Applications of First-Principles Method in Studying Fusion Materials

Transcription

1 Joint ICTP/CAS/IAEA School & Workshop on Plasma-Materials Interaction in Fusion Devices, July 18-22, 2016, Hefei Applications of First-Principles Method in Studying Fusion Materials by Guang-Hong LU ( 吕广宏 ) Beihang University

2 First-principles method - Electronic scale

3 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. 1D Schrodinger equation Wave function 2D Schrodinger equation Eigen value, Eigen function Stationary Schrodinger equation Energy, electron density

4 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 Schrödinger equation: Simple to write, yet hard to solve equation Calculation in the past 100 years: Physical models and theories to simplify of the equations

5 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

6 Let us start to learn how to do a simulation of fusion materials from an important issue

7 Bottleneck issues for future fusion reactor Two isotopes of H atomic nucleus: Deuterium (D), Tritium (T) He atomic nucleus with two protons D T He n free neutron Physical problem Plasma stability: long pulse, high power Tritium self-sustainment Materials problem Structure & properties under extreme future conditions (irradiation). 7

8 钨 : 最有前途的面对等离子体材料 Tungsten: Most promising PFM so far Advantages Disadvantages Role High melting point, high thermal conductivity low sputtering High DBTT; recrystallization brittleness; high Z Withstand H/He/Heat flux 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) Full-W Divertor

9 钨基材料面临的极端条件 : 三重辐照 Extreme conditions: 3-fold irradiations 中子辐照 Neutron SOL region 高热辐照 Heat 等离子体辐照 Plasma 壁材料 Wall Material

10 Hydrogen/helium Plasma Irradiation in metals Migration Solubility W surface Low solubility He, H Fast interstitial migration vacancy He, H Deep trapping in vacancy & grain boundaries, dislocations (defects) He & H agglomeration bubbles & blisters fuzz structure Precipitation of He in bubbles He & H trapping, clustering bubbles 11.3eV-He + 3.5x10 27 He + /m 2 TEM 38 ev-d D/m 2 Alimov et al., Phys.Scr S. Kajita et al., Nucl. Fusion 47(2007) 1358.

11 Sputtering Yield 溅射侵蚀 : 等离子体中钨杂质问题 Sputtering & Erosion: tungsten impurity W impurities Limit for W impurity in plasma < 20ppm Bubble-bursting & Sputtering Bursting PFM 等离子体 Plasma (W < 2 mg) ( 钨杂质 <2mg) PFM Energy (Sputtering threshold ) Sputtering data, Report IPP 9/82 (1993) crack/exfoliation Blistering on W Yamanishi, Yamanishi, Nucl Fusion Nucl Fusion (2007) (2007) Cross-section of ITER Fusion Engineering and Design 82(2007)

12 钨的溅射 Sputtering of tungsten Particle H/D/T 3 He/ 4 He C N O Ne Ar W E sput.th (ev) 458/229/ / W. Eckstein, Sputtering by Particle Bombardment, Experiments and Computer Calculations from Threshold to MeV Energies Incident energy > E sput.th long-duration exposure 100 ev~1kev Sputtering & damage Incident energy < E sput.th Interactions between H isotopes/he and surface W sputtering resistance decrease

13 Question: What is the physical mechanism for the H bubble formation in W? H molecule (H 2 ) Preliminary stage of H bubble formation

14 Mechanism for hydrogen bubble formation H bubble Process of H bubble formation Bubble control

15 Stability of H in the intrinsic W J. Nucl. Mater. 390, 1032 (2009) Tetrahedral interstitial site (TIS) Octahedral interstitial site (OIS) Substitutional site Single H atom prefers to occupy the tetrahedral interstitial site in W in comparison with the octahedral interstitial and substitutional case.

16 Two H atoms in the intrinsic W J. Nucl. Mater. 390, 1032 (2009) Distance between two H atoms: 2.2 augstrom H-H bond length in H 2 : 0.75 augstrom H 2 cannot be formed in intrinsic W

17 H occupation and accumulation at vacancy: optimal charge density W 2H 4H 6H Optimal charge density for single H embedded at a vacancy. 8H The isosurface of optimal charge for H for different number of H atoms at the monovacancy. W Such H segregation can saturate the internal vacancy surface, leading to the formation of the H 2 molecule and the preliminary nucleation of the H bubble. H Å 10H Y-L Liu & G-H Lu, Phys. Rev. B 79, (2009)

18 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)

19 Diffusion of H in intrinsic W 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 Yue-Lin Liu, Ying Zhang, G.-N. Luo, and Guang-Hong Lu, J. Nucl. Mater. (2009).

20 Hydrogen diffusion into vacancy Diffusion energy profile and the corresponding diffusion paths for H in W when the vacancy is present.

21 Optimal charge density for H in grain boundary H-B Zhou & G-H Lu, Nucl. Fusion (2010) The H-H binding energy ev (repulsion), equilibrium distance 2.15 Å. Second H atom addition makes isosurface of optimal charge density almost disappear.

