Dynamic measurements of electrical conductivity in

JOURNAL OF APPLIED PHYSICS 99, 023705 共2006兲

Dynamic measurements of electrical conductivity in metastable intermolecular composites Douglas G. Tasker,a兲 Blaine W. Asay, James C. King, V. Eric Sanders, and Steven F. Son DX-2, Los Alamos National Laboratory, Los Alamos, New Mexico 87545

共Received 25 April 2005; accepted 6 December 2005; published online 23 January 2006兲 Metastable intermolecular composite 共MIC兲 materials are comprised of a mixture of oxidizer and fuel with particle sizes in the nanometer range. Dynamic electrical conductivity measurements have been performed on a reacting MIC material. Simultaneous optical measurements of the wavefront position have shown that the reaction and conduction fronts are coincident within 160 ␮m. It has been observed that MICs, like high explosives, are insulators before reaction is initiated. Once reaction is induced, there is a conduction zone that corresponds with the reaction zone behind the reaction front. Unlike detonating high explosives 共HEs兲 where the conductivity profile is represented by an initial peak followed by an exponential decay of conductivity, the MIC conductivity profile is a gradual, irregular ramp which increases from zero over many microseconds. This supports other studies that show the MIC reaction process to be significantly different from detonating HEs. Static measurements of conductivity of pressed MIC pellets suggest that the electrical conduction is associated with chemical reaction in the MIC and not compaction effects alone. © 2006 American Institute of Physics. 关DOI: 10.1063/1.2163015兴 I. INTRODUCTION

Metastable intermolecular composites 共MICs兲, also known as superthermites, are comprised of a mixture of oxidizer and fuel with particle sizes in the nanometer range. These small particle sizes promote relatively fast kinetics with reaction front velocities of the order of 1 km/ s.1 In typical applications these materials are packed to densities of the order of 10%–30% of the theoretical maximum density 共TMD兲. To better understand the mechanism共s兲 of reaction propagation in these loose compacts, Asay et al. reported a systematic study of the possible modes of propagation.2 Radiation, convection, conduction, and acoustic/compaction modes were considered; of these four, convection was deemed the most likely mechanism of propagation. The work reported here extends these studies to investigate the electrical conductivity of reacting MICs. Much work has already been done to understand the dynamic electrical conduction in detonating high explosives. The methods that have been developed are used as tools for probing the detonation process; in particular, they can be used to study the effects of detonation wave stability and the roles of carbon3 and aluminum4,5 during the detonation process. Many solid explosives have been found to be good electrical insulators in their inert state.6 However, at the detonation front, peak conductivities of the order of 200 S / m have been observed. Behind the detonation front the conductivity falls exponentially over a short distance comparable to the reaction zone width; depending on the explosive these widths range from tens of microns to tens of millimeters. Consequently, there is a conduction zone that starts at the detonation front and extends a short distance behind it. In recent studies, it has been suggested that as the explosive a兲

Author to whom correspondence should be addressed; electronic mail: [email protected]

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molecular crystal is shock compressed, its electronic band gap is reduced. The transition of the insulating molecular explosive crystal to a semiconductor may account for the initial conduction peak at the detonation front.7 The predicted peak conductivities are consistent with the observed values. The conduction zone behind the detonation front has been correlated with the presence of carbon in the gaseous products.3 Before this study, it was not known if the unreacted MICs would behave as electrical insulators before the onset of reaction, nor was it known if electrical conduction would occur during reaction. The conduction mechanisms in reacting MICs were not expected to be the same as in detonating high explosives because the physics and chemistry of the two systems are so different. The ultimate goal of this study is to use the conductivity measurements as a tool to shed light on the reaction process in MICs. We report the first stages of this study where we have developed the methods of conductivity measurement. Dynamic electrical conductivity measurements have been performed on a reacting MIC mixture of aluminum and molybdenum trioxide 共MoO3兲, using a technique developed for measuring the electrical conductivity of detonating explosives8 and adapted to this study. MIC mixtures were prepared from 38% 80 nm Nanotechnologies aluminum plus 62% MoO3 by weight and the pressing densities, for the experiments reported here, were 0.44 g / cm3 共12% TMD兲.9 The original technique is due to Ershov et al.10 who measured the conductive region associated with the detonation wave of a solid explosive as it swept past a narrow slit in one of the pair of metal electrodes. In this work, a ⬃3-mm-thick layer of MIC was sandwiched between a pair of plane, parallel electrodes, and initiated with an electric match at one end. One electrode had one or more slits set in it; in this way the conductivity structure of the reaction front

