkady Krasheninnikov Senior scientist Doc. Flyura Djurabekova* Senior scientist Doc. Krister Henriksson Fusion reactor mat s Doc. Jani Kotakoski Nanostructures TU Wien, Austria Dr Olli Pakarinen* Ion tracks Dr Juha Samela* Sputtering and cratering Dr Carolina Björkas Fusion reactor mat'ls (FZ Jülich, Germany) Dr Lotta Mether Molecule deposition M Sc Jussi Polvi Processing of cellulose M Sc Katharina Vörtler Fusion reactor mat'ls M Sc Eero Holmström Damage in Si M Sc Helga Timko* Particle physics mat'ls (CERN, Switzerland) M Sc Ville Jansson Fusion reactor mat'ls (SCK-CEN, Belgium) M Sc Aarne Pohjonen* Particle physics mat'ls M Sc Stefan Parviainen* Particle physics mat'ls M Sc Marie Backman* Nanostructures in silica (Univ. Tennessee, USA) M Sc Avaz Ruzibaev* Particle physics mat ls M Sc Andrea Meinander Fusion reactor mat ls M Sc. Ane Lasa Fusion reactor mat ls M Sc. Mohammad Ullah M Sc Konstantin Avchachov* GaN and ZnO Ion tracks M Sc Andrey Ilinov Nanomechanics M Sc Laura Bukonte Particle physics mat ls B Sc Aleksi Leino* Nanostructures in silica Ms Harriet Åhlgren Nanostructures

4 0. Levels of molecular dynamics By increasing order of realism: Coarse-grained MD - Multimillions of objects - Now popular in biophysics Classical (analytical potential) MD - Hundreds of millions of atoms - Dominating by scopes of use Tight-binding MD - ~ A few hundred atoms - Has been used for some 20 years Density-functional theory MD - ~ One hundred atoms - Use widely increasing now Time-dependent density functional theory MD - ~ A few tens of atoms - Practical uses limited so far Relevant for sputtering simulations But because of need for statistics, classical still dominates! Kai Nordlund, Department of Physics, University of Helsinki 4

5 1. Brief review of interatomic potential philosophies The key part of any molecular dynamics algorithm is getting the forces acting between atoms (objects): Get forces F = - V(r (i) ) or F = F(Ψ) and a = F/m In many cases this is actually the only physics input (rest is numerical mathematics) Albeit in irradiation physics: also electronic stopping Hence crucial to get interatomic potential V(r (i) ) right But can this be done?? Atomic world is quantum mechanical! Kai Nordlund, Department of Physics, University of Helsinki 5

6 1. Brief review of interatomic potential philosophies - High-energy repulsive potential The behavior of high-energy (E kin >> 10 ev) ions is dominated by the high-energy repulsive potential Collisions between the atomic cores determines ion penetration depths and linear-cascade physical sputtering Irradiation physics Chemistry and materials science This part is usually not a problem: ZBL universal potential accurate to within ~5%, and DFT or Hartree-Fock methods can determine it to ~1% [K. Nordlund, N. Runeberg, and D. Sundholm, Nucl. Instr. Meth. Phys. Res. B 132, 45 (1997)]. Kai Nordlund, Department of Physics, University of Helsinki 6

7 1. Brief review of interatomic potential philosophies - Ionic potentials For highly ionic materials, it is easy to devise a potential for long ranges: Coulomb interaction For short distances a repulsive potential needs to be added V 1 r) 4 These are very well-developed for equilibrium situations In non-equilibrium charge transfer changes charge states Charge-transfer potentials exist, but are poorly developed Not so relevant for fusion reactors, as main materials are metallic or carbon-based 1 2 ( Vrepulsive 0 q q r ( r) Kai Nordlund, Department of Physics, University of Helsinki 7

