hermodynamics and ransport properties of ablated species · 2017. 11. 3. · thermodynamics and...

THERMODYNAMICS AND TRANSPORT PROPERTIES OF ABLATED SPECIES 61st COURSE OF THE INTERNATIONAL SCHOOL OF QUANTUM ELECTRONICS “HYPERSONIC METEOROID ENTRY PHYSICS”

ETTORE MAJORANA CENTRE FOR SCIENTIFIC CULTURE, Erice Sicily (ITALY) October 4, 2017

THERMODYNAMICS AND TRANSPORT PROPERTIES

OF ABLATED SPECIES

A D’Angola1,2, G. Colonna2, L. D. Pietanza2, M. Capitelli2, F. Pirani3, E. Stevanato4 and A. Laricchiuta2

1 Scuola di Ingegneria, Università della Basilicata, Potenza, Italy 2 PLASMI Lab CNR NANOTEC Bari, Italy

3 Dipartimento di Chimica, Biologia e Biotecnologie, Università di Perugia, Italy 4 Dept. of Engineering for Innovation, University of Salento, Lecce, Italy



ABLATED CHEMICAL SPECIES

!  ABLATIVE TPS!!  ABLATION for analysis of ROCKs !

!  METEOROID ABLATION during ENTRY in the ATMOSPHERE !

FELDSPAR!

OLIVINE! PYROXENE!QUARTZ!

MICA!



METEORITE CHEMICAL COMPOSITION



��

THE EQUILTHETA TOOL



Pascal André, William Bussière, David Rochette!Transport Coefficients of Ag-SiO2 Plasmas!Plasma Chemistry Plasma Process 27 (2007) 381!

!  Si-Si COLLISION INTEGRALs based on Hulburt Hischfelder fitting of ab-initio potentials!!  COLLISION INTEGRALs for polyatomic species based on simple relations!!  LOW-ORDER CHAPMAN-ENSKOG APPROXIMATION!!  TEMPERATURE RANGE (4,000-30,000 K)!

!  e-Si DIFFERENTIAL ELASTIC CROSS SECTION!!  ENERGY RANGE 1-103 eV!

R. Srivastava, W. Williamson Jr.!Differential and total cross sections for the elastic scattering of 1-1,000 eV electrons from silicon using the optical model!Journal of Applied Physics 65 (1989) 908!

LITERATURE SURVAY!

COLLISION INTEGRALS FOR BINARY INTERACTION INVOLVING SILICON-SPECIES



!  HIGH ORDER !!  ACCURATE INTERACTION POTENTIALS FOR POLYATOMIC SYSTEMS!!  RESONANT CHARGE TRANSFER PROCESS CONTRIBUTION!!  MULTIPLY IONIZED SPECIES!

CHEMICAL SYSTEM!

!  WIDE TEMPERATURE RANGE (500-40,000 K)!!  HIGH-ORDER CHAPMAN-ENSKOG APPROXIMATIONS (THIRD)!

internally consistent COLLISION INTEGRAL DATABASE!

TRANSPORT COEFFICIENTS!

CALCULATION FEATURES!


SiO2, SiC



CLASSICAL COLLISION INTEGRALS!


Multi-Potential Approach!

Si(3P)-Si(3P) Si(3P)-O(3P) Si(3P)-Si+(2P)!Si(3P)-C(3P)!C(3P)-Si+(2P)!



S. D. Peyerimhoff, R. J. Buenker, Chemical Physics 72 (1982)!

Si(3P)-Si(3P) INTERACTION!


1.0 2.0 3.0 4.0 5.0

-2.0

0.0

2.0

INTERNUCLEAR DISTANCE [Å]

POTE

NTI

AL

ENER

GY

[eV

]

21⌃+g1⌃+

g

1�g1⇧u

1⌃�u

1⇧g

1.0 2.0 3.0 4.0 5.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0


POTE

NTI

AL

ENER

GY

[eV

]

3⇧u

3⇧g

23⌃+u

3⌃+u

3�u

3⌃�g

2.0 4.0

-2.0

0.0

2.0


POTE

NTI

AL

ENER

GY

[eV

]

5⌃+g

5⇧g

25⌃+g

5⌃�u

MULTI-POTENTIAL APPROACH!



