Time dependent shock temperatures were measured for stainless steel (SS) films in contact with transparent anvils. The anvil/window material was the same as the driver material so that there would be symmetric heat flow from the sample. Inferred Hugoniot temperatures, T_h , of 5800–7500 K at 232–321 GPa are consistent with previous measurements in SS. Temperatures at the film‐anvil interface (T_i ), which are more directly measured than T_h , indicate that T_i did not decrease measurably during the approximately 250 ns that the shock wave was in Al_2O_3 or LiF anvils. Thus an upper bound is obtained for the thermal diffusivity of Al_2O_3 at the metal/anvil interface at 230 GPa and 6000K of κ≤0.00096 cm_2/s. This is a factor of 17 lower than previously calculated values, resulting in a decrease of the inferred T_h by 730 k. The observed shock temperatures are combined with temperatures calculated from measured Hugoniots and are used to calculate thermal conductivities of Al_2O_3. Also we note that since there was no measurable intensity decrease during the time when the shock wave propagated through the window, we infer from this that Al_2O_3 remained transparent while in the shocked state. Thus sapphire is a good window material to at least 250 GPa for shock temperature measurements for metals

Abelson, J. R.

Ahrens, Thomas J.

Bass, Jay D.

Fitzner, M.

Gallagher, Kathleen G.

Caltech Authors - Main

Shock temperature of stainless steel and a high pressure—high temperature
constraint on thermal diffusivity of Al 2 O 3
Kathleen G. Gallagher, Jay D. Bass, Thomas J. Ahrens, M. Fitzner, and J. R. Abelson 
 
Citation: AIP Conference Proceedings 309, 963 (1994); doi: 10.1063/1.46195 
View online: http://dx.doi.org/10.1063/1.46195 
View Table of Contents: http://scitation.aip.org/content/aip/proceeding/aipcp/309?ver=pdfcov 
Published by the AIP Publishing 
 
