In operando measurements of high explosives

An old saying goes, “the best way to survive a bomb explosion is to not be there,” but that is not an option for researchers who study high explosives in operando. High explosives can be triggered by shock waves to release their energy in the form of a detonation,¹ a supersonic shock driven by rapid chemical energy release. This is called the shock-to-detonation transition.^2,3 Both the triggering process and the subsequent detonation are examples of dynamic extreme conditions. Powerful shock waves produce extreme dynamic changes in pressure, temperature, and mechanical deformation.⁴ Because extreme conditions are produced by a rapidly moving excitation, high time and space resolution (in the work discussed here, 2 ns and 2 µm) is needed for detailed studies of shock compression of solids and liquids. Shock fronts, which represent the region of transition from ambient to extreme conditions, can be steep. In high explosive detonations, subnanosecond rise times have been observed.⁵ 

In some cases, the shock front rise is not the limiting factor in time resolution; it can also be limited by the shock transit time across the sample of interest, so experiments needing high time resolution often use thin samples. In condensed matter, a representative shock velocity would be on the order of 5–10 km/s,⁶ which corresponds to 5–10 µm/ns or 5–10 mm/μs, so a 10 µm thick sample can be shocked up in 1–2 ns.

The studies reported here used short-duration (typically 4 ns) shocks⁷ to trigger extreme chemical and mechanical changes in liquid or solid explosives. Short-duration shocks allow us to time-resolve the process of detonation formation. Understanding detonation formation on a tabletop can be the basis for improved microdetonation devices,⁸ and it provides insights into how detonations behave, how they can be controlled, and how they respond to external perturbations.

The short-duration shocks we use can be made powerful enough to produce pressures equal to or slightly greater than the leading edge of the detonation,⁹ so it will seem as if the detonation has already begun to form immediately after the shock is input to the explosive. Minimizing the time and run length to detonation allows us to use nearly the minimum amount of explosive material needed to observe the shock to detonation transition. In many cases, we can reduce the quantity of shocked explosives to 100 µg or less. The energy released from even the most powerful chemical explosives does not exceed 5 kJ/g,¹⁰ so even a complete detonation in our experiments releases no more than 0.5 J (enough to heat a gram of water by about 0.1 K). Since we enclose the explosive with thick (10 mm) glass windows, these experiments, however, violent the detonation, become intrinsically safe. They can also be conducted on a tabletop in a high-throughput format. Nevertheless, precautions should be taken by trained personnel to handle these explosives in the quantities (10 mg) used to fabricate multielement arrays.

We have developed a shock compression microscope that uses a tabletop pulsed solid-state laser (Nd:YAG) to launch a small (0.5 mm diameter) metal disk termed a “flyer plate” at hypersonic velocities (0–6 km/s or up to Mach 18).^7,11,12 These flyer plates are used to produce planar shocks in individual cylindrical charges of high explosive.¹³ Of course, such shocks expand radially, but for experiments where the run distance is significantly less than the flyer diameter, the shock can be viewed as planar. The tiny explosive charges are placed in the microscope equipped with the flyer launcher, a high-speed velocimeter, and various optical diagnostics to measure pressures and temperatures with high time and space resolution.^13,14

The shock compression microscope can be used to produce and study dynamic extreme conditions in inert materials¹⁵ and liquids¹⁶ as well as in explosives,¹³ so it has wide-ranging applications.¹⁶ Here, we will briefly describe shocked water as an example of dynamic conditions in liquid that has shock-induced chemistry but does not explode, but the emphasis will be on two explosive systems, a homogeneous liquid, nitromethane (CH₃–NO₂), and a microstructured plastic-bonded explosive (PBX) based on HMX, 1,3,5,7-Tetranitro-1,3,5,7-tetrazocane with chemical formula (CH₂–NNO₂)₄.