FITTING of ab-initio POTENTIALS!

!  Hulburt Hirschfelder!

!  repulsive exponential!





10.0

100.0

102 103 104

CO

LL

ISIO

N I

NT

EG

RA

L [

Å2 ]

TEMPERATURE [K]

P André, W Bussière, D Rochette, Transport Coefficients of Ag–SiO2 Plasmas Plasma Chem Plasma Process 27 (2007) 381–403!


Si(3P)-Si(3P) INTERACTION!




Si(3P)-O(3P)! Si(3P)-Si+(2P)!

10.0

100.0

102 103 104

COLL

ISIO

N IN

TEG

RAL

[Å2 ]

TEMPERATURE [K]

10.0

100.0

102 103 104

COLL

ISIO

N IN

TEG

RAL

[Å2 ]

TEMPERATURE [K]






CLASSICAL COLLISION INTEGRALS!


CLASSICAL COLLISION INTEGRALS!from fitting formulas!

INTERACTION POTENTIAL!

PHENOMENOLOGICAL APPROACH!AVERAGE INTERACTION!



10.0

100.0

102 103 104

COLL

ISIO

N IN

TEG

RAL

[Å2 ]

TEMPERATURE [K]

SiO-SiO!

Lennard Jones!

phenomenological!approach!

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

3.0 4.0 5.0 6.0 7.0 8.0

POTE

NTI

AL

ENER

GY

[eV

]


phenomenological!

Lennard Jones!4.25!



PHENOMENOLOGICAL APPROACH!



THEORETICAL resonant charge transfer cross section!

!!!

ASYMPTOTIC APPROACH!

RESONANT CHARGE TRANSFER IN SIMMETRIC ION-PARENT-ATOM COLLISIONS!

extended also to the treatment of resonant double charge transfer processes!

DEVOTO formula !for collision integrals!




60.0

70.080.090.0

100.0

200.0

10-2 10-1 100 101 102 103

RESO

NANT

CHA

RGE

EXCH

ANGE

CROS

S SE

CTIO

N [Å

2 ]

COLLISION ENERGY [eV]

asymptotic approach

close-couplingapproach

asymptotic approach!

close-coupling approach!

S. Sakabe & Y. Izawa, Atomic Data & Nuclear Data Tables 49 (1991)!B. M. Smirnov, Sov. Phys. Uspeki 44 (2001)!

EFFECTIVE diffusion-type COLLISION INTEGRAL for Si(3P)-Si+(2P) INTERACTION!


10.0

100.0

102 103 104

COLL

ISIO

N IN

TEG

RAL

[Å2 ]

TEMPERATURE [K]

inelastico

elastico

RESO

NA

NT

CHA

RGE

EXCH

AN

GE!

CRO

SS S

ECTI

ON

[Å2 ]!



TRANSPORT CROSS SECTIONs for e-Si(3P) INTERACTION!

integration of !quantum elastic !

differential cross section!

R. Srivastava and W. Williamson, Journal of Applied Physics 65 (1989)!




1.0

10.0

103 104

CO

LL

ISIO

N I

NT

EG

RA

L [

Å2 ]

TEMPERATURE [K]

COLLISION INTEGRALs for e-Si(3P) INTERACTION!


integration of !quantum elastic !

differential cross section!




��

THE EQUILTHETA TOOL



novel and efficient algorithms!

flexibility!

basic and advanced user

interface!

accurate fundamental atomic and molecular properties in the core DB!

reliability of results in extreme simulation conditions!

0 1 2 30

1

2

3

T [104 K]

Ental

pia S

pecifi

ca [1

08 J/k

g] p = 1atm

100 atm

10 atm

CHEMKINp = 1atm

Bacri&Raffanel, Plasma Chem.!Plasma Process. 7 (1987) 53, ibidem 9 (1989) 133

AIR

THE EQUILTHETA FEATURES



accurate of mixture transport and thermodynamic properties !


flexibility!


interface!






fast!



flexibility!


interface!







flexibility!

basic and advanced user interface!



complex mixtures in different simulation conditions !

fast!





