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
FIRST RESULTS OF REACTION PROPAGATION RATES IN HMX
AT HIGH PRESSURE
Daniel L. Farber, Anthony P. Esposito, Joseph M. Zaug,
John E. Reaugh, and Chantel M. Aracne
University of California, Lawrence Livermore National Laboratory,
7000 East Ave., Livermore, CA 94550
Abstract. We have measured the reaction propagation rate (RPR) in octahydro-1,3,5,7-tetranitro1,3,5,7-tetrazocine (HMX) powder in a diamond anvil cell over the pressure range 0.7-35 GPa. In
order to have a cross-comparison of our experiments, we conducted RPR experiments on nitromethane
(NM) up to 15 GPa. Our results on NM are indistinguishable from previous measurements of Rice and
Foltz. In comparison to high-pressure NM, the burn rates in solid HMX are 5-10 times faster at
pressures above 10 GPa. Numerical simulations of the burn rate of pressurized HMX were also
performed for comparison to the results obtained. The simulated burn rates closely approximate the
observed rates at pressures up to 3 GPa. However, further refinement to the computational model is
required for the calculated burn rates to approach those observed at higher pressures.
INTRODUCTION
Rice and Foltz (1,2). Here we report the first
results of the RPR measurements on octahydro1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) over
the pressure range 0.7-35 GPa. In addition, we
report calculated RPR values for HMX from 0.1 to
30 GPa.
Presently there is a strong interest in firstprinciples modeling of chemical reactions in high
explosive (HE) materials. However, the validation
of these models requires experimental data at the
appropriate pressure and temperature conditions of
the reactions of interest. Because these reactions
occur over time scales of microseconds, they have
resisted experimental characterization of the
fundamental processes governing combustion and
detonation. The diamond anvil cell (DAC) is well
suited for studying these reactions because it
provides a high-pressure, variable-temperature
sample environment, as well as a window for
spectroscopic study of reactions within the DAC.
The reaction propagation rate (RPR) of an HE
material can be studied directly by confining the
material within the DAC and initiating combustion
with a focused laser pulse. Our experimental
approach is a modification of the earlier work of
EXPERIMENTAL
The experimental setup is presented in Figure 1.
The apparatus and procedure employed were
similar to those used by Rice and Foltz (1,2).
Samples were contained in a DAC consisting of
two opposed 0.25 carat diamonds with culet
diameters of 0.5-1.0 mm. Lateral confinement of
the -50 //m thick samples was achieved using
Inconel 718 or rhenium gaskets with 150-400 jum
hole diameters. Ruby powder was deposited onto
the surface of the back diamond for determination
of the initial pressure using the ruby fluorescence
pressure scale.
1015
>L Argon Ion Laser
'488 nm
/r
FIGURE 2. Streak camera records of reacting HMX.
The vertical dimension is time, where the edge-to-edge
length is 3.2 //s, and the horizontal dimension is distance,
where the edge-to-edge length is 353 //m. The parallel
vertical lines are due to the undisturbed laser speckle
pattern being streaked in time. Deflagration within the
sample disturbs the speckle pattern from the point where
the ignition pulse strikes the sample. The disturbance
moves outward from this point, resulting in the pattern
shown here. (A) HMX sample at 21 GPa. The
corresponding RPR is 223 m/s. (B) HMX sample at 35
GPa recorded with the same streak duration as in Fig. 3 A.
The corresponding RPR is 641 m/s.
FIGURE 1. Schematic layout of RPR experimental
apparatus as described in the text. The following
abbreviations have been used: DAC: diamond anvil cell;
NF: holographic notch filter; SF: spatial filter.
Both sample illumination and excitation for
ruby fluorescence were provided by an argon ion
laser operating at 488 nm and ~3 W (Lexel model
95). The cw 488 nm beam was passed through a
spatial filter and defocused into the DAC in order to
fully illuminate the sample. Sample ignition was
provided by a Q-switched Nd:YAG laser (New
Wave MiniLase 11-20), frequency-doubled to 532
nm, with pulses of ~9 ns duration. During optical
alignment, the 532 nm pulse energies were kept
below 0.1 /J to prevent accidental ignition. The
532 nm beam was made collinear with the 488 nm
beam using a holographic bandpass filter, and was
focused to a ~5 //m spot size in the center of the
sample region illuminated by the 488 nm beam.