Nitromethane (NM) has served for decades as a model system for the shock-to-detonation transition.^14,17 Since it is transparent, we can see inside the liquid during this transition. The detonation velocity is 6.2 km/s, the reaction zone width is 11 ns or equivalently 70 µm, the pressure is 11.2 GPa (1 GPa = 10⁹ J/cm³ = 10 000 bars), and the temperature is 3400 K.⁹ The intent of the NM work is to understand how to produce detonations in the minimum possible volume and to understand the mechanisms of detonation formation in enough detail to develop kinetic models for chemical energy release needed for predictive, experimentally validated models of explosive performance.¹⁸ 

HMX is the most powerful explosive in widespread use.¹⁹ It can produce a 10 km/s detonation shock with a pressure of 40 GPa and a temperature of about 3500 K in a reaction zone ∼20 ns or 200 µm in length.²⁰ In PBX, HMX crystals are combined with small quantities of polymer binder, which coats the crystals and binds them together to impart mechanical stability and reduced sensitivity to external insults.²¹ The PBX microstructure has local configurations that can concentrate shock energy. In these regions of concentrated energy, HMX can be ignited to produce an ensemble of so-called “hot spots”²² with a distribution of sizes and temperatures. Many, perhaps most hot spots are too small to ignite nearby material, so we focus our attention to the larger, hotter hot spots (termed “critical hot spots”)²³ that can cause reactions to spread to nearby HMX crystals across insulating polymer gaps in a process called deflagration. Deflagration is a reaction in a medium where fuel and oxidizer are premixed, as is the case for both NM and HMX, which contain fuel (e.g., C-atoms) and oxygen (e.g., NO₂) on the same molecule. Since reactant mixing is not required, the rate-limiting step in deflagration propagation is heat transfer.

There is a long list of possible PBX structures that can produce hot spots, including voids, interfaces, and so forth,²² but no definitive answers yet as to the nature of the PBX local configurations that produce the critical hot spots.²² This controversy could be answered if we could see the hot spots inside the PBX and watch them ignite and grow. The problem with seeing hot spots is that PBX is opaque conglomerates, and it is impossible to see deep inside them with optical probes. Here, we will describe a method that allows us to watch individual HMX crystals ignite, grow, and create deflagrations.

This paper is arranged as follows: 1. What is a shock wave, 2. How are flyer plates launched, 3. Shock compression microscope, 4. Optical pyrometry, 5. What is a plastic explosive, 6. What is a detonation, 7. Inside a transparent liquid explosive, and 8. Inside a plastic-bonded explosive.

“What is a shock wave?” is illustrated in Fig. 1 for the case of a shock produced by a planar impact, which is commonly used since shocks in this geometry are the easiest to interpret.²⁴ Figure 1 illustrates a planar impact at velocity v with a material initially at density ρ₀.²⁵ An acoustic wave packet is launched when the impact produces a negligible density increase in the material [Fig. 1(b)]. The acoustic frequencies comprising the wave packet disperse, and the acoustic wave front broadens. In contrast, Fig. 1(c) illustrates a higher-velocity impact that causes the material to flow, leading to a density increase behind a shock front. This single-stage impact produces an irreversible adiabatic compression where temperature, density, and pressure increase. A shock is a nonlinear excitation, and the shock front tends to steepen up as it propagates,⁴ as illustrated in Figs. 1(d) and 1(e). Think of the shock front in Fig. 1(d) as being composed of a weaker leading shock and a stronger trailing shock. The stronger shock propagates faster, so the shock steepens up.

Early studies of shocks in condensed matter relied primarily on velocity measurements, particularly the two velocities, U_s the shock velocity, and U_p, the velocity imparted to the material by the impact.⁶ Assuming conservation of mass, energy, and momentum across the shock front leads to the Rankine–Hugoniot equations, which give the density and pressure behind the shock front as⁶ 

and

However, the Rankine–Hugoniot equations do not deal with temperature explicitly. To obtain temperatures, an equation of state such as the Mie–Gruneisen equation of state is needed. So while pressures and densities can be determined with velocity measurements, the temperature cannot. Temperature measurements are one of the biggest problems in shock compression science.

There are many other methods to produce extreme conditions. For example, a sample can be placed in a container then pressurized and heated. However, heating and pressurizing a container can take minutes or hours. Chemical materials may have decomposed long before the final state is reached. Irradiation by a pulsed laser also produces dynamic extreme conditions. Laser irradiation primarily couples to the electrons, so a lot of the laser energy is transformed into hot electrons, producing massive ionization and heating. A flyer plate impact produces dynamic extreme conditions by compressing bulk material, which minimizes ionization. A flyer plate impact produces dynamic mechanical deformation in a way that these other methods do not.

