by Guang-Hong LU （吕广宏）

Beihang University

Applications of First-Principles Method in Studying Fusion Materials

Joint ICTP/CAS/IAEA School & Workshop on Plasma-Materials Interaction in Fusion Devices, July 18-22, 2016, Hefei

First-principles method - Electronic scale

first principles According to the interaction between nucleus and electrons based on quantum mechanics principles, first principles method finds the solution to the Schrodinger equation through series of approximations and simplifications.

Wave function

Eigen value, Eigen function

Energy, electron density

1D Schrodinger equation

2D Schrodinger equation

Stationary Schrodinger equation

Difficulties in solving the Schrödinger equation

• Dirac (1929):

The difficulty is only that the exact application of quantum theory leads to equations much too complicated to be soluble.

• Large number of strongly interacting atoms in a solid

• Calculation in the past 100 years: Physical models and theories to simplify of the equations

Schrödinger equation：

Simple to write, yet hard to solve equation

Outline

Introduction (first principles)

Introduction (history of first principles)

Basic principles

• calculation of total energy

• electron-electron interaction (DFT)

• Bloch’s theorem – periodic system

• electron-ion interaction (pseudopotential)

Supercell technique

Computational procedure

Future

5

Let us start to learn how to do a simulation of fusion materials

from an important issue……

Physical problem

Structure & properties under extreme

future conditions (irradiation).

Plasma stability:

long pulse, high power

Materials problem

7

Two isotopes of H atomic nucleus:

Deuterium (D), Tritium (T)

He atomic nucleus

with two protons

free neutron

2 3 4

1 1 2D T He n

Bottleneck issues for future fusion reactor

Tritium self-sustainment

钨：最有前途的面对等离子体材料 Tungsten: Most promising PFM so far

8

Advantages

Role

High melting point, high thermal conductivity

low sputtering

Withstand H/He/Heat flux

Disadvantages High DBTT; recrystallization brittleness; high Z

Full-W Divertor 等离子体研制的穿管型钨铜偏滤器部件小模块 (W-Cu monoblock by CAS-IPP)

钨基材料面临的极端条件：三重辐照 Extreme conditions: 3-fold irradiations

SOL region

壁材料 Wall Material

中子辐照 Neutron

高热辐照 Heat 等离子体辐照

Plasma

surface

vacancy W

He & H trapping, clustering ⇒ bubbles

Precipitation of He in bubbles

He, H

He, H

Hydrogen/helium Plasma Irradiation in metals

• Low solubility

• Fast interstitial migration

• Deep trapping in vacancy & grain boundaries,

dislocations (defects)

He & H agglomeration

bubbles & blisters

fuzz structure

Migration

Solubility

TEM

11.3eV-He+ ➜ W @1250K,

3.5x1027He+/m2

S. Kajita et al., Nucl. Fusion 47(2007) 1358. Alimov et al., Phys.Scr. 2009

38 eV-D+W @530K

1027 D/m2

Sputtering data, Report IPP 9/82 (1993)

Sp

utt

erin

g Y

ield

Energy (Sputtering threshold )

W impurities

Yamanishi, Nucl Fusion (2007)

等离子体

(钨杂质 <2mg)

crack/exfoliation

Fusion Engineering and Design 82(2007)1720–1729

Limit for W impurity in

plasma < 20ppm

Blistering on W

Bursting

Bubble-bursting &

Sputtering

Yamanishi, Nucl Fusion (2007)

PFM

PFM

Cross-section of ITER

Plasma

(W < 2 mg)

溅射侵蚀: 等离子体中钨杂质问题 Sputtering & Erosion: tungsten impurity

钨的溅射 Sputtering of tungsten

Particle H/D/T 3He/4He C N O Ne Ar W

Esput.th(eV) 458/229/154 164/120 50 45 44 39 27 25

W. Eckstein, Sputtering by Particle Bombardment, Experiments and Computer Calculations from Threshold to MeV Energies

Interactions between H isotopes/He and surface W

sputtering resistance decrease

long-duration exposure 100 eV~1keV

Sputtering & damage

Incident energy

> Esput.th

Incident energy

< Esput.th

Question:

What is the physical mechanism for the H

bubble formation in W?

