《1. Introduction》

1. Introduction

Energetic materials (EMs) store large quantities of chemical energy, which can be released rapidly upon thermal or mechanical stimuli [1–4]. According to the amount of stored chemical energy and release rate, EMs are generally classified into explosives (primary or secondary explosives), propellants, and pyrotechnics [3,5]. Sustained interest in EMs has been driven by their wide civil and military applications as well as basic science [6]. A thorough understanding of mechanical, physical, and chemical processes in EMs is required not only to predict and control their performance, but also to address increasing environmental and safety concerns of EMs [1,7].

Thermomechanical, physical, and chemical processes in EMs during manufacturing and processing or under external stimuli such as shock compression, involve multiple temporal and spatial scales [6,8]. Microstructures (lattice defects, voids, cracks, interfaces, etc.) created during manufacturing and processing, ranging from sub-nanometers to millimeters [9,10], can impact their responses to external stimuli, and their subsequent chemical kinetics and overall performance [11,12]. Under thermal or mechanical stimuli, such microstructures may lead to strain, stress, or heating localizations, resulting in local chemical reactions (‘‘hot spots”) [13–16]. Upon external stimulation, mechanical and physical (e.g., plastic deformation [17,18], phase transition [19,20], and hot spot formation) and chemical (e.g., chemical kinetics [12,21] and carbon condensate formation [22,23]) processes in EMs span temporal scales from femtoseconds to microseconds, and spatial scales from single molecules and lattices to micrometers or larger. For example, shock-induced chemical initiation usually occurs at the molecular level and sub-picosecond scale [15,24–28]. Up to the mesoscale, the propagating shock wave interacts with the complex microstructure of an EM, yielding phase transitions and hot spots; the shock-to-detonation transition (SDT) [29] is manifested at the macroscale. The temporal scales in manufacturing and processing and external stimulation involve 100 fs in laser ablation [30,31], 100 ns in plate impact loading [32–34], 100 μs in split Hopkinson pressure bar (SHPB) loading [35,36], 10 ms in combustion shock tube [37,38], and 100 s in manufacturing. Given the multiple temporal and spatial scales inherent in EMs at various stages of their life cycles, reliable engineering simulations must resort to physics-based predictive models that incorporate multiscale structures and physical and chemical dynamics [6,7,39], calling for temporally and spatially resolved measurements.

While static [9,40–42] or macroscale [18,34] characterizations of EMs have been routine, resolving structure and physical and chemical dynamics at the micro- and mesoscales and appropriate temporal resolutions have been a diagnostics challenge. Since the physical and chemical events in EMs upon external stimuli occur in extreme conditions [6,18,33], the diagnostics should be nondestructive and penetrating, with high spatial and temporal resolutions. Conventional techniques, such as optical microscopy with matching reflective index [43], confocal scanning laser microscopy [44], polarized light microscopy [33], and scanning electron microscopy [45], can only provide surface measurements, and should be complemented with diagnostics having see-through capability and proper temporal resolutions, or providing extra information. The remarkable progress in X-ray sources, terahertz (THz) sources, detectors, and spectroscopy and imaging systems [46,47] offer opportunities to address the diagnostics challenges for EMs. For example, advanced synchrotron X-ray sources [46,48] and X-ray free electron lasers (XFELs) [49,50] provide femtosecond- and picosecond-scale pulse durations, and unprecedentedly high spatial and temporal resolutions to resolve structure and physical and chemical dynamics in EMs.

Here, we present a brief review on novel X-ray and optical diagnostics for EMs that are either emerging or already exist but are rarely applied to EMs. These diagnostics are targeted for such scientific questions and engineering problems as defects, strengths [51], deformations [18], hot spots, phase changes, reactions, and shock sensitivities [52,53]. This review emphasizes their capabilities of temporally and/or spatially resolved measurements. In addition, basic principles of measurement and data analysis, and illustrative examples for these are presented. In Section 2, we present two-dimensional (2D) and three-dimensional (3D) X-ray imaging techniques including X-ray phase contrast imaging (PCI), X-ray computed tomography (CT), X-ray diffraction (XRD), coherent diffraction imaging (CDI), and small angle X-ray scattering (SAXS). Section 3 addresses THz and optical absorption and emission spectroscopy including THz absorption spectroscopy, pyrometry and laser-induced breakdown spectroscopy (LIBS), and ultrafast imaging interferometry, which includes onedimensional (1D) and 2D velocity interferometer system for any reflector (VISAR) and transient imaging displacement interferometry (TIDI). Section 4 presents a summary of this review.

