MULTISCALE MODELING OF BERYLLIUM IN FUSION ENVIRONMENT

KIT  – University  of  the  State   of  Baden-­Wuerttemberg   and  

INSTITUTE  OF  APPLIED  MATERIALS  (IAM-­AWP),  Atomistic  Modeling  and  Validation  Group,  Department  of  Metallic  Alloys  

MULTISCALE  MODELING  OF  BERYLLIUM  IN  FUSION   ENVIRONMENT

D.  Bachurin ¹ ,  V.A.  Borodin ^2,3 ,  M.G.   Ganchenkova ³ ,  A.  Möslang ¹ ,  Ch.  Stihl ¹ ,  P.  Vladimirov ¹

1

Karlsruhe  Institute  of  Technology,  Germany

2

NRC  Kurchatov Institute,  Moscow,    Russia

3

NRNU  MEPhI,  Moscow,    Russia

Outline

• Beryllium  in  Fusion  Reactor

• Be  as  plasma  facing  material

• Be  in  T-­breeding  pebble  bed

• Simulation  methods

• Atomic  displacement  cascades  in  Be  &  Fe

• Adsorption  and  desorption

• H ₂ dissociative  adsorption  on  (0001)Be

• Hydrogen  surface  adsorption  sites

• H ₂ adsorption  on  precovered surface

• Hydrogen  interaction  on  Be  surface

• Hydrogen  associative  desorption

• Surface  energy  modification  by  H

• Clean  surface  energies

• Surface  energy  with  hydrogen

• Faceting  of  H-­covered  bubble

• Conclusions

Poster  #  Po3-­57 Poster  #  Po4-­80

Poster  #  Po4-­79

Beryllium  in  fusion  reactor

ITER  Torus   cross-­section

TBM  ITER  – 2  t DEMO  – 300  t

Be:  680  m ²   or 12.5  t Be  is  considered  as  plasma  facing  material

and  as  effective   neutron  multiplier for  tritium   breeding  blanket  (HCPB)

Hydrogen  isotopes  and  impurities  are   implanted  into  Be  first  wall  tiles

He  and  T  are  produced  in  Be  under  neutron   irradiation  in  the  first  wall   and  blanket

Be  swelling   occurs  under  neutron  irradiation   at  elevated  temperatures.  T  and  He  are  

accumulated  inside  gas  bubbles

Accumulated  T  poses  serious  safety  and  

waste  disposal  problems

Beryllium  in  fusion  reactor

ITER  Torus   cross-­section

TBM  ITER  – 2  t DEMO  – 300  t

Be:  680  m ²   or 12.5  t Be  is  considered  as  plasma  facing  material

and  as  effective   neutron  multiplier for  tritium   breeding  blanket  (HCPB)

Hydrogen  isotopes  and  impurities  are   implanted  into  Be  first  wall  tiles

He  and  T  are  produced  in  Be  under  neutron   irradiation  in  the  first  wall   and  blanket

Be  swelling   occurs  under  neutron  irradiation   at  elevated  temperatures.  T  and  He  are  

accumulated  inside  gas  bubbles

Accumulated  T  poses  serious  safety  and   waste  disposal  problems

Understanding  of  atomic  scale  mechanisms  of  tritium  trapping  and  

release  is  necessary  for  assessment  of  radioactive  inventory  as  well  as  

for  prediction  of  tritium  behavior  under  accidental  conditions

Be  as  plasma  facing  material  in  fusion  reactor

Be

Co -­d ep osi tio n

n

n

n

E _n ≥ 2.7  MeV:

# 𝐵𝑒 𝑛, 2𝑛 𝐵𝑒 ^'

' 𝐵𝑒 → 2𝛼

E _n ≥ 0.71  MeV

# 𝐵𝑒 𝑛, 𝛼 ⁺ 𝐻𝑒

+ 𝐻𝑒 → 𝐿𝑖 ⁺ + 𝑒 ^/ + 𝜈̅ ₂

+ 𝐿𝑖 (𝑛, 𝑡)𝛼

Im plantation

Be  as  plasma  facing  material  in  fusion  reactor

Be

Co -­d ep osi tio n

n

n

n

E _n ≥ 2.7  MeV:

# 𝐵𝑒 𝑛, 2𝑛 𝐵𝑒 ^'

' 𝐵𝑒 → 2𝛼

E _n ≥ 0.71  MeV

# 𝐵𝑒 𝑛, 𝛼 ⁺ 𝐻𝑒

+ 𝐻𝑒 → 𝐿𝑖 ⁺ + 𝑒 ^/ + 𝜈̅ ₂

+ 𝐿𝑖 (𝑛, 𝑡)𝛼

Im plantation

• Helium  and  hydrogen  isotopes  are  produced  in  Be  by  nuclear  transmutations   as  well  as  implanted  from  the  hot  plasma.

• He  and  H  can  be  trapped  within  vacancies  and  vacancy  clusters  produced  in  

displacement  cascades  by  neutron  irradiation  and  facilitate  formation  of  gas  

filled  bubbles.  

Be  Pebble  Bed  of  T-­breeding  Blanket

He  +  H ₂ inlet

He  +  H ₂ +HT

outlet

Be  Pebble  Bed  of  T-­breeding  Blanket

He  +  H ₂ inlet

He  +  H ₂ +HT

outlet

Complexity  of  the  problem  (1):  Irradiation

Radiation  source:

Neutrons,  Plasma  Ions,   Fission/Transmutation  Products

Atomic  displacement  cascades Primary  damage:  PKA,  

point  defects,  clustering

He,  H,  transmutation   products

Irradiation  Environment:  

Temperature,  Stress Defect  clustering  &  

annihilation Diffusion Radiation  induced  

segregation

Voids Precipitate  

evolution Dislocation  loops  &  

network

Co-­evolution  of  all  µs  features Bubbles

R.  Stoller,  S.  Zinkle et  al.,   DOE  Workshop  on  Adv.  

Comp.  Mat.  Sci.  2004

Complexity  of  the  problem  (2):  Tritium

Adsorption,   Desorption Interaction  with

surface

Occlusion  / Absorption Diffusion,   Dissolution

Retention  / Release Trapping  on  

vacancies,   gas  bubbles,  

dislocations

Void  /  Bubble

Complexity  of  the  problem  (2):  Tritium

Adsorption,   Desorption Interaction  with

surface

Occlusion  / Absorption Diffusion,   Dissolution

Retention  / Release Trapping  on  

vacancies,   gas  bubbles,  

dislocations

Traps  evolve  (mutate)  

• during  irradiation  or  

• even  during  annealing

Void  /  Bubble

Outline

• Beryllium  in  Fusion  Reactor

• Be  as  plasma  facing  material

• Be  in  T-­breeding  pebble  bed

• Simulation  methods

• Atomic  displacement  cascades  in  Be  &  Fe

• Adsorption  and  desorption

• H ₂ dissociative  adsorption  on  (0001)Be

• Hydrogen  surface  adsorption  sites

• H ₂ adsorption  on  precovered surface

• Hydrogen  interaction  on  Be  surface

• Hydrogen  associative  desorption

• Surface  energy  modification

• Clean  surface  energies

• Surface  energy  with  hydrogen

• Faceting  of  H-­covered  bubble

• Conclusions

Simulation  methods

Density  Functional  Theory  (ab initio)

VASP  4.6  /  VASP  5.3

Generalized  Gradient  Approximation   (GGA)

Pseudopotentials:  

Plain  Augmented  Waves  (PAW)

Gamma  centered  Monkhorst-­Pack  k-­point   grid   ≥ 13x13x13

Energy  cutoff  =  450  eV

Ab initio Molecular  Dynamics  (VASP)