��

THE EQUILTHETA TOOL



5000 10000 15000 200000

20

40

60

80

100

5000 10000 15000 2000010–5

10–4

10–3

10–2

10–1

100

101

5000 10000 15000 200000.0

1.0

2.0

3.0

5000 10000 15000 200000.0

1.0

2.0

3.0TEMPERATURE [K]

MO

LE F

RACT

ION

SiSi+

Si2+

Si3+Ar2+

Ar+

Ar

Ar

Si(10%)

Si

e

TEMPERATURE [K]

SPEC

IFIC

EN

THA

LPY

[MJ/k

g]

Si(50%)

TEMPERATURE [K] TEMPERATURE [K]

VIS

COSI

TY [1

0-4 k

g/m

.s]

THER

MA

L CO

ND

UCT

IVIT

Y [W

/m.K

]Si

Si(50%)

Si(10%)

Si

Si(50%)

Si(10%)

(a) (b)

(c) (d)

Ar/Si 1:1 !

THERMODYNAMICS AND TRANSPORT COEFFICIENTS OF SILICON-BASED PLASMAS

Ar-Si PLASMA pressure = 1 atm!COMPARISON with the LITERATURE!

Ar/Si !

Ar/Si !Ar/Si !



5000 10000 15000 200000

20

40

60

80

100

5000 10000 15000 2000010–5

10–4

10–3

10–2

10–1

100

101

5000 10000 15000 200000.0

1.0

2.0

3.0

5000 10000 15000 200000.0

1.0

2.0

3.0TEMPERATURE [K]

MO

LE F

RACT

ION

SiSi+

Si2+

Si3+Ar2+

Ar+

ArSi Si (c)

Si2Si3

Ar

Si(10%)

Si

e

TEMPERATURE [K]

SPEC

IFIC

EN

THA

LPY

[MJ/k

g]

Si(50%)


VIS

COSI

TY [1

0-4 k

g/m

.s]

THER

MA

L CO

ND

UCT

IVIT

Y [W

/m.K

]Si

Si(50%)

Si(10%)

Si

Si(50%)

Si(10%)

(a) (b)

(c) (d)

Gu L, Arntsberg A E and Bakken J A 1991 Proc. 10th Int. Symp. Plasma Chemistry (Bochum, Germany, 4–9 August 1991) Ed U Ehlemann et al paper 1.1-6 !Ar-Si PLASMA pressure = 1 atm!

COMPARISON with the LITERATURE!

Ar/Si 1:1 ! Ar/Si !

Ar/Si !Ar/Si !




5000 10000 15000 200000

20

40

60

80

100

5000 10000 15000 2000010–5

10–4

10–3

10–2

10–1

100

101

5000 10000 15000 200000.0

1.0

2.0

3.0

5000 10000 15000 200000.0

1.0

2.0

3.0TEMPERATURE [K]

MO

LE F

RACT

ION

SiSi+

Si2+

Si3+Ar2+

Ar+

ArSi Si (c)

Si2Si3

Ar

Si(10%)

Si

e

TEMPERATURE [K]

SPEC

IFIC

EN

THA

LPY

[MJ/k

g]

Si(50%)


VIS

COSI

TY [1

0-4 k

g/m

.s]

THER

MA

L CO

ND

UCT

IVIT

Y [W

/m.K

]Si

Si(50%)

neglecting Si-Si+ charge-exchangeSi(10%)

Si

Si(50%)

Si(10%)

(a) (b)

(c) (d)

Ar-Si PLASMA pressure = 1 atm!COMPARISON with the LITERATURE!

Ar/Si 1:1 ! Ar/Si !

Ar/Si !Ar/Si !

Gu L, Arntsberg A E and Bakken J A 1991 Proc. 10th Int. Symp. Plasma Chemistry (Bochum, Germany, 4–9 August 1991) Ed U Ehlemann et al paper 1.1-6 !




SiO2 PLASMA pressure = 1 atm!P André, W Bussière, D Rochette, Transport Coefficients of Ag–SiO2 Plasmas Plasma Chem Plasma Process 27 (2007) 381–403!

