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
SHOCK TEMPERATURE OF NaCl MEASURED WITH WIDE-BAND
OPTICAL RADIOMETRY
Toshiyuki Ogura1, Kazutaka G. Nakamura1, Hisataka Takenaka2, and Ken-ichi Kondo1
Materials and Structures Laboratory, Tokyo Institute of Technology, 4259 Nagatsuta, Midori, Yokohama 2268503, Japan
2
NTT Advanced Technology Corporation, 3-9-11, Midori, Musashino, Tokyo 180-8585, Japan
Abstract. Shock temperature of NaCl was measured with time-resolved (3-nanosecond resolution)
wide-band optical radiometry observing the radiation ranging from 0.6 to 13 jim in the pressure range
between 17 and 43 GPa. In case of samples above 2000 K, the emitted radiation was measured with a
visible to near-IR radiometer (0.6-1.6 jum). This radiation associated with a phase transition which arises
at the defect sites such as dislocations. An IR radiometer sensitive to 9-13 urn was used to measure the
bulk temperature below 1000 K. In the mixed-phase region between 23 and 33 GPa, thermal
heterogeneity was observed in shock-loaded NaCl. In the low-pressure phase (Z?l) between 17 and 21
GPa, the shock temperature obtained with IR radiometer was almost 400 K lower than the values
obtained by Fritz et al.1
problem for measuring low shock temperature below
2000 K because of an insufficient emission in a
visible wavelength range. For NaCl in the pressure
range below 45 GPa, while the radiometric
technique revealed the nature of local hot spot,3 it
was impossible to determine the bulk temperature.
The thermal information of the bulk is indispensable
not only for constructing EOS but also for
understanding the mechanism of the phase transition
under dynamic high pressure loading. In a previous
study, the infrared radiometry was developed for the
purpose of observing low shock temperature.4
In this study, we measured the shock temperature
of NaCl by observing shock-induced emission at the
wavelength between 0.6 and 13 |um. An isothermal
compression curve was derived from experimentally
determined shock temperature data and compared
with the available NaCl pressure standards.
INTRODUCTION
Mechanical properties of sodium chloride (NaCl)
under high pressure have been pursued by various
methods, x-ray analysis, shock and particle velocity
measurements, and ultrasonic measurements. These
experimental devotions were succeeded in the
construction of high pressure EOS of NaCl by
Decker,2 which is utilized as a pressure standard
below 30 GPa. The shock wave data by Fritz et al.l
play an important role on this pressure standard. In
their treatment, the shock temperature, however, was
derived from Hugoniot with assumptions on
thermodynamic parameters. It is desirable to
determine the shock temperature experimentally
without any assumption.
Optical radiometry has been usually used for
shock temperature measurement. It has, however, a
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0.10
(a)
£0.05
0.00
4-COLOR RADIOMETER
-
IR RADIOMETER
1
0
1
Time [>s]
2
3
FIGURE 1. The schematic drawing of the experimental setup
for shock temperature measurement.
EXPERIMENT AND DATA ANALYSIS
Shock wave was generated by a plate-impact
method with a flyer accelerated with 20mm-bore,
double-stage light-gas gun at Tokyo Institute of
Technology. The copper impactor 1.7-3.7 km/s
brought NaCl single crystal ([100] or [111]
perpendicular to the shock wave front) to the
pressure 17-43 GPa.
Emission between 0.6 and 13 urn from shockloaded NaCl was observed using wide-band optical
radiometric system shown in Fig. 1. The system
consisted of the 4-channel visible - near IR
radiometer (3-ns temporal resolution, silicon and
InGaAs optical device) sensitive to 0.6-1.6 um
emission and the 1-channel IR radiometer (HgCdTe
device cooled to 76 K) sensitive to 9-13 jam.
The temporal change of the IR (9-13 jam)
emission was analyzed in order to derive the
temperature with the equation;
0.2
0.4
Time [us]
FIGURE 2. The temporal change of the emission from shockloaded NaCl. (a) infrared (9-13 jam) at 21 GPa, (b) near IR (1.1
\im) at 24 and 43 GPa.