Time  step  0.3  fs

Run  duration  ~3000-­4000  steps  (~1  ps) Simulation  cell  size:  4x4x2  =  64  atoms Temperature:  200-­1000  K

k-­point  grid:  7x7x7 Energy  cutoff  250  eV

Atomistic  kinetic  Monte  Carlo  &  CE   code  MAPS

Molecular  Dynamics

Potential:  ABOP  (Bjorkas et  al.,  ver.I)  +   ZBL  repulsion

Simulation  cell:  

640,000  atoms

Periodic  boundary  conditions

Cascades:  

0,5  to  10  keV PKAs;;  10  cascades  at  each   energy  within  0.5-­3  keV

Т  =  600  К

Annealing  duration:  until  interstitials  run   away  sufficiently  far  from  vacancies  in   order  to  make  further  recombination   improbable  (typically  0.7  -­ 1  ns)

Barriers

Nudged  elastic  band  (NEB) Ab  initio  MD

Dimer  method  for  the  saddle  point  search

Approach:  Multiscale modelling

Length  scale

Ti m e   sca le

10^-­3 10^-­2 10^-­1 10⁰ 10¹ 10² 10³ 10⁴ 10^-­10

10^-­9 10^-­8 10^-­7 10^-­6 1x10^-­5

C_i  =  (K₀K_vs/K_ivK_is)^1/2 Quai-­Steady

State Ci=Cv=(K0/Kiv)^1/2 Linear  Buildup

Ci=Cv=K0t

Low  T,  low  sink  density  limit

Ci  ,  Cv  

Time,  s  C_i  C_v

τ1  =  (K0Kiv)-­1/2 τ2  =  (KisCs)-­1 τ3  =  (KvsCs)-­1

C_v  =  (K₀K_is/K_ivK_vs)^1/2

Rate  Equations,   Cluster  dynamics, Mesoscale  models Molecular  Dynamics

with  empirical interaction  potentials First  Principles

quantum  mechanical   electronic  structure

calculations

=  Ab  initio

Lattice kMC

Object kMC

Outline

• Beryllium  in  Fusion  Reactor

• Be  as  plasma  facing  material

• Be  in  T-­breeding  pebble  bed

• Simulation  methods

• Atomic  displacement  cascades  in  Be  &  Fe

• Adsorption  and  desorption

• H ₂ dissociative  adsorption  on  (0001)Be

• Hydrogen  surface  adsorption  sites

• H ₂ adsorption  on  precovered surface

• Hydrogen  interaction  on  Be  surface

• Hydrogen  associative  desorption

• Surface  energy  modification

• Clean  surface  energies

• Surface  energy  with  hydrogen

• Faceting  of  H-­covered  bubble

• Conclusions

Poster  #  Po3-­57

Atomic  displacement  cascades  in  Be  vs  Fe

Peak damage 650 7000

After  ballistic  stage 60 40

After  annealing  @  600  K 30 25

Cascade  stage 3  keV Be  è Be displ.

5  keV Fe  è Fe displ.

Be Fe

• More  extended  cascades  in  Be  with  lower  defect  density Poster  # Po3-­57

• Higher  recombination  rate  in  Be  after  ballistic  step

• After  annealing  nearly  the  same  number  of  defects  survived

Atomic  displacement  cascades  in  Be  and  Fe

Cascade  stage 3  keV Be  è Be displ.

5  keV Fe  è Fe displ.

