Multiscale Modelling of Microstructure Evolution under Radiation Damage of Steels Based on Atomistic to Mesoscale Methods

(1)

Centre

of

Excellence

for

Nuclear

Materials

Workshop

Materials

Innovation

for

Nuclear Optimized

Systems

December 5-7, 2012, CEA – INSTN Saclay, France

Christophe DOMAIN

EDF R&D (France)

Multiscale Modelling of Microstructure Evolution under

Radiation Damage of Steels Based on Atomistic to

Mesoscale Methods

Workshop

organized

by:

Christophe

GALLÉ,

CEA/MINOS,

Saclay

–

[email protected]

(2)

Workshop

Materials

Innovation

for

Nuclear

Optimized

Systems

December 5-7, 2012, CEA – INSTN Saclay, France

Multiscale Modelling of Microstructure Evolution under Radiation Damage

of Steels Based on Atomistic to Mesoscale Methods

Christophe DOMAIN

1, 2

1_{EDF R&D - MMC (Moret sur Loing, France)} 2

EDF-CNRS joint laboratory EM2VM (Study and Modeling of the Microstructure for Ageing of Materials)

Structural metallic materials used in nuclear facilities are submitted to irradiation which induce the creation of large amounts of point defects, which leads to modifications of the microstructure and the mechanical properties. In nuclear power plants, the main structural materials are: the pressure vessel (ferritic steels), the internal structure (austenitic steels).

In order to simulate the microstructure evolution with the objective to predict it, multiscale modelling tools are developed (Fig. 1). For this purpose different simulation methods are used and developed in order to treat the different physical phenomena occurring at different time scales and length scales:

ab initio, classical molecular dynamics, kinetic Monte Carlo, dislocation dynamics, phase field [1]. These simulations are very CPU demanding and take advantage of the development of High Performance Computing machines.

Finite elements

ab initio

Molecular dynamics

Mesoscopic

Multi-scale

modelling

1nm3

0 - ps

ns (10-30nm)3

cm3

µm3

h-year s - h

(30-100nm)3

m3

40 years

Micro-macro

Dislocation dynamics



Finite elements

ab initio

Molecular dynamics

Mesoscopic

Multi-scale

modelling

1nm3

0 - ps

ns (10-30nm)3

cm3

µm3

h-year s - h

(30-100nm)3

m3

40 years

Micro-macro

Dislocation dynamics



 



EPJ Web of Conferences 51, 02004 (2013) DOI: 10.1051/epjconf/20135102004

(3)

Workshop

Materials

Innovation

for

Nuclear

Optimized

Systems

December 5-7, 2012, CEA – INSTN Saclay, France

Fig. 1: Multiscale modelling scheme applied within the PERFORM-60 project to the pressure vessel and internal material microstructure.

The microstructure evolution under irradiation is obtained starting from the neutron spectrum to obtain the primary damage (displacement cascades), followed by the evolution of the point defects formed and their accumulation (Fig. 2).

Spectre de neutron

1.E+08 1.E+09 1.E+10 1.E+11 1.E+12

1.E-08 1.E-06 1.E-04 1.E-02 1.E+0 0 1.E+0 2 F lu x (n /c m2 /s ) 1.E-08 1.E-05 1.E-02 1.E+01 1.E+04

1E-051E-041E-031E-021E-011E+00 1E+01 EPKA (MeV)

P K A F lu x ( P KA /µ m 3/M e V /s ) PWR Neutron spectrum PKA spectrum Primary damage Short term evolution Interactions defects -dislocations Exper. resolvable defects

Spectre de neutron

1.E+08 1.E+09 1.E+10 1.E+11 1.E+12

1.E-08 1.E-06 1.E-04 1.E-02 1.E+0 0 1.E+0 2 F lu x (n /c m2 /s ) 1.E-08 1.E-05 1.E-02 1.E+01 1.E+04

1E-051E-041E-031E-021E-011E+00 1E+01 EPKA (MeV)

P K A F lu x ( P KA /µ m 3/M e V /s ) PWR 1.E-08 1.E-05 1.E-02 1.E+01 1.E+04

1E-051E-041E-031E-021E-011E+00 1E+01 EPKA (MeV)

P K A F lu x ( P KA /µ m 3/M e V /s ) PWR Neutron spectrum PKA spectrum Primary damage Short term evolution Interactions defects -dislocations Exper. resolvable defects

Fig. 2: Microstructure modelling under irradiation.

