Near-optimal combination of high performance and insensitivity in a shock compressed high explosive single crystal

For more than a century, the inherently stored chemical energy in high explosives (HEs) has been extensively utilized in a wide range of industrial and military applications.^1–3 The term high explosive typically refers to a composite consisting of a large mass fraction (∼95%) of high explosive crystals in a polymeric binder. A defining feature of high explosives, which is central to many applications, is the phenomenon of detonation—a high pressure shock wave, self-supported by an exothermic chemical reaction within and/or behind the shock front, which propagates through the explosive material.^3–5 Detonation can be caused by external impartation of a shock wave into the high explosive, either intentionally (e.g., using a detonator) or unintentionally (e.g., accidental impact). Thus, shock wave sensitivity is an important consideration regarding the safe use of high explosives.

Throughout the long history of HE development and use, high performance (detonation wave velocity, pressure, and reaction products) and safety (avoiding unwanted detonation) have been key—and sometimes competing—objectives.^1,2,6–8 High performance has been the primary motivation for developing more energetic and denser HE crystals, while enhanced safety for specific applications has motivated the development of insensitive high explosives (IHEs) that are less sensitive to shock wave initiation than conventional HEs. Although IHEs such as 2,4,6-triamino-1,3,5-trinitrobenzene (TATB) have been developed and used extensively, their performance compares unfavorably with that of many conventional HEs, such as hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX) or octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX).^6–8 Achieving the optimal combination of high performance and shock insensitivity is a long-standing and important goal for HE science and technology.

To characterize and model HE performance for various applications, considerable effort has gone into developing a theoretical understanding of the detonation process.^3–5 The first successful approach, developed by Chapman⁹ and Jouguet^10,11 more than a hundred years ago, incorporated the following idealized picture of detonation—conversion of the unreacted HE to the final reaction products is assumed to occur instantaneously within the propagating detonation wave front.^3–5 Using this idealized theory, the propagation velocity of a steady self-supporting detonation wave and the resulting detonation pressure are unique for each HE material, and together they define the Chapman–Jouguet (C–J) state for that material.^3–5 Although subsequent theoretical developments allowed for reactions to occur in a finite reaction zone behind the detonation wave front and for more complex energy release mechanisms,^3–5 the C–J model continues to be used to characterize and rank HE performance.^6,7

High performance conventional HEs typically exhibit relatively short reaction times (a few nanoseconds), where the chemical energy is completely released within or immediately behind the shock wave. For example, the detonation response of pentaerythritol tetranitrate (PETN) is well described by the C–J theory, including the assumption of an instantaneous reaction.¹² In contrast, IHEs typically exhibit reaction times that extend to hundreds, or even thousands, of nanoseconds.^13–16 Due to their extended reaction zone, such IHEs are not well described by the classical detonation theory and are referred to as nonideal explosives.^16,17 The relatively complex response of nonideal IHEs presents challenges for performance characterization—due partly to the need for large sample sizes^13–15,18—and for modeling.^16,17 Therefore, IHEs having short reaction zones (or near instantaneous reaction) constitute a very desirable scientific and technological development.

Although composite (or polymer-bonded) IHEs have been studied extensively, the detonation wave response of IHE single crystals has not been reported. Such studies constitute an important need because they provide insight into the intrinsic response of IHE crystals, avoiding complexities inherent to the shock compression response of composite explosives. In addition, studies of shock compressed IHE single crystals can provide experimental results that can be compared more readily with theoretical calculations, such as molecular dynamics and first principles quantum mechanical calculations, compared to results from composite IHEs.

Among IHE crystals, 1,1-diamino-2,2-dinitroethene (C₂H₄N₄O₄, known as DADNE or FOX-7)^19–21 has a particularly simple molecular structure (Fig. 1) and is attractive for shock compression experiments because of the following factors: (1) significantly lower sensitivity to impact, compared to conventional HEs such as RDX or HMX,^8,19 (2) detonation performance predicted to be similar to that of RDX,^19,22 (3) large body of experimental work under static compression,^23–32 and (4) availability of single crystals having sizes suitable for plate impact experiments.

