CP620, Shock Compression of Condensed Matter - 2001
edited by M. D. Furnish, N. N. Thadhani, and Y. Horie
© 2002 American Institute of Physics 0-7354-0068-7/02/$ 19.00
INVESTIGATION OF LIQUID-SOLID PHASE TRANSITION USING
ISENTROPIC COMPRESSION EXPERIMENTS (ICE)
Jean-Paul Davis, Dennis B. Hayes, James R. Asay, Phillip W. Watts ,
Paul A. Flores*, and David B. Reisman1^
Sandia National Laboratories, Albuquerque, NM 87185
Bechtel Nevada - Los Alamos Operations, Los Alamos, NM 87544
1
Lawrence Livermore National Laboratory, Livermore, CA 94550
Abstract. Isentropic ramp-wave loading of materials is a novel method to study the kinetics of
phase transitions, particularly in regimes that cannot be accessed by shock-loading techniques. The
Sandia Saturn accelerator produces magnetically driven planar ramp waves of 200-300 ns rise time
in an aluminum drive plate, which then propagate into a material sample. In this way, molten tin
initially at 600-700 K was isentropically loaded to 160-220 kbar, driving it across the liquid-solid
phase boundary. VISAR measurements at a sapphire window interface show possible evidence of
nonequilibrium freezing in tin with a characteristic transition time around 100 ns. Improved experimental techniques are needed to verify this conclusion.
INTRODUCTION
USEFULNESS OF THE ICE TECHNIQUE
An isentropic compression loading technique
has recently been developed at Sandia National
Laboratories* using fast pulsed power to provide
planar magnetic loading of material samples over
several hundred nanoseconds.1 Dubbed "Isentropic
Compression Experiments" (ICE), this method is
well-suited to the study of structural phase transitions, especially those not accessible by Hugoniot
measurements. One transition of interest is freezing
of metals, which, to the authors' knowledge, has
never been observed experimentally under high
strain-rate conditions. Liquid-solid transitions can
be accessed with relative ease using the ICE technique by pre-heating low-melting-point metals such
as tin to the liquid state. This paper presents some
computational results for dynamic loading of molten tin as well as initial results from the first experiments on molten tin performed at Sandia.
Figures 1-3 show how the ICE technique can
access freezing transitions in tin that cannot be
detected using shock-loading techniques. These
plots present results from one-dimensional hydrodynamic calculations using an equilibrium threephase model for tin, described in the next section.
In Fig. 1, phase boundaries, Hugoniot curves, and
ICE loading paths are shown together in the p-T
plane. Due to opposite curvature of the melting line
and Hugoniot curve, the Hugoniot starting from an
initial temperature of 700 K never enters the mixedphase region. The 600-K Hugoniot enters the
mixed-phase region, but never completely transforms to the y-solid phase, instead returning to the
liquid at about 240 kbar. Along the quasi-isentropic
ICE loading paths, however, the temperature remains low and the tin can transform completely to
the y-solid phase. If the transition is far from equilibrium, the ICE loading may follow a metastable
path in a super-cooled liquid state as indicated in
Fig. 1 for an initial temperature of 700 K.
* Sandia is a multi-program laboratory operated by Sandia
Corporation, a Lockheed Martin Company, for the United States
Department of Energy under Contract DE-AC04-94AL85000.
221
produces a shock wave of peak stress about 20 kbar
over the equilibrium transition stress on the ICE
loading path for 600 K. Even at this low overstress,
the partial freezing is overdriven, obscuring information about the transition. The stress histories
shown for ramp-wave loading in Fig. 3, however,
give a clear indication of the stress upon entering
and exiting the mixed-phase region, for propagation
distances small enough to avoid shock formation.
After a shock forms in the mixed-phase region, the
transition is quickly overdriven as shown for a
propagation distance of 0.8 mm.