The point defects created (vacancy and self interstitials) under irradiation often interact with the solute elements present in the materials. Solutes can precipitate and/or segregate on point defect clusters (loops or voids) or extended defects (dislocations, grain boundaries). These modifications of the microstructure affect directly the mechanical properties of the materials. Thus, modelling should take into account the most important solute elements in the chemical composition of the industrial alloys.

For the pressure vessel steels (for which an important international efforts is done in particular thanks to the PERFECT [2] and PERFORM-60 european projects) the evolution of the microstructure of dilute Fe alloys as complex as Fe-CuNiMnSiP-C under irradiation are modelled using a multiscale approach based on ab initio, molecular dynamics and kinetic Monte Carlo (KMC) simulations. In these atomic KMC simulations, both self interstitials and vacancies, isolated or in clusters, as well as carbon atoms are modelled [3]. The short term evolution of the microstructure is simulated. The medium to long term evolution of the microstructure is obtained by object KMC and cluster dynamics, considering a “grey” material. The interaction of some of these defects with dislocations are characterised by molecular dynamics in order to be used in mesoscopic dislocation dynamics. A similar approach is developed for austenitic materials modelled by a concentrated FeCrNi alloy (

γ

-Fe70Cr20Ni10). The thermal ageing (without irradiation) of FeCr alloys will also be presented.

In the framework of the european projects dedicated to the pressure vessel steels and the austenitic steels, the multiscale modelling methods of the microstructure have been capitalised within two tools (RPV and INTERN) [4].

References

[1] C. S. Becquart, C. Domain, Metallurgical and Materials Transactions A 42 (2011) 852. [2] Spetial Issue: PERFECT project. Journal of Nuclear Materials, 406 (2010).

(4)

Multiscale Modelling of

Microstructure Evolution

under Radiation Damage of

Steels Based on Atomistic

to Mesoscale Methods

C. Domain

1 _{, C.S. Becquart}

2 _,

G. Adjanor

1 _{, G. Monnet}

1 _,

J.B. Piochaud

2 _{, R. Ngayam-Happy}

1,2

1 EDF R&D

Dpt Matériaux & Mécanique des Composants

Les Renardieres, Moret sur Loing, France

2 UMET, Université de Lille 1

Villeneuve d’Ascq, France

F P 7 P r o je c t

F P 7 P r o j e c t

P E R F O R M 6 0

F P 7 P r o j e c t

P E R F O R M 6 0

(5)

Lifetime extension: Materials ageing

prediction

Lifetime extension: Materials ageing

prediction

• To improve quantitative predictions

of ageing of irradiated structural

materials in nuclear power plants in

order to gain margins.

• Challenge: to predict the evolution

of hundred of tons over more than

40 years based on physical

phenomena occurring at the

nanometer scale and picosecond

times (10

-12

_s)

• Construction and improvement of

multiscale modelling methods

allowing to better take into account

the material composition and

(6)

Microstructure evolution of Fe alloys under irradiation

RPV Fe ferritic alloys

- microstructure modelling

short & long term evolution

- plasticity

Austenitic alloys

- FeNiCr AKMC RIS modelling

30 ××××30 ××××140 nm3

Si P MnNi Cu

25 nm

2

5

n

m

8 nm

2

9

n

m

Si+P+Mn+Ni+Cu

3 nm

[A. Volgin PhD

SAT@GPM Rouen ]

(7)

Finite elements

ab initio

Molecular dynamics

Mesoscopic

Multi-scale

modelling

+ experimental validation

1nm

3

0 - ps

ns

(10-30nm)

3

cm

3

µm

3

h-year

s - h

(30-100nm)

3

m

3

40 years

Micro-macro

Dislocation

dynamics

Barbu, CEA

Pareige, U. Rouen

F P 7 P r o j e c t

P E R F O R M 6 0

F P 7 P r o j e c t

P E R F O R M 6 0

(8)

Classical Molecular Dynamics

(atomic forces derived from empirical potentials)

System size

Elementary

Mecanisms

Time

1nm

3

_(10-30nm)

3

_(30-100nm)

3

_µm

3

cm

3

ns

s - h

h-

year

0 - ps

Finite Elements

ab initio

(forces and energies determined from the electronic structure -- Density

Functional Theory (DFT))