8 1. Brief review of interatomic potential philosophies - Metallic potentials For purely metallic materials, the so-called EAM-like potentials are highly successful EAM = Embedded Atom Method Common is that (almost all) can be written in the simple functional form Vi Vrepulsive ( rij ) Fi ( rij ) neighbours j Based on Effective-Medium Theory, can also be considered a (gross) simplification of Density-Funtional theory Idea: positively charged atom cores are embedded in the negative electron gas Electron density given by (r ij ), embedding energy by F(r ij ) Kai Nordlund, Department of Physics, University of Helsinki 8

9 1. Brief review of interatomic potential philosophies - Covalently bonded potentials For covalently bonded materials, a wide range of different approaches exist The angle between bonds is important in covalently bonded materials, so they have an angular term That is unfortunately about the only common feature Obvious approach: include a 3-body term for angles: V ( r) V ( r ij ) i, j 2 V3 ( rij, rik, ijk ) i, j, k where the function is constructed to have minima at the bonds between angles For instance Stillinger-Weber potential, molecular mechanics potentials, ReaxFF, Kieffer potentials Kai Nordlund, Department of Physics, University of Helsinki 9

10 Log Energy/bond 1. Brief review of interatomic potential philosophies - Covalently bonded potentials A better motivated approach is actually the bond-order potentials, which start from Pauling s theory of chemical bond order and construct a potential based on that Abell s idea -> Tersoff s first practical implementation -> Brenners extension to bond conjugation V V ( r ) b ( r, r, ) V ( r ) ; b i repulsive ij ijk ij ik ijk attractive ij ijk neighbours Conforms to Pauling s theory of bond strength weakening and bond length increasing with # of bonds Can also be motivated by 2 nd moment approximation of tight- binding => also metals! Kai Nordlund, Department of Physics, University of Helsinki 10 dimer 1 coordination of i GRA DIA SC DFT or expt. data BCC Bonding distance FCC

11 1. Brief review of interatomic potential philosophies - Covalently bonded potentials Many other concepts exist as well For instance: Kieffer-like potentials: fit each coordination separately Modified EAM: extend EAM with angular term - Coordination dependence often bad ReaxFF - Molecular-mechanics-inspired - Fit each application separately Bond-order potentials by Pettifor et al - Modern, but not so many fits yet Kai Nordlund, Department of Physics, University of Helsinki 11

12 1. Brief review of interatomic potential philosophies - The really hard part The really hard part is the potential fitting! It needs hard work and lots of effort, and always leads to compromises Computers cannot compromise humans needed Some testing (like melting point) cannot be automated Kai Nordlund, Department of Physics, University of Helsinki 12

13 1. Brief review of interatomic potential philosophies So what to make of this?? There is no unique way to say that one potential is superior to the other Some fits may be outright lousy (e.g. negative elastic constants), many potentials have false (experimentally nonexistent) minima - These can be ruled out But how to choose among good-quality fits? Comparison with experiments in application of interest!! But: then predictive power is lost And experiments not always reliable either Potential-to-potential comparisons! If functional forms are independent, can be quite good way! Kai Nordlund, Department of Physics, University of Helsinki 13

14 2. MD sputtering and sticking calculations Formalism 1: Independent simulations 5Å 5Å.. Border cooling Kai Nordlund, Department of Physics, University of Helsinki 14

15 2. MD sputtering and sticking calculations Formalism 2: cumulative simulations 5Å y x Kai Nordlund, Department of Physics, University of Helsinki 15

16 2. MD sputtering and sticking calculations Example of independent event Kai Nordlund, Department of Physics, University of Helsinki 16

17 2. MD sputtering and sticking calculations Example from cumulative bombardments Kai Nordlund, Department of Physics, University of Helsinki 17

18 2. MD sputtering and sticking calculations Pros and cons Single-impact simulations: + Corresponds best to low-fluence experiments (e.g. FIM) + Easy to set up and run + Trivially parallellizable for statistics - Surface morphology perfect and static, may not correspond to experiments Cumulative simulations: + Likely corresponds best to high-fluence experiments - Requires automatic analysis between stages - Not parallelizable for statistics - Most relevant case for fusion Kai Nordlund, Department of Physics, University of Helsinki 18