H molecule (H2)

Preliminary stage of H bubble formation

H bubble

Bubble

control

Process of H bubble formation

Mechanism for hydrogen bubble formation

Tetrahedral interstitial site (TIS)

Octahedral interstitial site (OIS)

Substitutional site

Stability of H in the intrinsic W J. Nucl. Mater. 390, 1032 (2009)

Single H atom prefers to occupy the tetrahedral interstitial site in W in comparison with the octahedral interstitial and substitutional case.

Distance between two H atoms: 2.2 augstrom

Two H atoms in the intrinsic W J. Nucl. Mater. 390, 1032 (2009)

H-H bond length in H2: 0.75 augstrom

H2 cannot be formed in intrinsic W

Optimal charge density

for single H embedded

at a vacancy.

W

2H 4H 6H

8H

The isosurface of optimal

charge for H for different

number of H atoms at the

monovacancy.

W

10H

H2 0 .78Å

Y-L Liu & G-H Lu, Phys. Rev. B 79, 172103 (2009)

Such H segregation can saturate the internal vacancy

surface, leading to the formation of the H2 molecule

and the preliminary nucleation of the H bubble.

H occupation and accumulation at vacancy: optimal charge density

Trapping of H in monovacancy

Monovacancy traps up to 10 H.

Average H embedding energy inside a vacancy is lower than that at TIS

far away from the vacancy

Y-L Liu and G-H Lu, Phys Rev B (2009)

Diffusion of H in intrinsic W

Yue-Lin Liu, Ying Zhang, G.-N. Luo, and Guang-Hong Lu, J. Nucl. Mater. (2009).

Site 1, 2 and 4:

tetrahedral interstitial

sites.

Site 3: octahedral

interstitial site.

The arrows show the

corresponding diffusion

paths.

The energy barrier is 0.20 eV via the optimal diffusion path: t→t path

Diffusion energy profile and the corresponding diffusion paths

for H in W when the vacancy is present.

Hydrogen diffusion into vacancy

Optimal charge density for H in grain boundary

H-B Zhou & G-H Lu, Nucl. Fusion (2010)

The H-H binding energy -0.13 eV (repulsion), equilibrium distance 2.15 Å.

Second H atom addition makes isosurface of optimal charge density almost

disappear.

Phys. Rev. B 79, 172103 (2009);

Nucl. Fusion 50, 025016 (2010);

J. Nucl. Mater. 434, 395 (2013)

Enough space to provide an optimal charge density

Metal

Vacancy or vacancy-like

defects（GB, dislocation ）

Vacancy-trapping mechanism of H in metals

plasma

irradiation

H pressure（GPa） strain

retention nucleation growth blistering

Bubble

control

Process of H bubble formation

Hydrogen bubble growth: strain effect

First-principle calculation

The H solution energy is a linear monotonic

function of the triaxial strain.

Linear elasticity theory

Tetrahedron interstitial site (TIS)

Octahedron interstitial site (OIS)

Phys. Rev. Lett. 109, 135502 (2012); NIMB 269, 1731 (2011)

Dissolution of H in W under the isotropic strain

H in W/Mo/Fe/Cr under the triaxial strain

25

Dissolution of H in W under the biaxial strain

26

H-B Zhou & G-H Lu. Phys. Rev. Lett. (2012)

The solution energy of H “effectively” decreases with the

increasing of both signs of anisotropic strain, due to the

movement of H forced by strain.

H in W/Mo/Fe/Cr under biaxial strain

27

Phys. Rev. Lett. 109, 135502 (2012)

H accumulation Bubble formation Anisotropic strain in W

Enhancing H solubility

Bubble growth

……

Enhancing effect of anisotropic strain on H dissolution is also

applicable to other bcc metals.

H bubble

region

Strain-triggered cascading effect on H bubble growth

Phys. Rev. B 79, 172103 (2009);

Nucl. Fusion 50, 025016 (2010);

J. Nucl. Mater. 434, 395 (2013)

Remove all existing vacancies

Dope elements to occupy vacancy center: H2 not formed

Metal

Vacancy or vacancy-like

defects（GB, dislocation ）

Hydrogen bubble control based on mechanism

Methods

Synergistic behaviors of H & He in intrinsic W

30

• Solution energy of H: 0.76 eV, 0.23eV lower than that of TIS in W without He.