22 Vacancy-trapping mechanism of H in metals Metal Vacancy or vacancy-like defects(gb, dislocation ) Phys. Rev. B 79, (2009); Nucl. Fusion 50, (2010); J. Nucl. Mater. 434, 395 (2013) Enough space to provide an optimal charge density

23 Hydrogen bubble growth: strain effect plasma irradiation H pressure(gpa) strain Process of H bubble formation retention nucleation growth blistering Bubble control

24 Dissolution of H in W under the isotropic strain Tetrahedron interstitial site (TIS) Octahedron interstitial site (OIS) First-principle calculation Linear elasticity theory The H solution energy is a linear monotonic function of the triaxial strain. Phys. Rev. Lett. 109, (2012); NIMB 269, 1731 (2011)

25 H in W/Mo/Fe/Cr under the triaxial strain 25

26 Dissolution of H in W under the biaxial strain 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. 26

27 H in W/Mo/Fe/Cr under biaxial strain 27

28 Strain-triggered cascading effect on H bubble growth H bubble region Enhancing effect of anisotropic strain on H dissolution is also applicable to other bcc metals. H accumulation Bubble formation Anisotropic strain in W Bubble growth Enhancing H solubility Phys. Rev. Lett. 109, (2012)

29 Hydrogen bubble control based on mechanism Metal Vacancy or vacancy-like defects(gb, dislocation ) Phys. Rev. B 79, (2009); Nucl. Fusion 50, (2010); J. Nucl. Mater. 434, 395 (2013) Methods Remove all existing vacancies Dope elements to occupy vacancy center: H 2 not formed

30 Synergistic behaviors of H & He in intrinsic W H. B. Zhou & G-H Lu, Nucl. Fusion (2010) 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 30

31 Suppressing H bubble via inert gas elements 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 Hevacancy complex. Inert gas elements cause a redistribution of charge density inside the vacancy to make it not optimal for the formation of H 2 molecule, which can be treated as a preliminary nucleation of the H bubbles. H-B Zhou & G-H Lu, Nucl. Fusion 50, (2010)

32 Reduced retention of D by He in experiments without doped-he Reduced by an order of magnitude with doped-he M.J. Baldwin, Nucl Fusion 51, (2011) O.V. Ogorodnikova, J Appl Phys 109, (2011) Effect of He on D retention 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.

33 D bubble suppression with D-He/Ne plasma exposure noble gas(he/ne/ar):close shell structure Experiment:He M.J. Baldwin, Nucl Fusion 51, (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. Experiment:Ne J Nucl Mater 463, 1025 (2015)

34 You can manage systems at any scales using the first-principles method with sufficiently high computer capability & advanced algorithms.

35 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 36

37 Critical H concentration for formation and rapid growth of H bubble Metal First principles (absolute zero) Thermodynamics parameters (Formation energy/traping energy/diffusion barrier) input thermodynamics model (finite temperature ) Critical concentration H-vacancy complex concentration Effective diffusion coefficient sequential multi-scale method L. Sun, S. Jiin, and G.-H. Lu, to be published

38 Thermodynamic model Two kinds of H dissolved in W Interstitial H atom mh-vacancy complexes Gibbs free energy changes with H f m f G n E n E m TS+ pv HI HI HV HV m Interstitial H 3H 6H 1H mh-v complex In equilibrium with H 2 gas The energy reaches a minimal value with respect to H concentration when the system reaches equilibrium.

39 Thermodynamic model The equilibrium process of the interstitial H and mh-v complexes can be treated as independent Interstitial H concentration Formation energy c HI f nhi NI EHI exp( ) N N k T M M B H-V complex concentration c HV mmax m mmax f mn m HV m EHV m exp( ) N k T m M m Key parameters: Formation energy, maximal number B E E E f HI H TIS BULK H f 1 m m EHV EHV EBULK EBULK m H N H chemical potential ( T 0 K) ( T, p) H H H M c c c H HI HV

40 H Concentration vs. pressure at different temperatures c c c H HI HV c c HI HV f nhi NI EHI exp( ) NM NM kbt mmax f m m EHV m exp( ) kt m B Critical pressure The accumulation of H into vacancy Sharp increase of H concentration beyond certain H pressure Originate from the increase of H in H-vacancy complexes

41 Definition of critical H concentration/pressure Exist a critical concentration associated with critical P at certain T Definition c m HV c HI Different mh-v complex has different grow rate 300K m c min [ c ( m) c ( m)] H HV HI c p H c min m p H Critical H concentration: minimal value of H concentration at the H-V complex which is equal to that at the interstitial

42 Critical H concentration for H bubble formation Considerable H-V complexes form and rapidly grow The formed H-V complexes will combine to form larger cluster, leading to H bubble formation

43 Critical H concentration for H bubble formation: Comparison with experiments Red:H bubble formation Black:No H bubble formation Experimental value Experiments: Peng, Lee and Ueda, J Nucl Mater 438 (2013) S1063 The methodology may contribute to evaluation of the H-induced bubble formation of metallic PFMs in further fusion reactor.

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

46 Thanks for your attention!