Elementary Processes and Thermodynamic Properties of ...

3rd CRP – I.A.E.A., Vienna 2016

ROBERTO CELIBERTO

Dipartimento di Ingegneria Civile, Ambientale, Edile, del Territorio e di Chimica

Politecnico di Bari (Italy)

and

Istituto di Nanotecnologia - CNR, Bari (Italy)

Elementary Processes and Thermodynamic

Properties of Hydrogen and Helium Plasmas

High-density hydrogen plasma

Debye plasma: 𝑽(𝒓) =𝒆𝟐

𝒓∙ 𝒆−𝒓/𝝀𝑫 (𝝀D = Debye radius)

Non-ideal effects

• Self-energy (surrounding plasma influence):

𝑬 =𝒑𝟐

𝟐𝒎- self-energy term =

𝒑𝟐

𝟐𝒎-

𝒆𝟐

𝟐𝝀𝑫

• Alteration of the bound states energy:

HY = E Y 𝐇 =𝒑𝒆𝟐

𝟐𝒎𝒆-𝒆𝟐

𝒓∙ 𝒆−𝒓/𝝀𝑫 -

𝒆𝟐

𝟐𝝀𝑫

- Finite number of bound states- Lowering of bound states- Lowering of the ionization potential (Mott effect)

High-density hydrogen plasma

Debye plasma: 𝑽(𝒓) =𝒆𝟐

𝒓∙ 𝒆−𝒓/𝝀𝑫 (𝝀D = Debye radius)

Non-ideal effects

𝒆− + 𝒑+ ⇆ 𝑯

• Ionization degree from Saha equation (including self-energy and bound states)

• Lowering of the ionization potential at high densitiescauses full ionization (pressure ionization)

EXCITED-STATE KINETICS AND RADIATION TRANSPORT IN LOW-TEMPERATURE PLASMAS

THE SELF-CONSISTENT MODEL

G Colonna, G D’Ammando, LD Pietanza, M Capitelli,Plasma Physics & Controlled Fusion, 57, 014009 (2015)

Hydrogen and helium

1s2


THE SELF-CONSISTENT MODEL



SHOCK TUBE RESULTS: TEMPERATURES



SHOCK TUBE RESULTS: LEVEL DISTRIBUTION AND EEDF

Ionization limit

n = 2 n = 2

Ionization limit


𝐇+ 𝐇𝐞𝐇+ ⟶𝐇𝐞+ 𝐇𝟐+

Quasi-Classical Trajectory (QCT) method

Quantum-Mechanical Close-Coupling (QM-CC) method

QCT –– F. Esposito, C.M. Coppola, D. De Fazio J. Phys. Chem. A, 119, 12615 (2015).QM-CC –– D. De Fazio, Phys. Chem. Chem. Phys., 16, 11662 (2014)

Exit channel

Ramachandran et al, Chem. Phys. Lett., 469, 26 (2009)

Entrance channel

H…H distance (a.u.)He…H distance (a.u.)

En

erg

y (

eV

)

H-H = 2.074 (a.u.)

He-H = 1.927 (a.u.)

He+H2+

HeH++H

MRCI (cc-pv5z)

Fitted at (M = 6)

Calculated

MRCI (cc-pv5z)

Fitted at (M = 6)

Calculated


(Gamallo et al,J Phys. Chem., 2104)

(Bovino et al, Astron. Astrophys., 2011)

QM-CC

QM-WP

QM-CS/NIP

QCT



(Rutherford & Vroom, J. Chem. Phys, 1973)Exp.

QM-CC

QCT



v = 0

QM-CC

Solid lines

QCT

Dashed lines



j = 0

v = 0v = 2

v = 4

Exp.: Rutherford & Vroom,J. Chem. Phys, 1973)

QCT results



QM-CC

Solid lines

QCT

Dashed lines



Billing’s semiclassical method:

• Classical description of the gas-phase atoms (trajectories)

• Quantum mechanical description of surface

• Recombination coefficient (gH) and probability are calculated

Unit cell for

W(110) plane

Cristal used in

the calculations

M. Rutigliano, D. Santoro and M. Balat-Pichelin, Surface Science, 628, 66 (2014)

Hydrogen recombination on tungsten at high temperature: experiment and molecular dynamics simulation

a

H-atom interaction

potentials

a


H2-molecule interaction potential for T site

a

eV eV

H2-molecule interaction potential for T site

H

r

H

zH

xH

yH

a

eV eV

H𝑎𝑑𝑠 ∗ W 110 + H𝑔𝑎𝑠 ⟶ H2𝑔𝑎𝑠 +W(110)

H𝑎𝑑𝑠 ∗ W 110 + H𝑔𝑎𝑠 ⟶H𝑎𝑑𝑠 ∗ W 110 + H𝑔𝑎𝑠

H𝑎𝑑𝑠 ∗ W 110 + H𝑔𝑎𝑠 ⟶H𝑎𝑑𝑠 ∗ W 110 + H𝑔𝑎𝑠

H𝑎𝑑𝑠 ∗ W 110 + H𝑔𝑎𝑠 ⟶ H𝑎𝑑𝑠 ∗ W 110 +H𝑎𝑑𝑠∗ W 110

H𝑎𝑑𝑠 ∗ W 110 + H𝑔𝑎𝑠 ⟶H𝑔𝑎𝑠 +H𝑔𝑎𝑠 +W 110

H𝑎𝑑𝑠 ∗ W 110 + H𝑔𝑎𝑠 ⟶ (H2)𝑎𝑑𝑠 ∗ W 110

Molecular

recomb.