• H-He binding energy in intrinsic W: 0.23 eV; attractive interaction

H. B. Zhou & G-H Lu, Nucl. Fusion (2010)

H-B Zhou & G-H Lu, Nucl. Fusion 50, 115010 (2010)

Inert gas elements cause a redistribution of charge density inside the

vacancy to make it “not optimal” for the formation of H2 molecule, which

can be treated as a preliminary nucleation of the H bubbles.

Inert gas element（He/Ne/Ar）: closed shell electronic structure

Optimal charge isosurface for a single H

embedded at He-vacancy complex.

Atomic configuration of H at He-

vacancy complex.

Suppressing H bubble via inert gas elements

O.V. Ogorodnikova, J Appl Phys 109, 013309 (2011)

Helium is the product of fusion reaction, and thus the H bubble may be able to

be suppressed by controlling the content of He in fusion process.

Effect of He on D retention

without doped-He

with doped-He

Reduced by

an order of

magnitude

M.J. Baldwin, Nucl Fusion 51, 103021 (2011)

Reduced retention of D by He in experiments

D bubble suppression with D-He/Ne plasma exposure

noble gas（He/Ne/Ar）：close shell structure

Experiment：Ne

J Nucl Mater 463, 1025 (2015)

Experiment：He M.J. Baldwin, Nucl Fusion 51, 103021 (2011)

Helium is the product of fusion, it is thus possible to control the He concentration in the fusion

product to realize the H isotope bubble control.

You can manage systems at any scales using the first-principles method

with sufficiently high computer capability & advanced algorithms.

First-principles method - Manage system with any scale (theoretically)

36

A connection between atomic and macroscopic levels

（sequential multiscale）

First-principles method

Elastic constants Binding energy Energy barrier

mechanics thermodynamics kinetics

Critical

concentration

First principles

（absolute zero）

Thermodynamics parameters

（Formation energy/traping

energy/diffusion barrier）

input

H-vacancy complex

concentration

Effective diffusion

coefficient

sequential multi-scale method

L. Sun, S. Jiin, and G.-H. Lu, to be published

thermodynamics model

（finite temperature ）

Critical H concentration for formation and rapid growth of H bubble

Metal

+mff m

HI HI HV HV

m

G n E n E TS pV

1H

3H

6H

Interstitial H

mH-V complex

In equilibrium with H2 gas

Two kinds of H dissolved in W

Gibbs free energy changes with H

• Interstitial H atom

• mH-Vacancy complexes

The energy reaches a minimal value with respect to H

concentration when the system reaches equilibrium.

Thermodynamic model

The equilibrium process of the interstitial H and mH-V complexes can be treated as independent

Key parameters: Formation energy, maximal number

exp( )f

HI I HIHI

M M B

n N Ec

N N k T

• H-V complex concentration

max max

exp( )mfm mm

mHV HVHV

m mM B

mn Ec m

N k T

f

HI H TIS BULK HE E E

1mf m

HV HV BULK BULK H

M

E E E E mN

( 0 ) ( , )H H HT K T p

H chemical potential

Formation energy • Interstitial H concentration

H HI HVc c c

Thermodynamic model

• Sharp increase of H concentration beyond certain H pressure

• Originate from the increase of H in H-vacancy complexes

exp( )f

HI I HIHI

M M B

n N Ec

N N k T

max

exp( )mfm

m HVHV

m B

Ec m

k T

H HI HVc c c

Critical

pressure

The accumulation of H

into vacancy

H Concentration vs. pressure at different temperatures

Exist a critical concentration associated with critical P at certain T

Definition

m

HV HIc c

Different mH-V

complex has different

grow rate

Critical H concentration: minimal value of H concentration at

the H-V complex which is equal to that at the interstitial

min [ ( ) ( )]c

m

H HV HIc c m c m

minc

m

H Hp p

300K

Definition of critical H concentration/pressure

• Considerable H-V complexes form and rapidly grow

• The formed H-V complexes will combine to form larger

cluster, leading to H bubble formation

Critical H concentration for H bubble formation

The methodology may contribute to evaluation of the H-induced bubble

formation of metallic PFMs in further fusion reactor.

Red：H bubble formation

Black：No H bubble formation

Experimental value

Critical H concentration for H bubble formation: Comparison with experiments

Experiments： Peng, Lee and Ueda, J Nucl Mater 438 (2013) S1063

44

First-principles method - Manage system with any scale (theoretically)

Thanks for your attention!