a new embedded-atom method interatomic potential … · a new embedded-atom method interatomic...

A NEW EMBEDDED-ATOM METHOD INTERATOMIC POTENTIAL FOR TUNGSTEN-HYDROGEN SYSTEM

Li-Fang Wang1, Fei Gao2, Xiao-Lin Shu1, Guang-Hong Lu1*

1 School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, People’s Republic of China2 Department of Nuclear Engineering and Radiological Science, University of Michigan, Ann Arbor, MI, United States

OUTLINE

► Background: • An investigation of interatomic potentials for W-H system

► Potential formalism and parametrization

► Results and discussion• Basic Point defects• Interaction of H atoms with other defects (H atoms, SIAs, vacancies) in BCC W• Thermal properties: H diffusion

► Conclusions

An investigation of interatomic potentials for W-H system

► BOP-type potentials:• W-C-H_Juslin (2005)[Juslin N, Erhart P, Träskelin P, et al. Analytical interatomic potential for modeling nonequilibriumprocesses in the W–C–H system[J]. Journal of Applied Physics, 2005, 98(12): 123520.]

• W-H-He_Li (2012)[Li X C, Shu X, Liu Y N, et al. Analytical W–He and H–He interatomic potentials for a W–H–He system[J]. Journal of Nuclear Materials, 2012, 426(1): 31-37.]

► EAM-type potentials：• W-H-He_Bonny (2014)[Bonny G, Grigorev P, Terentyev D. On the binding of nanometric hydrogen–helium clusters in tungsten[J]. Journal of Physics: Condensed Matter, 2014, 26(48): 485001.]

A COMPARISON

Background

► Basic Properties

First Principles POT_Juslin POT_Li POT_Bonny1 POT_Bonny2

, 4.25 4.05 4.04 5.89 -17.65

, 1.00 1.04 1.18 3.65 -19.86

, 1.38 1.40 0.86 3.99 -19.48

∆tet-oct)

0.38 0.36 0.32 0.34 0.38

0.21 0.37 0.20 0.22 0.21

1.41 0.59 2.03 1.24 1.33

Position(H in V)

0.10 off OIS

0.08 off OIS

0.19 off OIS

Center of vacancy

0.35 off OIS

-4.74 -4.75 -4.75 NAN NAN

An investigation of interatomic potentials for W-H systemBackground

Too slow because of the long cutoff

OUTLINE




► Conclusions

Potential formalism and parametrization

► W-W interaction: two choices

5 4 3 2 15 4 3 2 1 0 1 2

30

2 20 1 2

10,

V( ) ,

( ) ( ) exp( )

( ) ( ),( )

0,

ZBL ij i

ij ij ij ij ij ij ij

ATPOT

ATPOT ij ij ij

ij c ij ij ij cij

ij

V r r

r a r a r a r a r ar a r r r

V

V r B b r r

r r c cr c r r rr

r r

2( ) ,0,

i d i d

i d

r r r rr r

( ) iF A

3

1

3

1

21 2

( ) ( ) ( )

( ) ( ) ( )

( )

n

i i ii

n

i i ii

F F

x a x x

x a x x

F x a x a x

A. EAM_WW_Marinica B. EAM_WW_Acland&Juslin

W-W interaction evaluationFP EAM2_Marinica EAM_ModAcland

3.56 3.49 3.636.71 6.48 6.836.93 6.83 6.8611.05 12.01 10.4811.68 12.73 10.4211.49 12.73 10.429.84 10.86 10.22

9.548 10.40 9.531.78 1.85 1.4

[Marinica M C, Ventelon L, Gilbert M R, et al. Interatomic potentials for modelling radiation defects and dislocations in tungsten[J]. Journal of Physics: Condensed Matter, 2013, 25(39): 395502.][Juslin N, Wirth B D. Interatomic potentials for simulation of He bubble formation in W[J]. Journal of Nuclear Materials, 2013, 432(1): 61-66.]

2 3 2 3

†

*

2 ( ) - ( )1

†

0†0

0

( ) ( )[ ( ) 2 ( )] [1 ( )]

[ 2 ] ( )

( ) 0.5{1 tanh[15( 0.9)]}

( ) 4.74(1 )

( ), 0.074 , 0.4899

H ij H H ij H

HH ij ij mol ij H H ij HH

k r k k r kHH H c ij

ij ij

amol ij

ij

r s r E r F s r

k e e f r

S r r

E r a e

r ra r nm

r

► H-H interaction2 3 2 3

5 5

2 ( ) - ( )1

26 94

0 0mod 0

0

53

2 86 7

9

1

[ 2 ] ( )

( 2 ) ( )( ),

( 0.5643 )( ),

( )