19 2. MD sputtering and sticking calculations Examples of reliability studies: Au Au irradiation of Au, EAM vs. CEM potential vs. experiment Conclusion obvious: CEM better [J. Samela et al, Nucl. Instr. Meth. Phys. Res. B 239, 331 (2005)] Kai Nordlund, Department of Physics, University of Helsinki 19

20 2. MD sputtering and sticking calculations Examples of reliability studies: Au Au 5 irradiation of Au, CEM potential vs. experiment Even cluster sputtering yields pretty well reproduced! Note the Y numbers [J. Samela et al, PHYSICAL REVIEW B 76, (2007)] Kai Nordlund, Department of Physics, University of Helsinki 20

21 2. MD sputtering and sticking calculations Examples of reliability studies: Si Ar irradiation of Si 6 potentials, none agrees perfectly But SWM, EDIP good [J. Samela et al, Nucl. Instr. Meth. Phys. Res. B 255, 253 (2007)] Kai Nordlund, Department of Physics, University of Helsinki 21

22 2. MD sputtering and sticking calculations Examples of reliability studies: sticking Sticking of CH3 radicals on dangling bonds on C Tight-binding MD showed good agreement Classical MD (Brenner potential) much worse [Träskelin et al, J. Appl. Phys. 93, 1826 (2003)] Kai Nordlund, Department of Physics, University of Helsinki 22

23 2. MD sputtering and sticking calculations Examples of reliability studies: C -> Si Potential-to-potential comparison of sticking, implantation and sputtering of C -> Si Tersoff-like potential (Erhart-Albe) vs. Kieffer potential ( Ludo ) Kai Nordlund, Department of Physics, University of Helsinki 23

24 2. MD sputtering and sticking calculations Be - Be self-sputtering ev Be ion irradiation flux ~ m -2 s room temperature Threshold ev Yield agrees with exp. Exp. values only at kev energies Be does not amorphize Like a typical metal Kai Nordlund, Department of Physics, University of Helsinki 24

25 2. MD sputtering and sticking calculations WC preferential sputtering D -> WC erosion yields vs. experiments Surface concentration changes with fluence: Experiment at 300 ev D on WC: 63 ± 10 at.% /(10 18 ions/cm 2 ) Simulation at 300 ev D on WC: crystalline: 57 ± 7 at.% /(10 18 ions/cm 2 ) amorphous: 110 ± 10 at.% /(10 18 ions/cm 2 ) Kai Nordlund, Department of Physics, University of Helsinki 25

26 2. MD sputtering and sticking calculations An aside: the incredible case of graphene Thanks to aberration-corrected TEM, every atom in graphene can be observed in situ during electron irradiation [Courtesy of Jannik Meyer and Jani Kotakoski] Kai Nordlund, Department of Physics, University of Helsinki 26

27 2. MD sputtering and sticking calculations An aside: the incredible case of graphene All defects and sputtering can be reproduced! DFTMD simulations, but classical also works pretty well Might be good to validate C potentials for fusion [Courtesy of Jannik Meyer and Jani Kotakoski] Kai Nordlund, Department of Physics, University of Helsinki 27

28 2. MD sputtering and sticking calculations What to make of the reliability issue? Classical MD is not fully reliably predictive in absolute numbers Except maybe if several independently potentials are available and can be crosschecked But at low energies more reliable than BCA Overall, why is there not more validation against experiments? Because it is difficult And scientifically; understanding mechanisms is more exciting than getting the numbers exactly right! Kai Nordlund, Department of Physics, University of Helsinki 28

29 3. MD sputtering calculations for fusion Background For fusion the materials of most interest are H, Be, W, C We have recently completed our potential for this full system Now getting statistics But as only one potential is available, we cannot crosscheck H He C W Be H He C W Be [WCH: Juslin et al, J. Appl. Phys. 98, (2005)] 2002 others [BeCWH: Björkas et al, J. Phys.: Condens. Matter 21 (2009) ; BeW: Björkas et al, J. Phys. Condens. Matter fast track 22 (2010) ] Kai Nordlund, University of Helsinki 29

