When energetic materials are subjected to high-velocity impacts, the first steps in the shock-to-detonation transition are the creation, ignition, and growth of hot spots. We used 1–3.2 km s−1 laser-launched flyer plates to impact powdered octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine, a powerful explosive, and monitored hundreds of emission bursts with an apparatus that determined temperature and emissivity at all times. The time-dependent volume fraction of hot spots was determined by measuring the time-dependent emissivity. After the shock, most hot spots extinguished, but the survivors smoldered for hundreds of nanoseconds until their temperatures spiked, causing a hot spot growth spurt. Depending on the impact duration, the growth spurts could be as fast as 300 ns and as slow as 13 μs.

When a high-velocity impact launches a shock wave into an energetic material (EM), the shock interacts with the material's microstructure, creating pressure and temperature jumps with complex spatial and temporal profiles.1,2 EM ignition begins in regions where the shock inputs the most energy, the so-called hot spots.3 If hot spots attain a critical size and temperature, they expand into the surrounding EM and coalesce to produce a deflagration, a rapid burning throughout the EM charge.4 With charges having the appropriate geometry, the deflagration may transition into a detonation, a constant-velocity shock sustained by EM reactions. Hot spots therefore play a crucial role in the shock-to-deflagration and shock-to-detonation transitions, and understanding hot spots is needed to control the sensitivity of EM to insults such as impacts or fires.

Much has been written about the hot spots,5 but they are seldom observed6 and the detailed dynamics of hot spot growth have not been explored. In this study, we describe experiments that use a high dynamic range emission apparatus7 coupled to a laser flyer plate launcher8–10 to study hot spot growth induced by km s−1 impacts with the energetic material HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine), in the form of small beds of ultrafine11 4(±3) μm HMX powder. HMX is an insensitive high-performance EM that detonates with a velocity of 9.1 km s−1 at 39 GPa, with temperatures in the 2800–3300 K range.12 

The prevailing picture of hot spot criticality, which determines whether hot spots extinguish or grow without restraint, is based on a seminal paper by Tarver and co-workers.4 Those authors used a three-stage model for HMX thermal decomposition based on the gradual heating measurements extrapolated to the far faster shock conditions to predict the critical temperature and the time-to-explosion versus hot spot size for HMX. For example, they computed that a 0.1 μm hot spot must be 1250 K, but a 1 mm hot spot need be only 800 K.4 The time-to-explosion for 4 μm HMX, the average particle size used here, was 10 μs.4 Subsequently, Barua and co-workers showed how shocking an HMX-based explosive with realistic microstructure created a statistical distribution of hot spot sizes and temperatures, and used the Tarver criteria to determine which of the hot spots went critical.2 

Our experimental method was described in detail previously.7 The concept of the present study is schematically depicted in Fig. 1. On a borosilicate glass window (Chemglass), we fabricated a shock target array consisting of 186 tiny polyimide wells 1 mm in diameter and 38 μm thick, filled with ∼30 μg of ultrafine 4(±3) μm HMX powder.7 This was a fluffy powder, and the mean HMX density was 0.56 g cm−3, about 1/3 of the single-crystal density.11 Laser-launched Al 1100 flyer plates 0.5 mm in diameter8,10 produced planar impacts10 in the HMX at velocities ranging from 1–3.2 km s−1. The flyer velocities and the instant of shock emergence from the HMX were measured with a high-speed photon Doppler velocimeter (PDV).8 Figure 1(e) shows an example of velocity profiles at the flyer/window interface (no HMX) or at the HMX/window interface, using a thin (100 nm) tungsten mirror deposited on the window (witness plate). Tungsten was chosen for its 6203 K boiling point; HMX boiled off a Ag mirror within a few nanoseconds. This flyer was a 50 μm Al flyer at 2.5 km s−1, and t = 0 denotes shock emergence from the mirror. The 2.5 km s−1 signal prior to t = 0 comes from the flyer plate within a few microns of the mirror, which was not a complete opaque. With glass only, the flyer accelerated glass to a steady speed (Up) of 1.65 (±0.05) km s−1 for 8 ns. The steadily driven shock durations measured in glass were varied from 2.5 ns to 16 ns by changing the Al foil thickness from 12–75 μm.8 After the shock passed through the porous HMX, the steadily driven shock speeds and durations decreased. In this case, the shock exiting HMX accelerated glass to a steady speed of 1.35 (±0.05) km s−1 for 2 ns.