《2. X-ray diagnostics》

2. X-ray diagnostics

Advanced synchrotron and XFEL X-ray sources with high brilliance, high coherence, high repetition rate, and short pulse duration allow for in situ, real time, multiscale measurements on a wide range of materials and processes [49,50,54,55]. Common Xray diagnostics are imaging in real space, diffraction and scattering in reciprocal space, and spectroscopy. X-ray spectroscopy is beyond the scope of this review and will not be discussed.

Different X-ray diagnostics involve different length scales and thus, different spatial resolutions. Fig. 1(a) illustrates three types of X-ray diagnostics: imaging (including PCI and CT), scattering (including SAXS), and XRD, with a typical length scale of micrometer and sub-micrometer, 1–100 nm, and lattice spacing (Å), respectively [46,56]. CDI is carried out in the Fourier space via phase retrieval and can achieve a spatial resolution of sub-nanometer scale. Such a rich suite of X-ray diagnostics renders structural characterization of EMs at multiple spatial scales feasible.

《Fig. 1》

Fig. 1. In situ multiscale measurements with X-rays. (a) Schematic diagrams of XRD, SAXS/CDI, and PCI/CT techniques. Typical data of XRD, SAXS and digital image correlation (DIC) are shown. Here, qx and qy are basic vectors of reciprocal space, x and y are basic vectors of real space. (b) Experimental setup for gas-gun loading along with X-ray imaging and diffraction/scattering diagnostics shown in (a), and an optical interferometry system (Doppler pin system (DPS)). Loading can be delivered with materials testing systems (MTSs), SHPBs, lasers, magnetic-driven devices, shock tubes, and so on. Inset: time-structure of a typical synchrotron filling mode. BCDI: Bragg CDI.

For single-bunch synchrotron X-ray measurements, loading devices, X-ray shutters, X-ray pulse train, and detectors are timed against a radio frequency signal from the synchrotron, which serves as the master clock of synchronization among these four key components [46]. The temporal characteristics, i.e., pulse width and pulse separation of the X-ray pulse train, are dictated by the time structure of electron bunch filling. Fig. 1(b) inset shows an example of the standard filling pattern at the Advanced Photon Source: Pulse width is ~80 ps, and pulse separation is 153.4 ns. Correspondingly, the highest temporal resolution for X-ray measurements is limited by pulse width (~100 ps), and the framing rate, by pulse separation. For comparison, the highest temporal resolution in XFEL experiments is 10–100 fs; the shortest pulse separation is approximately 10 ms for linac coherent light source (LCLS), 1 μs for LCLS-II, and 220 ns for European XFEL. For microsecond-level resolution, the time structure of a synchrotron filling mode becomes irrelevant and the X-rays can be treated as a continuous wave, while temporal resolution is achieved with electronic shutters of detectors. Considering different temporal resolutions, physical and chemical processes in EMs can be investigated at multiple temporal scales, in addition to multiple length scales.

EMs can be subjected to different stimuli or loading, such as lasers, gas-guns, SHPBs, materials testing systems (MTSs), and shock tubes, with different loading rates, event durations, and stress and temperature conditions. The setup for synchrotronbased, in situ, real time, multiscale X-ray measurements [57], implemented with gas-gun loading, is shown in Fig. 1(b) as an example [56]. The projectile launched by a gas-gun impacts an EM target, inducing physicochemical changes, which are probed with X-ray imaging and diffraction, as well as an optical velocimeter. Since the event duration is of 100–1000 ns for gas-gun loading, single-bunch X-ray measurements are required.

《2.1. X-ray PCI and digital image correlation》

2.1. X-ray PCI and digital image correlation

Propagation-based PCI extracts phase information as well as ensures the attenuation of an X-ray beam passing through a material [58,59]. A heterogeneous phase object induces spatial variations in the phase of X-rays, Φ(x, y), and local curvature in the transmitted wave front. The intensity change, I(x, y), during propagation and interference of such wave fronts is proportional to the Laplacian of this phase distribution, , yielding edge enhancement [58].

Therefore, PCI is particularly suitable for high-resolution imaging of low-density materials like EMs. Currently, advanced X-ray PCI based on synchrotron radiation and XFELs allows for in situ, real-time imaging of internal deformation, damage, and reaction dynamics under dynamic loading, at 100 ps [46,56] and 10– 100 fs [49,50] temporal resolutions, respectively.

Polymer bonded explosives (PBXs) are the most widely used insensitive high explosives [33,60]. Defects within crystals at the crystal-binder interface in the partially-dissolved crystal-binder region or within the binder itself may all contribute to hot spot nucleation [13,14] and initiate deflagration or detonation in abnormal conditions. High-speed synchrotron X-ray PCI has been utilized to characterize deformation and damage of PBXs under dynamic loading with ultrasound [35], SHPB [35,61], and gas gun [62,63]. The temporal and spatial resolutions can reach ~1 μs and 1–10 μm, respectively [46,48]. Fig. 2(a) displays the PCI images of an octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocin (HMX)-based PBX sample with sparsely distributed crystal particles [35] under SHPB loading. The crystal particles can be clearly distinguished from the polymer matrix (which has a similar density) due to edge enhancement. The crystal-matrix delamination (at 95 μs) and particle breakage (at 240 μs) are manifested in the high-resolution PCI images.

