1. Development of analytical bond- order potentials for the Be-C-W-H system C. Björkas, N. Juslin, K. Vörtler, H. Timkó, K. Nordlund Department of Physics, University of Helsinki K. Henriksson Department of Chemistry, University of Helsinki P. Erhart Lawrence Livermore National Laboratory, Livermore, USA Joint TFE-SEWG - Material Migration and Material Mixing meeting

2. 2 Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Motivation We all want to understand what is going on in a fusion reactor Erosion, redeposition, formation of mixed materials,... Ideally we would be able to test every possible situation that could occur But, experiments are timely and difficult The interesting phenomena take place at the atom- level and at very small time scales Hence, they are hardly accessible to experiments Therefore Molecular Dynamics (MD) can be used

3. 3 Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas MD Approximations: Atoms treated as objects with no internal structure No electronic structure calculations done -May include electronic stopping and electron- phonon coupling as friction E.g. 41·10 6 atoms, 72 x 72 x 72 nm, 35 ps, 1024 processors = 36 h

4. 4 Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas MD algorithm Give atoms initial positions r 0 Calculate forces F = V(r) and a = F/m Move atoms: r = r + v t + 1 / 2 a t 2 + correction terms Advance time: t = t + t Repeat until done

5. 5 Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Potentials Only with a reliable interatomic potential can we model things correctly A potential must at least be able to reproduce: Ground state properties and non-equilibrium processes such as different phases, melting point, defect structures and energetics,... Otherwise we don't know what will happen:

6. 6 Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Potentials To model plasma-wall interactions, we need potentials for the Be-C-W-H system W-W, W-H, C-C and H-C made earlier [Brenner PRB 42 (1990) 9458 and Juslin et al. JAP 98 (2005) 123520] Now we develop Be-C, Be-Be, Be-H and Be-W

7. 7 Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Potentials Many different forms of potentials exist Simple pair potentials, EAM, MEAM, BOP We chose the BOP formalism It is based on Linus Pauling's bond order concept It can describe: The angular dependency of covalent bonds Breaking of bonds It has successfully been applied to many systems e.g. Si, C, SiC, W, Pt, Zn, ZnO, GaAs, GaN, Fe,...

8. 8 Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas BOP: Formalism Bond Order the strength of the bond between two atoms depends on the surroundings of the bond

9. 9 Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas BOP: Formalism

10. 10 Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas BOP: Construction There are all in all 11 parameters that must be specified Constructing a potential means finding suitable values for these Done by fitting to different experimental or DFT values of both ground state and hypothetical phases Not a trivial task!

11. 11 Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Beryllium Be has hcp as ground phase bcc and fcc may also exist Potential vs. experiments c Z = 12

12. 12 Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Beryllium Be Pauling plot

13. 13 Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Be-H The Be-H potential was fitted to molecules and H defects in Be Almost the right ground state interstitial H in Be Most of Be-H n molecules ok D and T are also modellable with this potential

14. 14 Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Be-C Be-C poorly known experimentally Only one phase observed, the ionic antifluorite Be 2 C Potential vs. experiments rbrb a

15. 15 Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Be-C We ensured that there are no false minima Cooled a random melt (Be:C = 2:1) to zero K The atoms crystallized into the antifluorite structure The correct Be 2 C really is the ground structure of the potential

16. 16 Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Be-W Complex phase diagram: Be 2 W, Be 12 W, Be 22 W seen

17. 17 Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Be 2 W Initial test of the Be 2 W phase: What becomes of the ideal hexagonal Laves structure? DFT: E coh = -7.03 eV/atBOP: E coh = -6.72 eV/at a = 4.46 Å a = 4.70 Å c/a = 1.64 c/a = 1.60

18. 18 Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Self sputtering 20 – 100 eV Be ion irradiation flux ~2·10 28 m -2 s -1, @ room T Sput. threshold 20 – 50 eV Yield agrees with extrapolated exp. Be does not amorphize

19. 19 Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas C irradiation of Be At 1500 K Layers of Be 2 C are formed close to the initial Be surface Sputtering threshold 20 - 50 eV

20. 20 Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Conclusions Potentials for pure Be, Be-H, and Be-C ready and tested Simulations with them already in process Be-W potential under development

21. 21 Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Joint TFE-SEWG Material Migration and Material Mixing meeting - Carolina Björkas Thank you.