Recently, the shock compression response of FOX-7 single crystals was examined in plate impact experiments.^33,34 These experiments represented the first examination of a shock compressed IHE single crystal and provided wave profile measurements³³ and time-resolved Raman spectra³⁴ for FOX-7 single crystals shock compressed to ∼20 GPa. Significantly, neither the continuum results (wave profiles) nor the Raman results showed any indications of the onset of a chemical reaction. Because Raman spectroscopy measurements in shock compressed high explosives are a particularly sensitive indicator of chemical reaction onset,^35–37 these results have unequivocally demonstrated that FOX-7 single crystals are strongly insensitive to shock wave initiation.^33,34 The ∼20 GPa or higher threshold for FOX-7 is in marked contrast to Raman measurements in PETN or RDX, which showed the onset of chemical decomposition around 5–6 GPa.^36,37

To examine the detonation response of FOX-7 single crystals, shock compression experiments at higher pressures are required. Previous experiments on several composite HEs have shown that significant insight into the detonation response can be obtained by examining HEs shock compressed to pressures exceeding the C–J pressure (resulting in overdriven detonations).^3,4,38–44 Thus, we conducted well-characterized plane shock wave experiments to measure wave profiles to examine the detonation response of FOX-7 single crystals shock compressed to 64 GPa—almost twice the calculated C–J pressure.²² These wave profiles—the first reported for either conventional or insensitive HE single crystals shocked above the C–J pressure—revealed steady overdriven detonations that exhibited classic C–J detonation behavior with chemical decomposition completed within the detonation front. For an IHE to display a C–J detonation response was extremely unexpected. Furthermore, measurements of detonation profiles at pressures above the C–J state provide insight into the equation of state (EOS) for the FOX-7 detonation products—an important determinant of HE performance.

Our results for FOX-7 single crystals reveal a near-optimal combination of high performance and insensitivity to shock initiation—the first such finding, to the best of our knowledge, for a high explosive crystal.

The experimental configuration shown schematically in Fig. 2 and the experimental techniques used in this work are the same as described in Ref. 33. Hence, only a brief summary of the methods is presented here.

Powdered FOX-7 was provided by Dr. Joel R. Carney of the Naval Surface Warfare Center-Indian Head Division (NSWC-IHD). Single crystals were grown from a solution of FOX-7 in dimethyl sulfoxide (DMSO) by slow evaporation at room temperature.²⁶ Although two high temperature structural phases of FOX-7 are known,^45,46 the crystals used in this study had the ambient α structure (monoclinic, P2₁/n).²¹ The single crystals were cleaved parallel to the {101} plane (the ac plane in Fig. 1) to obtain samples having 1–2 mm lateral dimensions and thicknesses of ∼250 μm (Table I). Because the FOX-7 single crystals are extremely fragile, considerable care was required in sample handling and preparation. The cleaved and polished single crystals having {101} faces were bonded to a 1050 Al buffer⁴⁷ and a LiF window⁴⁸ using epoxy. Prior to bonding, an Al mirror was deposited on the sample side of the LiF window. The {101} crystal faces of FOX-7 are the only ones currently accessible for plate impact experiments.

Plate impact experiments were carried out using the configuration shown in Fig. 2. Using a two-stage light gas gun,⁴⁹ 1050 Al flyers (C101 Cu flyer⁴⁸ for experiment 1) were impacted onto the Al/FOX-7/LiF target assemblies; the measured impact velocities are listed in Table I. Particle velocity histories were measured at the FOX-7/LiF interface using a velocity interferometer system (VISAR)⁵⁰ having 0.7 ns time resolution. In addition, velocity histories were measured at three locations at the back of the Al buffer to measure impact tilt and to enable determination of the shock wave arrival at the Al/FOX-7 interface.

Ten plate impact experiments were conducted on FOX-7 single crystals shock compressed to pressures ranging from 25 to 64 GPa. The measured particle velocity histories at the FOX-7/LiF interface for all ten experiments are shown in Fig. 3. At 25 GPa pressure (experiment 1), the measured wave profile is a flattopped single wave, very similar to those measured previously at pressures up to 21 GPa.³³ Although not shown, we note that the 25 GPa wave profile is well matched using the material model developed previously³³ for unreacted FOX-7 wave profiles to 21 GPa. Thus, wave profiles for FOX-7 single crystals show no indications of a chemical reaction for shock compression to 25 GPa.