Strain mapping across an EM sample, which highlights strain localizations and mechanical energy deposition, is crucial for understanding hot spot formation. X-ray projections of microstructures (e.g., crystal particles in PBX) can provide natural speckles for correlation analysis to track displacement/strain fields [64–66]. The calculation principle and procedure for X-ray digital image correlation (DIC) is similar to those for conventional optical DIC [67]. However, X-ray DIC provides smaller (50 μm or less) speckles and higher spatial resolution (10 μm or better) [68] due to PCI. The deformation dynamics can be resolved for local areas, e.g., particle–matrix interfaces in PBX. X-ray DIC is more advantageous when internal features (e.g., explosive crystal particles) are used to produce speckles through PCI [57,69]. Internal deformation can be studied on a length scale beyond optical DIC. Optical DIC is limited to low temperatures and may fail at or close to the detonation limit. On the other hand, X-ray DIC provides a flexible method for measuring both surface and internal deformation fields depending on how speckles are prepared, and opens new horizons for “2.5D” strain measurements. In addition, X-ray DIC can be combined with XRD to provide lattice-scale deformation mechanisms [48,57], as detailed in Section 2.4.

Fig. 2(b) presents the first study on X-ray DIC for strain mapping around a preset internal void in an aluminum plate under dynamic tension [64]. Lagrangian tensile (E11) and shear (E12) strain concentrations are observed to nucleate and grow around the void with increasing loading. The displacement and strain errors are below 0.01 pixels and 0.01%, respectively.

《Fig. 2》

Fig. 2. (a) X-ray PCI image sequence of PBX under SHPB compression; (b) X-ray PCI image sequence of void growth in an aluminum plate under dynamic tension; (c) corresponding Lagrangian shear strain (E12) and tensile strain (E11) fields. (a) Reproduced from Ref. [35] with the permission of AIP Publishing, ©2016; (c) reproduced from Ref. [64] with the permission of AIP Publishing, ©2014.

《2.2. In situ and dynamic CT and mesoscale finite element modeling》

2.2. In situ and dynamic CT and mesoscale finite element modeling

Laboratory- or synchrotron-based CT serves as a unique tool for nondestructive, 3D characterization of microstructures of a variety of materials [70–72] including EMs [10,43,73,74]. With the rapid development of X-ray sources, in situ CT is gaining popularity in resolving deformation and failure of explosives or simulants under mechanical loading (e.g., handling, transport, or green compaction) [75–78]. Various loading cells including miniature MTS were designed for in situ CT scanning [71,72]. Although laboratory CT can be used for in situ testing, synchrotron CT usually provides a much better combination of penetration and temporal and spatial resolutions [72]. Fig. 3(a) presents an example of CT characterization on a columnar granular packing under compression [70]. Particle rotation and breakage are clearly revealed in the 3D images, consistent with stress drops in the force displacement curve. 3D morphology of particles, intra-granular pores, and crack networks can be quantified via topological analysis including gyration tensor and fractal [70,79].

3D displacement/strain fields can be deduced from volume image sequences via digital volume correlation (DVC) [72,73,75]. For PBX samples, crystal particles serve as natural speckles for DVC. Various incremental DVC algorithms were developed for 3D deformation mapping [80]. 3D correlation criteria were proposed to establish the correspondence between reference and current frames, similar to DIC. Iterative correlation was usually used to achieve high accuracy. Fig. 3(c) [73] presents 3D microstructures from CT characterization and the corresponding DVC analyses for polymer-bonded sugar (PBS), an explosive simulant. Evolution of the axial displacement field in the PBS sample is well correlated to its heterogeneous microstructure, as well as debonding and particle breakage.

With synchrotron sources, the temporal resolution of CT can be increased to ~5 ms (208 tomograms per second) [81]. Such a dynamic CT has been applied to dynamic processes including foaming [81,82], sintering [83], and cracking [84,85]. Fig. 3(b) presents two representative 3D images of a bubble structure captured at 1 Hz. The velocity field of bubbles is quantified via particle imaging velocimetry (PIV) [86]. Such information is useful for understanding packing dynamics, for instance, during compaction of explosive crystals. Although the sub-second temporal resolution is insufficient to resolve highly transient impact or shock events, dynamic CT can capture the deformation dynamics of PBXs at low loading rates or map void production and fluid flow in PBXs during manufacturing and processing, or under thermal decomposition [87]. Recently, a high-speed CT system was demonstrated based on flash X-ray radiography with multiple sources and detectors at a sub-microsecond temporal resolution and a submillimeter spatial resolution [88], while the number and quality of tomograms remain to be improved via integrating more X-ray sources and detectors. Such techniques are promising for studying the shock detonation of EMs.