Mesoscopic

(grain, set of grains)

Kinetic Monte Carlo

(diffusion)

[Rate theory/cluster dynamics]

(cf. T Jourdan)

Dislocation Dynamics

001 100 1nn

1nn

0.4 µm

Microscopy and chemical analysis

Tomographic atom

probe

Prog. de surveillance

Positon

annhilation

SANS

(9)

AKMC

Solute interactions (Cu, Ni, Mn, Si)

(interface energies,

mixing energies …)

Ab initio

Solute diffusion by

- vacancy mechanisms

- interstitial mechanisms

Parameterisation

cohesive model

Experimental data and

Thermodynamical data

Experimental

validation:

TAP, SANS, SAXS, PA, TEP

εεεεFe-V_1nn εεεεFe-Si_2nn ) 2 ( ) ( ) 1 ( ) ( ) 2 ( ) ( ) 1 ( ) ( ) 2 ( ) ( ) 1 ( )

(

3

8

6

4

3

4

_Fe _Fe _Fe _Fe _Fe _X _Fe _X _X _X _X _X

mixing

E

=

−

ε

₋

−

ε

₋

+

ε

₋

+

ε

₋

−

ε

₋

−

ε

₋

) 2 ( ) ( ) 1 ( ) ( ) 2 ( ) ( ) 1 ( )

(

6

4

3

8 )

(

Z _V _Z _V _Z _Z _Z _Z _Z

formation

V

E

=

ε

₋

+

ε

₋

−

ε

₋

−

ε

₋

) 1 ( ) ( ) 1 ( ) ( ) 1 ( ) ( ) 1 ( ) ( ) 1 ( )

(V X Fe V Fe X Fe Fe V X binding

E

₋

=

ε

₋

+

ε

₋

−

ε

₋

−

ε

₋

Objective:

Simulation formation of solute rich complexes

(observed by TAP) under irradiation

TAP, Pareige, U. Rouen

15x15x50 nm Cu

Mn

Ni Si

(10)

Atomistic Kinetic Monte Carlo (AKMC)

Treatment of multi-component systems on a rigid lattice

Substitutional elements

Interstitial elements

Diffusion by 1nn jumps

Via vacancies

Via interstitials

Jump Probability:

Residence Time Algorithm applied to all events

Vacancy and Interstitial jumps

Frenkel Pairs and Cascade flux for irradiation

Average time step:













−

=

Γ

kT

Ea

X

ν

exp

∑

Γ

=

∆

k j jk

t

,

1 Environment dependant form of activation energy Ea

ν

X

= attempt frequency

Γ_1,1 Γ2,1

Γ_2,2 Γ_1,2

v₁ v2

v₃

Γ_3,1

3,2

Γ

Γ_1,1 Γ_1,8 Γ_2,1

Γ

2,7

Γ Γ

3,2

3,7

Γ_1,1 Γ2,1

Γ_2,2 Γ_1,2

v₁ v2

v₃

Γ_3,1

3,2

Γ

Γ_1,1 Γ2,1

Γ_2,2 Γ_1,2

v₁ v2

v₃

Γ_3,1

3,2

Γ

Γ_1,1 Γ_1,8 Γ_2,1

Γ

2,7

Γ Γ

3,2

3,7

Γ_1,1 Γ_1,8 Γ_2,1

Γ 2,7 Γ Γ 3,2 3,7

2 )

(

X

Ef

Ei

Ea

=

_i

+

−

Code: LAKIMOCA

(11)

AKMC irradiation simulation conditions

For electron irradiation

: Frenkel Pair (FP) flux

For neutron irradiation

: flux of

• 20 keV and 100 keV cascades debris obtained by Molecular Dynamics

(R. Stoller, J. Nucl. Mater. 307-311 (2002) 935)

• Frenkel Pairs

surface

cascades

Paires de Frenkel

Cascades

Paires de

Frenkel pairs

Frenkel

PBC

Typical simulation box:

1.01 ××××

10

-17

_cm

3

_boxes

(12)

Cohesive energy model (bcc)

2 )

(

X

Ef

Ei

Ea

=

_i

+

−

+

) ( 1 j nnTens l X E

+

) ( 1 j i nnComp

l dumb X

E −

• dumbbell - dumbbell

E_b(dumb - dumb) 1nn & 2nn

SIA:

