Quantum chemical calculations and MD simulations for Be

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2 Quantum chemical calculations and MD simulations for Be Institute of Ion Physics University of Innsbruck Michael Probst Michael Stefan Alexander Ivan Andreas Györoek Huber Kaiser Sukuba Mauracher Be-CRP IAEA VIE June

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4 1 Electron impact ionization cross sections (EICSs) Electron impact ionization cross sections of beryllium-tungsten clusters Ivan Sukuba, Alexander Kaiser, Stefan E. Huber, Jan Urban, Michael Probst Eur. Phys. J. D (2016) 70: 11.

5 Last meeting: Beryllium hydride cross sections. We wanted to modernize the EICS calculations a little bit: use at least 2 independent methods (BEB and DM) work to incorporate a third method (optical potential) use good global geometry optimization algorithms extend the EICS to cover excited states / ionic states Example: BeW results.

6 DM:, ln / 1 / BEB: / ln 1 1 ln, /, /, 4 / From QC calculations

7 Be n W cluster, n=1-12, all singlet states Optimization by simulated annealing (Born-Oppenheimer molecular dynamics with TURBOMOLE)

8 Be n Wcluster, n= BeW DM Singlet Triplet BeW BEB 15 Cross sections for S and T spins: 5 15 Be 2 W (I) Be 2 W (I) σ ( -16 cm 2 ) 15 5 Be 2 W (II) Be 2 W (II) Be 2 W (III) Be 2 W (III) Be 3 W Be 3 W Energy (ev) Energy (ev)

9 Be n Wcluster, n=1-12 Cross sections: BeW Be 2 W DM DM fit BEB BEB fit Be 7 W Be 8 W σ ( -16 cm 2 ) Be 3 W Be 4 W Be 9 W Be W Be 5 W Be 11 W Be 6 W Energy (ev) Be 12 W Energy (ev)

10 In Be 8 W, different geometries are close in energy. Their cross sections are similar to each other: σ ( -16 cm 2 ) DM BEB Energy (ev) I II III IV V

11 2 MD of Be-D sputtering (Ivan Sukuba et al.)

12 Sputtering yield as a function of the temperature of a Be surface hcp - Be surface (0001), 32x32x45(60)A 3 ~4700 atoms for 25 and 50 ev impact energies and ~6300 atoms for 70 and 80 ev energies impacts.

13 Sputtering yield as a function of the temperature of a Be surface 1) Be sputtering non-cumulative events Impact energies: 25, 50, 70, 80 ev

14 Sputtering yield as a function of the temperature of a Be surface 1) BeD sputtering non-cumulative events Impact energies: 25, 50, 70, 80 ev

15 Sputtering yield as a function of the temperature of a Be surface 1) D reflected non-cumulative events Impact energies: 25, 50, 70, 80 ev

16 Sputtering yield as a function of the temperature of a Be surface For D, Be and BeD leaving the surface there is little, if any effect of the surface temperature T, at least if T is in the range 420 to 720K. Compare: 1eV corresponds to 100K Be boils at 3240K (cohesive energy) Experiments show a definite T-dependence Mechanism of T influencing sputtering?

17 Further MD-related works: surface dependence trajectory analysis

18 3 Stability of BeH molecules Reaction Thermodynamics Be BeH BeH 2 and other equilibria Alexander Kaiser Ivan Sukuba Stefan Huber Michael Probst Not yet published

19 Calculations: G f und H f values (free formation energies and - enthalpies) for various neutral, cationic and anionic Be x H y species. G values (free energies of reactions) and equilibrium constants at different temperatures for the various interconversion reactions of neutral and ionic Be x H y species have been calculated. This gives the equilibrium concentrations of these molecules The electron-impact cross sections of these molecules have also been calculated.

20 What we aimed for: Stability analysis Enthalpy and Free energy of reactions Transition states (in progress) Rate constants for various BeD 2 and BeD 3 channels Ab initio methods: Accuracy of the G4 method of theory is very good! also CCSD, QCISD Basic formulas: G = G 0 + RT ln(q r )= RT ln(q r /K eq ) Q r reaction quotient - initial concentrations Sputtering yields from MD simulations and experiments (not used yet, but data available) ln(q r /K eq ) determines the direction of the reaction Eyring equation for rate constants k(t)= k B T/ h exp(- G /RT) All values are calculated

21 Motivation Discrepancies between MD results and experiment at high temperatures ( 500 K) Data for ERO (need for data in general) BeD1-3 molecules Few experimental data If, only for BeD (spectroscopic data) Theoretical data only for BeD Explanation of reactivity of BeD2 and BeD3