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FIG. 2. Schematic of conductivity measurement technique. The brass conductors C apply an electric field E across the MIC and carry a current I through the conduction wave, CW. The wave moves from right to left with a wave speed D. S is a slit, L is a low inductance loop bridging the slit, and RC is a Rogowski coil. The Rogowski coil output is M dl / dt, where M is the mutual inductance of the coil. FIG. 1. SEM micrograph of a loose packed 40% 80 nm Al+ 60% MoO3. The large sheets are the MoO3.

as it passed each slit could be measured. Fiber-optic probes were used to determine the position of the reaction front relative to the conductivity front. It was considered possible that the conduction mechanism in MIC compositions is purely physical and not associated with the reaction. In the unreacted and porous MIC, the aluminum particle agglomerates are insulated by ⬃2-nm-thick oxide layers and the gases of the interstitial voids. Figure 1 shows a scanning electron microscope 共SEM兲 image of a low-density MIC. By compressing the porous material ahead or in the vicinity of the reaction front the aluminum particles and agglomerates could be forced into closer contact, thereby abrading their oxide surfaces and moving them close enough together that breakdown could more readily occur on a microscopic level. Moreover, the insulating MoO3 sheets would be likely to fracture. In other experiments with various loading densities, i.e., various porosities, combustion pressures of between 14 and 22 MPa 共⬃2 – 3.5 ksi兲 have been measured in this MIC by Bockmon et al.11 and Asay et al.12 In fact, McAfee et al. observed small pressure precursor details that were of the order of 0.3–0.6 MPa. A porous material has little strength; therefore it cannot support a significant pressure rise until its pores have collapsed. So, the observations of Asay et al. are consistent with the arrival of a compaction wave prior to combustion.13 To determine whether the conduction was due to compaction or not, the MIC was statically pressing to pressures up to 20 MPa, then the pressure was released and the conductivity was measured.

trodes, as shown in Fig. 2. As the reaction entered the electrodes the circuit was completed by conduction through the conduction zone. Current I then began to flow through the reaction zone of the MIC and along the electrodes. The bottom electrode had a 10-␮m-wide slit in it, which was shunted with a low inductance loop 共⬃2.5 nH兲. The rate of change of current, dl / dt, was measured in that loop with a Rogowski14 coil. The data shown later suggest that the conduction zone was more than 10 mm wide, so the slit was negligibly thin by comparison. Thus, as the conduction zone traversed the slit at x = x⬘ 共see Fig. 3兲 the current to the left of the slit, IL, was IL = w

冕

x⬘

␴共x兲E共x,t兲dx,

共1兲

0

where w is the width of the conductors in contact with the MIC; E共x , t兲 is the electric field as a function of distance x and time t; ␴共x兲 is the conductivity profile as a function of x. If the Rogowski coil is connected as shown in Fig. 2 it produces a voltage Vr共t兲 = M共dIL / dt兲 where M is the mutual inductance of the coil with the shunt loop. As E is independent of x, Eq. 共1兲 may be used to express the measured Rogowski voltage Vr共t兲 in terms of the conductivity as a function of time, Vr共t兲 = M

d dIL = wM dt dt

冋冕

x⬘

E共t兲␴共t兲 . dx

0

= wME共t兲␴共t兲共dx/dt兲.