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Shock Temperature of Stainless Steel and a High Pressure - High Temperature 
Constraint on Thermal Diffusivity of Al2Oa. 
Kathleen G.Gallagher*, Jay D.Bass, Thomas J.Ahrens*, M.Fitzner and J.R.Abelson 
California Institute of Technology*, Pasadena nd University of Illinois, Urbana 
Abstract 
Time dependent shock temperatures were measured for stainless teel (SS) films in contact with transparent anvils. The 
anvil/window material was the same as the driver material so that there would be symmetric heat flow from the sample. 
Inferred Hugoniot emperatures, Th, of 5800-7500K at 232-321GPa re consistent with previous measurements in SS. 
Temperatures at the fihn-anvil nterface (T,), which are more directly measured than Th, indicate that Ti did not decrease 
measurably during the approximately 250ns that the shock wave was in A1203 or LiF anvils. Thus an upper bound is 
obtained for the thermal diffusivity of A1203 at the metal/anvil interface at 230GPa nd 6000K of ~ < O.O0096cm2/s. This 
is a factor of 17 lower than previously calculated values, resulting in a decrease of the inferred :/'a by 730k. The observed 
shock temperatures are combined with temperatures calculated from measured ttugonlots and are used to calculate thermal 
conductivities of A1203. Also we note that since there was no measurable intensity decrease during the time when the 
shock wave propagated through the window, we infer from this that A1203 remained transparent while in the shocked state. 
Thus sapphire is a good window material to at least 250GPa for shock temperature measurements for metals. 
In t roduct ion  
There have been several studies on the shock tempera- 
tures of iron using optical measurements of the interface 
radiation to infer the Planck temperatures and emissivi- 
ties. These interface temperatures, Ti are used to infer 
the Hugoniot temperature, Th, as a function of shock 
pressure. Several authors have suggested that optical ra- 
diation in these experiments is not actually emitted from 
the metal-window interface and some light may be com- 
ing from the shocked anvil material[I]. There is also an 
uncertainty in the values of the constants, such as the 
thermal diffusivity of the anvil material, that are used in 
the calculation of Th from T/. Since the calculations of 
McQueen et al, 1970 [2] predict a lower shock tempera- 
ture for 304 stainless teel (SS) than for iron, this study 
focuses on the shock temperatures and thermal proper- 
ties of SS. If there is a systematic difference between the 
measured shock temperatures of SS and iron, and those 
differences are consistent with the predictions, then it 
can be inferred that the optical radiation is coming from 
the metal-anvil nterface, rather than from within the 
shocked anvil. Also two different anvil materials are used 
and the consistency of the observed interface tempera- 
tures can be used to infer that a non-significant contri- 
bution of the radiation is originating within the anvil. 
Additionally, a new target configuration is used to 
constrain the thermal diffusivity of the anvil. The previ- 
ous configuration [3] used metal drivers and 10pro thick 
films so that the there would be no predicted ecrease in 
the interface temperature with time. Thus the Ti could 
be related to the Th as in Tan and Ahrens 199014]. The 
new, or "sandwich" configuration has a thinner film of 1 
#rn and the same material for the anvil and the driver. 
This allows heat to diffuse out of the hot metal into the 
relatively colder anvil material so that the temperature 
is expected to decrease at the interface. The magnitude 
of the temperature decrease with time is dependent on 
the thermal diffusivities of the metal and the anvil. Since 
the thermal conductivity of the metal is well constrained 
by the Weideman-Franz law, we are effectively measuring 
the thermal diffusivity of the anvil at high pressure. We 
assume that specific heats axe well known for both me- 
dia. It could be argued that some or all of the decrease 
in radiation with time could be due to the anvil material 
becoming opaque [5]. However, for film thicknesses of 
10 pro, no measurable t mperature d crease is expected 
due to thermal diffusion. Thus if we employ 10 prn films 
and observe no measurable t mperature decrease, then 
we can conclude that the anvil material remains trans- 
parent. 
Methods  
Previous tudies used the target configuration shown in 
Figure (1 a). For this configuration the interface tem- 
perature is not expected to decrease with time and it is 
dependenton the Th [4]. Two shots, indicated by "S" in 
Figure 4, used a "sandwich" configuration as shown in 
Figure (1 b). Here the driver and the anvil materials are 