At pressures near the calculated C–J pressure (∼35 GPa),^19,22 the wave profiles for experiments 2–4 show large spikes (<10 ns duration), indicating a shock wave-induced chemical reaction. Further discussion of these three experiments is presented in the Sec. IV.

At higher pressures (44 GPa and above), the measured profiles are flattopped single waves corresponding to the propagating shock waves through the sample. These higher pressure profiles show that the shock-induced chemical reaction is completed within the shock front, implying reaction times less than the 0.7 ns time resolution of our measurements. These reaction times are significantly shorter than those reported for IHEs, such as TATB-based composites.^13,18,39 The reaction completion in the shock front is in agreement with the idealized C–J detonation theory.

The shock compression end states (or Hugoniot states) reached in each experiment were determined from the measured shock wave velocities and the measured impact velocities using standard impedance matching methods.⁵¹ The results are tabulated in Table I and shown in Fig. 4, along with the recently published results for unreacted FOX-7 single crystals shocked to 21 GPa.³³ 

For particle velocities (u_p) greater than 2.5 mm/μs, the measured shock wave velocities (U_s) shown in Fig. 4(a) are greater than the calculated C–J detonation velocity (8.80 mm/μs).²² These results, together with the wave profiles presented in Fig. 3, show that flattop or steady overdriven detonation waves develop very rapidly in FOX-7—requiring less than 250 μm of run distance from the impact surface. This finding contrasts with the multi-millimeter run distances required to establish steady detonations in TATB-based composite IHEs.^13,18

In experiments 1–3, the measured shock velocities (Table I) are significantly lower than the calculated C–J detonation velocity (8.80 mm/μs).²² Instead, they are in excellent agreement with the extrapolation of the unreacted FOX-7 shock velocities. The narrow (<10 ns) spikes in experiments 2 and 3—conducted to examine experimental reproducibility—occur after the arrival of the nearly flattop shock waves at the LiF window. Although these spikes indicate the onset of a shock-induced chemical reaction, the reaction onset is localized near the FOX-7/LiF interface—resulting from the increased pressure and temperature due to shock reflection from the LiF window.⁵² The shock velocity in experiment 4 (Table I) is again significantly lower than the calculated C–J detonation velocity, but, unlike the other experiments, the same cannot be associated with a flattop wave.

Figure 4(b) shows the pressure (P)–volume (V/V₀) states corresponding to the U_s–u_p results in Fig. 4(a). Due to the release of chemical energy in the detonation wave front, the P–V/V₀ Hugoniot states at 44 GPa and above have significantly larger volumes compared to the extrapolated Hugoniot curve for unreacted FOX-7. In particular, we note that the extrapolated unreacted Hugoniot curve does not appear to intersect the locus of the measured high pressure Hugoniot states, in contrast to previous results for several other common HEs.^53–55 Because the onset of chemical reaction for experiments 2 and 3 is localized near the FOX-7/LiF interface, as discussed above, the P–V/V₀ states corresponding to the initial jump in these experiments are consistent with the extrapolated unreacted Hugoniot curve. We note that Hugoniot states were not determined for experiment 4 because of the absence of a constant state following the initial jump.

The detonation products’ response at high pressures is important for quantifying the HE performance.^4,17 Because the measured Hugoniot states at 44 GPa and above presented here arise from steady detonations, they provide important insight into the reaction products response, including the detonation products’ equation of state (EOS). We used the well-established Jones–Wilkins–Lee (JWL) EOS^4,56–58 to fit the measured Hugoniot states, together with the calculated results for FOX-7 at the C–J point and along the expansion isentrope.²² The JWL EOS is defined by^4,56–58

where P is the pressure, V is the specific volume, E is the internal energy per unit volume, and A, B, R₁, and R₂ are constants. In the JWL EOS, ω is traditionally used to denote the Grüneisen parameter—usually denoted by Γ elsewhere and defined as $Γ=V(∂P/∂E)V$^51,59—which is assumed to be constant in Eq. (1).^4,56–58

The Hugoniot curve and the isentrope through the C–J point determined using the JWL EOS are shown in Fig. 4. The separation between these two curves is determined by the Grüneisen parameter. The JWL fit presented here results in Γ = 0.52, which is consistent with the values obtained from JWL fits for overdriven detonations in composite HEs.^39,40,44 The JWL parameter values from our fit are listed in Table II.