To illustrate the effects of flyer plate impacts on inert samples lacking mechanical strength, Fig. 2 uses a compendium of literature references to consider water impacted by an Al flyer plate.^26–32 Keep in mind that, as always, water is unique. Here, it is the relatively low density and high compressibility of the extended hydrogen-bonded network in water that leads to higher temperatures than would be expected in most other shocked inert solid or liquid chemicals. Knowing the shock equations of state (termed “Hugoniot”)⁴ of Al and water allows us to compute the fraction of momentum transferred from the flyer plate to the water, thus determining the input pressure (momentum flow per unit area) associated with a given flyer velocity. A complete equation of state is used to obtain the water temperature.³³ Prior measurements of electrical conductivity during shock are used to determine the ionic strength (pKw) of the water.³⁴ 

Figure 2 shows that a 5 km/s impact of an Al flyer plate on the water can produce pressures of 27 GPa and temperatures of 2200 K. When shocked, the water dissociates to create ion pairs, since creating ionic pairs from hydrogen-bonded water is associated with a volume decrease. It is possible to shock water into a liquid superionic fluid, a molten salt consisting only of H⁺ and OH⁻ (and their various associated structures).^35–37 However, even relatively modest impact velocities, such as from a high-power rifle bullet (1.2 km/s), can cause the pH to drop from ambient pH = 7 to pH = 3.7, more than a thousand-fold increase in [H⁺] concentration.

A detonation is a special kind of shock wave supported by energetic chemical reactions behind the shock front.¹ The distinguishing feature of a detonation is that, in a reference frame moving at the shock velocity, the shock profile does not change (Fig. 3).¹ For a cylindrical explosive, a steady detonation is possible only if the diameter is larger than a critical value, and the run distance is longer than the reaction zone. Detonations can be produced in charges with sufficient run distance but subcritical diameter, but such detonations decay rapidly and are termed unsteady detonations.

The structure of a simple detonation is illustrated in Fig. 3.³⁸ The leading edge of the detonation is termed the von-Neumann spike (VNS). Behind the VNS, the shock pressure and density decay as the condensed-phase explosive are transformed into an expanding gas. There is a critical plane behind the VNS termed the Chapman-Jouguet plane (CJ plane). Behind this plane, pressure waves generated by energy release from chemical reactions cannot propagate fast enough to reach the shock front, so chemical reactions behind the CJ plane cannot support the shock front. However, many explosives, especially those with Al particles, may continue to react behind the CJ plane and increase the destructive power of the explosive. Those reactions, however, destructive, do not affect the detonation shock. The region between the VNS and CJ plane is termed the “reaction zone.”^20,38 It is the region encompassing the chemical reactions that support the detonation.

Figure 4(a) shows the concept behind our 0.5 mm diameter flyer plate launcher,^7,11,12 which uses a Q-switched Nd:YAG laser that produces a 10 ns pulse with up to 2.5 J of energy to launch flyers from a metal foil bonded with epoxy to a glass substrate. Most often, we use 25 µm thick Al-1100 foil for the flyer plate, although thicker Al and other metals can also be used.^7,12 The laser beam profile must be uniform, otherwise different parts of the foil travel at different velocities and the flyer tears itself apart in flight.³⁹ We use a diffractive optic from Silios, Inc. (Peynier, France) to homogenize the beam.^16,40

The original concept for laser-launching of flyer plates involved generating an expanding plasma at the irradiated foil surface.⁴¹ However, it is desirable to minimize the ablation and heating of the foil, so we have developed a shock-assisted launching process that relies on the fact that Nd:YAG laser damage of glass windows occurs predominantly at the surface. We use a highly convergent laser beam that is below the damage threshold when it enters the glass substrate but far above the damage threshold at the foil/epoxy/glass interfaces [Fig. 4(a)].⁷ Up to 90% of the laser, pulse energy can be absorbed in this interface, greatly reducing laser heating of the foil.⁷ The laser energy absorbed at the glass–foil interface produces a shock that helps launch the flyer plate. The shot-to-shot velocity reproducibility is 2%.¹² 