(2)
where A, /?, T are absorption, reflection, and
transmission of the sample, respectively.
The temporal profile of 0.6-1.6 um emission
changed with the shock pressure as shown in Fig. 2
(b). While the emission obeyed Eq. (1) for the
pressure above 40 GPa, it peaked during the shock
duration for the pressure below 35 GPa. The 4-color
0.6-1.6 um spectrum was fitted to the graybody
spectrum;
', CD
where & is the emissivity and /^ is the corresponding
blackbody radiation. as and av are absorption
coefficients of the shocked and the unshocked NaCl,
respectively, d is the initial thickness of the sample.
The experimental record is shown in Fig. 2 (a) along
with the least square fit to Eq. (1). In order to
determine the value of £, the reflectivity of the shock
wave front was measured and Kirchhoff s relation
was applied;
s^e*'"-\
(3)
to determine the temperature, T, and the emissivity,
£, where A is wavelength and Cl and C2 are constants
(Q= 1.191xlO-16 W-m'-sr-1, C2= 1.439xlO-2m-K).
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5000
Hugoniot temperature below the phase transition
pressure 23 GPa. This is explained as follows; the
expected temperature is obtained by separating the
increase in internal energy induced by shock wave
into lattice compression part and thermal part,
o c
4000
£ 3000
8
shock ~ ^^compression "^ ^tL thermal •
!
&2000
—V— IR A NIRflOO]
T IRflll]
O Schmitt
A Kondo
D Kormer
O Ahrens
———Fritz
•••••Al'tshuler
---Isentrope
1000
0
10
20
30
40
50
60
70
(4)
On the other hand, it is reported that a large number
of defects such as slip surfaces, dislocations and
point defects are generated in the shock-compressed
solids. In considering dislocation, formation of
dislocations will consume the shock energy as the
form of strain energy. The new term should be added
toEq.(4),
80
Pressure [GPa]
FIGURE 3. The shock temperatures of NaCl below 80 GPa
determined with the wide-band optical radiometry along with the
data in the literatures.
shock ~
* compression + A/i thermal
defect
. (5)
Comparing with Eq. (4), the thermal part of the
internal energy can decrease the shock temperature.
Assuming the formation of the screw dislocation as
an example, the elastic strain energy per unit length
is written as;
RESULTS
The experimental results are shown in Fig. 3.
Above 35 GPa, the temperatures measured by the IR
(9-13 urn) observations are comparable with those
from the near-IR (0.6-1.6 um). These agree well
with the results by Kormer.5
Between 23 and 33 GPa, where the crystal is in
the mixed phase state of Bl (NaCl) and B2 (CsCl)
structures, the results obtained by the two methods
differ from each other. The IR temperatures keep
constant value around 800 K. In contrast, the nearIR temperatures are significantly higher values from
2000 to 4000 K and the brightness of the near-IR
emission is small (the emissivity is in the order of
0.01). All the values of temperatures differ from the
expected Hugoniot temperature obtained by Fritz et
al. (solid line in Fig. 3).
The IR temperatures become lower and approach
to the temperatures for the isentropic compression
(dashed line) below 23 GPa. The 0.6-1.6 um
emission becomes weaker abruptly and is below the
sensitivity of the radiometer.
The reflectivity of the shock wave front is 44% at
maximum at 19 GPa for the IR emission range.
,,5 Gb ,( R
E =——ln| —
4n
(6)
where G, b, R, r0 are shear modulus, Burgers vector,
grain size including dislocation considered, and
radius of dislocation core (almost equal to 5&),
respectively. Using Eq. (6) and the deviation of the
temperature from
the expected
Hugoniot
temperature, the dislocation density in shocked NaCl
is estimated to be 1017 m"2. This value is larger than
the typical density of 109 - 1016 in 2 . The point
defect-dislocation and the dislocation-dislocation
interactions may decrease the density.
