Schematic of the experimental setup for shock recovery of BC 3 samples ͑ left ͒ and for load characterization ͑ right ͒ . The explosive charge is 

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Context 1

... fixed positions along the tube. The passage of the detonation wave in the HE cylinder is accompanied by considerable heating which causes partial or total ionization of the air at the probe extremity, resulting in the emission of a flash recorded by a photodiode. The transit time over the 3 cm spacing between these chronometric probes provides a measurement of the mean detonation velocity at each shot ͑ Fig. 3 ͒ . Within the experimental uncer- tainty, this measured velocity is found to match the Chapman–Jouguet ͑ CJ ͒ value expected for the propagation of a steady detonation wave in a charge of diameter far greater than the critical diameter of both explosives ͑ Table I ͒ . The detonation pressure in this CJ regime is given in Table I for both NM and PBX. In this geometry, the detonation wave can be approximated as a planar front in the central region close to the symmetry axis, as confirmed by two-dimensional ͑ 2D ͒ simulations presented later. The temporal profile of the pressure pulse is basically triangular ͑ Taylor wave profile ͒ , with a steep compression to the CJ pressure followed by gradual unloading due to the expansion of the detonation gases. When the wave front reaches the interface with the anvil, a shock is transmitted into steel and another shock is reflected in the detonation products, due to the acoustic impedance mismatch across this interface. The pressure value behind those shock waves can be evaluated in a pressure-particle velocity diagram, at the 14,15 intersection of the steel adiabat and the symmetric of the Rayleigh line issued from the CJ state ͑ Fig. 4 ͒ . This simple impedance matching technique, based on a linear approxima- 16 tion of the Crussard curve of the detonation products and 17–19 data reported in the literature, leads to peak pressures of 21 GPa and 41 GPa for NM and PBX, respectively ͑ Table I ͒ . To test the consistency of these theoretical pressure values, as well as the validity of the planar approximation in the central region, and to account for the decay of the pressure pulse during its propagation through the steel cell from the interface with the HE to the sample location, Lagrangian simulations have been performed in 2D axisymmetric geom- 20 etry with the hydrocode RADIOSS . The detonation wave is initiated from the top as an input initial condition. It is as- sumed to propagate at the CJ velocity in the condensed explosive, which is instantaneously transformed into detonation products at the CJ pressure. A Jones–Wilkins–Lee 21 formulation was used for the equation of state of these 22 gaseous products, while a Johnson–Cook constitutive law accounts for the elastic-plastic behavior of steel, and a simple hydrodynamic description was used for the PVC tube. Simu- lations of the detonation propagation with or without the PVC tube lead to basically identical pressure profiles along the explosive charge, which indicates that the confining ef- fect of the tube can be neglected, as could be expected with regards to the high detonation pressures involved. Hence, to reduce time consuming calculations of sliding interfaces, this tube has been removed in the next computations. The pres- ence of the thin B-C chip embedded in the metal is disre- garded too, since it is expected to reach very rapidly the pressure and temperature conditions induced in the surround- ing steel, after a quick reverberation of compression waves throughout the chip thickness ͑ about 50 ␮ m ͒ . Figure 5 shows the pressure contours calculated within the left half of a PBX-steel assembly at successive times. It depicts the expansion of the detonation gases behind the shock wave ͓͑ a ͒ and ͑ b ͔͒ , which propagates at the CJ velocity ͑ Table I ͒ , then the pressure increase due to the impedance mismatch across the interface with steel ͑ c ͒ , and the transmission of a com- pressive pulse into the anvil, with a planar wave front in the vicinity of the symmetry axis. The calculated values of the transmitted pressure for NM and PBX are 20 GPa and 40.5 GPa, respectively, in very good agreement with the theoretical predictions ͑ Table I ͒ . Then, due to the unloading Taylor wave following the shock front, peak pressure decays during propagation in steel ͑ d ͒ . Meanwhile, release waves issued from the outer edges of the explosive charge propagating in both axial ͑ downward ͒ and radial ͑ inward ͒ directions lead to an increasing curvature of the wave front. Still, the compression wave reaching the sample, either 12 or 17 mm beneath the interface with the explosive, remains approximately planar ͑ e ͒ . Finally, the later interactions of lateral release waves produce tensile loading ͑ i.e., negative pressure ͒ above the sample location f , but in practice such tension cannot be sustained by the mechanical interfaces in the steel assembly ͑ see Fig. 1 ͒ , so it will not be transmitted to the