册共2兲

A. Dynamic measurements

From the optical measurements of velocity presented later, the wave speed of the reaction front, dx / dt was found to be a constant, D. So

A square cross-section column of the MIC, 3.175 mm on a side, was loaded between the parallel plane electrodes. First, it was determined that the unreacted MIC would not breakdown in the applied electric field, otherwise the technique would not work as breakdown would occur at random points throughout the cell inside and outside the reaction zone. Then a voltage was applied across the electrodes, thus introducing an electric field E into the unreacted MIC. The MIC was ignited with an electric match causing a reaction wave to sweep from right to left under the elec-

FIG. 3. Idealized conductivity profile shows conductivity ␴ as a function of distance x. The slit is at position x⬘.

II. TECHNIQUE


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FIG. 4. 共a兲 End view of test cell, as seen from the electric match, showing the MIC in the center, the two conductors C, the optical fiber cavity OC, and the PMMA insulators. 共b兲 Side view of test cell showing the slits S, H, the holes for the Rogowski probes, EM the electric match, and the insulator inserted at the end to prevent electrical breakdown.

Vr共t兲 = wMDE共t兲␴共t兲

or

␴共t兲 = Vr共t兲/wMDE共t兲.

共3兲

The field E共t兲 was obtained from the applied potential difference between the electrodes, P共t兲, divided by h the separation of the plates, 共E = P / h兲, and w, M, and D were constant. Hence the conductivity ␴共t兲 = ␴共x / D兲 was obtained. The basic apparatus in Fig. 4 is shown without the electrical connections and diagnostics. The MIC was contained by the top and bottom brass electrodes and the side poly共methyl methacrylate兲共PMMA兲 insulators, and had a cross section of 3.175⫻ 3.175 mm2. The MIC was initiated by an electric match on the left of Fig. 4共b兲. In the various experiments, one to four slits were placed in the top electrode to observe the conduction wave as it swept from left to right in the test cell. 共Only the data for the first two slits are reported here because the energy was dissipated too quickly in the circuit, see below.兲 To correlate the time of emission of light with the arrival of the conduction front, optical fibers were inserted through cylindrical cavities in a PMMA insulator adjacent to each slit, Fig. 4共a兲; fast photodiodes15 were attached to the other ends of the fibers to detect the optical signals. To prevent electrical breakdown across the end a 3.175-mm-thick PMMA or polyethylene wafer was inserted at the match end 共left in the figure兲. A photograph of the assembled cell is shown in Fig. 5. A resonant series LC circuit was designed to have a half period comparable to the expected transit time of a combus-

FIG. 6. Electrical circuit: V is the voltage measurement circuit; I is the current in the circuit; CT the current transformer that measures I; EM the electric match; RC the Rogowski coil adjacent to the slit; and L and C are the inductance and capacitance. Just one of the four slits and Rogowski coils are shown.

tion wave in the test cell, in fact, the period was found, to be too short as reported later. Figure 6 shows the 8 ␮F capacitor wired in series with a 30 ␮H inductor and the cell. Before igniting the MIC with an electric match the capacitor was charged to 2500 V and this voltage was thus applied to the electrodes of the test cell. Once the match was fired the reaction swept under the electrodes and current flowed in the circuit. The voltage across the cell was measured using a resistor and an isolated current-monitor,16 the power supply and voltage probe were attached separately in a four-point configuration to avoid contact resistance errors. The total current in the circuit was measured with a calibrated commercial current transformer.17 Great care was taken to isolate all peripheral equipment in the experiment from the main test cell circuit to avoid ground loops. In particular, all diagnostics were electrically isolated from the main circuit by using magnetically-coupled or optical sensors. Several different grounding arrangements were tried before the data reported here were obtained. B. Static measurements

To determine if the conduction was due to the compaction, a series of small pellets of the same MIC composition were statically pressed up to 20 MPa, released to atmospheric pressure, then their conductivities were measured with a low-energy milliohmeter18 in the four-point mode. III. RESULTS A. Dynamic measurements

FIG. 5. The assembled test cell showing the four holes and open slits in the bottom of the holes 共the slits at the top of the holes are filled with solder兲; the clear PMMA insulation; and the connectors for the current input and voltages diagnostics at the top rear of the picture. The length of the test cell with its insulation is 120 mm.