Ads/des

Exchange

Atomic

Ads

Molecular

ads

Des

Surface processes

The calculations have been performed for the 3F and T sites

Recom

bin

ation p

robabili

ty

H𝑎𝑑𝑠 ∗ W 110 + H𝑔𝑎𝑠 ⟶ H2𝑔𝑎𝑠 +W(110)

T = 1000 K



On the surface Above the surface

H atom trajectories


𝛾𝐻 =[Hrec]

[Htot]


𝑦 = 1.98 ∙ exp(−1693/𝑇)

TS = Tgas

𝛾𝐻 =[Hrec]

[Htot]


Electron-impact dissociation cross sections of vibrationally excited He2

+ molecular ion

𝐇𝐞𝟐+ 𝑿𝟐𝚺𝒖

+, 𝒗 + 𝒆 ⟶ 𝐇𝐞𝟐+ 𝑨𝟐𝚺𝒈

+ + 𝒆⟶ 𝐇𝐞 + 𝐇𝐞+ + 𝒆

R. Celiberto, K. Baluja, R. K. Janev and V. Laporta,Plasma Phys. Control. Fusion 58, 014024 (2015)


+, 𝒗 + 𝒆 ⟶ 𝐇𝐞𝟐∗ ⟶𝐇𝐞 +𝐇𝐞+ + 𝒆


+, 𝒗 + 𝒆 ⟶ 𝐇𝐞𝟐∗ ⟶𝐇𝐞𝟐

+ 𝒗′ + 𝒆

J. Royal and A. E. Orel 75, 052706 (2007)


+ molecular ion


+, 𝒗 + 𝒆 ⟶ 𝐇𝐞𝟐+ 𝑨𝟐𝚺𝒈

+ + 𝒆⟶ 𝐇𝐞 + 𝐇𝐞+ + 𝒆



+, 𝒗 + 𝒆 ⟶ 𝐇𝐞𝟐∗ ⟶𝐇𝐞 +𝐇𝐞+ + 𝒆


+, 𝒗 + 𝒆 ⟶ 𝐇𝐞𝟐∗ ⟶𝐇𝐞𝟐

+ 𝒗′ + 𝒆

J. Royal and A. E. Orel 75, 052706 (2007)

𝑨𝟐𝚺𝒈+

𝑿𝟐𝚺𝒖+


+ molecular ion


+, 𝒗 + 𝒆 ⟶ 𝐇𝐞𝟐+ 𝑨𝟐𝚺𝒈

+ + 𝒆⟶ 𝐇𝐞 + 𝐇𝐞+ + 𝒆


Adiabatic Nuclei Approximation

𝑨𝟐𝚺𝒈+

𝑿𝟐𝚺𝒖+


+ molecular ion


+, 𝒗 + 𝒆 ⟶ 𝐇𝐞𝟐+ 𝑨𝟐𝚺𝒈

+ + 𝒆⟶ 𝐇𝐞 + 𝐇𝐞+ + 𝒆


Adiabatic Nuclei Approximation

𝑨𝟐𝚺𝒈+

𝑿𝟐𝚺𝒖+

Outer Region

Single-center expansion…

Boundary of R-matrix box

Inner Region

Exchange,

Short-range correlation…


+ molecular ion

R-matrix method


+ + 𝒆 ⟶ 𝐇𝐞𝟐+ 𝑨𝟐𝚺𝒈

+ + 𝒆 ⟶ 𝐇𝐞 + 𝐇𝐞+ + 𝒆

e-


+ molecular ion

A2Σ𝑔+

X2Σ𝑢+

Xie J, Poirier B and Gellene G I

J. Chem. Phys. 122 184310 (2005)

R-matrix


+ molecular ion

Metropoulos A, Li Y, Hirsch G and Buenker R J

Chem. Phys. Lett. 198 266 (1992)

R-matrix


+ molecular ion

v = 0

Adiabatic

nuclei approx

Fixed-nuclei

Approx.

(Req = 2.04 a.u.)


+ molecular ion


+ molecular ion


+ molecular ion

v = 0

v = 0


+ molecular ion0

23

58

8

|Y|2

R

3rd CRP – I.A.E.A., Vienna 2016

ROBERTO CELIBERTO

Dipartimento di Ingegneria Civile, Ambientale, Edile, del Territorio e di Chimica

Politecnico di Bari (Italy)

and

Istituto di Nanotecnologia - CNR, Bari (Italy)

Elementary Processes and Thermodynamic

Properties of Hydrogen and Helium Plasmas

Elementary Processes and Thermodynamic Properties of ...

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