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
TEMPERATURE MEASUREMENTS OF SINGLE AND DOUBLE
SHOCK COMPRESSED LIQUID NITROGEN IN OVERTAKING
SHOCK WAVE CONFIGURATION
Alexei A.Pyalling, Vladimir Ya.Ternovoi, Alexander S.Filimonov
Institute for Chemical Physics Research RAS, Chernogolovka, 142432, Russia.
Abstract. In the present work the results of experiments on multiple shock compression of liquid
nitrogen are presented. It was suggested to use two step compression waves to determine temperature of
double compressed nitrogen not using window material. The proposed method can be used to determine
optical densities of shock compressed material and phase-transformation boundaries with high accuracy.
The abnormal speed of the secondary compression wave was registered after single compression to
40 GPa in nitrogen. The transport cross section of the electron-ion interaction in shock-compressed
liquid nitrogen was estimated.
INTRODUCTION
of sound, and compressibility of the material at shock
compression [7]
The behavior of nitrogen under extreme conditions have been studied in theoretical and in experimental works. The simplicity of structure and absence of difficult chemical transformations allows
one to create its equation of state iteratively, taking
into account additional physical effects. In previous
work [1] nitrogen was investigated at relatively low
pressures of shock compression ( P < 40 GPa ),
where it was appropriate to describe its behavior in
the model of molecular liquid [2]. However this theory was unable to describe experiments [3,4] when
nitrogen was compressed up to the pressure of 80
GPa. This required the inclusion of additional physical effects connected with dissociation [5] in the
model.
In the subsequent experiments [6] on double
shock compression of nitrogen was register the effect
of "shock cooling". After the reflection of a shock
wave in nitrogen from a sapphire window, the sharp
decrease of emission intensity was observed. Registered temperature dropped from 8-9 TK in the single
compression wave, to 7-8 TK in double-compressed
wave. It is possible to calculate the heat capacity of
the material having measured the temperature, speed
c
uv
2
(D-U)
—_______U
————————————
where D(U) is the shock wave velocity, U is the mass
velocity, and y is the Griineisen coefficient. If there
are no anomalies on the shock Hugoniot, then
D~a+bU, Ds>0, Dm<0, D>U; so, "shock cooling"
means a negative Griineisen coefficient. However,
the use of a window material for creating the doubleshocked states of nitrogen allows one to attribute the
diminishing of optical emission to the loss of transparency by sapphire window compressed to a pressure of ~ 70 GPa.
The aim of the present work was to conduct experiments allowing us to prove the presence or absence of anomalies in the behavior of nitrogen in the
area of the phase diagram. These data is of interest
also for the development of equation of state of hydrogen, since the same physical models are used for
describing these substances.
95
moment of rapid decrease of temperature) and to
determine its optical thickness more accurately then
in configuration A.
The optical thickness of the target material is determined according to the time of increase of emission from the shock-wave front (from zero level to
the stationary value). The time of emission increase
from the shock wave front is influenced significantly
by the geometry of the striker plate (striker is not
always perfectly flat) forming the preshock wave, so
there are always questions about the correct interpretation of the data observed.
In configuration B the parameters of the layered
system were selected to create high temperature in
the volume of the sample during the temperature
decrease of the shock front after the arrival of release
waves. Thus, the difference between the measured
temperature and the calculated temperature of the
shock wave front gives information about the optical
thickness of the sample.
EXPERIMENTAL SETUP
The experimental assembly consisted of a steel
container 20 mm in diameter (0.5 mm thick bottom)
filled with liquid nitrogen. The upper side the container was closed by the sapphire window, through
which we measured the emission intensity of nitrogen
during compression. The container was immersed in
a foam box surrounded by liquid nitrogen and cooled
to the temperature T0=77 K. The cooled target container was filled with nitrogen of high purity. The
temperature in the assembly was measured with a
chromel-cupel thermocouple. The optical measurement configuration was as in [7].
[Configuration A
EVALUATION OF EXPERIMENTAL DATA.
The equation of state of nitrogen was constructed
according to the referenced model [6]. This model,
for the description of behavior of molecular phase of
nitrogen, uses the variational model of soft spheres.
The free energy is written in the form:
FIGURE 1. Two experimental setups used to measure optical
densities and temperatures of single and double shock compressed
nitrogen; also shown is the pressure profile of nitrogen at a single
time during shock-compression; temperatures are measured both
in the case of non-transparent material and semi-transparent.
Fpu^Fu+FiM+Fel
where FU - free energy in an ideal gas approximation,
Fei- electron component contribution to the free energy, ^int - part of free energy taking into account the
interpartial interaction.
The experiments utilized two different setups
(Fig. 1). In the first (Config. A) the parameters of the
layered system were chosen to generate two-step
structure of the compression wave in nitrogen. The
layer of initially liquid nitrogen was loaded by two
shock waves with increasing intensities. Later a second shock wave caught up with the front of the first
shock wave and formed a single front of strong unitary compression. In the case of semi-transparent
materials it is possible to measure the temperature of
a weak single compression wave, the temperature of
double-shock compressed material and the temperature of an intense single shock compression. In this
configuration it is also possible to evaluate the optical thickness of the material of interest.