The flyer plate velocity profile is characterized using photon Doppler velocimetry (PDV),^7,42 as depicted in Fig. 4(b), where the flyer plate was used to launch a shock at a Pyrex glass flat in a vacuum. Our PDV is a compact 1.5 µm wavelength all-fiber interferometer,⁴³ where the flyer plate or the moving sample material acts as one mirror of the interferometer. Knowing the laser wavelength, the flyer velocity history can be reconstructed from a time-dependent interferogram.⁴⁴ Figure 4(c) shows a velocity history for a 75 µm thick Al flyer plate launched in a vacuum.¹² Due to the short duration of the laser pulse, the force imparted by the laser on the foil is impulsive, and a reverberating shock is produced in the flyer, leading to the damped oscillations in Fig. 4(c).⁷ The spacing between the launcher and the target, typically 0.3–0.5 mm, is adjusted so these oscillations have become minimal at the instant of flyer impact. In Fig. 4(c), the flyer terminal velocity was 1.4 km/s. When the flyer impacts the glass the velocity drops abruptly, but for a brief period thereafter the flyer/glass interface moves at U_p = 0.9 km/s [Figs. 4(c) and 4(d)]. From the tabulated Pyrex glass Hugoniot, we can use Eq. (2) to compute the pressure in the glass,^6,45 which is 9.8 GPa. This high pressure is steady for 13 ns [Fig. 3(d)] before the shock begins to dissipate.

The shock compression microscope, an inverted optical microscope with flyer launcher, PDV, and various optical diagnostics is depicted in Fig. 5(a).⁴⁰ Because shock measurements are inherently destructive, sacrificial samples are mass-produced in the form of an array of solid targets¹³ or liquid microcuvettes [Fig. 5(b)].⁹ The samples can be illuminated by a 2 µs flash lamp or a femtosecond laser pulse.¹⁶ Shocked energetic materials produce intense thermal emission that can be detected by a 32-channel optical pyrometer⁴⁶ and a nanosecond video camera.

In operando temperature measurements are made by spectral analysis of thermal emission, a method called optical pyrometry.⁴⁷ Our optical pyrometer [Fig. 5(c)] consists of a high-throughput aberration-free prism spectrograph with a linear array of 32 optical fibers in the image plane.⁴⁶ Each fiber is connected to a <1 ns photomultiplier and a 1.2 GHz digitizer. The pyrometer is calibrated using a tungsten halogen lamp, nominally 2900 K, that is spatially homogenized with an integrating sphere. The spectral radiance from the sphere was calibrated by the manufacturer (Labsphere). On each shot, the pyrometer outputs spectra at 32 wavelengths from 450 to 825 every 0.8 ns, out to 200 µs. To handle this large quantity of data, we use a logarithmic averaging procedure to produce a constant number of data points in each time decade.⁴⁶ 

Planck’s radiation law assumes a blackbody (perfectly absorbing of all radiation) in thermal equilibrium at temperature T. Wien’s high-temperature approximation, which is valid at the high temperatures studied here, can be written as⁴⁷ 

where C₁ = 3.72 × 10⁻¹⁶ W/m², C₂ = 1.439 × 10⁻² m K, and ε(λ) is the emissivity, where ε(λ) = 1 for a blackbody. S(T,λ) is the spectral radiance, the absolute intensity of emitted light in the wavelength range between λ and λ + dλ in one steradian, with SI units of W m⁻² sr⁻¹ nm⁻¹. In the graybody approximation, the emissivity <1 is assumed independent of wavelength.

Several complications arise when making optical pyrometry measurements of shocked energetic materials, primarily a spatially dependent temperature distribution (“hot spots”) and an emissivity that is <1 and wavelength dependent. According to the Stefan-Boltzmann law, the intensity of radiation integrated over all wavelengths emitted by a black body increases as T⁴.⁴⁷ We make measurements over the visible spectral range, and in this range, the intensity varies approximately as T⁶. So optical pyrometry with a spatially inhomogeneous temperature distribution tends to strongly emphasize hot spots.

When emissivity is <1 then, unlike a blackbody, thermal emission does not originate entirely from the surface. Emission from material below the surface may also be observed. For a non-graybody emitter with a wavelength-dependent emissivity, emission at different wavelengths can originate from different depths below the surface. When a steep shock front arrives and causes the sample to emit, the emission rise time will be different at different wavelengths.

Models have been derived for the emissivity wavelength dependence in various scenarios.⁴⁷ We have developed a method to verify whether the graybody approximation is valid over the wavelength range observed.^16,48 Equation (3) can be reformulated to yield⁴⁹ 

Equation (4) shows that if we plot the function Z vs 1/λ, for a graybody, a linear function will be obtained with a slope inversely proportional to T. There are multiple reasons this type of plot, which we call the “Z-plot,” might deviate from linearity. For example, atomic line or molecular band emission may be superimposed on the thermal emission.⁴⁶ In a Z-plot, such excess emission appears as a downward feature on the otherwise linear plot.