Peak damage 650 7000

After  ballistic  stage 60 40

After  annealing  @  600  K 30 25

U _ZBL (r)  =  Z _p Z _t f _ZBL (r ⁾

Be:  Z _p Z _t =  16 Fe:  Z _p Z _t =  676

Weaker  interaction  =>  closer  collisions  =>  lower  scattering  cross-­

section

Large  angle  scattering  =  repulsive  potential

Poster  # Po3-­57

• More  info  on  interstitial  defects  in  Be  &  Zr in  Po4-­57

Outline

• Beryllium  in  Fusion  Reactor

• Be  as  plasma  facing  material

• Be  in  T-­breeding  pebble  bed

• Simulation  method

• Atomic  displacement  cascades  in  Be  &  Fe

• Adsorption  and  desorption

• H ₂ dissociative  adsorption  on  (0001)Be

• Hydrogen  surface  adsorption  sites

• H ₂ adsorption  on  precovered surface

• Hydrogen  interaction  on  Be  surface

• Hydrogen  associative  desorption

• Surface  energy  modification by  H

• Clean  surface  energies

• Surface  energy  with  hydrogen

• Faceting  of  H-­covered  bubble

• Conclusions

Poster  #  Po4-­80

H ₂ dissociative  adsorption  on  (0001)Be

Beryllium

-­2.5 -­2.0 -­1.5 -­1.0 -­0.5 0.0

-­0.4 -­0.2 0.0 0.2 0.4 0.6 0.8

-­0.27  eV -­0.12  eV 0.75  eV

E n er gy,  e V

Z,  Angström

chemisoption state

desorption  barrier:

1.02  eV adsorption  barrier:

0.75  eV

H ₂ dissociative  adsorption  on  (0001)Be

H ₂ adsorption  on  Be  (0001)

shallow  physisorption   state?

H ₂

Vacuum

Poster  #  Po4-­80

H  on  Be(0001)  surface:  Adsorption  sites

• Two  stable  adsorption  sites  for  hydrogen  (hcp and  fcc)  exist  at   (0001)  Be  surface  at  low  coverage

• Hydrogen  coverage  calculated  as  a  fraction  of  occupied  sites  

(1ML  – all  hcp &  fcc sites  occupied)

H  interaction  on  (0001)  Be

1NN

1NN

2NN

2NN

3NN

3NN

• Hydrogen  atoms  at  the  surface  prefer  to  stay  far  from  each  other

H ₂ adsorption  on  H  pre-­covered  surface

• There  is  no  hydrogen  adsorption  on  fully  precovered (0.5  ML)  Be  (0001)  surface

• One  H-­vacancy  is  also  insufficient  for  H ₂ adsorption

all  hcp sites

occupied

H ₂ adsorption  on  H  pre-­covered  surface

H  coverage  0.5ML  with  two  adjacent  vacancies;;  

T=200K

• Two  hydrogen  vacancies  on  H-­covered  surface  are  required  for  H ₂ adsorption.  

• The  adsorption  energy  barrier  on  pre-­covered  surface  is  higher  than  for  the   clean  surface.

• The  energy  of  incident  molecule  should  be  in  a  rather  narrow  range!

E _k (H ₂ )=2.0  eV No  adsorption

E _k (H ₂ )=4.6  eV Adsorption!

E _k (H ₂ )=8.2  eV

No  adsorption

Hydrogen  at  Be(0001)  surface:  Desorption

Surface  coverage  0.5ML (half  of  sites  occupied  by  H)

hcp sites

T=900K

No  desorption

Surface  coverage  1.0ML (all    sites  occupied  by  H)

hcp-­fcc sites

Desorption!

Hydrogen  at  Be(0001)  surface:  Desorption

Surface  coverage  0.5ML (half  of  sites  occupied  by  H)

hcp sites

33  fs

Surface  coverage  1.0ML (all    sites  occupied  by  H)

hcp-­fcc sites

22  fs

H ₂

Hydrogen  at  Be(0001)  surface:  Desorption

Surface  coverage  0.5ML (half  of  sites  occupied  by  H)

hcp sites

33  fs

Surface  coverage  1.0ML (all    sites  occupied  by  H)

hcp-­fcc sites

22  fs

H ₂

• At  surface  coverage  of  0.5  ML  severe  surface  reconstruction  is  observed,  but   no  hydrogen  desorption  occurs.

• At  surface  coverage  of  1.0  ML  immediate  associative  desorption  occurs.

⇒ In  equilibrium  with  H ₂ gas  the  maximum  critical  H  coverage  is  0.5  ML.