In Config. B (Fig. 1) it is possible to determine
the sound velocity of shock-compressed nitrogen (the
The dissociation of nitrogen molecules was taken
into account by assuming ideal, non-interacting nuclear and molecular gases. From the condition of
minimum free energy we obtain
Fdis = min{l - x)F£* + 2xF^°m + F.m + xE& (V) +
The quantity Edis(V) is calculated at T=OK and assumed to be temperature independent. Edis(V) was
assumed to take the form
96
. j (y) = a 0 -fl 1 (V-V 0 ) z V<VQ
V>V0
fo (V) = a 0
EXPERIMENTAL RESULTS AND
DISCUSSION.
9
However, such construction of free energy of a
system, without interactions between various subsystems causes an abnormal form of the "cold" curve
(isotherm at temperature close to zero). At the pressure of "metallization" (atomic configuration is favorable, free energy of atomic and metal phase intersects) on the cold curve, there appears a sharp decrease of pressure. At non-zero temperatures this
results in the formation of quasi-VanDerVaals loops,
imitating the phase transition of first order.
This effect can be eliminated by the introduction
into the model of an additional parameter - occupation of state. We assume that the occupation of
molecular phase varies from 1 at normal density (the
hole system can as in molecular state, as in atomic
state) to 0 - at density of metallization (the system
can no longer be in a molecular state due to the large
density).
^W = ***&)/ Edis(V)>o
Three experiments in Config. A were conducted
(double shock-compression of nitrogen in a single
shock-wave). Two of them were done at relatively
low compression, with a striker plate velocity of 5-6
km/c (Fig. 2). In the third experiment the striker was
accelerated up to a velocity of 7.5 km/s in order to
produce significant dissociation of nitrogen in the
first compression wave (Fig. 4).
200
400
600
800
1000
Time, ns
FIGURE 2. Experiments in configuration A. Experimental data,
calculation of shock temperature and temperature to be measured.
In the first experiments good agreement between
theoretical and experimental temperature profiles
was achieved. There is a good agreement in the initial compression temperature, temperature of the
final, powerful single shock-wave compression, and
the initial profiles of temperature increase. Agreement between measured and calculated temperature
of double-shock compression is not as good. The
sound velocity calculated from these experiments is
in good agreement with theoretical calculation.
In Config. B two experiments were done, with
different initial velocities of the striker plate (Fig.3).
There is a good agreement between the experimental and calculated release profiles. This indicates
that the theory evaluates well the sound velocity of
shocked nitrogen and its volume dependence. Also,
the theory is good in predicting the tail of the release
wave when the temperature on the shock wave front
is lower then measured one, due to emission from the
internal, hot layers of nitrogen. But the time of increase of the emission from the shock-wave front
from zero to the stationary value (at the very beginning of the temperature profile) was predicted properly only for the experiment with lower shock-wave
This construction provides smoothness and monotony of isotherms at the density of metallization
and only slightly affects the behavior of isotherms far
from this density.
For all the experiments, ID gas-dynamic calculations were done, using the above experimental parameters. This allowed one to calculate temperatures
on the shock- wave front, and in the volume of nitrogen. Also, to make a comparison with experimental
temperature profiles, recalculation of emission intensity was performed taking into account the optical
thickness of nitrogen. According to the classical theory, the absorption coefficient depends on the number of electrons, frequency of light and frequency of
electron-atom interactions [8]:
where m is the electron mass, c velocity of light, e is
the electron charge, Ne and Na are the concentrations
of electrons and atoms respectively, q is the effective
frequency of electron-atom interactions, u is the
mean velocity of electrons, and otT is the transport
cross section of electron- atom interactions. Throughout, 0 tr was taken to be o tr = 4 A2.
97
parameters, due to the significant role of shape of
striker plate (non-flatness of plate) in the second
case.
ferent processes. These results cannot be described
using current model EOS of nitrogen, new physical
effects may likely have to be included.
1000
• Optical length obtained from
best fit of all experimental data
X Optical length based on the
temperature increase rate
of the first shock wave front ,
J 100
Shock wave temp
Recalculated temp
Experiment
400
600
800
1000
10
6
1200
Time, ns
FIGURE 3. Experiments in configuration B. Experimental data,
calculation of shock temperature and temperature to be measured.
The parameters of shock compression in the second experiment in configuration B were chosen to be
the same as parameters of the first compression in the
third experiment in configuration A (with high speed
striker) (Fig. 4). The main difference between these
two experiments was that in configuration B the nitrogen after single compression was unloading and in
configuration A nitrogen was double shockcompressed after the initial single compression.
7
8
Temperature, 10 3K
FIGURE 5. Calculated optical density of nitrogen.
The results of optical length estimation of nitrogen from present experimental data are shown on
Fig. 5.
This work was supported in part by Russian Fund
for Basic Researches Grant N 00-02-17550. The
authors thank V. K. Gryasnov and N. A. Afanas'ev
for their help.
REFERENCES
18
16
Single shock
formation
1.
14
£12
2.
£ 10
I 8
3.
4>
H
Shock wave Temp
Recalculated TempExperiment
4
2
100
200
300
400
500
Time, ns
600
4.
5.
700
FIGURE 4. Experiments in configuration A. High velocity. Single shock wave was not formed, contrary to the theory.
Theory was satisfactory in predicting the release
profile in configuration B and in predicting the sound
velocity in nitrogen. On the other hand, it was unable
to predict the time when the second shock wave
overtakes the first one in configuration A. On the
experimental profile there is no sharp increase in
temperature, which can be attributed to this observation. Therefore, two experiments gave two different
estimations of the sound velocity in nitrogen for dif-
6.
7.
8.
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