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
THERMODYNAMIC PARAMETERS AND EQUATION OF STATE
OF LOW-DENSITY SiO2 AEROGEL
M-V-Zhernokletov1*, T.S.Lebedeva1*, A.B.Medvedev1*, M.A.Mochalov1*,
A-RShuykin1*, V.E.Fortov2)
1) Russian Federal Nuclear Center - VNIIEF, Sarov, Russia, 607190
2) Institute of Extreme State Thermodynamics, Moscow, 127412
Abstract. This paper studies properties of low-density SiO2 aerogel of initial density p0 = 0.08 g/cm3,
0.15 g/cm3, and 0.19 g/cm3 in shock compression up to ~ 13 GPa pressures in plane- and semisphericalgeometry devices. Shock-wave velocities up to ~14 km/s, luminance temperatures up to -20000 K, light
absorptivity a ~ (1-4)103 cm"1 in a shock-compressed aerogel, and sound speed are measured with the
optical method in visible spectrum (X = 406, 498, 550, and 600 nm). Thermodynamic parameters of
liquid-state aerogel are calculated by the equation of state using the modified van der Waals model for
reactive mixtures.
INTRODUCTION
Institute were used. The experimentally measured
spectral transmission of aerogel in the 400...600nm
range is 60...80%, which allowed using the optical
method to measure cinematic and thermodynamic
parameters of SiO2 aerogel during its shock
compression.
The experimental scheme for simultaneous
measurement of shock wave velocity and luminance
temperatures at the front in the plane-wave
experiments is presented in Fig. 1.
The ~3-mm-thick SiO2 aerogel sample to be
studied was fastened in a cell evacuated down to
residual pressure no worse than 10"1 mm Hg and
covered with a sapphire substrate 2 mm thick. All
the measurements were performed with 4-channel
photoelectronic pyrometer [8], whose design appears
in Fig.l. The shock front emission in the aerogel was
formed to a parallel light beam through diaphragm
0 10 mm in the chamber casing and external
reflector (1) by objectives (2) and (4), then the beam
was directed to pyrometer (5).
Glass plates (11-14) distribute emission among
four photoelectric multipliers. To separate spectral
ranges, interference filters of -50% transmission at
wavelengths X = 406 nm, 498 nm, 550 nm, and 600
nm at 10 nm half-height bandwidth were used.
Silicon aerogels of a low initial density (0.0080.36 g/cm3) have been extensively used recently for
producing and studying nonideal plasma at high
local energy and temperature concentrations. Using
porous samples extends the material phase diagram
range accessible to dynamic experiments. Principal
experimental data for highly porous samples has
been obtained with dynamic methods through
material compression and irreversible heating at the
front of powerful shock waves generated by
condensed and nuclear explosive detonation [1-7].
Refs. [5-6] measure luminance temperatures in
addition to aerogel compressibility.
This paper measures thermodynamic parameters
of shock-compressed aerogel using a pyrometer of
visible spectrum (400... 600 nm). A wide
experimental data set is obtained with the optical
method and used to test the equation of state of lowdensity SiO2 aerogel.
MEASUREMENT METHOD AND
EXPERIMENTAL RESULTS.
Samples of initial density 0.08, 0.15, and
0.19 g/cm3 fabricated by Novosibirsk Catalysis
763
Typical oscillograms of radiation luminance
buildup at the shock front in aerogel are presented in
Fig. 2.
D,km/s
U, km/s
SiOz aerogel
10
0 - 0.008, • - 0.08, • - 0.15, V - 0.19, o - 0.27, V - 0.36 g/cm3
fitted data from this paper:
—————— D(U) = 0.556 + 0.868 U + 0.022 U2
FIGURE 3. Low-density aerogel Hugoniot
1- reflector; 2,4 - objectives; 3 - diaphragm; 5 - pyrometer
casing; 6, 7, 8,9,10 photoelectric multiplier; 11,12,13,14
deflection plates.