sample. Further characterization of the pressure loading is pro- vided by instrumented experiments described in Fig. 1 ͑ right ͒ . Thin piezoelectric films of polyvinylidene-fluoride ͑ PVDF ͒ are inserted at fixed positions in a steel cell in contact with the cylindrical charge of NM or PBX. Upon compression by the transmitted shock front, they deliver a sharp 23 current pulse. The mean shock velocities inferred from the measured transit times between the gauge positions are 3.92 km/s and 4.27 km/s for NM and PBX, respectively. They match the shock velocity calculated in the corresponding simulations within a 4% error. Such consistency implies a correct description of the pressure pulse evolution during its propagation, since shock velocity in steel strongly depends on shock pressure. Figure 6 shows the pressure profiles calculated at the sample position, either 12 or 17 mm deep below the interface, for both types of HE. Due to the elastic-plastic behavior of steel, the shock front splits ͑ more or less, depending on shock pressure ͒ into an elastic precursor to about 1.4 GPa ͑ Ref. 24 ͒ ahead of a sharp compression to a peak pressure ranging from 8 to 32 GPa, depending on the type of HE and sample location ͑ Table II ͒ . It is followed by gradual unloading to ambient pressure within about 2 ␮ s. According to the assumption of fast reverberation mentioned earlier, these profiles can be considered as the pressure loads applied onto the BC 3 sample. The temperature history is more difficult to assess, because shock-induced heating is uneasy to compute, due to the effect of an artificial viscosity used to damp nu- 17 merical oscillations following a discontinuity. Besides, the initial porosity, hard to evaluate in our B-C chips, is known to increase shock heating. Furthermore, shock temperature is followed by a residual, postrelease temperature significantly higher than the initial temperature. Finally, the time needed for thermal equilibrium between the steel and the BC 3 sample is essentially unknown. Values of shock temperature 25 in steel inferred from Hugoniot data are listed in Table II. They provide rough, lower estimates of the temperature in- troduced into the BC samples. The structure and phase composition of the t-BC 3 samples recovered after NM and PBX shock loading were characterized by both Raman scattering and x-ray diffraction. Raman spectroscopy provides an insight into lattice disorder. The impurity centers and defects break the transla- tional symmetry of the structure. As a result, the selection rules for the Raman active optical phonons near the center of the Brillouin zone ͑ q ϳ 0 ͒ are no longer applicable. Graphite and other graphitelike phases are examples of structures with 26 such defect-induced Raman lines. A highly ordered pyro- lytic graphite has two Raman active -point modes of E 2 g symmetry, that correspond to the low frequency ͑ 42 cm −1 ͒ interplane rigid-layer shear displacements and high frequency ͑ the so-called G band at 1581 cm −1 ͒ in-plane 27 displacements. Phases with imperfect graphitelike structure, in particular t-BC 3 , have additional defect-induced bands ͑ for instance the D band at 1350 cm −1 ͒ in their Raman spectra previously explained by the relaxation of the q ϳ 0 27,28 vector selection rule. The changes in the shapes and intensities of Raman bands are often used as an indication of structural changes in samples of graphitic structure. Raman spectra were collected using a micro-Raman spectrometer LABRAM ͑ Jobin-Yvon ͒ , of 800 mm focal length, equipped with a large 1024 pixel charge coupled device chip. The 100 ␮ m slit of the spectrometer gives a resolution of 0.3 to 1 cm −1 between 200 and 4000 cm −1 . Raman spectra were excited by the 488 nm line of an adjustable ionized argon laser. The power on the sample was less than 4 mW to avoid temperature effects on the Raman peaks positions. The scattered radiation was collected in a backscattering geometry. Two types of spectra have been observed in t-BC 3 recovered after NM-shock loading ͑ Fig. 7 ͒ . Type ͑ 4 ͒ is almost similar to the starting material ͑ 5 ͒ with a ratio I ͑ D ͒ / I ͑ G ͒ = 1.58 against 1.34 for the starting t-BC 3 sample, where I ͑ D ͒ and I ͑ G ͒ are the integrated intensity of the peaks D ͑ ϳ 1350 cm −1 ͒ and G ͑ϳ 1581 cm −1 ͒ , respectively. Type ͑ 3 ͒ shows additional peaks at 376, 525–575, 703, 870, and 1070 cm −1 . The peaks at 1357 and 1577 cm −1 are less broad than in spectrum ͑ 4 ͒ . Two second order peaks appear at 2690 and 2924 cm −1 . As suggested by the comparison shown in Fig. 8, these features indicate that part of the shocked t-BC 3 sample has undergone phase segregation into B 4 C and graphite. B 4 C is known to be a molecularlike structure constituted of B 11 C and B 12 icosahedra joined by a three atoms linear chain 29,30 ͑ C–B–C or C–B–B depending of the concentration of carbon ͒ . Its typical Raman spectrum is shown in Fig. 8 spectrum 1 over three main frequency domains: i 600– 1100 cm −1 assigned to the breathing modes of the icosahedra, ͑ ii ͒ 400– 580 cm −1 assigned to ...