)

( j k

mixed

l X X

E − Solute atoms Fe atom

εεεε

Fe-V_1nn

ε

Fe-Si_2nn

Vacancy:

FIA (C):

FIA

vacancy

solute

SIA

+

• solute - dumbbell

∑

_













−

+

−

+

−

+

=

i j j i j

l k j mixte l j nnTens l j i nnComp l f

dumb

E

dumb

X

E

X

E

X

E

dumb

E

, 1 1

)

(

)

(

)

(

)

(

∑

−

+

−

+

−

+

−

+

−

+

−

=

p i Y X n i X V m i X Fe l i V Fe k i V V j i Fe Fe

E

ε

₍() ₎

ε

₍() ₎

ε

₍() ₎

ε

₍( ) ₎

ε

₍() ₎

ε

₍() ₎

~ 100 ab initio data considered in the model

• RPV: 1nn and 2nn pair interactions

(13)

i = 1 or 2

X, Y = solute atoms

•

• )

(

)

(

)

(

)

(

)

(

)

(

)

(

)

(

)

(

)

(

i

Y

X

i

Fe

i

Y

Fe

i

X

Fe

i

Y

X

liaison

E

₋

=

ε

₋

+

ε

₋

−

ε

₋

−

ε

₋

Binary alloys

Ternary alloys…

Z = Fe or solute atom

)

1 (

)

(

)

1 (

)

(

)

1 (

)

(

)

1 (

)

(

)

1 (

)

(

lac

X

Fe

lac

Fe

X

Fe

lac

X

liaison

E

₋

=

ε

₋

+

ε

₋

−

ε

₋

−

ε

₋

)

2 (

)

(

)

1 (

)

(

3

4 )

(

_Z

cohésion

Z

E

=

ε

₋

+

ε

₋

)

2 (

)

(

)

1 (

)

(

)

2 (

)

(

)

1 (

)

(

6

4

3

8 )

(

Z

_lac

_Z

_lac

_Z

formation

lac

E

=

ε

₋

+

ε

₋

−

ε

₋

−

ε

₋

)

(

)

(

)

(

)

(

)

(

)

(

)

(

)

(

2 i

lac

i

Fe

i

lac

Fe

i

lac

liaison

E

₋

=

ε

₋

−

ε

₋

−

ε

₋

)

2 (

)

(

)

1 (

)

(

)

2 (

)

(

)

1 (

)

(

)

2 (

)

(

)

1 (

)

(

)

100 (

int

erface

2 Fe

Fe

4 Fe

X

2 Fe

X

2 X

X

E

=

−

ε

₋

−

ε

₋

+

ε

₋

+

ε

₋

−

ε

₋

−

ε

₋

)

2 (

)

(

)

1 (

)

(

)

2 (

)

(

)

1 (

)

(

)

2 (

)

(

)

1 (

)

(

3

8

6

4

3

4 _Fe

_Fe

_X

_Fe

_X

mélange

E

=

−

ε

₋

−

ε

₋

+

ε

₋

+

ε

₋

−

ε

₋

−

ε

₋

Ab initio data

Parameters

ε

Fe-Cu_1nn

ε

Si-Si_2nn

Adjustment on thermal annealing experiment

(14)

686+19 Fe atoms PAW GGA 300 eV - 1 kpoints

BGL run

512 CPU - ~24h

001

100 1nn

1nn

Fe-C

Local magnetic moment (µB)

Fe Cu Ni _Mn

Si -0,2

0 0,2 0,4 0,6 0,8 1 1,2

Fe-CuNiMnSi

Phys. Rev. B 69 (2004) 144112

Phys. Rev. B 65 (2002) 024103

Nucl. Inst. Meth. Phys. Res. B:

DFT:

(15)

Fe-0.2Cu-0.53Ni-1.26Mn-0.63Si (at.%) at 300°C

Flux: 6.5 10

-5

_dpa.s

-1

Dose: 1.3 10

-3

_dpa

V-solute complex

SIA-solute complexes

Small solute clusters

SIA

Cu

Si

Mn

Cu

Si

Mn

Cu

Si

Mn

Ni

Cu

Si

Mn

Cu

Si

Mn

Cu

Si

Mn

Ni

V

Point defect clusters = germs for precipitation

Neutron irradiation of FeCuNiMnSi alloys

Medium term evolution by atomic Kinetic Monte Carlo

(16)