Outline

• Beryllium  in  Fusion  Reactor

• Be  as  plasma  facing  material

• Be  in  T-­breeding  pebble  bed

• Simulation  method

• Atomic  displacement  cascades  in  Be  &  Fe

• Adsorption  and  desorption

• H ₂ dissociative  adsorption  on  (0001)Be

• Hydrogen  surface  adsorption  sites

• H ₂ adsorption  on  precovered surface

• Hydrogen  interaction  on  Be  surface

• Hydrogen  associative  desorption

• Surface  energy  modification  by  H

• Clean  surface  energies

• Surface  energy  with  hydrogen

• Faceting  of  H-­covered  bubble

• Conclusions

Poster  #  Po4-­79

Be  principal  surfaces

The  lowest  surface  energy  has  

• basal  (0001) plane,  

• followed  by  prismatic  I 11700 and  

• pyramidal  II 27112   surfaces  

The  last  two  being  very  close  in  energy.

Adsorbed  hydrogen  modifies  surface  energy

Single  hydrogen  atom  adsorption  results  in  notable   decrease  of  surface  energy in  most  of  the  cases.

How  multiple  hydrogen  adsorption  would  affect  the  surface  energy?

Adsorbed  hydrogen  modifies  surface  energy

• At  low  coverage:  

Decrease  of  E _surf due  to   single  H  adsorption

• At  high  coverage:

Increase  of  E _surf due  to   H-­H  repulsion

⇒ Complex  modification   of  hydrogen-­filled  gas  

bubble  faceting

Hydrogen  bubble  faceting

0  ML

0.08  ML

0.125  ML

0.21  ML 0.23  ML

0.5  ML Equal  H-­coverage  for  all  faces  

was  assumed Poster  #  Po4-­79

Shape  of  gas  bubbles  in  Be

S.P.  Vagin et  al.  J.  Nucl.  Mater.  

258-­263 (1998)  719-­723 V.  Chakin,  Z.  Ostrovsky,    J.  Nucl.  

Mater.   307–311 (2002)  657–663

n-­irradiated  (He-­bubbles) H-­implanted  (H-­bubbles)

Equilibrium  shape  of  bubbles  (Wulff construction)

HRTEM  investigations  of  a  8 nm  bubble  in  a  pebble  irradiated  at  686 K:  the   bubble  with  a  regular  hexagonal  form  and  with  an  elongated  shape

Taken  from:  M.  Klimenkov et  al.  J.  Nucl.  Mat.  443  (2013)  409-­413.

“Comparison”  with  experiment

basal

prismatic  type  I prismatic  type  II pyramidal  type  I pyramidal  type  II

0  ML 0.23  ML 0.5  ML

Equilibrium  shape  of  bubbles  (Wulff construction)

“Comparison”  with  experiment

Taken  from:  S.P.  Vagin et  al.  J.  Nucl.  Mat.  258-­263  (1998)  719.

Cavities  in  hydrogen-­implanted  beryllium  after  annealing  for  15  min  at  600°C.

basal

prismatic  type  I prismatic  type  II pyramidal  type  I pyramidal  type  II

0  ML 0.23  ML 0.5  ML

Displacements  cascades  in  Be  are  more  extended  then  in  Fe  with   lower  defect  clustering

H ₂ adsorption  and  desorption  on  clean  and  H  precovered Be(0001)   surface  has  been  studied

Hydrogen  atom  is  adsorbed  without  barrier,  while  ~0.8  eV  should  be   overcome  during  H ₂   molecule  adsorption

Hydrogen  adsorption  is  completely  blocked  by  H-­coverage  of  0.5  ML At  least  two  vacant  sites  are  necessary  for  H ₂ adsorption  on  H  

precovered surface

There  is  a  critical  H  surface  coverage  of  0.5ML,  above  which  non-­

activated  H ₂ desorption  occurs

H  repulsion  on  the  surface  results  in  severe  surface  reconstruction Adsorbed  H  significantly  modifies  surface  energy  of  various  Be  

surfaces,  so  that  equilibrium  shape  of  H-­covered  bubble  is  changed   drastically

Conclusions

Thank  you  for  your  attention!