An example of a pyrometer output matrix is shown in Fig. 6, where the sample was PBX formulated from HMX with a silicone polymer binder, and the flyer plate velocity was 4 km/s.¹⁶ The Z-plots are linear at all times. The slope is smallest at a shortest time when temperatures are high and it decreases with time as the shocked PBX cools down.

Nitromethane would ideally produce the maximum energy by decomposing to the lowest energy products, H₂O, N₂, and CO₂, but the NM molecules themselves do not have enough oxygen (negative oxygen balance), so some of the reaction products will include NO and CO and HCN.⁵⁰ The excess carbon condenses into a mixture of various allotropes, often with nitrogen and oxygen impurities.⁵¹ This condensate is called “soot.”

NM is viewed as a homogeneous explosive, a particularly simple case, but it is not really homogeneous. When shocked, gas is generated almost immediately, followed by soot precipitation. As described below, so-called “cellular structures” are formed spontaneously in the driven fluid flow.⁵² 

Although shocked NM chemistry is complicated, from an engineering point of view the most relevant quantities are the rates of heat release and work done by volume expansion. Experiments have shown that the heat release from shocked NM can be modeled as a two-step thermal explosion.^52–54 In the first step, heat release occurs primarily during the formation of water, which requires a C–N bond to break.⁵⁰ The other atoms in the reactive mixture form heterogeneous clusters containing carbon, oxygen, and nitrogen.⁵⁰ The first step triggers the subsequent release of energy released by breaking up these metastable clusters.^52,54

Because the shock produced in NM with our 0.5 mm flyer plates is below the critical diameter,⁹ we need to produce an unsteady detonation where the reaction is fully developed before edge effects quench it. So the NM explosive charge must, at minimum, be longer than the 70 µm reaction zone. We use a thin (25 µm) flyer plate that produces a shock slightly more powerful than the VNS at the leading edge of the detonation (Fig. 3) so the input shock already resembles the leading edge of the detonation and is immediately part way toward producing the full reaction zone.⁹ 

Figure 7(a) shows experimental results using PDV to measure the shock waveform as it breaks out of the NM into a glass window [Fig. 5(b)] located various distances downstream from the shock input.⁹ The two most interesting features of Fig. 7(a) are the large jump in shock pressure about 40 µm (6 ns) downstream, and the formation of a shock around 90 µm whose profile does not change, at least for the next 210 µm. This is an unsteady detonation that dissipates about 250 µm downstream. The detonation is produced in about 15 ns, close to the theoretical limit of 11 ns based on a 70 µm reaction zone and 6.2 km/s velocity.⁹ Figures 7(b) and 7(c) show associated pyrometry measurements of the detonation temperature 3430 ± 240 K.⁹ 

The large pressure jump around 6 ns [Fig. 7(a)] is due to a phenomenon seen in homogeneous explosives termed a “superdetonation.”^17,55,56 When a shock enters NM, as it travels downstream the NM near the shock entry, which has been heated the longest, eventually undergoes a two-stage explosion. The first explosion launches a shock wave that catches up to the input shock,⁵⁷ to create a higher-pressure merged shock around 5 ns. This merged shock, or superdetonation, then merges with the shock from the second NM explosion and decays into a detonation that persists for a brief time because it is an unsteady detonation due to the small sample size.⁵⁸ 

One of the motivations for detailed studies of NM is to develop theoretical models to describe the shock-to-detonation transition in such detail that its behavior can be predicted with confidence in any shock or detonation scenario.¹⁸ A critical ingredient in such predictions is a kinetic model for the generation of heat and work. Ordinary methods to measure chemical kinetics are not suitable for studying this extreme reaction, because the chemical species are moving at high speed, about Mach 18, and all the action takes place in a moving 70 µm thick reaction zone.