30 3. MD sputtering calculations for fusion Collecting data from MD for ERO plasma simulations Linking MD to plasma (ERO) simulations Air aim in sputtering calculations now is to provide sputtering and reflection yields for different surface concentrations in the ternary Be-C-W system In principle all intermediate concentration points should be covered! - Is there a way to interpolate?? Kai Nordlund, University of Helsinki 30

31 3. MD sputtering calculations for fusion Swift chemical sputtering of beryllium: D irradiation of pure Be Our simulations agree with plasma experiments done at the PISCES-B facility at low energies At higher energies with the rest Sputtering is seen at 7 ev! Kai Nordlund, University of Helsinki 31

32 3. MD sputtering calculations for fusion Swift chemical sputtering of beryllium: D irradiation of pure Be A large fraction of Be is eroded as BeD molecules at low energies Chemical sputtering! This fraction decreases with ion energy This collaboration came out of a previous IAEA meeting Kai Nordlund, University of Helsinki 32

33 3. MD sputtering calculations for fusion Swift chemical sputtering of beryllium: D irradiation of Be Kai Nordlund, University of Helsinki 33

34 3. MD sputtering calculations for fusion Swift chemical sputtering of BeC D irradiation on Be 2 C Carbide layers will form on beryllium surfaces This is believed to decrease the sputtering of pure Be and pure C Noticeable in our simulations C Be Kai Nordlund, University of Helsinki 34

35 3. MD sputtering calculations for fusion Swift chemical sputtering of BeC D irradiation on Be 2 C Are there any chemical effects present? Yes, molecules are sputtered! Same mechanism as in pure Be: the swift chemical sputtering mechanism Preferential sputtering of Be 15 ev case interesting Here, but not at 20 ev, one CD 3 and one CD 4 are released - Statistical fluctuations Kai Nordlund, University of Helsinki 35

36 3. MD sputtering calculations for fusion Swift chemical sputtering of BeC Irradiation of Be 2 C Molecules sputtered: mostly BeD Kai Nordlund, University of Helsinki 36

37 3. MD sputtering calculations for fusion Swift chemical sputtering of BeC Irradiation of Be 2 C Be C D Kai Nordlund, University of Helsinki 37

38 3. MD sputtering calculations for fusion Swift chemical sputtering of BeC Irradiation of Be 2 C Be C D Kai Nordlund, University of Helsinki 38

39 3. MD sputtering calculations for fusion Swift chemical sputtering of BeC D irradiation of WC Molecular sputtering was also observed in WC sputtering simulations (e.g. at 300 ev): A lot of different small molecules Very few hydrocarbons, WC-molecules and single C preferred Is the mechanism the same as in Be and Be 2 C? Kai Nordlund, University of Helsinki 39

40 3. MD sputtering calculations for fusion Sputtering of WC D irradiation of WC He C W D Kai Nordlund, University of Helsinki 40

41 3. MD sputtering calculations for fusion Sputtering of WC D irradiation of WC Detailed analysis showed that the mechanism is essentially the dimer physical sputtering one Synergetic movement of atoms in low-energy heat spikes Physical in nature, mostly seen during Ar sputtering So, not the same as during the low energy bombardments of beryllium and beryllium carbide Karetta and Urbassek Appl. Phys. A 55 (1992) 364 At lower energies, however, mechanism will again be swift chemical sputtering Kai Nordlund, University of Helsinki 41

42 3. MD sputtering calculations for fusion Sputtering of W D irradiation of pure W As a sanity check for our potentials, we also ran simulations of D bombardment of pure W Experiments show zero sputtering below ~ 200 ev, so we should also get none otherwise we are in trouble with our swift chemical sputtering results! Fortunately we do get zero sputtering, for at least 2000 D ions up to 200 ev Higher energies running still, physical sputtering now observed at 1000 ev, in agreement with experiments Kai Nordlund, University of Helsinki 42

43 3. MD sputtering calculations for fusion Phase formation in MD Observations of phase formation Our interatomic potentials aim to describe all crucial phases of the materials involved correctly. Hence they should be able to reproduce the central part of the phase diagrams to the extent they are known Be-W C - Be Kai Nordlund, University of Helsinki 43