In the mixed phase region between 23 and 33
GPa, the measured temperatures, both the IR and the
near-IR measurements, abruptly increase. This will
be explained by the disappearance of dislocations
and the release of the strain energy. It was reported
that the dislocation of the order of 1016 m"2 existed in
the shock-loaded steel recovered from 10.4 GPa and
that the density decreased when the shock pressure
exceeded the transition pressure because of the
DISCUSSIONS
The temperature obtained with the IR radiometer
is significantly lower than the expected continuum
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It is revealed that the EOS obtained from shock
temperature measurements is above the others by
5.9% in the pressure range 16-20 GPa when the
reflectivity of the shock front is negligible. Even if
the reflectivity of the shock front is assumed to be
44%, which is the maximum value measured at 19
GPa, our EOS is still higher by 4.9%. This value is
larger than the experimental error. It is, therefore,
concluded that the isotherm may be shifted to higher
pressure in the pressure range of 16-20 GPa.
By fitting the Birch-Murnaghan equation;8
30
20
O
10
———Decker (1971)
——— ftitz(1971)
— •••Brown (1999)
• This work
——— RtofB-Meq.
0.6
0.8
V/Vo
0.7
0.9
1.0
(8)
FIGURE 4. The isothermal compression curve at room
temperature obtained from Eq. (8) along with the available NaCl
pressure standards.
V0
it is possible to estimate the pressure derivative of
bulk modulus, K0". Using K0= 23.84 GPa and K0' =
5.352 (obtained from ultrasonic measurement below
3 GPa9), K0" becomes -0.30 GPa'1. This value is
smaller than that obtained from ultrasonic
measurements, -0.68 GPa"1. Using the EOS by Fritz
et al., K0" becomes -0.46 GPa"1.
rearrangement of atoms.6 The energy released from
dislocations will be converted to the thermal energy
and increase the temperature. Therefore, the
disappearance of dislocations and the release of the
elastic strain energy can generate the high
temperature regions heterogeneously scattered in
shocked solid. The extremely high temperature
ranging 2000-4000 K observed with the near-IR
(0.6-1.6 jLim) radiometer is considered to be due to
these hot spots.
ACKNOWLEDGEMENT
This work was supported by Core Research for
Evolutional Science and Technology (CREST)
program of Japan Science and Technology
Corporation (1ST).
DERIVATION OF THE 293 K ISOTHERMAL
COMPRESSION CURVE FOR NaCl
Using the temperature measurement data of NaCl
below the transition pressure, 293 K isothermal
compression curve was derived and compared with
the available NaCl pressure scale, i.e., the
calculation from atomic model by Decker2 and
Brown,7 and the shock wave data by Fritz et al.1 The
measured shock temperature was utilized to convert
the shock wave EOS to the isotherm under room
temperature using the equation,
dP_
dE
,
REFERENCES
1. Fritz, J. NL, Marsh, S. P., Carter, W. J., and McQueen, R.
G., in Accurate Characterization of the High Pressure
Environment, edited by E. C. Lloyd, National Bureau
of Standards, Washington DC, 1972, Vol. 326, pp. 201208.
2. Decker, D. L., J. Appl. Phys. 42, 3239 (1971).
3. Schmitt, D. R., Ahrens, T. J., and Svendsen, B., J. Appl.
Phys. 63,99(1988).
4. Fat'yanov, O. V., Ogura, T, Nicol, M. R, Nakamura, K.
G., and Kondo, K., Appl. Phys. Letters 77, 960 (2000).
5. Kormer, S. B., Sov. Phys. Uspekhi 11, 229 (1968).
6. Huo, D. T. C., and Ma, C. H., /. Appl. Phys. 46, 699
(1975).
7. Brown, J. M., J. Appl. Phys. 86, 5801 (1999).
8. Birch, F., J. Geophys. Res. 83, 1257 (1978).
9. Spetzler, H., Sammis, C. G., and O'Connell, R. J., J.
Phys. Chem. Solids 33, 1727 (1972).
(7)
with the Debye model of heat capacity and the
constant y/y . The result is shown in Fig. 4.
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