Simulation of phase transitions and material decomposition

in ultrashort laser–metal interactionM. Povarnitsyn*, K. Khishchenko, P. Levashov

Joint Institute for High Temperatures of RAS, Moscow, Russia*povar@ihed.ras.ru

15th APS Topical Conference on Shock Compression of Condensed MatterKohala Coast, Hawaii

29 June, 2007

Outline1. Problem setup main parameters2. Mechanisms of ultrashort laser ablation3. Numerical model

• Basic equations• Equations of state (EOSs)• Thermal decomposition model (homogeneous nucleation)• Mechanical decomposition model (spallation)

4. Results• Dynamics of ablation• Analysis of phase trajectories• Ablation in the case of different EOSs

5. Conclusions and future plans

MotivationLaser machining, micro- and nanostructuring, laser-induced plasma spectroscopy (LIPS), nanoparticle synthesis in vacuum or in a liquid solution, medical imaging, laser surgery, etc.

Setup parameters

laser

targets: Al, Au, Cu, etc. = 0.8 mkm,L = 100 fs, ( FWHM )F = 0.15 J/cm2

Single pulse, Gaussian profile

Actual questions: • Heat wave propagation ? • Melted zone depth ?• Cavitation and fragmentation ?• Parameters of the plume ?• Generation of nanoparticles, clusters and chunks ?• Ablation depth vs laser flux ?

Stages of ultrashort ablation

t = 0

1. Pulse L ~ 100 fs

~10 nm

t < 1 ps

2. Energy absorption by conduction band electrons

~100 nmt ~ 5 ps

3. Heat conductivity + electron-lattice collisions

V > 10 km/s

t > 10 ps

4. Thermal decomposition and SW and RW generation

V ~ 1 km/s

t ~ 100 ps

5. Mechanical fragmentation V < 1 km/s

Basic equations

Two-temperature single-fluid multi-material Eulerian hydrodynamics with sources of absorption and energy exchange

Interface reconstruction algorithm

(a) (b)

(c) (d)

(e)

D. Youngs (1987)

D. Littlefield (1999)

Specific corner and specific orientation choice makes only five possible

intersections of the cell

Symmetric difference approximation or some norm minimization is

used to determine unit normal vector

j+1

j

j-1

i-1 i i+1

U*t

U*

3D2D

Two-temperature semi-empirical EOS

“instant relaxation” 0

1

10

1

10

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Density, g/cm3

Al

l+g

Te

mp

era

ture

, kK

s

lg

s+g

s+l

CP

kinetic models

Stable EOS

1

10

1

10

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Density, g/cm3

l+g

(s)

(g)

(s+l)

(l)

Te

mp

era

ture

, kK

Al

s

lg

s+g

s+l

CP

“frozen relaxation”

Metastable EOS

Sp

Bn

1

10

1

10

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Density, g/cm3

l+g

(s)

(g)

(s+l)

(l)

Te

mp

era

ture

, kK

Al

s

lg

s+g

s+l

CP

Thermal decomposition of metastable liquid

Metastable liquid separation into liquid-gas mixture

Terms used: homogeneous nucleation; phase explosion; explosive boiling; critical point phase separation

liquid + gas

Model of homogeneous nucleation

V. P. Skripov, Metastable Liquids (New York: Wiley, 1974).

S. I. Tkachenko, V. S. Vorob'ev, and S. P. Malyshenko, J. Phys. D: Appl. Phys. 37, 495 (2004).

1

10

1

10

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Density, g/cm3

l+g

(s)

(g)

(s+l)

(l) T

em

pe

ratu

re,

kK

Al

s

lg

s+g

s+l

CP

0.9Tc<T<Tc

1

10

1

10

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Density, g/cm3

P = 0 GPa P = -2 GPa P = -5 GPa

l+g

(s)

(g)

(s+l)

(l)

Te

mp

era

ture

, kK

s

lg

s+g

s+l

CP

Mechanical spallation (cavitation)

P

P

P

Time to fracture is governed by the confluence of voids

liquid + voids

Spallation criteria

Minimal possible pressure

D. Grady, J. Mech. Phys. Solids 36, 353 (1988).

P < -Y0

Energy minimization

P

P

P

Dynamics of ablation of Al target

0

10

20

30

40

50

0

10

20

30

40-200 0 200 400 600

0

1

2

3

4D

ensi

ty (

g/cm

3 )

10 ps

-200 0 200 400 600

20 ps

-200 0 200 400 600

0

1

2

3

4

x (nm)

Den

sity

(g/

cm3 )

30 ps

-200 0 200 400 600

x (nm)

80 ps

Pre

ssur

e (G

Pa)

Pre

ssur

e (G

Pa)

TM

P

P

P

P

F = 5 J/cm2

-5

0

5

10

15

20

-200 0 200 400 600

-1

0

1

2

3

4

5

6

x (nm)

Den

sity

(g/

cm3 )

Pre

ssur

e (G

Pa)

Ablation dynamics of Al target

Al

= 0.8 mkm = 100 fsF = 5 J/cm2

Results with stable and metastable EOSs

1

10

1

10

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Density, g/cm3

Al

l+g

Te

mp

era

ture

, kK

s

lg

s+g

s+l

CP

1

10

1

10

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Density, g/cm3

l+g

(s)

(g)

(s+l)

(l)

Te

mp

era

ture

, kK

Al

s

lg

s+g

s+l

CP

SW

P ~ 0

P ~ Pmin<0

SW

P ~ 0

(l)

0.1 1

0

50

100

150

200

250

0

50

100

150

200

250

this work ablated depth melting depth

experiment Amoruso et al Colombier et al

simulation Komashko et al Vidal et al

De

pth

(n

m)

Fluence (J/cm2)

Ablation depth in Al target

1. Povarnitsyn et al, PRB 75, 235414 (2007); 2. Amoruso et al, Appl. Phys. 98, 044907 (2005); 3. Colombier et al, PRB 71, 165406 (2005); 4. Komashko et al, Appl. Phys. A 69, S95 (1999); 5. Vidal et al, PRL 86, 2573 (2001)

Conclusions and Outlook

1. Simulation results are sensitive to the models used: absorption, thermal conductivity, electron-lattice collisions, kinetics of nucleation, fragmentation criteria, EOS, etc…

2. Time-dependent criteria of phase explosion and cavitation in metastable liquid state were introduced into hydrodynamic model

3. Observed decomposition of ablated substance is due to:• thermal phase separation in the vicinity of critical point• mechanical fragmentation of liquid phase at high strain rates and

negative pressures

4. Usage of metastable and stable equations of state allows to take into account kinetics of metastable phase separation in metastable liquid

5. Ablation depth correlates with the melted depth

6. Treatment of individual droplets and bubbles will be introduced since their size may be comparable with the size of grid cells

Conclusions and Outlook

1. Simulation results are sensitive to the models used: absorption, thermal conductivity, electron-lattice collisions, kinetics of nucleation, fragmentation criteria, EOS, etc…

2. Time-dependent criteria of phase explosion and cavitation in metastable liquid state were introduced into hydrodynamic model

3. Observed decomposition of ablated substance is due to:• thermal phase separation in the vicinity of critical point• mechanical fragmentation of liquid phase at high strain rates and

negative pressures

4. Usage of metastable and stable equations of state allows to take into account kinetics of metastable phase separation in metastable liquid

5. Ablation depth correlates with the melted depth

6. Treatment of individual droplets and bubbles will be introduced since their size may be comparable with the size of grid cells