We have developed a method to detail the two stages of NM reaction by imaging structures in the shock front termed “cellular structures.”^52,54 Cellular structures and dark waves⁵⁸ are often seen in detonations of liquids or gases, and they are caused by interactions of the shock with the walls of the container. These “wall-stabilized” structures produce an imprint on the walls that can be analyzed post mortem.^59,60

The cellular structures we observe are different. They are transient structures generated without walls due to successive collisions between the downstream shock and the two shocks launched by the two-stage NM explosion behind the shock front.⁵² They represent structured regions of enhanced chemical reactivity observed as brighter thermal emission against a darker background. Figure 8 shows some typical structures observed at impact velocities below (3.3 and 3.7 km/s) and equal to (4.0 km/s) what is needed to produce a detonation in a short time.⁵² Figure 8(a) shows that in the subdetonation regime, the initial step involves the formation of small hot spots, which bloom and then dissipate. This demonstrates that shocked NM very quickly stops being a homogeneous explosive.

Figures 8(b) and 8(c) show two distinct types of cellular patterns. A chaotic fine-grained pattern at a shorter time and a larger, more coherent pattern with 110 µm cells. These two patterns result from the two shocks emitted by NM behind the leading shock front. The size of the cells increases further downstream because the two NM explosions produce highly diverging shocks. The size of the cells and knowledge of the shock velocity allows us to determine the times associated with the two successive NM explosions.⁵² 

Detonation formation in shocked PBX begins with hotspot formation, and the shock-to-detonation transition in PBX is quite different from a homogeneous explosive.⁶¹ Hotspot formation occurs promptly, but deflagration growth is hindered by the insulating polymer layers between HMX crystals. In the PBX experiments described here, a deflagration is created but it cannot evolve into a detonation because the samples are too small.

We have developed methods to mass-produce small cylindrical PBX charges [Fig. 9(a)] in the form of sacrificial arrays such as the one shown in Fig. 9(b).^62–64 The explosive material is mixed with a binder, compacted in a hydraulic press, and packed into small wells with a Teflon spatula. Then, the binder is allowed to cure. The array in Fig. 9(b) consists of 186 cylindrical charges 1 mm in diameter and 90 µm in length.

A minimal PBX consists of explosive crystals (a mixture of single crystals and fused polycrystals), binder, and voids. Voids are especially important as locations where hot spots can be formed.²² A nano x-ray computed tomography scanner (CT) can be used to detect the voids, as shown in Figs. 9(c) and 9(d) where the explosive was TATB (triamino trinitro benzene) or PETN (pentaerithritol tetranitrate). Voids in the TATB PBX are visible as small black regions [Fig. 9(c)]. We typically produce PBX with less than 5% volume fraction of voids.

Hot spots have been discussed for more than 70 years,⁶⁵ but real-time measurements have been frustrated by the opacity of PBX and the fleeting appearance of hot spots within a violent explosion. For these reasons, we do not really know which microstructure configurations produce critical hot spots. Figure 10(a) illustrates the problem of seeing hot spots. Following a flyer plate impact, thermal emission is produced at the shock front as well as behind the front. However, to observe this emission, light has to diffuse through a highly scattering medium of particles and binder, making it impossible to image hot spots in real time.

Our solution to this problem involves embedding individual crystals of PBX in a transparent polymer matrix in a traveling-wave geometry, where we can view the PBX through the polymer during the shock. Our first efforts involved a single (i.e., nominally defect-free) crystal of HMX, where we saw see hot spots appearing at the HMX-polymer interface.^66,67 These hot spots produced a deflagration that grew until it consumed the entire HMX crystal in about 200 ns, subsequently spreading into some of the surrounding polymer.

Recently, we have developed a method depicted in Fig. 10(b) where we can observe every crystal in a shocked PBX in real time. We fabricate a PBX wafer whose thickness is about the size of the largest crystal in the PBX. Figure 10(c) shows a random sample of HMX crystals used to fabricate the wafer. The wafer is nominally one crystal thick and there are no crystals hidden from view. We can input various kinds of shocks and observe the result. We can use a thin flyer plate that produces a 4 ns shock to get high time resolution. We can also use the flyer plate to initiate an explosive booster that will launch a detonation shock into the wafer.^63,64

In the experiments described here, we used a 30 µm thick wafer of HMX crystals with an epoxy binder to impart mechanical strength. The wafer was embedded in a silicone rubber binder (Sylgard 182). Figure 10(d) shows an image of the wafer taken with the nanosecond camera in visible light, where the bright regions are the higher refractive index HMX and the dark regions the polymer binder. In Fig. 10(e), we have used an image analysis routine to outline each crystal in red. The wafer had 76 identifiable HMX crystals.

