Shock-induced chemical decomposition and overdriven detonation in hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX) single crystals

Achieving high performance and safety have been key—and sometimes competing—objectives throughout the long history of high explosive (HE) development and their use.^1–5 The desire for high performance (detonation wave velocity, pressure, and reaction products) has motivated the development of HE crystals that are denser and more energetic, while enhanced safety (avoiding unwanted detonation) has been the motivation for developing insensitive high explosives (IHEs) that are less sensitive to shock wave initiation than conventional HEs (CHEs). A continuing goal of HE scientific activities is attaining the optimal combination of high performance and insensitivity.

Recently, wave profile measurements were reported⁶ for 1,1-diamino-2,2-dinitroethene (FOX-7) single crystals shock compressed to 64 GPa—almost twice the calculated Chapman–Jouget (C–J) pressure.⁷ These wave profiles—the first reported for HE single crystals shocked above the C–J pressure—in thin (∼250 μm) crystals revealed steady overdriven detonations that exhibited classic C–J detonation behavior:^8–10 completion of chemical decomposition within the detonation front—an unexpected finding for an IHE. Determination of the detonation products equation of state (EOS) and the C–J pressure (35 GPa) provided⁶ an experimental demonstration of performance similar to or better than the theoretically calculated response of hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX)⁷—a commonly used CHE. The high performance of FOX-7 relative to other IHEs, such as 2,4,6-triamino-1,3,5-trinitrobenzene (TATB), together with the observed shock insensitivity of FOX-7 to ∼30 GPa, revealed a near-optimal combination of high performance and insensitivity not previously reported for HE crystals.

Gaining insight into the differences in the shock compression and detonation response of IHEs and CHEs is important for guiding research efforts to further enhance the desired combination of high performance and insensitivity. In particular, wave profile measurements for CHE single crystals at high pressures—to complement the previous FOX-7 study⁶—are needed to better understand the intrinsic response of the HEs, avoiding the complexities inherent to the response of composite (or polymer-bonded) HE formulations. However, the peak pressures reached in previous wave profile measurements for shock compressed CHE single crystals—pentaerythritol tetranitrate (PETN),¹¹ octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX),¹² and RDX^13–15—have not exceeded 5 GPa (or ∼13 GPa for unsteady waves in PETN).¹⁶ Hence, wave profiles in CHE single crystals are needed at pressures comparable to the pressures examined in FOX-7.⁶ 

To address this need, we conducted well-characterized plane shock wave experiments to measure wave profiles in RDX single crystals to 63 GPa. Because the shock response of RDX single crystals can be examined along more than one orientation (unlike FOX-7), wave profiles were measured for [100]- and [111]-oriented RDX. The experiments were undertaken to address the following questions:

1. How does the shock sensitivity of RDX single crystals compare to that of FOX-7? In particular, at what pressures do shock-induced chemical decomposition features appear in the measured RDX wave profiles?

2. At what pressures do steady detonations develop within thin (∼250 mm) RDX crystals? Will such detonations exhibit an idealized C–J behavior at high pressures, similar to FOX-7?

3. What is the response of RDX detonation products (products Hugoniot curve and EOS) at pressures above the C–J state and how does it compare to that of FOX-7?

4. Does crystal orientation play a significant role in the shock compression and detonation response of RDX single crystals?

The experimental methods used to obtain wave profiles are presented in Sec. II. The experimental results, including the measured wave profiles, are presented in Sec. III. In Sec. IV, the results are analyzed and discussed to address the scientific questions noted above. The main findings of this work are summarized in Sec. V.

The experimental configuration, shown schematically in Fig. 1, and the experimental methods used in this work are similar to those described in Refs. 6 and 17. Hence, only a brief summary of the methods is presented here.

The RDX single crystals were grown at the Los Alamos National Laboratory (LANL) from stock produced by the Woolwich (HMX-free) process with additional purification before crystallization. The α-phase crystals (Pbca space group, ρ₀ = 1.806 g/cm³)¹⁸ were oriented along the [100] or [111] crystallographic direction, cut, and provided to us by Dr. Daniel E. Hooks of LANL. Typical lateral dimensions of the prepared samples were 7–8 mm. Each crystal was ground and polished to a thickness of ∼250 μm, comparable to the sample thickness used in the FOX-7 experiments.⁶ The polished RDX single crystals were bonded to a 1050 Al buffer¹⁹ and a [100]-oriented LiF window²⁰ using epoxy. Prior to bonding, an Al mirror was deposited on the sample side of the LiF window.