Several series of shots were fired before it was possible to reduce the cross talk between adjacent channels of Rogowski coil 共dl / dt兲 data to acceptable levels. This pickup was traced to the capacitive coupling of the coils to the lower electrode, which was exacerbated by small ground loops. After careful rewiring and grounding of the circuit, reasonable data were obtained. There remained a small common mode pickup signal from a ground loop; this is believed to have been between the grounds of the electric match power supply and the instrumentation ground. The metallic electrodes and electrical connectors survived each shot and could be reused after cleaning. The PMMA insulators were usually damaged.


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FIG. 8. Conductance of the complete test cell in Siemens 共reciprocal ohms兲 for shot 42104-5.

FIG. 7. Conductivity data and derivatives of optical fiber data at the first and second slits for 共a兲 shot 42104-4 and 共b兲 shot 42104-5. Conductivity 共S1 C and S2 C兲 in S / m; derivatives of optical fiber data 共S1 O and S2 O兲 in arbitrary units. The S1 C and S1 O data have been offset by +50 units in 共a兲 and the S2 C and S2 O data have been offset by +300 units in 共b兲 for clarity. The small offsets of the S1 C and S2 C data before arrival of conduction are due to ground loops. The conductivity data in both 共a兲 and 共b兲 were terminated when the applied field had decayed to zero 共at 50 and 40 ␮s, respectively兲. Point X in 共a兲 identifies one of the common features between the optical and conductivity data.

The results of the data analysis described by Eq. 共3兲 are shown in Fig. 7 for two consecutive experiments in nominally the same material. It was only possible to collect conductivity data for the first two of the four slits. This was because the cell resistance was high enough to dissipate all the electrical energy in the circuit after the wave had traveled 40 or 50 ␮s past the first slit, i.e., before the combustion wave arrived at the last two slits. By that time the electric field E共t兲 between the top and bottom electrodes had decayed to zero, and Eq. 共3兲 was no longer valid. It is hoped to make measurements at points further downstream from the electric match in future experiments. The top half of each graph shows the conductivity data and the bottom the corresponding fiber-optic signals. The fiber-optic data were numerically differentiated to improve the presentation of the arrival times in the figures and arbitrarily scaled to fit on the graphs. The times were arbitrarily zeroed at the start of conductivity for the first slit. Notice the “noisy” nature of the data and the slow rise in conductivity over several microseconds. The noise was not due to the instrumentation but was likely due to the stochastic nature of

the reaction in the test cell. The noise may also have been due to the irregularity of electrical contacts between the MIC and the electrodes. However, some features of the conductivity data 共such as point X兲 are mirrored in the optical data in Fig. 7共a兲. 关The optical sensitivity was set significantly higher for the fiber data in Fig. 7共b兲, so the signals clipped before these interesting structures could not be seen.兴 This suggests that the irregularities were not due to contact effects. Moreover, if the conduction was due to the reaction products, it is not clear what effect contact irregularities would have had. Spectral analysis of the conductivity data shows a noisy spectrum up to ⬃50 MHz, the limit of the slit resolution, with no dominant resonances. The measurements obtained in the first two slits were of reactive waves that had probably not reached the steady state. The conductivity rose steadily behind the reaction front over a period of 15– 25 ␮s and then fell more rapidly. This is different to the general behavior of detonating high explosives where the peak conductivity is at the detonation front and drops off exponentially behind the apparent reaction zone.8 With high explosives and MICs conduction is extinguished behind the conduction zone. This finite duration is also demonstrated by the overall resistance of the MIC in the test cell. Figure 8 shows the overall conductance of the cell obtained by dividing the total current flowing in the test cell by the voltage between the electrodes; inductance effects were negligible.19 It demonstrates that the structure of the conductivity data in Fig. 7 is due to the localized effects adjacent to the slits and not global effects in the electrical system. Figure 9 shows the conductivity data of Fig. 7 on a common plot for direct comparison of the profiles. The times between the arrivals of the waves at the two slits are the same, 25 ␮s, and the shapes are similar, but the magnitudes are significantly different. It is surmised that the magnitudes differ because of small scale differences in the packing of the material adjacent to the slits, but as yet there is no proof of this. It originally appeared that the conductivity fronts were detected before the arrival of the optical signals, but that was incorrect. The optical data were long, slowly rising signals, which made it difficult to detect the onset of light emission.