A thermodynamic equilibrium model of liquid
- solid transition may not be valid on the time scale
of an ICE ramp-wave. The nonequilibrium computational results in Fig. 4, which assume a very simple model for phase change kinetics, indicate sensitivity of the ICE technique to the characteristic time
for dynamic freezing. Thus, not only can the ICE
technique access phase transitions not detectable
using impact experiments, it can also provide experimental data on the kinetics of phase transitions.
Figure 2 shows in-situ stress-time histories in
molten tin at various Lagrangian distances from an
impact surface. The copper impactor at 800 m/s
1700-
liquid
1500
equilibrium
Hugoniot curves
1300
1100
equilibrium
ICE loading paths
y-solid ct(8)
500300
P-solid ct(
0
50
100
150
200
250
pressure (kbar)
300
FIGURE 1. Computed phase diagram of tin with equilibrium
Hugoniot curves (dashed) and ICE loading paths (solid gray) for
initial temperatures of 600 K and 700 K.
uu -
0.0 5mm
80- \
6040-
0.2mm
\O.lmm /
-^
THREE-PHASE MODEL FOR TIN
0.4mm
The continuum calculations presented in the
previous section were performed using a threephase model for tin based on assumptions introduced by Horie and Duvall2 concerning a homogeneous mixture of structural phases; common particle
velocity, common pressure and temperature, and no
interfacial energy between phases. The calculation
method follows that developed by Andrews3 and
extended to N phases by Hayes.4 Each of the
20-
n0
50
100
150
200
time from impact (ns)
FIGURE 2. In-situ longitudinal stress histories in tin initially at
600 K impacted by copper at 800 m/s, computed under the
assumption of equilibrium freezing.
400-
200
time (ns)
FIGURE 3. In-situ longitudinal stress histories at 0.2 mm
intervals in tin initially at 600 K subjected to ICE ramp-wave
loading, computed under the assumption of equilibrium freezing. Load profile based on real Saturn current pulse. Disturbances correspond to mixed-phase region.
200
time (ns)
250
FIGURE 4. In-situ longitudinal stress histories (at a Lagrangian
distance of 0.4 mm from loading surface) for tin initially at 700
K, computed using the present kinetics model.
222
Aluminum drive (0.6mm)
Pymoeeram 9608 insulator (2.0mm)
phases (oc-solid, y-solid, and liquid) has its own
equation of state (EOS), and extensive properties of
the mixture are mass-averaged over all phases. For
the EOS of each phase, a Mie-Griineisen form was
assumed with constant cv, constant T/v, and the
reference p(v) curve given by a Birch isotherm.
Parameter and reference-state values for the three
phases of tin were taken from Mabire and Hereil.5
The phase boundaries in Fig. 1 were computed
by solving for states where the Gibbs free energies
of two phases are equal. Kinetics were introduced
by a simple phenomenological model wherein the
mass fraction rate of change for a given phase is
proportional to the sum of the differences in Gibbs
free energy from each other phase.3 The model was
implemented in the one-dimensional computer code
WONDY.6 It is important to note that the present
model, based solely on macroscopic thermodynamics, is not intended to illuminate the underlying
physics of dynamic freezing. Rather, the goal is to
connect experimental data to continuum modeling.
Confidence in the present model was obtained by
successful comparison (not shown) to the impact
data of Mabire and Hereil,5 which indicate melting
upon release from Hugoniot states.
A]
1
o
Stepped tin sample (0.4mm & 0.7mm)
Stepped sapphire wiridow (2.3mm & 2.0mm)
FIGURE 5. Sketch of experiment configuration showing
thicknesses of the various material layers.
turb the wave entering the molten tin. Pyroceram
9608, a glass ceramic made by Corning, was chosen
because previous impact experiments7 indicated a
ramp-generating behavior up to 200 kbar. This
nonlinear elastic response prevents the input ramp
wave from shocking up over the long propagation
distance required for thermal insulation. Since
Pyroceram 9608 is no longer manufactured, the
present work used material from a small batch recreated by the Corning Cells Group. Results from
recent impact experiments on the new Pyroceram
9608 indicate that it does not reproduce the same
ramping behavior seen in the original material.