FIGURE 1. Experimental scheme and measuring cell design
Shock front luminosity
in aerogel
12
Shock wave release to
sapphire substrate
2 6
2 4
2 2
2 0
0
time 200ns/div
upper beam - X = 406nm, lower beam - A, = 498nm
10
20
30
(E -E
40
50
O ),
k J/g
60
70
n - 0.008, • - 0.08, • - 0.15, T - 0.19, o - 0.27, V - 0.36 g/cm3
___- calculation by equation of state for POO= 0.15 g/cm3;
FIGURE 4. Aerogel luminance temperatures vs. shock
compression energy
FIGURE 2. Oscillograms of shock front emission in SiO2 aerogel
and sapphire substrate
The oscillogram provides the strict time of the
shock wave arrival at aerogel and an abrupt signal
burst at the time of the shock wave arrival at the
aerogel-sapphire interface, which allows the shock
wave velocity to be measured. Material mass
velocity behind the shock front was calculated
through intersection of the wave beam with
unloading isentropes of screen material (aluminum)
that had been computed by the equation of state with
taking into account melting [9,10].
Compressibility and luminance temperatures up
to 13GPa were measured with semi-spherical
geometry device MZ-4 [11].
The results of this paper along with the data on
shock compressibility and luminance temperatures
of aerogel with initial density 0.008, 0.27, and 0.36
g/cm3 from refs. [5-6] are given in Fig. 3 and Fig. 4.
The measurement accuracy is 0.5% for shockwave velocity, ~ 1% for mass velocity, ~ 5% for
luminance temperatures.
The measured luminance temperatures in the 2 <
P < 13 GPa pressure range were obtained by
comparison between the front emission amplitude
and the reference source emission.
Sound speed in the shock-compressed aerogel
was measured with the "overtaking" method [8].
The experiment used a sample of poo = 0.15 g/cm3
and thickness increased up to ~ 7 mm, so that the
rarefaction wave on the side of the impactor
definitely overtake the shock wave in the sample. A
typical oscillogram for the emission in aerogel at
764
Previously, the model had been successfully
employed for the description of experimental data
for various materials, both individual and mixed, in
a wide range of states [9,10]. This is a covolume
model. Variability of the covolume (intrinsic particle
volume)
reflects
compressibility.
Mixture
composition is found from the condition of
minimum free energy. At high temperatures, Saha
equations are solved.
The calculations included the following
molecules, atoms, and ions: SiO2, SiO, Si, Si2, O, O2,
Si+, Si++, O+, <9++, etc., and electrons. When
selecting the covolumes of Si and O2, experimental
data on shock compressibility of these constituents
were taken into consideration. It was assumed that
covolume of Si2 was equal to that of Si, covolume of
O was the same as in O 2 - When selecting the
covolume of molecular SiO2 and attraction, the data
on silica glass density, isothermal compressibility,
and sublimation energy were used. The covolume of
SiO was considered as adjustment covolume because
of missing data for behavior of this constituent at
high pressures. Covolume considered to be not
varied during ionization. Only were considered main
electronic states of particles. We treat the molecules
using
rigid
rotator-harmonic
oscillator
approximation. Ionization potential was assumed
constant.
The description of the experimental data by the
model under discussion at relatively low pressures is
presented in Fig.7.
shock compression pressure P = 6.59 GPa at
wavelength A, = 406 nm appears in Fig. 5.
FIGURE 5. Oscillogram of shock front luminosity
The calculated data for motion of the shock
wave (SW) and rarefaction waves (RW) in this
device and experimentally measured time At = (799
± 4) ns were used to estimate sound speed in shockcompressed aerogel as Cs = 3.8 km/s.
1 o Vr, K
•- aerogel (POO = 0.15 g/cm3),
• - silica glass (p™ = 2.205 g/cm3)
FIGURE 6. Light absorptivity vs. temperature for aerogel and
silica glass shock compression.
20000 W Pbo=0.32
O.I
Light absorptivity was measured by recording
radiation luminance buildup with time during the
shock wave propagation through aerogel, which was
related to the increase in thickness of the material
layer compressed by the shock wave and its
transparency [12]. The obtained results averaged for
the visible spectrum (400-600nm) are presented in
Fig.6 along with data for silica glass from ref. [13].
; T=10000 K
15-
ft g/cfo
EQUATION OF STATE OF SiO2.