As seen in Fig. 3, all of the measured wave profiles show a small jump in particle velocity in the later portions of the profile. This jump is due to the arrival of a reflected wave that originates at the FOX-7/LiF interface and then reverberates between the Al buffer and the LiF window. Thus, the measured arrival time of the small reverberating wave provides key information about the sound speed in the FOX-7 detonation products, which, in turn, provides an important constraint on the detonation products EOS.

To examine this constraint, numerical simulations were carried out to match the wave profiles—including the small jump in particle velocity at later times—measured at 44 GPa and above. Wave profiles were calculated using the well-established finite-difference, artificial viscosity approach⁶⁰ in a wave propagation code.⁶¹ Because the chemical reaction in shock compressed FOX-7 is completed within the shock front for pressures of 44 GPa and higher, no further reaction was considered in the detonation products’ EOS, and the same was described using the Mie–Grüneisen EOS,^51,59

where P_H and E_H are the pressure and specific energy, respectively, on the Hugoniot curve. The Grüneisen parameter Γ was assumed constant, consistent with the JWL EOS formulation. To calculate the wave profiles for shock compression to 44 GPa and higher, the Hugoniot curve used to determine P_H and E_H in Eq. (2) incorporated a smooth transition from the unreacted FOX-7 Hugoniot curve to the FOX-7 detonation products’ Hugoniot curve, as shown in Fig. 5. We note that the smooth transition used is for numerical convenience and has no bearing on the findings.

The calculated wave profiles (red curves) are shown in Fig. 6, together with the measured wave profiles (black curves). The calculated profiles provide a good match to the measured shock wave arrival times and the measured peak particle velocities. However, the calculated arrival time of the small reverberating wave is early compared to that in the measured profile, showing that the sound speed determined from the detonation products EOS is too high. To better match the reverberating wave arrival time, the Grüneisen parameter in the EOS was increased to Γ = 1.3. As shown in Fig. 6, the Mie–Grüneisen EOS with Γ = 1.3 (green curves) provides a good match over the entirety of the measured wave profiles, including the arrival time and amplitude of the small reverberating wave.

The sonic condition^3,4 at the C–J point implies that the shock wave velocity, the Lagrangian sound speed of the detonation products, and the sum of the Eulerian sound speed and the particle velocity are all equal at that state.⁴⁰ As discussed in Ref. 40, this condition can be used, together with sound speed determinations for the detonation products, to determine the C–J state.

The sound speed in a shock compressed fluid, such as the FOX-7 detonation products, is determined using^40,59

where P_H is the Hugoniot pressure, V is the specific volume, $dPH/dV$ is the slope of the Hugoniot curve at P_H, and Γ is the Grüneisen parameter. To determine the sound speed for the FOX-7 detonation products in each experiment, Eq. (3) was used, together with the JWL Hugoniot curve in Fig. 4 and Γ = 1.3. We note that Eq. (3) determines the Eulerian sound speed, the velocity of an acoustic wave in the compressed fluid. The Lagrangian sound speed, more amenable to direct experimental determination, is defined by

As seen in Fig. 7, the shock wave velocity, the Lagrangian sound speed, and the sum of the Eulerian sound speed and the particle velocity all converge at the U_s–u_p state corresponding to a pressure of 35 GPa—experimentally confirming the calculated C–J pressure.²² Thus, the calculated C–J state is consistent with the measured wave profiles at 44 GPa and above.

The measured wave profiles for FOX-7—shock compressed above the C–J state—represent the first such measurements for an HE single crystal and have provided important insight into the shock compression response and chemical energy release for this IHE. The lack of a chemical reaction in the wave profile measured at 25 GPa demonstrates the strong shock insensitivity of FOX-7 single crystals, compared to conventional HEs such as PETN or RDX.^36,37

The steady detonations observed at 44 GPa and above (Fig. 3) enable two key findings regarding the FOX-7 response at pressures above the C–J state: (1) The shock-induced chemical reaction is completed within the measured shock front, indicating rapid (<0.7 ns) reaction times. (2) An overdriven detonation wave develops within 250 μm of run distance from the impact surface. These two findings show that the response of FOX-7 single crystals, shock compressed above the C–J pressure, is well described by the classical Chapman–Jouguet detonation theory.^3–5 Such detonation behavior has not been previously reported for shock compressed IHEs and is in contrast to the significantly longer reaction times reported for TATB-based composite HEs.^13,18,39