Fiber-coupled velocity interferometry (VISAR)
was used to measure time-resolved particle velocity
of the tin/sapphire interface.
EXPERIMENT CONFIGURATION
A pre-molten tin sample was obtained using
small 25-W resistance heater cartridges with feedback control. These heated a tubular copper boat
that defined the lateral extent of a 6.9-mm diameter
cell holding the molten tin. The copper was
clamped between a stepped sapphire window and a
ceramic insulator (12-mm diameter) to define the
axial extent of the tin sample. The insulator was
itself bonded to the aluminum drive plate that forms
part of the anode on the Saturn accelerator. As
shown in Fig. 5, magnetic loading is applied to the
opposite side of the drive plate, sending an unsteady
hydrodynamic stress wave into the series of material
layers. Layer thicknesses are shown in Fig. 5.
The most challenging requirement in these experiments is the thermal insulator between the metallic drive plate (part of an enormous heat sink in
the form of Saturn's power-flow hardware) and the
tin sample. Materials with low thermal conductivity
tend to have high elastic limits that adversely per-
RESULTS
Two molten tin experiments were performed on
the Saturn accelerator, using two different anode
geometries (to obtain different current densities and
hence different peak pressures) and different initial
temperatures. Two heating cells were used on each
experiment; one with the stepped tin sample, the
other with a sapphire window mounted directly on
Pyroceram. Figures 6-7 present VISAR data from
these shots. Note that differences in signal delay
times have not been accounted for.
In shot 2925 (Fig. 6), an untested method was
223
1.0
time (us) uncorrected
1.1
1.2
1.3
time (us) uncorrected
1.4
1.5
FIGURE 6. VISAR velocity records from Saturn shot 2925
(peak pressure approx. 220 kbar, initial temperature 600 K).
FIGURE 7. VISAR velocity records from Saturn shot 2926
(peak pressure approx. 160 kbar, initial temperature 700 K).
used to bond the sapphire window to the pre-heated
Pyroceram. The bond evidently failed, leaving a
small gap that resulted in an impact. In shot 2926
(Fig. 7), the heater without a tin sample was left at
room temperature, and the Pyroceram/sapphire
bond appears to have maintained its integrity. In
this case, however, a useful measurement of the
ramp wave exiting the Pyroceram was prevented by
early (relative to the ramp rise-time) arrival of edge
waves at the probe location. This was due in part to
use of two off-center probes for redundancy (shot
2925 used only one centered probe).
The tin/sapphire interface velocity at which
freezing is expected to initiate was computed using
the model described earlier, and is indicated on
each of Figures 6-7. The experimental data show a
distinct two-wave structure that, based on other
experiments using Pyroceram (not shown), is
probably due to a disturbance generated in the new
Pyroceram 9608 insulator material. In Fig. 6, the
second wave is overtaking the first wave, consistent
with a double-ramp wave having entered the tin
from the Pyroceram. If the plateau were due to
freezing, it would be expected to occur at a higher
velocity in Fig. 7 due to the higher initial temperature (cf. Fig. 1); instead, it appears at the same velocity. Nonequilibrium dynamic freezing may
cause the change in curvature with propagation seen
at the top of the first wave. If so, then comparison
to nonequilibrium computations would suggest a
characteristic time for freezing on the order of 100
ns. It should be noted that, based on the results in
Figures 3-4, the present experiments are only expected to detect freezing if it occurs with a charac-
teristic time of less than 400-500 ns.
FUTURE WORK
Further experiments are planned using a sapphire insulator in place of the Pyroceram to provide
an unperturbed ramp wave up to 300 kbar (within
the elastic regime of sapphire under ICE loading).
Though sapphire has an order of magnitude higher
thermal conductivity, the heating cell was overdesigned by a wide margin. Also being considered
are LiF windows to increase signal reading time.
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224
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