the same and the metal is lpm thick. In this geometry, 
after the shock wave traverses the metal, the thin metal 
is sandwiched between cooler anvil material. The result- 
ing heat flow should symmetric about the center plane 
of the metal film and is simple to model. Moreover, heat 
conduction occurs such that, on the time scale of the 
9 1994 American Institute of Physics 963 
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964 Shock Temperature of Stainless Steel 
present experiments (,~ 250ns), the interface tempera- 
ture can be observed to decrease. 
Figure 1: Target configurations a) previous target with a 
metal driver and a thick film. b) "sandwich" configura- 
tion with a thin film and anvil material same as driver. 
Calculations ummarized in Figure 6 show that a re- 
solvable temperature decrease of 500 K should be de- 
tectable in a -,, 250ns time interval. This is the ap- 
proximately the time required for the shock propagation 
through the anvil. 
The radiation from the target was measured using a 6 
channel pyrometer (Figure 2). The radiation calibration 
was performed with a tungsten ribbon filament lamp and 
the procedure was similar to that of Boslough and Ahrens 
[5]. 
Shock experiments were performed on the Caltech 
two stage light gas gun. Projectile velocities are in the 
range of 5.4km/s to 6.8km/s, resulting in shock pres- 
sures between 231 - 321GPa. Tantalum flier plates were 
employed and the shock pressures were calculated using 
the same parameters for equation of state of Ta, SS, 
A1203 and LiF as in our previous work [6], and refer- 
ences therein. 
Calcu la t ions  
The observed radiation intensities, corrected with the cal- 
ibration data, are then fit to the Planck function using an 
iterative least squares method to obtain the Ti and emis- 
sivity, ~. e was assumed to be wavelength independent 
for this calculation. Then the temperature was corrected 
from Ti to the shock Hugoniot temperature, Th (Figure 
4) as explained by Bass et al 198916]. The temperature 
was calculated at a series of times for each shot. We as- 
sumed a simple melting line and neglected the difference 
between solidus and liquidus. From these measurements 
we find that the melting point of SS is 5800 K + 300K 
at 250GPa. We see that there is a systematic difference 
between the shock temperatures for iron and those for SS 
which agree with the calculations by McQueen et al 1970 
Figure 2 :6  channel optical pyrometer. Lens projects tar- 
get image onto optical fiber bundle. Bundle is split into 
6-subbundles which lead to 6 50nm wide optical filters 
6 photodiodes and 6 linear amplifiers. Resultant signals 
are recorded on oscilloscopes. 
[2]. Additionally the time dependence of interface tem- 
peratures for the sandwich shots show that Ti decreases 
by no more than 5 K in 250 ns. (figure 5) The flatness 
of the radiation versus time curves for all pressures and 
film thicknesses and anvil materials implies that the LiF 
and A1203 anvils are not becoming measurably opaque 
under shock loading to 140 and 240 GPa respectively. 
1000o 
M,~ LIQUID /As  
,c x~c .~  
~ 04\0~ SOLID 
0 . . . . .  i , ,  i ,  
0 100 2oo 300 
Pressure (GPa) 
Figure 3: The phase diagram of stainless teel from shock 
temperature measurements. Open andsolid symbols are 
observed interface temperatures and inferred tlugoniot 
temperatures; Circles and triangles are data from LiF 
and Al20a windows; arrow represents pressure at which 
melting is observed by Hixon et al [7]. 
Also heat is not diffusing out of the thin films and 
into the A1203 anvils at a rate fast enough to cause a 
measurable temperature decrease. The heat conduction 
can be modeled by a symmetric boundary value problem 
with the ordinary heat flow equation, equation (1). 
d2T 1 dT 
- (1) dz 2 ~r dt 
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K. G. Gallagher et al. 965 
ID  [-, 
10000 
50OO 
0 , . i  i . . . .  , 
0 100 200 300 
LIQUID 
9 / 
..o"~?,'" 9 
y SOLID 
Pressure (GPa) 
Figure 4: Comparison of the Shock temperatures of iron 
and stainless teel Open symbols are data for iron, solid 
symbols are for stainless teel. Circles are for LiF, tri- 
angles are for A1203 anvils 
Here T is the temperature of the medium at position, 
x, and time, t, and n is the thermal diffusivity. The initial 
tempcrature distribution is shown in figure 6, as to and 
is described by the equations (2) and (3). 
T(t = O,x < xo) = T1 (2) 
T(t = 0, z > xo) = 0 (3) 
The diffusivities of the three regions are approximated 
to be that of the anvil material, however, because the 
anvil diffusivity is much lower than that of of the metal 
by a factor of 103, so the anvil's thermal conductivity 
controls heat conduction from the metal. This approxi- 
mation allows an analytic solution to the problem. 