Because of the Chapman–Jouguet detonation in FOX-7 single crystals, significant insight into the FOX-7 detonation products response was obtained from our measurements. In particular, the detonation products’ EOS for FOX-7 single crystals was determined to pressures almost twice that of the C–J state. Although product EOSs for composite HEs shock compressed above the C–J point have been developed previously using measured overdriven detonation states^38–41 and using thermochemical equilibrium calculations,⁴⁴ the FOX-7 products’ EOS presented here is the first for an HE single crystal. This development is important because the reaction products’ EOS is a key determinant of HE performance.^4,16

The small wave reverberation observed in the measured profiles (Fig. 3) provided information about the off-Hugoniot response of the detonation products, and our measurements of the reverberation time resulted in additional constraints on the detonation products’ EOS. Numerical simulations showed that the Grüneisen parameter (Γ = 1.3) required to match the wave profiles at 44 GPa and above (Fig. 6) was more than a factor of two larger than that required to match the response of detonation products for FOX-7 and other HEs^39,40,44,57 at relatively large expansions (V/V₀ > 3). Therefore, our results suggest that the assumption of constant Γ is likely not accurate for FOX-7 detonation products—and perhaps also for the detonation products of other HEs—over volume ranges that encompass both highly compressed and highly expanded states.

Extrapolation of sound speeds for shock compressed FOX-7—determined using the detonation products’ EOS—and the U_s–u_p Hugoniot curve for the detonation products provided a determination of the FOX-7 C–J state. The resulting C–J pressure (35 GPa) for FOX-7 provides experimental demonstration of its high performance—relative to other IHEs, such as TATB—suggested by theoretical calculations.^19,22

The near-optimal combination of high performance Chapman–Jouguet detonation response and strong insensitivity to shock initiation exhibited by FOX-7 single crystals—not previously reported for any HE—is a significant and somewhat unexpected scientific finding. The insensitivity of FOX-7 can be understood—at least in part—in terms of a compression-induced phase transformation to a TATB-like crystal structure and the concomitant strengthening of the FOX-7 hydrogen-bonding network.^30,32,34 In contrast, a detailed understanding of the high performance and Chapman–Jouguet detonation behavior presented here for FOX-7 will require theoretical studies. Some preliminary insight can be gained by noting that the chemical stoichiometry for decomposition of FOX-7 is the same as that of RDX and HMX. Thus, FOX-7 detonation is expected to result in the formation of significantly less solid carbon, compared to carbon-rich IHEs such as TATB. The formation of solid carbon particles in the detonation products is the primary mechanism responsible for the late-time exothermic reactions that result in nonideal detonation behavior in TATB and other carbon-rich IHEs.^13,16,39,62 The results presented here are expected to provide an impetus on two scientific fronts: (i) detailed theoretical understanding of the FOX-7 detonation performance and shock insensitivity, and (ii) guiding the development of other HE crystals that may further enhance the performance and insensitivity observed in shock compressed FOX-7.

In conclusion, we note that DADNE or FOX-7—based on the experimental findings presented here—provides the desired combination of excellent detonation performance and strong shock insensitivity long sought in a high explosive crystal. As such, FOX-7 appears to be superior to the currently available HE crystals in applications where this combination is a key requirement. We recognize that the deployment of HE crystals in an application encompasses many technical issues^6,7 not covered in our work. How the FOX-7 scientific findings demonstrated here can be translated into its practical use in HE applications is a question best answered by those possessing the necessary expertise in such matters.

The authors thank N. Arganbright and K. Zimmerman for their expert assistance with the plate impact experiments. The FOX-7 single crystals were grown by N. Arganbright, Z. Dreger, and Y. Tao. This work was supported by the Office of Naval Research (Grant No. N00014-19-2047) and the Department of Energy/National Nuclear Security Administration (Cooperative Agreement No. DE-NA0003957). Y.M.G. would like to dedicate this study to two outstanding individuals (Dr. Richard Miller and Dr. Judah Goldwasser, both deceased) who strongly encouraged a physicist to get involved in understanding chemical decomposition in shock compressed high explosives.

The data that support the findings of this study are available within the article.