The emission bursts resulting from flyers hitting HMX must be attributed to HMX shock-induced reactivity.7 Control experiments were previously performed to show that emission from the flyer hitting glass or hitting a charge of inert alumina powder was orders of magnitude weaker.7 An example of an HMX spectral radiance transient with a 2.5 ns duration, 1.8 km s−1 impact, selected from a library consisting of hundreds of shots, is shown in Fig. 2(a). Although we previously described the method to determine time-dependent temperatures,7 now we have added the capability of determining time-dependent graybody emissivities. A graybody model describes a spatially homogeneous thermal emitter with just two parameters, temperature T and wavelength-independent emissivity ε < 1. The temperature can be determined from the spectral distribution (Figs. 1(a) and 1(b)), and the emissivity from the absolute spectral radiance. When hot spots are present, the graybody emitter will have a spatially inhomogeneous temperature distribution (Figs. 1(c) and 1(d)). The emission detector will measure the spatially averaged emissivity Φ. Since thermal emission detectors are most sensitive to the hottest parts of the emitter, an emitter with hot spots can be approximately described by Φ = εV*, where ε is the emissivity of a uniformly heated emitter and V* is the volume fraction of hot spots. In our experiments, we determined ε under conditions where we were confident that the sample was uniformly hot, i.e., it was one large hot spot. Then at any time, the volume fraction of hot spots V* = Φ/ε. While our experiments determine the volume fraction of hot spots V*, they say, nothing about the sizes or size distributions of the hot spots, other than the hot spots must be smaller than the 50 μm diameter probed volume.

Figure 2 shows an example of our analysis for a 2.5 ns duration, 1.8 km s−1 impact with HMX. Figure 2(a) shows the time-dependent spectral radiance. Figure 2(b) shows graybody fits and error bounds (95% confidence limits) at the four example times indicated by arrows in Fig. 2(b). The values of T and Φ at all times, obtained by repeating this analysis, are shown in Fig. 2(b) along with the total radiance (the wavelength integral of the spectral radiance). A jump in radiance not accompanied by a corresponding temperature jump indicates a jump in emissivity Φ.

Figure 3 shows examples of time-dependent graybody temperatures and emissivities for 5 ns duration HMX impacts at velocities ranging from 1.4 to 3.2 km s−1. Below 1.4 km s−1 (not shown), we observed greatly reduced emission signals. Log (time) plots were used to emphasize the different stages of heat generation over the entire duration (10 ns–100 μs) of the emission bursts. To deal with the time zero problem in log(time) plots, we think of time zero as the instant of impact, and we used the convention that the time the shocks emerged at the HMX-glass interface, as determined by PDV, was 10−8 s,7 since it took several nanoseconds for the shock to propagate through the HMX. Gaps in the data stream, especially near 100 ns, indicate where the emission intensity dropped below the noise floor. We obtained five data sets at each velocity to assess reproducibility.7 The temperatures were quite reproducible, since they depended fundamentally on HMX ignition chemistry. The emissivities were also quite reproducible except at times >10 μs when the HMX was burning out and the emission signals were the weakest. Some charges burned for tens of microseconds longer than others.

Figure 3 shows there were always two temperature spikes followed by two emissivity spikes. The first temperature spike occurred during the shock (slightly after 10−8 s in Fig. 3), where temperature spiked to ∼6500 K and then cooled over the next 100 ns to ∼3000 K. The corresponding emissivity spiked a few nanoseconds later (see, e.g., the guide lines in Figs. 3(a) and 3(b)). Around 0.3 μs, the temperatures spiked a second time to ∼4500 K, and the spikes lasted for hundreds of nanoseconds. These second temperature spikes were followed by second emissivity spikes. At the highest impact velocities (Figs. 3(e) and 3(f)), the spatially averaged emissivities Φ attained maximum values of ∼0.3 after the first temperature spike and ∼0.2 after the second temperature spike. These maximal values of Φ indicate the HMX was homogeneously heated, i.e., the HMX was a single uniformly hot emitter. The value of Φ ≈ 0.3 after 10 ns is interpreted as the visible emissivity of spatially homogeneous shock-compressed HMX reacting at high pressure. The value of Φ ≈ 0.2 after a few hundred nanoseconds is interpreted as the ambient-pressure visible emissivity of spatially homogeneous ignited HMX. Smaller values of Φ at times >100 ns, therefore, indicate spatially inhomogeneous ignition, i.e., hot spots, as depicted in Figs. 1(c) and 1(d). The volume fraction V* of hot spots at any instant after the shocks have unloaded can be estimated from the data in Fig. 3 by dividing the value of Φ by about five.