44 3. MD sputtering calculations for fusion Phase formation in MD C irradiation of Be Gratifyingly enough, we do see a lot of phases formed! Initial surface ev C ion irradiation flux ~ m -2 s 1500 K Layers of Be 2 C are formed! Kai Nordlund, University of Helsinki 44

45 3. MD sputtering calculations for fusion Phase formation in MD Random mixtures of Be and C When making cells of random Be- C composition, we do see phase separation of BeC starting from random mixtures! As expected from DFT calculations of phases and a single-intermetallic type phase diagram layered BeC BeC cell, mixed simulations) Kai Nordlund, University of Helsinki 45

46 3. MD sputtering calculations for fusion Collecting data from MD for ERO plasma simulations Ongoing sims Consider the observed BeC phase segregation In a macroscopically phase segregated region, a randomly cut surface will have regions of both types of phases in amounts proportional to the composition => it is sufficient to simulate sputtering and reflection from all existing pure and well-defined intermetallic/alloy phases, and use linear interpolation in between!(?) Kai Nordlund, University of Helsinki 46

47 3. MD sputtering calculations for fusion Collecting data from MD for ERO plasma simulations Ongoing sims Kai Nordlund, University of Helsinki 47

48 3. MD sputtering calculations for fusion Collecting data from MD for ERO plasma simulations Ongoing sims Kai Nordlund, University of Helsinki 48

49 3. MD sputtering calculations for fusion Conclusions BeCWH part BeCWH potential developed Swift chemical sputtering observed so far in: C Si Be BeC WC But not W Simulations to collect database for ERO input for low-e D bombardment in progress Kai Nordlund, University of Helsinki 49

50 Conclusions on interpolation The observation that phase segregation occurs even on MD timescales is actually very encouraging!! Instead of: Only existing phases needed*(?): * There are no known intermediate ternary phases Kai Nordlund, University of Helsinki 50

51 Interpolation scheme Linear interpolation between phases? But should solubility limits be considered? Be 22 W Be 12 W Be Be 2 W Be 2 C W W 2 C WC Kai Nordlund, University of Helsinki 51 C

52 CMS HIP Simulations of H and He effects in W Kalle Heinola, Krister Henriksson, Tommy Ahlgren, Katharina Vörtler and Kai Nordlund Department of Physics University of Helsinki, Finland

53 Multiscale calculation of H retention with Rate Equations: Hydrogen in the bulk is free (=mobile) or trapped E.g. system with hydrogen and monovacancies (V 1 ), diffusion (free particles ) source term (implantation ions, defects) trapping (R ab from MD) detrapping In real life: several defect types trap Hydrogen evolution of defects is time & temperature dependent HELSINGIN YLIOPISTO HELSINGFORS UNIVERSITET UNIVERSITY OF HELSINKI Heinola / ITPA-DSOL Meeting 53

54 Multiscale calculation of H retention with Rate Equations: Analytical method, real time & length scales, no limitations in the number of particles HELSINGIN YLIOPISTO HELSINGFORS UNIVERSITET UNIVERSITY OF HELSINKI Heinola / ITPA-DSOL Meeting 54

55 Multiscale calculation of H retention with Rate Equations: Analytical method, real time & length scales, no limitations in the number of particles System with hydrogen, vacancies (V n ), interstitials (I n ), grains, energetics from DFT sink strength and reaction radii from MD HELSINGIN YLIOPISTO HELSINGFORS UNIVERSITET UNIVERSITY OF HELSINKI Heinola / ITPA-DSOL Meeting source term from BCA, MD, experiments, etc 55

