Transcript PRESSURE OF THE LATTICE

Simulation of phase transitions
and material decomposition
in ultrashort laser–metal interaction
M. Povarnitsyn*, K. Khishchenko, P. Levashov
Joint Institute for High Temperatures of RAS, Moscow, Russia
*[email protected]
15th APS Topical Conference on Shock Compression of Condensed Matter
Kohala Coast, Hawaii
29 June, 2007
Motivation
Laser machining, micro- and nanostructuring, laser-induced plasma
spectroscopy (LIPS), nanoparticle synthesis in vacuum or in a liquid
solution, medical imaging, laser surgery, etc.
Outline
1. Problem setup main parameters
2. Mechanisms of ultrashort laser ablation
3. 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
Setup parameters
 = 0.8 mkm,
L = 100 fs, ( FWHM )
F = 0.15 J/cm2
Single pulse, Gaussian profile
laser
•
•
•
•
•
•
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 ?
targets: Al, Au, Cu, etc.
Stages of ultrashort ablation
1. Pulse L ~ 100 fs
t=0
~10 nm
2. Energy absorption by conduction
band electrons
3. Heat conductivity +
electron-lattice collisions
4. Thermal decomposition and
SW and RW generation
5. Mechanical fragmentation
t < 1 ps
V > 10 km/s
~100 nm
t ~ 5 ps
t > 10 ps
V ~ 1 km/s
V < 1 km/s
t ~ 100 ps
Basic equations
Two-temperature single-fluid multi-material Eulerian
hydrodynamics with sources of absorption and
energy exchange
Interface reconstruction algorithm
2D
3D
j+1
U*t
j
U*
(a)
(b)
(c)
(d)
j-1
i-1
i
i+1
D. Youngs
(1987)
D. Littlefield
(1999)
Symmetric difference
approximation or some
norm minimization is
used to determine unit
normal vector
(e)
Specific corner and specific orientation
choice makes only five possible
intersections of the cell
Two-temperature semi-empirical EOS
Metastable EOS
Stable EOS
Al
g
10
s+l
l+g
1
1
Temperature, kK
Temperature, kK
g
l
CP
10
Al
10
l
CP
(g)
10
s+l
Bn
l+g
Sp
(l)
1
1
s
s
s+g
0.0
0.5
1.0
1.5
s+g
2.0
2.5
3.0
3.5
0.0
0.5
3
(s+l) (s)
1.0
1.5
2.0
2.5
3.0
3
Density, g/cm
Density, g/cm
“instant relaxation”   0
“frozen relaxation”   
kinetic models
3.5
Thermal decomposition of metastable liquid
Al
Temperature, kK
g
10
l
CP
(g)
10
s+l
liquid + gas
l+g
(l)
1
1
Metastable liquid
separation into
liquid-gas mixture
s
s+g
0.0
0.5
(s+l) (s)
1.0
1.5
2.0
2.5
3.0
3.5
3
Density, g/cm
Terms used: homogeneous nucleation; phase explosion; explosive boiling; critical
point phase separation
Model of homogeneous nucleation
0.9Tc<T<Tc
Al
V. P. Skripov, Metastable Liquids (New
York: Wiley, 1974).
Temperature, kK
g
10
l
CP
(g)
10
s+l
l+g
(l)
1
1
s
S. I. Tkachenko, V. S. Vorob'ev, and
S. P. Malyshenko,
J. Phys. D: Appl. Phys. 37, 495 (2004).
s+g
0.0
0.5
(s+l) (s)
1.0
1.5
2.0
2.5
3
Density, g/cm
3.0
3.5
Mechanical spallation (cavitation)
P
P = 0 GPa
P = -2 GPa
P = -5 GPa
Temperature, kK
g
10
CP
(g)
l
10
P
s+l
P
l+g
(l)
1
1
liquid + voids
s
s+g
0.0
0.5
(s+l) (s)
1.0
1.5
2.0
2.5
3
Density, g/cm
3.0
3.5
Time to fracture is
governed by the
confluence of voids
Spallation criteria
Minimal possible pressure
P
P < -Y0
P
Energy minimization
P
D. Grady, J. Mech. Phys. Solids 36, 353 (1988).
Dynamics of ablation of Al target
F = 5 J/cm2
4
50
10 ps
20 ps

3

30
P
P
1
20
10
0
4
0
-200
0
200
400
600
200
400
600

M
40
30
T

3
Density (g/cm )
0
80 ps
30 ps
3
-200
2
20
P
P
1
10
0
0
-200
0
200
x (nm)
400
600
-200
0
200
x (nm)
400
600
Pressure (GPa)
Density (g/cm )
2
Pressure (GPa)
40
3
Ablation dynamics of Al target
20
5
= 0.8 mkm
 = 100 fs
F = 5 J/cm2
15
3
Density (g/cm )
4
10
3
2
5
Al
1
0
0
-1
-5
-200
0
200
x (nm)
400
600
Pressure (GPa)
6
Results with stable and metastable EOSs
Al
g
Temperature, kK
l
CP
10
10
s+l
P~0
l+g
1
1
s
SW
s+g
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
3
Density, g/cm
Al
Temperature, kK
g
10
l
CP
(g)
10
P ~ Pmin<0
s+l
P~0
l+g
(l)
1
1
(l)
s
s+g
0.0
0.5
(s+l) (s)
1.0
1.5
2.0
2.5
3
Density, g/cm
SW
3.0
3.5
Ablation depth in Al target
250
200
Depth (nm)
150
250
this work
ablated depth
melting depth
experiment
Amoruso et al
Colombier et al
simulation
Komashko et al
Vidal et al
200
150
100
100
50
50
0
0
0.1
1
2
Fluence (J/cm )
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