The data in Fig. 3 show that the first emissivity spikes that appeared during the shock decayed nearly to zero as the shocks unloaded. This indicates that hot spots created during the shock were mostly extinguished. However, there must have been surviving hot spots, no more than a few percent of the observed volume, which smoldered for a few hundred nanoseconds after the shock before a new second stage of exothermic chemistries caused their temperatures to spike. These second temperature spikes were followed by emissivity jumps that are interpreted as hot spot growth spurts that ultimately ended up igniting all the HMX in the probed volume. The hot spot growth spurts must have been caused by the temperature spikes, rather than vice versa, since emissivity maxima always appeared after temperature maxima. The times between impact and the second emissivity maxima in Fig. 3 were ∼500 ns. This is the approximate time for ignited hot spots to grow and coalesce to homogeneously ignite the HMX.

We previously showed that we could significantly alter HMX chemical kinetics by changing the shock durations from 2.5 ns to 16 ns.7 This happens because, under even the extreme conditions of detonation shocks, the main HMX heat-producing reactions take 20 ns or more.13,14 The termination of these short-duration shocks interrupts chemical heat production at different stages of reaction, so they leave behind different post-shock reactive mixtures. The shortest-duration shocks leave behind the greatest amount of stored chemical energy.

The effects of shock duration are illustrated in Fig. 4, where the impact velocities were about 2 km s−1. With all shock durations in Fig. 4, we saw the two temperature spikes followed by the two emission spikes. After the shocks unloaded, a small fraction of the hot spots smoldered until their temperatures spiked a second time, igniting hot spot growth spurts. The smoldering times (time between impact and the second temperature peak) for 2.5, 5, 10, and 16 ns shock durations were 300 ns, 200 ns, 500 ns, and 600 ns, respectively. The durations of the corresponding hot spot growth spurts (the 10%–90% emissivity rise times) were 280 ns, 370 ns, 1 μs, and 13 μs.

Our HMX samples consisted of low-density powders, so the quite high ∼6500 K temperatures during the first temperature spikes were due, in part, to powder compactification.7 However, once the powder was compactified and the shock unloaded, the subsequent hot spot growth dynamics were properties of hot spots in dense HMX. The picture of hot spot dynamics that emerges from our experiments is as follows. Most of the hot spots created by shock extinguished after the shock unloads. The surviving hot spots smolder at ∼3000 K for times that depend on shock duration, but were typically a few hundred nanoseconds. The smoldering HMX hot spots pass through different stages of reaction until an exothermic stage causes a temperature spike to 4000 or 4500 K around 0.3 μs. These temperature spikes induced hot spot growth spurts. The durations of these growth spurts were faster with shorter shock durations where the chemical energy stored in the smoldering hot spots was greatest. Consequently, the hot spot growth spurts occurred in a few hundred nanoseconds with shocks ≤5 ns, but took several microseconds with 10–16 ns shocks.

Our experimental results reveal that the dynamics of hot spot growth in a prototypical energetic material, HMX, are considerably more complex than envisioned by existing theoretical models. The principle reason for this complexity stems from the complicated multistage reaction kinetics15 of the energetic material that, additionally, are sensitive to shock duration. Unlike the chemical energy-production schemes used in hot spot thermal explosion models4 that capture the behavior of EM under conditions of slow to moderately fast heating,4 the extreme temperature excursions associated with shock compression cause the HMX chemical energy to be released in bursts that cause temperature spikes. The magnitudes and durations of these spikes depend not only on HMX chemistries but also on the detailed nature of the input shock and the interactions of the shock with the sample microstructure. The hot spots created by shock smolder for hundreds of nanoseconds before their temperatures spike. Depending on the input shock duration, the subsequent hot spot growth spurts that ignite the entire volume of the EM charge can be as fast as 300 ns and as slow as 13 μs.

The research described in this study was based on the work supported by the U.S. Air Force Office of Scientific Research under Award Nos. FA9550-14-1-0142 and FA9550-16-1-0042, the U.S. Army Research Office under Award No. W911NF-13-1-0217 and the Defense Threat Reduction Agency under Award No. HDTRA1-12-1-0011. Will P. Bassett acknowledges the support from the Stewardship Sciences Academic Alliance Program from the Carnegie-DOE Alliance Center, under DOE Award No. DE-NA0002006.

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