56 Multiscale calculation of hydrogen retention in W: Computational tools Energetics from first-principle calculations DFT (density functional theory) with VASP W properties: bulk bcc, fcc and A15 as well as W 2 molecule W point defect properties (mono-vacancy and SIA) W (100) surface reconstruction H diffusivity in W and on the (100) surface H detrapping from W mono-vacancy W(100) surface 111 SIA HELSINGIN YLIOPISTO HELSINGFORS UNIVERSITET UNIVERSITY OF HELSINKI Heinola / ITPA-DSOL Meeting Ahlgren, Heinola, et al, J. Appl. Phys. 107, (2010) Heinola, Ahlgren, J. Appl. Phys. 107, (2010) Heinola, Ahlgren, Phys. Rev. B 81, (2010) Heinola, Ahlgren, et al, Phys. Rev. B 82, (2010) 56

57 Multiscale calculation of hydrogen retention in W: Computational tools Energetics from first-principle calculations DFT (density functional theory) with VASP Defect properties in clusters with MD MD potential from DFT + experiments clustering & annihilation radii (R) W in W projected ranges with low energies thousands of W atoms Vacancy cluster properties Frenkel pair annihilation radius HELSINGIN YLIOPISTO HELSINGFORS UNIVERSITET UNIVERSITY OF HELSINKI Heinola / ITPA-DSOL Meeting Ahlgren, Heinola, et al, J. Appl. Phys. 107, (2010) 57

58 Multiscale calculation of hydrogen retention in W: Computational tools Energetics from first-principle calculations DFT (density functional theory) with VASP Defect properties in clusters with MD MD potential from DFT + experiments Initial damage profile with MD & BCA (binary collision approx.): damage profile vs. depth per implanted ion immediate SIA & vacancy clustering: I 1-5, V 1-10 HELSINGIN YLIOPISTO HELSINGFORS UNIVERSITET UNIVERSITY OF HELSINKI Heinola / ITPA-DSOL Meeting 58

59 Multiscale calculation of hydrogen retention in W: Computational tools Energetics from first-principle calculations DFT (density functional theory) with VASP Defect properties in clusters with MD MD potential from DFT + experiments Initial damage profile with MD & BCA (binary collision approx.): damage profile vs. depth per implanted ion HELSINGIN YLIOPISTO HELSINGFORS UNIVERSITET UNIVERSITY OF HELSINKI Final damage profile with Rate Equations t i+1 = t i + Δt diffusion trapping, detrapping clustering e.g. D implantation 30 RT, annealing for 24 hrs 59

60 Validation of the Multiscale method: Rate Equations vs. Implantation experiments Rate Equation results: Same input parameters as in the experiments: 5, 15, 30 kev/d and D/cm 2 D implantation 30 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) HELSINGIN YLIOPISTO HELSINGFORS UNIVERSITET UNIVERSITY OF HELSINKI Heinola / ITPA-DSOL Meeting Theory: Ahlgren, Heinola, et al. Phys. Rev. B (2010), submitted 60

61 Validation of the Multiscale method: Rate Equations vs. Implantation experiments 5 kev D in W Rate Equation results: Specification of each defect type Hydrogen trapping to each defect Majority of hydrogen in mono-vacancies (V 1 ) with all implantation energies High implantation energy number of larger defects increase HELSINGIN YLIOPISTO HELSINGFORS UNIVERSITET UNIVERSITY OF HELSINKI Heinola / ITPA-DSOL Meeting G+ρ is the only adjustable parameter (G+ρ is dislocation and grain boundary sinks) C is the inherent C impurity concentration [Plansee] Ahlgren, Heinola, et al., Phys. Rev. B (2010), submitted 61

62 Multiscale method: Rate Equations Retention & recycling Accumulation of D to the W surface in the course of implantation Hydrogen recycling! HELSINGIN YLIOPISTO HELSINGFORS UNIVERSITET UNIVERSITY OF HELSINKI Heinola / ITPA-DSOL Meeting Ahlgren, Heinola, et al., Phys. Rev. B (2010), submitted 62

63 Conclusions - W Bubble formation and trapping in W by H and He is dramatically different 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 Implantation and diffusion of D in W (@ RT) and grain boundaries and impurities included in the system 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 Kai Nordlund, University of Helsinki 63

64 Conclusion-conclusions Simulating sputtering yields is quite a challenge! But also lots of fun! Kai Nordlund, University of Helsinki 64