Plate impact experiments were conducted using the configuration shown in Fig. 1. Using a two-stage gun,²¹ 1050 Al flyers were impacted onto the Al/RDX/LiF target assemblies (a powder gun was used to launch C101 Cu flyers²⁰ for experiments 1–4); Table I shows the measured impact velocities, together with other experimental parameters. A velocity interferometer system (VISAR)²² having 0.7 ns time resolution was used to measure particle velocity histories at the RDX/LiF interface. In addition, velocity histories were recorded at three locations at the Al buffer/RDX interface to measure the impact tilt and to determine the shock wave arrival time.

Twelve plate impact experiments were conducted on RDX single crystals shock compressed to pressures ranging from 15 to 63 GPa. The measured particle velocity histories at the RDX/LiF interface for all 12 experiments are shown in Fig. 2. The measured wave profiles for many of the experiments show a large jump in particle velocity to a near-constant state, followed by a small jump at a later time. The small jump is due to a reflected wave that originates at the RDX/LiF interface and then reverberates between the Al buffer and the LiF window.

At 15 GPa (experiments 1 and 2), the measured velocity profiles for both RDX orientations show an initial jump followed by a slow increase in particle velocity; this velocity increase is more rapid for [100] RDX than for [111] RDX (Fig. 3). The observed slow velocity increase indicates the onset of shock wave-induced chemical decomposition in RDX single crystals, with the reaction progressing more rapidly for [100] RDX.

At 20 GPa (experiments 3 and 4), the large initial jump is again followed by a slow increase in velocity, with the velocity increasing more rapidly for [100] RDX than for [111] RDX (Fig. 4). However, for both orientations, the increase in velocity at 20 GPa is somewhat more rapid than at 15 GPa—especially for the [111] orientation—suggesting that the decomposition rate increases with shock pressure.

At 31–32 GPa (experiments 5 and 6), approaching the calculated C–J pressure (∼35 GPa),⁷ the initial jump and slow increase in velocity are followed by a second velocity jump and significant velocity fluctuations (Fig. 5). The second velocity jump occurs at a significantly earlier time than that expected for the reflected reverberation wave noted earlier. Therefore, the second velocity jump for experiments 5 and 6 suggests the onset of a rapid shock-induced chemical reaction that arises subsequent to the initial slow reaction onset. The second jump occurs at a later time for [111] RDX, compared to [100] RDX. The onset of a rapid chemical reaction is also indicated in experiments 7 and 8, where the measured wave profiles show an initial spike followed by a significant reduction in velocity (Fig. 5); however, the measured profiles for [100] RDX and [111] RDX are quite similar. Further discussion of experiments 5–8 is presented in Sec. IV.

At higher pressures (51 GPa and above), the measured profiles are flat-topped single waves. These flat-topped profiles show that the shock wave-induced chemical reaction is completed within the shock front, implying reaction times less than the 0.7 ns time resolution of our measurements. Completion of the reaction within the shock front is consistent with the idealized C–J detonation theory.

The analyses conducted on our measured RDX results—and presented in this section—are similar to those carried out previously for FOX-7 single crystals.^6,17 However, unlike the previous FOX-7 work, the RDX results presented here encompass two different crystal orientations ([100] and [111]). Therefore, in this section, the results for [100] RDX and [111] RDX will be compared with each other and with the previous results for FOX-7 single crystals.^6,17

For each experiment, the shock compression end states (or Hugoniot states) were determined from the measured shock wave velocities and the measured impact velocities using standard impedance matching methods.²³ The results are tabulated in Table II and shown in Fig. 6.