0 5 10 15 20 25

1 7 13 19 25 31 37 43 49 55 61 67 73 79

R

ép

ar

tit

io

n

d

es

e

sp

èc

es

Numéro de l'amas

SIA Vac P Ni Mn Si Cu

• The biggest solute clusters are associated with PD clusters

−

In agreement with induced segregation mechanism to account for solute clusters formation

• Clusters associated with interstitial clusters are enriched in Mn, and P/Ni

• Clusters associated with vacancy clusters are enriched in Si/Cu/Mn (mostly) and Ni

• I-Solute complexes

>>>>

V-Solute complexes

Cluster ID

V-Solute

SIA-Solute

Pure solute

Fe – CuMnNiSiP (at.%) alloys

(17)

All Solute clusters

AKMC

Simulation

Average composition

(nb solute & vac & int / cluster)

Solute clusters

Atom Probe [Meslin et al.]

Experimental results

0 20 40 60 80

Fe - Cu Fe - Mn Fe - MnNi Fe - CuMnNi 16M ND5

N o m b re m o y e n p a r a m a s P Ni Mn Si Cu 62 mdpa 62 mdpa 100 mdpa 62 mdpa 62 mdpa 0 5 10 15

Fe - Cu Fe - Mn Fe - M nNi Fe - CuMnNi Fe

-CuMnNiSiP P Ni Mn Si Cu 5,1 mdpa 24,33 mdpa 18,53 mdpa 18,09 mdpa 14,38 mdpa 0 10 20 30 40

Fe - Cu Fe - M n Fe - M nNi Fe - CuMnNi Fe -CuM nNiSiP N o m b re m o y e n p a r a m a s _SIA Vac P Ni Mn Si Cu 5,1 mdpa 18,09 mdpa 18,53 mdpa 0 5 10 15 20

Fe - Cu Fe - Mn Fe - MnNi Fe - CuMnNi Fe -CuMnNiSiP N o m b re m o y e n p a r a m a s _SIA Vac P Ni Mn Si Cu 5,1 mdpa 24,33 mdpa 18,53 mdpa 18,09 mdpa 14,38 mdpa 0 5 10 15

Fe - Cu Fe - Mn Fe - M nNi Fe - CuMnNi Fe -CuMnNiSiP N o m b re m o y e n p a r a m a s SIA Vac P Ni Mn Si Cu 5,1 mdpa

24,33 mdpa 18,53 mdpa 18,09 mdpa 14,38 mdpa

(18)

Vacancy

X

Y

X

Y

X

Y

SIA

Compressive atoms

Tensile atoms

∑

_













−

+

−

+

−

+

=

i j j i j

l k j mixte l j nnTens l j i nnComp l f

dumb

E

dumb

X

E

X

E

X

E

dumb

E

, 1 1

)

(

)

(

)

(

)

(

∑

−

+

−

+

−

+

−

+

−

+

−

=

p i Y X n i X V m i X Fe l i V Fe k i V V j i Fe Fe

E

ε

₍( ) ₎

ε

₍( ) ₎

ε

₍( ) ₎

ε

₍( ) ₎

ε

₍( ) ₎

ε

₍( ) ₎

1nn (and 2nn) pair interactions

(no reliable FeNiCr EAM

potentials for thermodynamical

and defect properties)

(19)

FeNiCr interaction parameters

adjustment on DFT data (

Fe

₇₀

Ni

₁₀

Cr

₂₀

)

Cohesive energies

X-X terms

Binding energies in dilute

γ

-Fe

X-Y terms

Chemical interactions in the Bulk

Vacancy-solute interactions

Fe

Ni

Cr

(20)

TNES & RIS profil

TNES results:

RIS results:

Cr enrichment

Cr depletion

Ni depletion

Ni enrichment

→

Coherent with experimental results

TNES

RIS

(21)

Long term microstructure

modelling Object Kinetic Monte Carlo

Objects:

- vacancy

- self interstitial

- dilute solute (with vacancy interactions)

- sink (e.g. grain boundaries, …)

- trap (e.g. impurities, …)