( )

ij ij

i i

i Hc

k r k k r kWH c ij

k r k rH i c i

HH

H

iH i i i

i

r rc i

k e e f r

k r e e f rr r r

r Ar r r

kF k k

k

f r e

*

*

=

( ) ( / )H H H

H H H

S

F F S

► W-H interaction

► identical transformation [Angelo J E, Moody N R, Baskes M I. Trapping of hydrogen to lattice defects in nickel[J]. Modelling and Simulation in Materials Science and Engineering, 1995, 3(3): 289.][Baskes M I, Sha X, Angelo J E, et al. Trapping of hydrogen to lattice defects in nickel[J]. Modelling and Simulation in Materials Science and Engineering, 1997, 5(6): 651.].



properties , , ,∆tet-oct)

Position(H in V)

Position1(H in V)

Position2(H in V)

reference 4.25 1.00 1.38 0.38 1.41 0.10off OIS 1.40 0.10

off OIS0.90off OIS -4.74

properties

reference 0.74 -2.95 -9.69 -0.47 -0.11 -0.04 0.01 0.000 -0.03 -0.05

► Database

► Fitting code

MATLAB

Nonlinear least-squares method (nonlinear data-fitting)

► Potential Profile

OUTLINE




► Conclusions

H point defectsResults and Discussion

► Basic PropertiesFirst

Principles POT_present POT_Juslin POT_Li POT_Bonny1 POT_Bonny2

, 4.25 4.00 4.05 4.04 5.89 -17.65

, 1.00 1.05 1.04 1.18 3.65 -19.86

, 1.38 1.40 1.40 0.86 3.99 -19.48

∆tet-oct)

0.38 0.35 0.36 0.32 0.34 0.38

0.21 0.22 0.37 0.20 0.22 0.21

1.41 1.12 0.59 2.03 1.24 1.33

Position(H in V)

0.10 off OIS

0.12 off OIS

0.08 off OIS

0.19 off OIS

Center of vacancy

0.35 off OIS

-4.74 -4.72 -4.75 -4.75 NAN NAN

Binding energy of two H atoms in different TIS of BCC W

First H

(7)

(4)

G(9)

F(8)E(6)

D(5)

C(3)

B(2)

A(1)

H

(10)

Interaction between H atoms in bcc WResults and Discussion

Interaction between H atoms and SIAs in bcc WResults and Discussion

Model： System with single [111] SIA

1~10 H atoms are added around the SIA randomly and then the system is energetically minimized

Repeating above process for 10000 times

The most stable configuration is chosen to calculate the binding energy of H atoms to SIA.

Interaction between H atoms and SIAs in bcc W

[111] SIA of BCC W

Results and Discussion

Configuration of the H atoms binding to SIA by POT_PresentThe [111] SIA structure predicted by Pot_Juslin

is unstable

Interaction between H atoms and single vacancy in BCC W

Configuration

Interaction between H atoms and vacancies in bcc WResults and Discussion

Consistent with FP results.[Ohawa,prb]

1~10 H atoms are added in the vacancy randomly and then the system is energetically minimized Repeating above process for 2000 times The most stable configuration is chosen to calculate the binding energy of H atoms to the single vacancy.


Interaction between H atoms and vacancy cluster in BCC W.

Hydrogen-vacancy cluster Size:

Number of vacancies: m=2~10

(Binding energies of vacancy clusters are tested.)

Number of H atoms: n=1~10*m

(Randomly placed in the vacancy clusters repeatedly until the most stable configuration is appeared)

Binding energy of vacancy cluster

Pot_Marinica

Interaction between H atoms and vacancy cluster in BCC W.


(n/m) (m/n)

Thermal diffusion of H atoms in bcc W

/

Experiment . 0.39 —

Pot_Present 7.15 0.25 0.22

Pot_Juslin 2.70 0.34 0.37

Pot_Bonny1 9.31 0.22 0.22

Pot_Bonny2 6.97 0.28 0.21

Results and Discussion

1000~3000K, 0.3% H atoms diffusion in bcc WArrhenius fit of diffusion data

OUTLINE




► Conclusions

Conclusions

► A new embedded-atom method (EAM) interatomic potential fortungsten-hydrogen system is developed ;

► The new W-H potential is thoroughly assessed compared with firstprinciples calculations and other interatomic potential results;

► Basic point defect properties of W-H system, interaction between Hatoms and other defects of bcc W, and thermal diffusion of H in W are allderived, and the new EAM potential perform reliable calculationscompared with first-principles’ prediction and other interatomic potentials’results.

The End

Thank you for your attention.

a new embedded-atom method interatomic potential … · a new embedded-atom method interatomic...

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