For particle velocities (u_p) greater than 2.6 mm/μs, the measured shock wave velocities (U_s) shown in Fig. 6(a) are greater than the calculated C–J detonation velocity for RDX (8.76 mm/μs).⁷ These results, together with the wave profiles presented in Fig. 2, show that the development of steady overdriven detonation waves in RDX single crystals requires less than 250 μm of run distance from the impact surface at sufficiently high pressures, similar to the response reported previously for FOX-7.⁶ These findings for RDX and FOX-7 are in contrast to the multi-millimeter run distances reported for establishing steady detonations in TATB-based composite IHEs.^24,25

For particle velocities less than 2.6 mm/μs, the measured shock velocities are significantly lower than the calculated C–J detonation velocity.⁷ As shown in Fig. 6(a) (red dotted-dashed curve), the U_s–u_p results for u_p < 2.6 mm/μs are fitted well using the nonlinear relationship²⁶ 

where c₀ = 2.525 mm/μs is the ambient bulk sound speed determined using the RDX elastic constants;²⁷ this finding is in contrast to the linear U_s–u_p relationship calculated for unreacted RDX (black dotted-dashed curve).²⁸ In addition, a linear U_s–u_p relationship was also determined previously for unreacted FOX-7 (green dotted-dashed curve).^6,17 Although the reason for the nonlinear U_s–u_p relationship measured for RDX is not clear, the measured wave profiles shown in Figs. 3–5 suggest that the Hugoniot states in Fig. 6 likely do not correspond to completely unreacted RDX. For experiments 5 and 6, the second jump in the RDX wave profiles—which contrasts with the large spikes observed for FOX-7 (Fig. 5)— occurs subsequent to the arrival of the shock wave at the LiF window. Therefore, the onset of a rapid chemical reaction—indicated by the second jump—is localized near the RDX/LiF interface and results from the increased pressure and temperature due to the reflection of the shock wave from the LiF window.²⁹ For experiments 7 and 8, the measured shock velocities (not shown in Fig. 6; see Table II) are significantly lower than the calculated C–J detonation velocity. However, unlike the other experiments, these velocities cannot be associated with a nearly flat-top wave.

Figure 6(b) shows the pressure (P)–volume (V/V₀) states corresponding to the U_s–u_p results in Fig. 6(a). Due to chemical energy release in the detonation wave front, the P–V/V₀ Hugoniot states at 51 GPa and above have significantly larger volumes compared to the extrapolated Hugoniot curve for RDX (red dot-dashed curve). The results show that the P–V/V₀ Hugoniot responses for [100] RDX and [111] RDX are similar over the range of pressures examined here. We note that Hugoniot states were not determined for experiments 7 and 8 because a near-constant state following the initial jump was not observed.

The measured Hugoniot states at 51 GPa and above arise from steady detonations. Therefore, they provide important insight into the detonation products response, including the products equation of state (EOS). We used the well-established Jones–Wilkins–Lee (JWL) EOS^9,30–32 to fit the measured RDX Hugoniot states, together with the calculated results for RDX at the C–J state and along the expansion isentrope.⁷ The JWL EOS is defined by^9,30–32

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 Eq. (2), ω is traditionally used to denote the Grüneisen parameter—usually denoted elsewhere by Γ and defined as $Γ=V(∂P/∂E)V$^23,33—which is assumed to be constant in the JWL formulation.^9,30–32

The Hugoniot curve and the isentrope determined using the JWL EOS are shown in Fig. 6 (red solid and red dashed curves, respectively). The JWL fit presented here results in Γ = 0.51, which is consistent with the values obtained from JWL fits for overdriven detonations in FOX-7 single crystals⁶ and in composite HEs.^34–36 The parameter values obtained from our JWL fit are listed in Table III.

Also shown in Fig. 6 is the Hugoniot curve determined previously for the FOX-7 detonation products (green solid curve).⁶ The FOX-7 products Hugoniot curve lies above that of RDX in the P–V/V₀ plane, suggesting higher performance for overdriven detonations.

As discussed in Sec. III, the small jump in particle velocity in the later portions of the measured wave profiles (Fig. 2) is due to a reflected wave that originates at the RDX/LiF interface and then reverberates between the Al buffer and the LiF window. Therefore, for experiments at 51 GPa and above, the measured arrival time of the reverberating wave provides information about the sound speed in the RDX detonation products, which provides an important constraint on the detonation products EOS.

