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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
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)
EXCITED-STATE KINETICS AND RADIATION TRANSPORT IN LOW-TEMPERATURE PLASMAS
SHOCK TUBE RESULTS: TEMPERATURES
G Colonna, G D’Ammando, LD Pietanza, M Capitelli,Plasma Physics & Controlled Fusion, 57, 014009 (2015)
EXCITED-STATE KINETICS AND RADIATION TRANSPORT IN LOW-TEMPERATURE PLASMAS
SHOCK TUBE RESULTS: LEVEL DISTRIBUTION AND EEDF
Ionization limit
n = 2 n = 2
Ionization limit
G Colonna, G D’Ammando, LD Pietanza, M Capitelli,Plasma Physics & Controlled Fusion, 57, 014009 (2015)
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
𝐇+ 𝐇𝐞𝐇+ ⟶𝐇𝐞+ 𝐇𝟐+
(Gamallo et al,J Phys. Chem., 2104)
(Bovino et al, Astron. Astrophys., 2011)
QM-CC
QM-WP
QM-CS/NIP
QCT
𝐇+ 𝐇𝐞𝐇+ ⟶𝐇𝐞+ 𝐇𝟐+
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)
(Rutherford & Vroom, J. Chem. Phys, 1973)Exp.
QM-CC
QCT
𝐇+ 𝐇𝐞𝐇+ ⟶𝐇𝐞+ 𝐇𝟐+
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)
v = 0
QM-CC
Solid lines
QCT
Dashed lines
𝐇+ 𝐇𝐞𝐇+ ⟶𝐇𝐞+ 𝐇𝟐+
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)
j = 0
v = 0v = 2
v = 4
Exp.: Rutherford & Vroom,J. Chem. Phys, 1973)
QCT results
𝐇+ 𝐇𝐞𝐇+ ⟶𝐇𝐞+ 𝐇𝟐+
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)
QM-CC
Solid lines
QCT
Dashed lines
𝐇+ 𝐇𝐞𝐇+ ⟶𝐇𝐞+ 𝐇𝟐+
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)
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
M. Rutigliano, D. Santoro and M. Balat-Pichelin, Surface Science, 628, 66 (2014)
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
M. Rutigliano, D. Santoro and M. Balat-Pichelin, Surface Science, 628, 66 (2014)
M. Rutigliano, D. Santoro and M. Balat-Pichelin, Surface Science, 628, 66 (2014)
On the surface Above the surface
H atom trajectories
M. Rutigliano, D. Santoro and M. Balat-Pichelin, Surface Science, 628, 66 (2014)
𝛾𝐻 =[Hrec]
[Htot]
M. Rutigliano, D. Santoro and M. Balat-Pichelin, Surface Science, 628, 66 (2014)
𝑦 = 1.98 ∙ exp(−1693/𝑇)
TS = Tgas
𝛾𝐻 =[Hrec]
[Htot]
M. Rutigliano, D. Santoro and M. Balat-Pichelin, Surface Science, 628, 66 (2014)
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)
𝐇𝐞𝟐+ 𝑿𝟐𝚺𝒖
+, 𝒗 + 𝒆 ⟶ 𝐇𝐞𝟐∗ ⟶𝐇𝐞 +𝐇𝐞+ + 𝒆
𝐇𝐞𝟐+ 𝑿𝟐𝚺𝒖
+, 𝒗 + 𝒆 ⟶ 𝐇𝐞𝟐∗ ⟶𝐇𝐞𝟐
+ 𝒗′ + 𝒆
J. Royal and A. E. Orel 75, 052706 (2007)
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)
𝐇𝐞𝟐+ 𝑿𝟐𝚺𝒖
+, 𝒗 + 𝒆 ⟶ 𝐇𝐞𝟐∗ ⟶𝐇𝐞 +𝐇𝐞+ + 𝒆
𝐇𝐞𝟐+ 𝑿𝟐𝚺𝒖
+, 𝒗 + 𝒆 ⟶ 𝐇𝐞𝟐∗ ⟶𝐇𝐞𝟐
+ 𝒗′ + 𝒆
J. Royal and A. E. Orel 75, 052706 (2007)
𝑨𝟐𝚺𝒈+
𝑿𝟐𝚺𝒖+
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)
Adiabatic Nuclei Approximation
𝑨𝟐𝚺𝒈+
𝑿𝟐𝚺𝒖+
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)
Adiabatic Nuclei Approximation
𝑨𝟐𝚺𝒈+
𝑿𝟐𝚺𝒖+
Outer Region
Single-center expansion…
Boundary of R-matrix box
Inner Region
Exchange,
Short-range correlation…
Electron-impact dissociation cross sections of vibrationally excited He2
+ molecular ion
R-matrix method
𝐇𝐞𝟐+ 𝑿𝟐𝚺𝒖
+ + 𝒆 ⟶ 𝐇𝐞𝟐+ 𝑨𝟐𝚺𝒈
+ + 𝒆 ⟶ 𝐇𝐞 + 𝐇𝐞+ + 𝒆
e-
Electron-impact dissociation cross sections of vibrationally excited He2
+ molecular ion
A2Σ𝑔+
X2Σ𝑢+
Xie J, Poirier B and Gellene G I
J. Chem. Phys. 122 184310 (2005)
R-matrix
Electron-impact dissociation cross sections of vibrationally excited He2
+ molecular ion
Metropoulos A, Li Y, Hirsch G and Buenker R J
Chem. Phys. Lett. 198 266 (1992)
R-matrix
Electron-impact dissociation cross sections of vibrationally excited He2
+ molecular ion
v = 0
Adiabatic
nuclei approx
Fixed-nuclei
Approx.
(Req = 2.04 a.u.)
Electron-impact dissociation cross sections of vibrationally excited He2
+ molecular ion
Electron-impact dissociation cross sections of vibrationally excited He2
+ molecular ion
Electron-impact dissociation cross sections of vibrationally excited He2
+ molecular ion
v = 0
v = 0
Electron-impact dissociation cross sections of vibrationally excited He2
+ 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