applications of first-principles method in studying fusion ... · applications of first-principles...
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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!