To examine this constraint, we carried out numerical simulations to match the wave profiles—including the small particle velocity jump at later times—measured at 51 GPa and above. The wave profile calculations utilized the well-established finite-difference, artificial viscosity approach³⁷ in a wave propagation code.³⁸ Because the chemical decomposition in RDX shock-compressed to 51 GPa and above is completed within the shock front, no further reaction was considered and the detonation products response was described using the Mie–Grüneisen EOS,^23,33

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 wave profiles, the Hugoniot curve used to determine P_H and E_H in Eq. (3) incorporated a smooth transition from the RDX Hugoniot curve [Eq. (1)] to the RDX detonation products Hugoniot curve, as shown in Fig. 7. The smooth transition was incorporated for numerical convenience and has no bearing on the findings.

The wave profiles calculated using Γ = 0.51 (red curves) are shown in Fig. 8, 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 particle velocities. However, the calculated arrival time of the small reverberating wave is early compared to the measured profile, indicating that the calculated detonation products sound speed is too high. As shown in Fig. 8, the Mie–Grüneisen EOS with Γ = 1.05 (green curves) provides a somewhat better match to the measured wave profiles. However, the calculated reverberating wave arrival time is too late for experiments 9 and 10 and too early for experiments 11 and 12.

These results show that the wave profiles at 51 GPa and above cannot all be matched by calculations using a single Γ value, in contrast to previous calculations for FOX-7.⁶ As shown in Fig. 8, a good match to all of the wave profiles at 51 GPa and above is obtained from calculations using Γ = 0.95 (blue dashed curves) for experiments 9 and 10 and Γ = 1.25 (blue solid curves) for experiments 11 and 12. Both of these Γ values are significantly larger than that obtained from the JWL fit for RDX (Γ = 0.51) and are somewhat smaller than the Γ value obtained previously for FOX-7 (Γ = 1.30).⁶ 

As noted previously,³⁵ the sonic condition^8,9 at the C–J point of a steady detonation 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 the C–J state. Similar to the previous FOX-7 study,⁶ this condition was used, together with sound speed determinations for the detonation products, to determine the C–J state for RDX. The sound speeds in the RDX detonation products were determined using^33,35

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. In Eq. (4), the JWL Hugoniot curve for RDX in Fig. 6 was used, together with Γ = 0.95 for experiments 9 and 10 and Γ = 1.25 for experiments 11 and 12. We note that c_E in Eq. (4) is the Eulerian sound speed, the acoustic wave velocity in the compressed fluid. The Lagrangian sound speed is defined by

As shown in Fig. 9, 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 C–J pressure of 35 GPa—providing experimental confirmation of the calculated C–J pressure.⁷ Thus, the calculated C–J state is shown to be consistent with the measured wave profiles at 51 GPa and above, similar to the previous finding for FOX-7.⁶ 

The results and analyses presented here for RDX single crystals—a conventional HE—complement those reported previously for FOX-7 IHE single crystals,^6,17 providing important insight into the differences in the shock compression and detonation response of IHEs and conventional HEs. The comparisons presented here between the shock compression responses of RDX and FOX-7 are particularly useful because they involve the intrinsic response of conventional HE and IHE single crystals, rather than the significantly more complex response of composite (or polymer-bonded) HE formulations.

The wave profile features indicating the onset of a chemical reaction, observed for RDX at 15 and 20 GPa (Figs. 2–4), demonstrate the considerably higher shock sensitivity of RDX single crystals relative to FOX-7 single crystals, which showed no sign of chemical decomposition to ∼30 GPa (Figs. 3 and 4).^6,17 Approaching the C–J pressure, the onset of relatively slow reaction rates in the shock compressed RDX crystals gives way to much faster reactions (Fig. 5). Compared to FOX-7,⁶ the energy release in RDX is slower and occurs over a considerably wider pressure range.