22 Input to G and k calculations QC data components: BeH_ log 8.31E 03 kj/(molk) Eelec E 06 Hartree/MolK ZPE TCEnergy ZPE+Evib+Erot+Etrans TCEnthalpy ZPE+Evib+Erot+Etrans+RT TCGibbs Eelec+ZPE Eelec+Thermal Energy Eelec+TCEnergy Eelec+thermal Enthalpy Eelec+TCEnthalpy Eelec+thermal free energy Eelec+TCGibbs

23 The reaction network. Free energies as function of temperature G4 reaction free energies ΔG r0 ( Ochterski approach from gaussian calculations) K kj/mol kj/mol kj/mol kj/mol kj/mol kj/mol kj/mol kj/mol kj/mol kj/mol kj/mol kj/mol kj/mol ΔG r 0 ΔG r 0 ΔG r 0 ΔG r 0 ΔG r 0 ΔG r 0 ΔG r 0 ΔG r 0 ΔG r 0 ΔG r 0 ΔG r 0 ΔG r 0 ΔG r 0 T BeD BeD 2 BeD 2 BeD 2 BeD BeD BeD 2 BeD 2 BeD 2 BeD 2 BeD 2 BeD BeD 2 Be+D Be+D 2 BeD+D Be+2D Be + D Be + D Be + D 2 Be + D 2 Be + D + D Be +2 D BeD + D Be + D + e Be + D 2 + e product product product anion anion anion unstable unstable unstable

24 The reaction network. Free energies as function of temperature Table 11 continued G4 calculations of reaction free energies K kj/mol kj/mol kj/mol kj/mol kj/mol kj/mol kj/mol kj/mol kj/mol ΔG 0 r ΔG 0 r ΔG 0 r ΔG 0 r ΔG 0 r ΔG 0 r ΔG 0 r ΔG 0 r ΔG 0 r T BeD 3 BeD 3 BeD 3+ BeD 3+ BeD 3+ BeD 3+ BeD 3 BeD 3 BeD 3 BeD 2 +D BeD +D 2 BeD + +D 2 BeD + D + 2 BeD 2+ +D BeD 2 + D + BeD 3 + e BeD 2 + D BeD + D product anion unstable

25 Enthalpy and Free energy as function of temperature (kj/mol) At low T BeD 2 is much favoured over Be and D 2 At 00K both BeD 2 and Be+D 2 are equally probable

26 4 DFT of Be 2 W and Be 12 W surfaces Surface binding energies of beryllium /tungsten alloys Gyoeroek, Michael; Kaiser, Alexander; Sukuba, Ivan; Urban, Jan; Hermansson, Kersti; Probst, Michael Journal of Nuclear Materials (2016), 472,

27 Surfaces of Interest o pure Be - hexagonal close packed (0001) o pure W - body centered cubic (001) o Be 2 W (001) o o Be 12 W (001) 27

28 o VASP Density functional theory Widely used in materials science Plane waves, LAPWs as basis sets PBE functional Periodic systems 28

29 2. Methods Surface Model o periodic boundary conditions o vacuum depth 8 [Å] o orientation (001) 29

30 2. Methods Surface Binding Energy & Cohesive Energy E - single atom energy E - total energy of the surface slab with a single surface vacancy E - total energy of the slab with the clean surface E - total bulk energy - number of atoms of each species n 30

31 Surface Binding Energies: Pure Metals structure vacancy SBE [ev] no. of neighbor s Be hcp (0001) distance [Å] (number of neighbors) DFT ABOP W Be W-W Be-Be Be (3) (6) W bcc (001) W (4) (5) 31

32 Alloys: Geometric Arrangement 32

33 Results Surface Binding Energies vacanc y SBE [ev] no. of neigh -bors distances [Å] (number of neighbors in parentheses) Be 12 W (001) DFT W Be Be-W Be-Be Surface A Surface A Surface A Be (α) (1) Be (γ) (1) W(β) (4) (4) (4) (1), (2) (1), (2) (2) 2.4 (2), (2) (1), (2) Surface B Be (δ) (1) 2.4 (3), (2) 33

34 Comparison DFT vs. ABOP - Be 2 W

35 Comparison DFT & ABOP Be 12 W

36 Cohesive energy correlations

37 Conclusions: Increasing tungsten content stabilizes the whole material (against sputtering). Preferential sputtering of Be (only). One case where there is a large discrepancy with BOP

38 Thank you!