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,

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

2Joint TFE-SEWG Material Migration and Material Mixing meeting

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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



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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. 41·106 atoms, 72 x 72 x 72 nm, 35 ps, 1024

processors = 36 h



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MD algorithm

Give atoms initial positions r0

Calculate forces F = V(r)and a = F/m

Move atoms: r = r + v t +1/2 a t2 + correction terms

Advance time: t = t + t

Repeat until done



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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:



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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



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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, ...



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BOP: Formalism

Bond Order ≈ the strength of the bond between two

atoms depends on the surroundings of the bond



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BOP: Formalism



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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!



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Beryllium

Be has hcp as ground phase bcc and fcc may also exist

Potential vs. experiments

c

Z = 12

BOP exp.

-3.32 eV -3.32 eVa 2.3 Å 2.29 Åc/a 1.57 1.57B 120 Gpa 116.8 Gpa

1560 K

Ecoh

Tmelt 1550±50 K

αV 38.2·10-6 1/K 29.0·10-6 1/K



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Beryllium

Be Pauling plot



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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

Interstitials BOP DFT I DFT IIBT (eV) 1.22 0.8 1.58O (eV) 1.46 unstable 1.79Ground state (T) (eV) 1.04 0.8 1.58

BT to O 0.43 0.38migration barrier (eV)

Molecules BOP DFT

Be-H

-1.3 -1.3

1.34 1.34

-1.65 -2.13

1.35 1.33

-1.31 -1.35

1.41 1.47

EC

(eV)

rb (Å)

Be-H2 linear

EC

(eV)

rb (Å)

Be-H3 D3h

EC

(eV)

rb (Å)



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Be-C

Be-C poorly known experimentally Only one phase observed, the

ionic antifluorite Be2C

Potential vs. experiments

rb

a BOP exp.

-5.34 eV -5.4 – -5.85 eVa 4.57 Å 4.34 ÅB 227 Gpa > 233 Gpa

3150±50 K 2670 K

Ecoh

Tmelt

αV 4.5·10-6 1/K 5.8·10-6 1/K



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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

2C really is the ground structure of the

potential



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Be-W

Complex phase diagram: Be2W, Be

12W, Be

22W seen



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Be2W

Initial test of the Be2W phase: What becomes of the

ideal hexagonal Laves structure?

DFT: Ecoh

= -7.03 eV/at BOP: Ecoh

= -6.72

eV/at

a = 4.46 Å a = 4.70 Å

c/a = 1.64 c/a = 1.60



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Self sputtering

20 – 100 eV Be ion irradiation flux ~2·1028 m-2s-1 , @ room T

Sput. threshold 20 – 50 eV Yield agrees with extrapolated exp.

Be does not amorphize



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C irradiation of Be

At 1500 K

Layers of Be2C are formed close

to the initial Be surface

Sputtering threshold 20 - 50 eV



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Conclusions

Potentials for pure Be, Be-H, and Be-C ready

and tested Simulations with them already in process

Be-W potential under development



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Thank you.

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,

Documents

material mixing meeting

usa joint tfesewg

h slide

w slide

potential slide

bond slide

formalism slide

h potential