The flat-topped single waves observed at 51 GPa and above (Fig. 2) show that RDX, like FOX-7, can exhibit steady overdriven detonation waves within 250 μm of run distance from the impact surface at sufficiently high pressures, and these detonation waves are well-described by the classic Chapman–Jouguet (C–J) detonation theory.^8–10 Interestingly, the shock pressures required to observe this behavior are higher for RDX than for FOX-7, despite the significantly greater sensitivity of RDX to the onset of chemical decomposition at lower pressures.

Because of the C–J detonation exhibited by the RDX single crystals, the measured wave profiles provided significant insight into the RDX detonation products response. In particular, the detonation products EOS for RDX single crystals—a key determinant of HE performance^9,39—was determined to pressures almost twice that of the C–J state, similar to the analysis carried out previously for FOX-7.⁶ The FOX-7 products Hugoniot curve lies above that of RDX in the P–V/V₀ plane (Fig. 6), suggesting higher performance for FOX-7 at overdriven detonation conditions.

Our arrival time measurements for the small reverberation wave observed in the measured profiles (Fig. 2) provided additional constraints on the detonation products EOS. Numerical simulations using a single constant Grüneisen parameter were unable to match the measured wave profiles at 51 GPa and above (Fig. 8), in contrast to previous results for FOX-7.⁶ The Grüneisen parameters used to match the overdriven detonation wave profiles for RDX at 51 GPa (Γ = 0.95) and at 63 GPa (Γ = 1.25), while somewhat smaller than that used in similar calculations for FOX-7,⁶ were significantly larger than those required to match the response of detonation products for RDX, FOX-7,⁶ and other HEs^31,34–36 at relatively large expansions (V/V₀ > 3). Therefore, our results for RDX—together with the previous results for FOX-7⁶—suggest that the constant Γ assumption incorporated in the JWL EOS^9,30–32 is not a good assumption for modeling the detonation products response of HEs over volume ranges that encompass both highly compressed and highly expanded states.

Using the detonation products EOS, sound speeds were determined for shock compressed RDX and were used, together with the detonation products Hugoniot curve, to determine the C–J state for RDX. The resulting C–J pressure (35 GPa) for RDX single crystals is the same as that reported previously for FOX-7 single crystals,⁶ providing experimental confirmation for previous calculations.⁷ 

Our results have also provided insight into the role of crystal orientation on the shock compression response of RDX crystals. Figures 2–5 show that the chemical decomposition develops more rapidly for [100] RDX, compared to [111] RDX, indicating that [100] RDX is somewhat more sensitive under shock compression. However, the orientation dependence reported here for the RDX response is significantly less pronounced than that reported previously for PETN.¹⁶ At pressures above the C–J state, the Hugoniot response and detonation products EOS are similar for [100] RDX and [111] RDX. This finding is consistent with the hypothesis that the chemical reactions involved in the overdriven detonation response depend primarily on the structure of the RDX molecules and not on the crystal orientation. Although a corresponding examination of the role of crystal orientation on the shock compression and detonation response of FOX-7 single crystals is very desirable, crystal orientations other than {101} are not available—likely due to the layered crystal structure of FOX-7.⁴⁰ 

The above results and findings demonstrate the usefulness of comparing the response of different HE single crystals to shock compression below and above the C–J pressure. Extension of the same approach to other HE single crystals is expected to provide fruitful insights. Also, the experimental results and findings presented here are expected to motivate theoretical studies to further understand the observed differences in the response of RDX and FOX-7 single crystals over a broad range of pressures below and above the C–J pressure. Such efforts are needed to provide a more detailed understanding of detonation performance and shock insensitivity for IHE and CHE single crystals and to guide the development of HE crystals that further enhance the high performance and insensitivity observed for shock compressed FOX-7.⁶ 

N. Arganbright and K. Zimmerman are acknowledged for their expert assistance with the plate impact experiments. The RDX single crystals used in this work were provided to us by Dr. Daniel E. Hooks of Los Alamos National Laboratory. 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).

The authors have no conflicts to disclose.

J. M. Winey: Conceptualization (equal); Formal analysis (lead); Supervision (equal); Writing – original draft (lead); Writing – review & editing (equal). Y. Toyoda: Investigation (lead). Y. M. Gupta: Conceptualization (equal); Supervision (equal); Writing – review & editing (equal).

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