transit in sample 
q g 
so.o [ - -  .... ! i1 . . . .  
i , t :  
~o 40.0 ..... . . . . .  ~ :~ ' -  ::,-~' : ;  
. . . . . . . . . . . . . . . . . . .  PL . . . . . . . . .  
2o.o  : - , /Sx~ - - : : - -  : :  . . . . .  
<1 0.0 
0.0 0.5 1.0 
A Time 0' s) 
Figure 5: Time dependence of interface radiation from 
sandwich configuration with 1 /~rn SS, shot #'s  246 and 
247 
1 T a-x  a -z  T=To+: , {erf[~] + erf[~]} (4) 
Figure 6 shows that in order to get a 50 K decrease, 
which is the smallest resolvable, we would require a time 
of ~ 300 ns, which is about the time of our cxperiments. 
Since we did not see this temperature decrease we can 
use this information to calculate a bound to the thermal 
diffusivity, n. 
= pCp/K < .00046cm2/s (5) 
Where p is the density, Cp is the heat capacity and 
K is the thermal conductivity. Since K is the least well 
constrained of the three variables, we can assume that 
the major uncertainty is due to inadequate knowledge of 
K. We thus calculate that K <_ 0.84W/mK. This value 
is 4.5 times lower than that predicted by the method of 
Tan and Ahrens, 199013]. Upon substituting this value 
into the calculated value for Th to obtain a revised value 
of 6600k for shot 247, which is 730K less than the value 
previously calculated. 
, / .~  x 
7500 to / / t2~!~tt  
5000 V fa  I 
2 
2500 14 
0 ' 
-2 0 2 
Distance {/~m) 
Figure 6: Analytical model of heat flow from an initial 
temperature distribution, at t0 (Eq. 4) 
Conclus ion 
For stainless teel shocked up to 321 GPa in the sandwich 
configuration, with 1 #m films, the best fit temperature 
at the interface decreases no more than 5 K after 250 ns. 
The constancy of the radiation intensity with time im- 
plies that sapphire shocked to 250 GPa is not becoming 
measurably absorptive. Within the errors of the mea- 
surement, enough heat is not conducting out of the film 
into the sapphire to create a measurable t mperature dif- 
ference at the interface. Since the diffusivity of A1203 is 
much less than that for SS, A1203 limits heat conduction 
at the interface. Thus we may apply our simple model of 
the sandwich configuration to determine that the diffu- 
sivity of AltOs is _< .00046cm2/8 at 321Gpa and 5800K. 
This is a factor of 4.5 lower than the calculated value of 
Bass and Ahrens [6]. 
In addition, the measured shock temperatures of the 
stainless steel samples were consistent independent of the 
anvil material (LiF or A1203). Moreover below 250 GPa 
good agreement exists between our previous iron shock 
temperature data [8, 6] and recent data of Yoo et. al. 
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966 Shock Temperature of Stainless Steel 
[9] using diamond anvils. On the other hand, theoret- 
ically and experimentally there was a systematic differ- 
ence between Th data for iron and stainless teel films 
films between 500 to 1500K and 220 and 300 GPa. This 
difference is consistent with the calculated temperature 
difference by McQueen et al 1970. However McQueen's 
temperature calculation assumed a value of 3R for iron 
and not the 5R value found theoretically by Bonness et. 
al. [10]. 
References 
[I] W.J.Nellis and C.S.Yoo. J. Geophys. Res., 95:p. 
21749-21752, 1990. 
[2] R. G. McQueen, S. P. Marsh, J.W.Taylor, J.N.Fritz, 
and W.J.Carter. In High Velocity Impact Phenom- 
ena. R.Kinslow (ed.), Academic Pre~s, New York, p. 
294-419, 1970. 
[3] T.J.Ahrens, H.Tan, and J.D.Bass. High Pressure 
Research, 2, p. 145-157, 1990. 
[4] H.Taa and T.J.Ahrens. High Pressure Research, 2:p. 
159-182, 1990. 
[5] M.B.Boslough. Rev. Sci. Instr., 60:p. 3711-3716, 
1989. 
[6] T.J.Ahrens, J.D.Bass, and J.R.Abelson. In 
S.Schmidt, J.Johnson, and J.Davidson, editors, 
Shock Compression of Condensed Matter. Elsevier 
Science Publishing, Amsterdam, p. 851-857, 1989. 
[7] R.S.Hixon, R.G.McQueen, and J.N.Fritz. The shock 
hugoniot of 316 ss and sound velocity measurements. 
In presented at the APS/AIRAPT conference on 
High Pressure Science and Technology, 1993. 
[8] J.D.Bass, B.Svendsen, and T.J.Ahrens. In 
M.H.Manghnani and Y.Syono, editors, High Pres- 
sure Research In Mineral Physics, pp. 393-402. 
Terra Scientific, 1987. 
[9] C.S.Yoo, N.C.Holmes, M.Ross, D.J.Webb, and 
C.Pike. Phys. Rev. Lett., 70:p. 3931-3934, 1993. 
[10] D.A.Boness, J.M.Brown, and A.K.McMahan. Phys. 
Earth. Planet. Inter., 42, p. 227-240, 1986. 
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Shock Temperature of Stainless Steel and a High Pressure - High Temperature Constraint on Thermal Diffusivity of Al_2O_3

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Shock Temperature of Stainless Steel and a High Pressure - High Temperature Constraint on Thermal Diffusivity of Al_2O_3

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