Transmitted light from the sample was magnified
(~10x) and focused onto a 10-50 //m-wide slit, and
was then magnified (9.5x) after the slit. For ruby
fluorescence measurements, the emission was
focused onto the entrance slit of a /1.8 spectrograph
(Kaiser Optics), and detected by a liquid-nitrogen
cooled CCD camera (Princeton Instruments).
After pressure measurements, the laser speckle
pattern from the DAC, due to illumination by the
488 nm beam, was directed to an EG&G L-CA-20
electronic streak camera (Polaroid film type 57,
3000 speed) operating at streak durations between
1.8 and 10 jus. Ignition pulse energies were
determined by a Molectron EPM 2000 energy
meter, and were in the range of 1-10 /J. A
holographic notch filter placed before the streak
camera slit was used to attenuate the 532 nm light
to prevent over-exposure of the streak image.
Typical streak images are shown in Figure 2.
Samples consisted of ultrafine HMX containing
less than 0.7% RDX, with a uniform grain size of
-3 jum. In addition, RPR studies of nitromethane
(NM) were conducted for comparison with the
previous data of Rice and Foltz (1). Figure 3
presents a comparison of NM burn rates obtained
by Rice and Foltz with those obtained in our
laboratory. Our results are essentially indistinguishable from those previously obtained.
I
40-
CO
a-g
o c
1
S
.9,
+-*
u
5
10
Pressure (GPa)
20
FIGURE 3. Pressure dependence of the RPR for NM.
The data obtained in our laboratory are shown in large
circles over the RPR data obtained by Rice and Foltz (1).
1016
RESULTS AND DISCUSSION
I
a
Table 1 presents the experimental RPR values
obtained in the present study on HMX in the
pressure range 0.7-35 GPa, and those calculated for
pressures between 0.1 and 30 GPa (see below). The
data presented in Table 1 have been plotted in
Figure 4; also depicted in Fig. 4 is a best-fit curve
to strand burner data on LX-04 (85 wt% HMX, 15
wt% Viton-A) obtained by Maienschein et al. (3).
There is good agreement between the experimental
and calculated values for pressures up to 3 GPa;
however, at higher pressures the data sets diverge.
Direct numerical simulations of a propagating
planar flame front were made using ALE-3D, an
arbitrary Lagrange-Eulerian computer simulation
program under development at this laboratory. In
these simulations, the program was exercised as
though it were a one-dimensional Lagrange
program with plane symmetry. The simulations
include heat transfer by conduction, and a
simplified global reaction scheme fitted to onedimensional time-to-explosion experiments (4).
The first of the three reactions is endothermic, the
second moderately exothermic, and the third
3.0
3.7
7.7
9.1
11
12
13
14
21
25
30
35
,*
CO
a:
^
g
'to
10
&
1
'"^ *
— --< i. ——s-\ i--i / s''
D)
2
a.
o
^i_.
^-^"
01
"^\
r
--X
CO
4r
^A P
0.01 X
0. 01
0.1
1
10
Pressure (GPa)
FIGURE 4. Pressure dependence of the reaction
propagation rate for HMX and LX-04. Values obtained
in this study on pure HMX are indicated by the points
(diamonds: experimental; squares: calculated), while the
thick curve is the best fit to strand burner data on LX-04
from Maienschein et al. (3). The thin curve fits to the
data are present to guide the eye, and are described by the
following equations:
fit to experiment: RPR =
(pressure)A1.81; to calculation: RPR = (pressure)A0.67.
TABLE 1. Experimental and Calculated Reaction
Propagation Rates for HMX._______________
Pressure (GPa)
0.1
0.7
1.0
1.7
2.8
j> .
"2.
100
exothermic. Four equations of state are required:
the solid unreacted material; the solid endothermic
product; moderately exothermic gas, described as a
relatively high molecular weight gas; and the final
products of HMX decomposition. The latter two
gas equations of state were described by
interpolating tables constructed using CHEQ, a
thermochemical equilibrium computer program (5).