10000 20000 30000 400001022

1023

1024

10000 20000 30000 400000.0

1.0

2.0

3.0SPEC

IES

DEN

SITY

[m-3

]Si

Si+

Si2+

Si3+

O2+

O+

O

e

SiO

O2

TEMPERATURE [K]

10000 20000 30000 400000

1

2

VIS

COSI

TY [1

0-4 k

g/m

.s]

10000 20000 30000 400000

4

8

12

TEMPERATURE [K]

THER

MA

L CO

ND

UCT

IVIT

Y [W

/m.K

]

10000 20000 30000 400000.0

0.5

1.0

1.5

2.0

2.5

0.0

0.5

1.0

1.5

2.0

Cp S

PECI

FIC

HEA

T [1

04 J/

kg.K

] ELEC

TRIC

AL

CON

DU

CTIV

ITY

[104

S/m

]

λRREA

CTIVE TH

ERMA

L CO

ND

UCTIV

ITY [W

/m.K

]





10000 20000 30000 400001022

1023

1024

1025

10000 20000 30000 400000.0

1.0

2.0

3.0SPEC

IES

DEN

SITY

[m-3

]Si

Si+

Si2+

Si3+

O2+

O+

O

e

SiO

O2

TEMPERATURE [K]

10000 20000 30000 400000

1

2

VIS

COSI

TY [1

0-4 k

g/m

.s]

10000 20000 30000 400000

4

8

12

TEMPERATURE [K]

THER

MA

L CO

ND

UCT

IVIT

Y [W

/m.K

]

10000 20000 30000 400000.0

0.5

1.0

1.5

2.0

2.5

0.0

0.5

1.0

1.5

2.0

Cp S

PECI

FIC

HEA

T [1

04 J/

kg.K

] ELEC

TRIC

AL

CON

DU

CTIV

ITY

[104

S/m

]

λRREA

CTIVE TH

ERMA

L CO

ND

UCTIV

ITY [W

/m.K

]

SiO2 PLASMA pressure = 30 atm!P André, W Bussière, D Rochette, Transport Coefficients of Ag–SiO2 Plasmas Plasma Chem Plasma Process 27 (2007) 381–403!





SiC PLASMA pressure = 1 atm!


10000 20000 30000 400000.0

0.5

1.0

MO

LE F

RACT

ION

Si

Si+Si2+

Si3+C2+C+

C

e

SiC

C2

TEMPERATURE [K]

10000 20000 30000 400000

1

2

VIS

COSI

TY [1

0-4 k

g/m

.s]

1 atm

10

100 atm

10000 20000 30000 400000

5

10

15

20

TEMPERATURE [K]

THER

MA

L CO

ND

UCT

IVIT

Y [W

/m.K

]EL

ECTR

ICA

L CO

ND

UCT

IVIT

Y [1

04 S

/m]

10000 20000 30000 400000.0

1.0

2.0

3.0

1.0

1.2

1.4

10000 20000 30000 400000.0

1.0

2.0

3.0

(Cp)SiC

10000 20000 30000 400000.0

1.0

2.0

3.0

0.2

0.4

0.6λR

λint

THERM

AL CO

ND

UCTIV

ITY [W

/m.K

]

Cp S

PECI

FIC

HEA

T [1

04 J/

kg.K

]Cp

SPE

CIFI

C H

EAT

[104

J/kg

.K]

ISENTRO

PIC COEFFICIEN

T

1 atm

10 atm

100 atm

1 atm

10 atm

100 atm(Cp)SiO2

γSiCγSiO2



CONCLUSIONS AND FUTURE PERSPECTIVES

!  an accurate and extended database of energy levels for atom and molecular silicon species has been created for the calculation of internal partition functions!

!  a complete database of collision integrals (up to high orders) for interactions involving silicon species has been derived, adopting a combined multi-potential—phenomenological approach and accounting for the resonant inelastic channels!

!  all the collision integrals have been fitted with analytical expressions for an easy implementation in transport computational modules!

!  the core databases of the EquilTheTA tool have been updated and extended !

!  thermodynamic properties, equilibrium composition and transport coefficients for Si, Si/Ar, SiO2 and SiC plasma mixtures have been derived at different values of the pressure in a wide temperature range!

!  effect of different mixture ratios !

!  extension to metals (Fe, Al, Mg, Ca …)!

!

hermodynamics and ransport properties of ablated species · 2017. 11. 3. · thermodynamics and...

Documents