Context 2

... 2,4,6-trinitramine ͒ . In the case of NM, the detonation was driven from the top by a ϳ 30 g pentrite initiator. Three optical probes were inserted at fixed positions along the tube. The passage of the detonation wave in the HE cylinder is accompanied by considerable heating which causes partial or total ionization of the air at the probe extremity, resulting in the emission of a flash recorded by a photodiode. The transit time over the 3 cm spacing between these chronometric probes provides a measurement of the mean detonation velocity at each shot ͑ Fig. 3 ͒ . Within the experimental uncer- tainty, this measured velocity is found to match the Chapman–Jouguet ͑ CJ ͒ value expected for the propagation of a steady detonation wave in a charge of diameter far greater than the critical diameter of both explosives ͑ Table I ͒ . The detonation pressure in this CJ regime is given in Table I for both NM and PBX. In this geometry, the detonation wave can be approximated as a planar front in the central region close to the symmetry axis, as confirmed by two-dimensional ͑ 2D ͒ simulations presented later. The temporal profile of the pressure pulse is basically triangular ͑ Taylor wave profile ͒ , with a steep compression to the CJ pressure followed by gradual unloading due to the expansion of the detonation gases. When the wave front reaches the interface with the anvil, a shock is transmitted into steel and another shock is reflected in the detonation products, due to the acoustic impedance mismatch across this interface. The pressure value behind those shock waves can be evaluated in a pressure-particle velocity diagram, at the 14,15 intersection of the steel adiabat and the symmetric of the Rayleigh line issued from the CJ state ͑ Fig. 4 ͒ . This simple impedance matching technique, based on a linear approxima- 16 tion of the Crussard curve of the detonation products and 17–19 data reported in the literature, leads to peak pressures of 21 GPa and 41 GPa for NM and PBX, respectively ͑ Table I ͒ . To test the consistency of these theoretical pressure values, as well as the validity of the planar approximation in the central region, and to account for the decay of the pressure pulse during its propagation through the steel cell from the interface with the HE to the sample location, Lagrangian simulations have been performed in 2D axisymmetric geom- 20 etry with the hydrocode RADIOSS . The detonation wave is initiated from the top as an input initial condition. It is as- sumed to propagate at the CJ velocity in the condensed explosive, which is instantaneously transformed into detonation products at the CJ pressure. A Jones–Wilkins–Lee 21 formulation was used for the equation of state of these 22 gaseous products, while a Johnson–Cook constitutive law accounts for the elastic-plastic behavior of steel, and a simple hydrodynamic description was used for the PVC tube. Simu- lations of the detonation propagation with or without the PVC tube lead to basically identical pressure profiles along the explosive charge, which indicates that the confining ef- fect of the tube can be neglected, as could be expected with regards to the high detonation pressures involved. Hence, to reduce time consuming calculations of sliding interfaces, this tube has been removed in the next computations. The pres- ence of the thin B-C chip embedded in the metal is disre- garded too, since it is expected to reach very rapidly the pressure and temperature conditions induced in the surround- ing steel, after a quick reverberation of compression waves throughout the chip thickness ͑ about 50 ␮ m ͒ . Figure 5 shows the pressure contours calculated within the left half of a PBX-steel assembly at successive times. It depicts the expansion of the detonation gases behind the shock wave ͓͑ a ͒ and ͑ b ͔͒ , which propagates at the CJ velocity ͑ Table I ͒ , then the pressure increase due to the impedance mismatch across the interface with steel ͑ c ͒ , and the transmission of a com- pressive pulse into the anvil, with a planar wave front in the vicinity of the symmetry axis. The calculated values of the transmitted pressure for NM and PBX are 20 GPa and 40.5 GPa, respectively, in very good agreement with the theoretical predictions ͑ Table I ͒ . Then, due to the unloading Taylor wave following the shock front, peak pressure decays during propagation in steel ͑ d ͒ . Meanwhile, release waves issued from the outer edges of the explosive charge propagating in both axial ͑ downward ͒ and radial ͑ inward ͒ directions lead to an increasing curvature of the wave front. Still, the compression wave reaching the sample, either 12 or 17 mm beneath the interface with the explosive, remains approximately planar ͑ e ͒ . Finally, the later interactions of lateral release waves produce tensile loading ͑ i.e., negative pressure ͒ above the sample location f , but in practice such tension cannot be sustained by the mechanical interfaces in the steel assembly ͑ see Fig. 1 ͒ , so it will not be transmitted to the sample. Further characterization of the pressure loading is pro- vided by instrumented experiments described in Fig. 1 ͑ right ͒ . Thin piezoelectric films of polyvinylidene-fluoride ͑ PVDF ͒ are inserted at fixed positions in a steel cell in contact with the cylindrical charge of NM or PBX. Upon compression by the transmitted shock front, they deliver a sharp 23 current pulse. The mean shock velocities inferred from the measured transit times between the gauge positions are 3.92 km/s and 4.27 km/s for NM and PBX, respectively. They match the shock velocity calculated in the corresponding simulations within a 4% error. Such consistency implies a correct description of the pressure pulse evolution during its propagation, since shock velocity in steel strongly depends on shock pressure. Figure 6 shows the pressure profiles calculated at the sample position, either 12 or 17 mm deep below the interface, for both types of HE. Due to the elastic-plastic behavior of steel, the shock front splits ͑ more or less, depending on shock pressure ͒ into an elastic precursor to about 1.4 GPa ͑ Ref. 24 ͒ ahead of a sharp compression to a peak pressure ranging from 8 to 32 GPa, depending on the type of HE and sample location ͑ Table II ͒ . It is followed by gradual unloading to ambient pressure within about 2 ␮ s. According to the assumption of fast reverberation mentioned earlier, these profiles can be considered as the pressure loads applied onto the BC 3 sample. The temperature history is more difficult to assess, because shock-induced heating is uneasy to compute, due to the effect of an artificial viscosity used to damp nu- 17 merical oscillations following a discontinuity. Besides, the initial porosity, hard to evaluate in our B-C chips, is known to increase shock heating. Furthermore, shock temperature is followed by a residual, postrelease temperature significantly higher than the initial temperature. Finally, the time needed for thermal equilibrium between the steel and the BC 3 sample is essentially unknown. Values of shock temperature 25 in steel inferred from Hugoniot data are listed in Table II. They provide rough, lower estimates of the temperature in- troduced into the BC samples. The structure and phase composition of the t-BC 3 samples recovered after NM and PBX shock loading were characterized by both Raman scattering and x-ray diffraction. Raman spectroscopy provides an insight into lattice disorder. The impurity centers and defects break the transla- tional symmetry of the structure. As a result, the selection rules for the Raman active optical phonons near the center of the Brillouin zone ͑ q ϳ 0 ͒ are no longer applicable. Graphite and other graphitelike phases are examples of structures with 26 such defect-induced Raman lines. A highly ordered pyro- lytic graphite has two Raman active -point modes of E 2 g symmetry, that correspond to the low frequency ͑ 42 cm −1 ͒ interplane rigid-layer shear displacements and high frequency ͑ the so-called G band at 1581 cm −1 ͒ in-plane 27 displacements. Phases with imperfect graphitelike structure, in particular t-BC 3 , have additional defect-induced bands ͑ for instance the D band at 1350 cm −1 ͒ in their Raman spectra previously explained by the relaxation of the q ϳ 0 27,28 vector selection rule. The changes in the shapes and intensities of Raman bands are often used as an indication of structural changes in samples of graphitic structure. Raman spectra were collected using a micro-Raman spectrometer LABRAM ͑ Jobin-Yvon ͒ , of 800 mm focal length, equipped with a large 1024 pixel charge coupled device chip. The 100 ␮ m slit of the spectrometer gives a resolution of 0.3 to 1 cm −1 between 200 and 4000 cm −1 . Raman spectra were excited by the 488 nm line of an adjustable ionized argon laser. The power on the sample was less than 4 mW to avoid temperature effects on the Raman peaks positions. The scattered radiation was collected in a backscattering geometry. Two types of spectra have been observed in t-BC 3 recovered after NM-shock loading ͑ Fig. 7 ͒ . Type ͑ 4 ͒ is almost similar to the starting material ͑ 5 ͒ with a ratio I ͑ D ͒ / I ͑ G ͒ = 1.58 against 1.34 for the starting t-BC 3 sample, where I ͑ D ͒ and I ͑ G ͒ are the integrated intensity of the peaks D ͑ ϳ 1350 cm −1 ͒ and G ͑ϳ 1581 cm −1 ͒ , respectively. Type ͑ 3 ͒ shows additional peaks at 376, 525–575, 703, 870, and 1070 cm −1 . The peaks at 1357 and 1577 cm −1 are less broad than in spectrum ͑ 4 ͒ . Two second order peaks appear at 2690 and 2924 cm −1 . As suggested by the comparison shown in Fig. 8, these features indicate that part of the shocked t-BC 3 sample has undergone phase segregation into B 4 C and graphite. B 4 C is known to be a molecularlike structure constituted of B 11 C and B 12 icosahedra joined by a three atoms linear chain 29,30 ͑ C–B–C or C–B–B depending of the concentration of carbon ͒ . Its typical Raman spectrum is shown ...