The numerical simulation is ignited by raising
the temperature of one face of the one-dimensional
slab to the approximate flame temperature. That
face is also maintained as a constant pressure
boundary, and the opposite face has no normal
displacement. After an initial transient the flame
propagates as a steady, constant velocity process
through the initially cold but pressurized HMX
reactant. This steady velocity is then recorded.
Repeating the calculations with different initial
pressures provides the simulation results of flame
speed as a function of pressure. The spatial
resolution (zone-size) needed to resolve the flame
Rate (m/s)
Experimental
Calculated
0.5
4.3 ± 0.8
2.6
9.5 ±2.5
11.0 ±2.0
3.8
9.3 ± 0.9
53.0 ±5.3
152 + 5.5
186+19
7.0
228 ± 18
242 ± 23
222 ± 23
257 ± 26
9.0
641 ± 70
1017
front depends on pressure and flame speed. Higher
flame speed requires finer mesh resolution to
capture the spatial gradient. Lower pressure
requires finer mesh resolution to capture the spatial
gradient in the product gas. For these Lagrange
simulations, the gas products, and so the finitedifference zones, expand much more at low
pressure than at high pressure. In our simulations
the zone-size was typically a few nanometers, and
the flame thickness a few hundred nanometers.
The Arrhenius chemical reaction rates used in
these simulations are temperature-dependent, but
not pressure-dependent. The observed pressure
dependence in the simulations comes from the
separation of hot gas products from the cold surface
that is large for the low-density, low-pressure
products, and is small for the high-density, highpressure products. A second-order effect is the
change of thermal conductivity with density.
Although there are many parameters used to
describe the mechanical, chemical, and thermal
properties of the four species used in these
simulations, none are specifically fit to or
determined by flame propagation.
They are
obtained independently. The factor of two or three
difference between theory and experiment at low
pressure is undoubtedly due to deficiencies in the
thermal and chemical properties used, which were
taken from near-atmospheric pressure experiments.
Nevertheless, we consider the agreement with
experiment to be surprisingly good. The substantial
deviation from the measured flame propagation
speed and our simulations at high pressure is
apparently due to the inadequacies of our simplified
and global chemical reactions that were determined
by ODTX experiments at roughly 0.1 GPa. We
anticipate further research in this area.
The significance of the experimental results is
that they may constrain the physics and chemistry
behind our canonical model of initiation and growth
of reaction in explosives from hot spots. We feel
that time-resolved temperature, and, to a lesser
degree, pressure measurements under the RPR
experimental conditions are required to confidently
guide future computational developments. In all
such models, it is postulated that the hot spots, once
formed, link up by the mechanism of laminar flame
spreading. Knowing the ratio of the flame spread
velocity at high pressure, on the order of 35 to 50
GPa, to the detonation velocity is the necessary
coupling between the average separation of hot
spots and the thickness of the reaction zone of a
quasi-planar detonation front.
ACKNOWLEDGEMENTS
*This work was performed under the auspices
of the U.S. Department of Energy by the Lawrence
Livermore National Laboratory under contract
number W-7405-Eng-48. We thank C. M. Tarver
for his support of this work.
REFERENCES
1. Rice, S.F., and Foltz, M. F., Combustion and Flame
87, 109-122 (1991).
2. Foltz, M. F., Propellants, Explosives, Pyrotechnics
18, 210-216 (1993).
3. Maienschein, J. L., and Chandler, J. B., "Burn Rates
of Pristine and Degraded Explosives at Elevated
Temperatures and Pressures," Eleventh International
Detonation Symposium, Snowmass, CO, 1998.
4. McGuire, R. R., and Tarver, C. M., "Chemical
Decomposition Models for the Thermal Explosion of
Confined HMX, TATB, RDX, and TNT Explosives,"
Seventh Symposium (International) on Detonation,
Annapolis, MD, 1981.
5. Ree, F. H., J. Chem. Phys. 81, 1251-1263 (1984).
1018