COMPARISON WITH THE EXPERIMENT
Thermodynamic properties of liquid and
gaseous silicon dioxide at high pressures and
temperatures were calculated including vaporization,
dissociation, and ionization of constituents by the
modified model of van der Waals equation of state.
Experiment: • -[2],———— - [3], o, • - [4],
+, T - [5-6], A,<fr -this paper.
Initial densities of the samples are specified near the computed
curves. T=2000K, 10000K, and 20000K are isotherms.
FIGURE 7. Porous quartz Hugoniots.
765
One can see a satisfactory agreement between
the experimental and calculated data. An exception
are results from refs. [6] at initial density 0.36g/cm3.
Fig. 8 depicts porous quartz Hugoniots in the
pressure range up to lOOGPa, and Fig. 9 gives those
in the pressure range up to 3TPa. The interpretation
of the results at high pressures depends on the
equation of state of reference material. A
displacement in some data [1, 7] when using the
equation of state of aluminum from [9,10] is
indicated in Fig. 9 with arrows.
this may be equilibrium radiation shielding because
of a high light absorptivity at the shock front.
This model of the equation of state of aerogel
does not reproduce the temperature "shelves"
depending on shock compression energy noted in
Refs. [5-6].
The calculated sound speed at P = 6.59 GPa
agrees with the experimental value within the
measurement error (10-15)%.
REFERENCES
1.
2.
3.
4.
5.
6.
Experimental data for p =0.19 and 0.32 g/cm3 from ref. [4]. The
other data is from [1]. The notations are the same as in Fig. 7
FIGURE 8. Porous quartz Hugoniots up to lOOGPa pressure
7.
200000 K
=2 €
1.75
Poo -
100000 K
2-
9.
1.35
S.
10.
T=1000K
11.
12.
13.
P, g/cm3
Experimental data from refs. [1,7]. The notations are the same as
in Fig.7
FIGURE 9. Continuous and porous quartz Hugoniots up to 3GPa
pressure
The calculated aerogel temperature as a function
of shock compression energy appears in Fig.7. The
measured values are seen to lie lower, than they
should according to the computation. A reason for
766
Simakov G.V., Trunin R.F. Izv. AN SSSR. Fizika
Zemli, 1990,No.ll,p.72
Holmes N.C., See E.F. In: Shock Compression of
Condensed Matter -1991, pp.91-94. 1992 Elsevier
Science Publishers B.V.
Holmes N.C. In: High-Pressure Science and
Technology- 1993, pp.153-156. 1994 American
Institute of Physics
Vildanov V.G., Gorshkov M.M. et al. In: Shock
Compression of Condensed Matter- 1995, pp. 121124. American Institute of Physics. NY, 1996
Gryaznov V.K., Nikolayev D.N., Ternovoy V.Ya.,
Fortov V.E. et al. Khimicheskaya Fizika, V. 17, No.2,
pp. 33-37.
Nikolaev D.N., Fortov V.E., Filimonow A.S., Kvitov
S.V., Ternovoi V.Ya. In: Shock Compression of
Condensed Matter - 1999, pp. 121-124. American
Institute of Physics, NY, 2000.
Trunin R.F., Podurets M.A., Simakov F.V. et al.
ZhETF, 1995, V.108, No.3(9), pp.851-861.
Kormer S.B., Sinitsyn M.V., Kirillov G.A., Urlin
V.D. ZhETF, 1965, V. 48, No. 4, pp. 1033-1048.
Medvedev A.B. Voprosy Atomnoj Nauki i Tekhniki.
Ser. Teor. i Prikl. Fizika. 1992, No.l, pp. 23-29.
Kopyshev V.P., Medvedev A.B. Sov. Tech. Rev. B.
Therm. Phys. Rev. Vol. 5. 1993. pp.37-93
Altshuler L.V., Trunin R.F., Krupnikov K.K., Panov
N.V. UFN, 1996, V.166, No.5, pp.575-581.
S.B.Kormer. UFN, 1968, V. 94, p. 641.
Sugiura H, Kondo K, Sawaoka. J.Appl.Phys., 1982,
Vol.53, No.6, pp.4512-4514.