Figures 11(a) and 11(b) show the time-dependent radiance and temperature from the polymer-embedded wafer shocked with a 4.3 km/s flyer plate. This radiance and temperature profile obtained with our pyrometer is a spatial average over a 0.4 mm diameter region at the center of the shock produced by the 0.5 mm diameter flyer plate. The two peaks in the radiance are associated with the shock ignition of hot spots and the growth of a deflagration throughout the wafer.

Figure 12 shows an eight-frame video of the shocked wafer that allows us to spatially resolve the thermal emission. In each frame, the white outlines represent the 76 crystals and the red patches represent thermal emission. Of course, the crystals do not remain intact during the shock and deflagration; the white outlines are presented as a static reference to show which crystals produced the thermal emission.

The images show distinct hot spots at shorter times. Some of them disappear. Others in the upper right hand and lower right hand corner seemingly appear out of nowhere long after the 4 ns shock. Ultimately, the entire wafer is consumed by deflagration. The hot spots that disappear were those with high temperatures but such low thermal mass that they could not induce reactions in nearby crystals. Such subcritical hot spots can be produced, for example, by compression of gas in small pores.⁶⁸ The delayed appearance of hot spots occurs at sites where the shock produced hot spots that were initially too cold to produce thermal emission above our noise floor of about 1800 K. When those hot spots eventually ignited the HMX, the temperature jumped and the thermal emission spiked. Three hot spots grew and merged to produce deflagration throughout the entire wafer.

Figure 13(a) shows the thermal emission intensity trajectories for all 76 crystals. The sum of these trajectories, plus thermal emission from regions between crystals, is equal to the radiance in Fig. 11(a). We can identify some structures associated with subcritical and critical hot spots. Crystals denoted 1 and 2 in Fig. 13(b) produced hot spots that died out quickly while crystals denoted 3, 4, and 5 were at the center of the critical hot spots.

To understand which configurations suppress or enhance hotspot formation in shocked energetic microstructures, it is useful to have experimental methods that produce enough data for machine learning analysis. The PBX wafers we made were 5 cm², and allowing a generous spacing between flyer impacts, we can get at least 50 shots per wafer.

Studying high explosives in operando means watching them with high time and space resolution as a powerful shock wave passes through them, causing heat release and rapid volume expansion. Here, we discussed doing this not by watching a large bomb explode from a distance,⁶⁹ but on a tabletop in an intrinsically safe high-throughput mode.

The technology that makes these in operando measurements possible is the hypervelocity laser flyer launcher, the velocimeter that acts as a dynamic pressure gauge, an optical pyrometer that measures time-dependent spatial-averaged temperatures, and a high-speed camera that measures the locations where thermal emission appears.

The ability to produce detonations and determine where hot spots are created and how they evolve in time in a high-throughput mode where the explosive composition, microstructure, and input shock can be varied generates the information needed to build predictive models of explosives performance. Watching a detonation grow and decay helps us understand how detonations interact with various external perturbations, such as obstacles in their path and interactions with other detonations. Obstacles in the path can be used to vary the explosive output. Interactions between multiple detonations, if cooperative, can result in conditions much more extreme than possible from a single detonation.

Finally, although the focus of this paper was on high explosives, this technique is quite general as to its ability to study other condensed matter systems in dynamic extreme conditions of high pressure and temperature.

The research described in this study was based on work at the University of Illinois, supported by the U.S. Air Force Office of Scientific Research under Award Nos. FA9550-19-1-0227, FA9550-19-1-0318, and FA9550-21-1-0448, and by the U.S. Army Research Office under Award No. W911NF-19-2-0037.

The authors have no conflicts to disclose.

Dhanalakshmi Sellan: Sample preparation (equal); Data acquisition (equal); Data analysis (equal); Review and editing (equal). Xuan Zhou: Sample preparation (equal); Data acquisition (equal); Data analysis (equal); Review and editing (equal). Lawrence Salvati III: Instrument development and support (equal); Data analysis (equal); Structural characterization (equal) Review and editing (equal). Shiva Kumar Valluri: Review and editing (equal); Data analysis (equal); Structural characterization (equal). Dana D. Dlott: Supervision (equal); Funding acquisition (equal); Concept development (equal); Writing and editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.