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FIG. 9. Comparison of conductivity data in S / m vs time for shots 42104-4 and 42104-5. Shot 42104-4 data for the first and second slits are labeled 4-1 and 4-2; similarly for shot 42104-5 they are 5-1 and 5-2. The data have been offset for clarity as follows: 4-2 offset by 0; 5-2 offset by 100 S / m; 4-1 offset by 400 S / m; and 5-1 offset by 500 S / m.

However, by differentiating the optical data, as shown in Fig. 7 the signals for both shots arrived simultaneously, within the resolution of the optical data. The time resolution of the Ershov technique is determined by the electrical response of the Rogowski coil 共⬍1 ns兲 and the time it takes the reaction wave to sweep across the width of the slit, ␦x. It turns out that sweep time is the dominant factor. The measured wave speeds D for the mixtures reported here were ⬃650 m / s. For ␦x = 10 ␮m that translates to a time resolution of ␦t = ␦x / D or ⬃15 ns. The time resolution of the optical fibers is determined by the width of the cone of light that the fibers admit, and light scatter. Light scatters ahead of the luminous reaction front because the material is not optically dense at the loading densities used in these experiments. Also, the reaction front is fairly diffuse 共as evidenced by the large reaction zone length, approximately 25 ␮s or 15 mm, Fig. 7兲. For the shots reported here the resolution was ⬃250 ns at a wave speed of 650 m / s, this corresponds to a spatial resolution of 160 ␮m. The wave velocities of the reactive fronts, as determined from the optical data, were 605 and 704 m / s for the two shots, see Fig. 10 for the 42104-5 data. However, there were only three points recorded for shot 42104-4 and four points for shot 42104-5 and the standard errors for the two veloci-

FIG. 10. Fiber-optic time of arrival data for shot 42104-5 recorded at the four points adjacent to the four slits. The wave velocity was 704 m / s with a standard error of 49 m / s.

ties were 20 and 49 m / s, respectively, Given the relatively large errors and the small samples the two velocities were not significantly different. B. Static measurements

To verify that the conduction was not due to simple mechanical compaction 共without reaction兲, a series of small pellets of the same MIC composition 共38% 80 nm Nanotechnologies aluminum plus 62% MoO3 by weight兲 were statically pressed to pressures up to 20 MPa then relieved back to the atmospheric pressure. The test sample densities ranged from 0.76 to 1.30 g / cm3 at atmospheric pressure as shown in Table I. A low-energy milliohmeter was used to avoid ignition of the MIC composition. The first ten samples were pressed many hours before the conductivity tests and the 11th was pressed within 5 min of the measurement. None of the first ten samples conducted. There was a concern that the aluminum may oxidize so quickly that the statically pressed samples would never conduct, i.e., the abrasive action of rapid dynamic compaction may be necessary to initiate conduction. In case a “freshly” pressed sample might conduct, a sample 共11兲 was pressed to 1.30 g / cm3 and the conductivity was measured within 5 min of the pressing. This pellet, like the others, did not conduct. 共It should be noted that pressed MIC pellets remain reactive

TABLE I. Pressing data and conductivities of MIC pellets.

Pellet

Mass 共mg兲

P 共MPa兲

Diam 共cm兲

Height 共cm兲

Density 共g / cm3兲

% TMD

␴ 共S / m兲

1 2 3 4 5 6 7 8 9 10 11

97.05 97.75 98.00 98.40 148.00 146.00 145.60 147.70 170.90 171.90 170.10

1.54 1.54 6.27 6.27 10.97 10.97 15.67 15.67 20.37 20.37 20.37

0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95

0.180 0.180 0.140 0.140 0.190 0.190 0.165 0.170 0.188 0.190 0.185

0.7607 0.7661 0.9876 0.9916 1.0989 1.0841 1.2449 1.2257 1.2825 1.2764 1.2972

20.7% 20.9% 26.9% 27.0% 29.9% 29.5% 33.9% 33.4% 34.9% 34.8% 35.3%

0 0 0 0 0 0 0 0 0 0 0


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almost indefinitely, i.e., they have a long shelf life, so extensive oxidation could not have occurred in these samples.兲 IV. DISCUSSION