- dislocation

- foreign interstitial atoms

He in austenitic alloys

C or N in ferritic or austenitic alloys

Annihilation

Interstitial loop

Emission

Interstitial cluster

Vacancy cluster Traps

Electrons

Neutrons

Frenkel pairs

cascade +

Emission

+ +

Recombination

200nm PBC or surface

dislocation

He cluster

Mixed He vacancy cluster

SIA-Loop

Nanovoi

d

Solute

clusters

P-segregatio

n

Ma

trix

Da

ma

ge

Precipitatio

n

Se

gr

eg

ati

on

(22)

Annihilation

Interstitial loop

Emission

Interstitial cluster

Vacancy cluster traps

Vacancy loop

+ Emission

Migration

+

Recombination

>300nm PBC or surface

sinks dislocation

Input required:

Mobility: diffusion coefficient

Local interaction rules: Interaction and binding energies

Long term simulation of the microstructure under

irradiation of Fe by object kinetic Monte Carlo

1E+23 1E+24 1E+25 1E+26

0.0001 0.001 0.01 0.1 1

set 1 PBC set 2a PBC set 3a PBC experimental min max

D

e

n

s

it

y

(

m

-3

)

0.0009 0.009

0.23

0 0.5 1 1.5 2 2.5 3 3.5

(23)

(param Set II)

7 10

-11

_dpa/s

7 10

-5

_dpa/s

DEFECT POPULATION at 0.1 dpa

343K

Long term simulation of the microstructure:

(24)

Atom-meso transition

Meso-continuum transition

Homogenization

Mechanical properties

RVE

mechanics

Physics modeling

Irrad. microstructure

10 nm

Dislocation-defect

10 µm

Collective dislocation behavior

10 µm

(25)

Critical stress for (110) screw dislocation (temperature, strain rate)

0 100 200 300 400 500

0 100 200 300 400

T (K)

MD Simulations

Experiments

Critical Stress (MPa)

[Domain et al.]

Critical stress for (112) edge dislocation (temperature, strain rate )

0

200

400

600

800

0

50

100

150

200 Τ (Κ)

τ

c

(MPa)

Antitwinning direction

Twinning direction

[Terentyev et al.]

Screw core structure: compact

ab initio

EAM: Mendelev03

EAM: Ackland04

(26)

0

25

50

75

100

125

150

1 Alloy Friction

Forest dislocation

Carbides

Shear stress (MPa)

Lath geometry

Initial state

2 voids

Irradiated state

CRSS

∆

Irradiation strengthening in RPV

(27)

R

P

V

-2

o

r

IN

T

E

R

N

-1

CONVOLVE

LONG_TERM

IRRAD

HARD

neutron spectrum

temperature

+ composition

composition

+ mobility rules and diffusion coefficients

+ energetics of clusters

+ sinks densities

+ time steps and total irradiation time

pinning forces of the clusters

+ slip system

+ shear modulus

∆τ

(t)

pka spectrum

source term

clusters distributions f(t)

RPV-2

INTERN-1

Integration: RPV & INTERN plateforms

F P 7 P r o j e c t

P E R F O R M 6 0

F P 7 P r o j e c t

P E R F O R M 6 0

(28)

Dislocation dynamics cristalline law of Fe

alloys (at low temperature)













−

=

kT

G

l

b

T

_scs app

c D screw

)

(

∆

exp

)

,

(

₂ 2

τ

ν

τ

υ

b

v

(

,

T

)

b

ed

s

(

,

T

)

s

ed

s

sc

s

sc

s

ρ

τ

ρ

υ

τ

γ

&

=

+

Orowan Law for plastic flow

DD velocity of scew dislo













−

=

∑

c

s

u

su

s

g

K

a

b

ρ

γ

ρ

&













_∆













∆

−

=

o

s

eff

o

s

sc

c

D

s

sc

s

kT

G

kT

G

l

b

τ

υ

ρ

γ

4 ₂

exp

sinh

3 &

Dislocation density evolution law

[Naamane, Monnet, Devincre]

(29)

0

100

200

300

0

10

20

30

40

50 50K

350K

250K

200K

150K

100K

γ

(%)

Stress (MPa)

[Kuramoto 1979]

Finite elements simulations:

stress strain curves

(30)

Uncertainties

Statistics

Complexity

(chemistry, clusters, interfaces)

Time-scale

(fs, ps, years)

Integration

(codes, database,

methods, …)

Length-scale

(Angstrom, meter)

Material Multiscale Modeling Challenge

Accuracy

(31)