From the optical data and the conductivity data it was observed that the luminous and conduction fronts were coincident within the resolution of the experiment, i.e., ⬃160 ␮m. Unlike detonating explosives, where the conductivity profile is represented by a sharply rising initial peak followed by an exponential decay of conductivity,8 the MIC conductivity profile was a gradual, irregular ramp which steadily increased from zero over many microseconds. Assuming that the luminous region in the MIC corresponded to the reaction zone, this suggests that the reaction zone thicknesses and reaction rates are different in MICs compared to detonating high explosives 共HE兲 as is to be expected. In detonating HE it is thought that the conduction is due to a combination of pressure and temperature-induced 共unreacted兲 conductivity,7 followed by the coagulation of unburned carbon in the product gases.3 It remains to be determined what the conduction mechanism is in MICs; it could be due to a combination of chemical and physical processes. But as MIC reaction occurs more slowly than in HE, the products must be released more slowly, leading to a slower rise in conductivity. It is noted that the conductivity measurements obtained in the first two slits were of reactive waves that had probably not reached steady state. The results showed a noisy spectrum with a bandwidth extending from 0 to ⬃50 MHz with no dominant resonances. The SEM image of Fig. 1 shows the MoO3 has sheet dimensions and spacing of tens of microns. So this 50-MHz-wide spectrum is also consistent with the time it would take for the combustion wave to sweep across the MoO3 particles. However, the interaction with aluminum particles 共ca. 25 nm across兲 would be too fast to resolve because each particle would be swept by the wave in ⬃40 ps and the Rogowski coil and slit combination had a resolution of 10 ns. So the “noise” may be a structure due to the stochastic reaction associated with individual MoO3 flakes. Some structure of the conductivity profiles is replicated in the optical data, which suggests that contact irregularities do not account for the noise. For the two experiments reported here, the times between the arrivals of the waves at the two slits are the same, 25 ␮s, and the shapes are similar, but the magnitudes are significantly different. Presumably the magnitudes differ because of small scale localized differences in the packing of the material adjacent to the slits. Some variations can be explained because the reactive waves had probably not reached steady state in the first two slits. The static conductivity measurements of the MIC pellets showed that they do not conduct when pressed to 20 MPa, i.e., at pressures comparable to those observed in dynamic combustion experiments. The initial evidence, although not conclusive, suggests that the conduction observed in the dynamic experiments is due to the reaction in the MIC, not compaction. However, the failure to conduct in the static experiments could be due to a number of reasons other than

the absence of reaction. For example, the electric field applied by the milliohmeter may have been too small to overcome the effects of oxide on the aluminum surfaces; or the oxide may grow so fast 共on a microsecond time scale兲 that only the abrasive action of rapid dynamic compaction will allow conduction or both. It will be interesting to continue the dynamic conductivity studies on MICs with different particle sizes and compositions in an effort to gain further insight into the conduction and reaction processes. V. CONCLUSIONS

The first dynamic electrical conductivity measurements on a reacting MIC material have been performed and they have shown that the reaction and conduction fronts are coincident within the resolution of the experiment, i.e., 160 ␮m. The unreacted MIC was also found to be an insulator. Static tests have demonstrated that the conduction occurs during the reaction process and is not caused by purely physical processes associated with compaction of the unreacted MIC. The results are consistent with those of Ref. 2, specifically that the reactive wave appears very different from classical detonation, as is to be expected given the significant differences between the chemistry and physical structures of these materials. Some structure of the conductivity data is reproduced in the differentiated optical data, which suggests that the irregularities in the data are due to the stochastic nature of the MIC reaction. This study has demonstrated that dynamic electrical conductivity measurements can be performed on MICs. As with detonating high explosives3–7 it is planned to use this tool in future studies to explore the physics and chemistry of reaction in MICs. ACKNOWLEDGMENTS

The authors acknowledge the excellent technical assistance rendered by Alan Novak and proof reading of the manuscript by Elena Phillips, both of DX-2, Los Alamos National Laboratory. This study was supported in part by the US Department of Defense, Joint Munitions Program. 1

C. E. Aumann, G. L. Skofronick, and J. A. Martin, J. Vac. Sci. Technol. B 13, 1178 共1995兲. 2 B. W. Asay, S. F. Son, J. R. Busse, and D. M. Oschwald, Propellants, Explos., Pyrotech. 29, 216 共2004兲. 3 B. Hayes, Fourth Symposium (International) on Detonation, White Oak, MD, October 1965 共Office of Naval Research, Department of the Navy, Arlington, VA, 1965兲, pp. 595–601. 4 S. D. Gilev, 12th Symposium (International) on Detonation, San Diego, CA, 11–16 August 2002 共Office of Naval Research, Department of the Navy, Arlington, VA, 2002兲. 5 R. J. Lee and P. K. Gustavson, Shock Compression of Condensed Matter2003, edited by M. D. Furnish, Y. M. Gupta, and J. W. Forbes, AIP Conf. Proc. No. 706 共AIP, Melville, NY, 2003兲, p. 1273. 6 D. G. Tasker, Naval Surface Warface Center Report No. NSWC TR 85360 共Naval Surface Warfare Center, White Oak, MD, 1985兲. 7 K. F. Grebenkin, Shock Compression of Condensed Matter-2005, Baltimore, MD, 2005 共to be published兲. 8 D. G. Tasker and R. J. Lee, Proceedings of the Ninth Symposium (International) on Detonation, Portland, OR, 1989 共Office of Naval Research, Department of the Navy, Arlington, VA, 1989兲, p. 396. 9 The TMD is 3.67 g / cm3 based on the crystal density being 4.696 g / cm3 for MoO3 and 2.700 g / cm3 for the aluminum at STP in a 38:62 mixture.


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A. P. Ershov, P. I. Zubkov, and L. A. Luk’yanchikov, Combust., Explos. Shock Waves 10, 776 共1974兲. 11 B. S. Bockmon, M. L. Pantoya, S. F. Son, B. W. Asay, and J. T. Mang, J. Appl. Phys. 98, 064903 共2005兲. 12 B. W Asay, S. F. Son, J. R. Busse, and D. M. Oschwald, Shock Compression of Condensed Matter-2003, edited by M. D. Furnish, Y. M. Gupta, and J. W. Forbes, AIP Conf. Proc. No. 706 共AIP, Melville, NY, 2003兲, p. 827. 13 For further details of compaction waves see, for example, J. M. McAfee, B. W. Asay, A. W. Campbell, and J. B. Ramsay, Proceeding of the Ninth Symposium (International) on Detonation, Portland, OR, 1989 共Office of Naval Research, Department of the Navy, Arlington, VA, 1989兲, p. 265. 14 The Rogowski coil was wound on the core of a RG223 cable with a pitch of ⬃50 turns/ cm. Prior to the experiment the sensitivity 共mutual inductance, M兲 of the Rogowski coil was calibrated by short-circuiting the

J. Appl. Phys. 99, 023705 共2006兲 assembly and comparing the dl / dt signature with total current measured with the current transformer. M was typically ⬃30 nH and each coil had a response time of ⬃1 ns. 15 DET210 High Speed Silicon Detector, ThorLabs, 435 Route 206, P.O. Box 366, 共973兲 579-7227, Newton, NJ 07860-0366; 1 ns resolution. 16 This is a standard technique for high-voltage circuits. The current through a high voltage 1 k⍀ resistance was measured with a current transformer. 17 Pearson Electronics Model 411 current transformer. 18 The milliohmeter was a Hewlett Packard HP 4338A with the following specifications: test frequency of 1 kHz, signal current⬍ 10 mA rms, and signal voltage of 20 mV peak. 19 The maximum inductance of the test cell was 24 nH and the maximum rate of change of current was 45 MA/ s. Hence the maximum error in voltage was ⬃0.1% due to cell inductance.