Moreover, 3D microstructures of PBXs obtained from dynamic CT can be used as inputs to and for comparison with finite element modeling (FEM) [67,89]. Details on the simulation procedures, material models, and parameters [89–91] are beyond the scope of this review. Fig. 3(d) shows that mesoscale FEM reproduces well the crystal-binder delamination and intergranular cracking [67]. However, 2D meshes with a limited number of crystal particles were employed in previous studies for simplicity [67,89]. The appropriate size for a 3D representative volume element at which macroscale behaviors can be adequately described remains to be elucidated [67,76]. With higher-resolution images and advanced image processing, mesoscale FEM with realistic, complex 3D configurations can be exceedingly useful for studying quantitatively the structure–property relations of PBXs, especially under high-rate, thermal-mechanical loading [20,90]. Meanwhile, phase transition and chemical reaction dynamics can be integrated into mesoscale FEM via user subroutine programs, e.g. UMAT/VUMAT [92].

《Fig. 3》

Fig. 3. (a) Force–displacement curve and 3D tomograms from in situ testing of a granular packing under compression with a miniature MTS at the displacements marked on the curve. (b) Dynamic CT characterizations of a foaming process at 1 Hz, displaying two tomograms (left) and displacement field u (right) obtained from PIV. (c) 3D axial displacement fields of a granular packing under quasi-static compression. (d) 2D FEM model based on a tomogram of a PBX sample (left) and simulated 2D maximum principal strain fields εmp (right) at two volumetric strains. (a) Reproduced from Ref. [70] with the permission of Elsevier, ©2020; (b) and (c) reproduced from Ref. [73] with the permission of Elsevier, ©2012; (d) reproduced from Ref. [75] with the permission of MDPI, ©2017.

《2.3. XRD, CDI, and SAXS》

2.3. XRD, CDI, and SAXS

2.3.1. XRD

XRD is essentially a manifestation of electron density distribution of atoms in an ordered/disordered lattice via scattered Xrays. Moreover, it is an indispensable tool for nondestructive determination of crystal structure, phase component, phase change and pathway, grain size, texture, deformation (including strain tensor), and indirectly residual stress and strength. XRD can be conducted on polycrystalline and single-crystal solids, as well as on liquids.

For instance, to elucidate the polymorphic structure of 1,3,5- trinitrohexahydro-1,3,5-triazine (RDX), a widely used explosive first synthesized in 1899 [93], has been investigated under ambient and high pressures regarding its polymorphism with combined single-crystal and powder diffraction. At ambient conditions, RDX exists as stable α-RDX and metastable β-RDX. Their crystal structures were obtained largely with single-crystal XRD [94–98]. RDX has a complex phase diagram, as determined with the diamond anvil cell (DAC) technique [19,40,99] and is rich in polymorphs, including γ-, δ-, ε-phases and the recently discovered ξ- and η-RDX [100].

Static-compression diffraction experiments on RDX were primarily conducted with DAC [40,101,102]. For shock compression, both ex situ and in situ XRD measurements were conducted on RDX [103,104], but no data have been published for the latter till date. Despite that, though dynamic XRD with a synchrotron or XFEL source has been well-established for shock compression [46,56,105,106], its applications to EMs are just emerging.

To illustrate the feasibility of applying transient X-ray diffraction (TXD) to investigating EMs under shock compression, we perform XRD simulations on single-crystal (Fig. 4) [102,107] and polycrystalline RDX (Fig. 5), regarding its phase change, equation of state, and strength upon simulated plate impact loading. In the simulations, diffraction intensity, I, of a simulated structure at scattering vector q is the product of structure factor F(q )with its complex conjugate, F* (q ) [108,109], i.e.,

with

where i denotes the imaginary unit, rj is the position of the jth atom in an atomic configuration; fj is atomic scattering factor of the jth atom and depends on q.

For the α → γ phase transformation of RDX at ~4.0 GPa [101,110] (Figs. 4(a) and (b)), we calculate the corresponding single-crystal diffraction patterns with typical synchrotron and XFEL sources. We choose the first harmonic of a synchrotron undulator source (an 18 mm period and 13 mm gap) at the Advanced Photon Source with an 8% bandwidth (Fig. 4(g)). It is noteworthy that the undulator bandwidth is tunable, an advantage for singlecrystal diffraction. The single-crystal diffraction patterns (Figs. 4(c) and (d)) display drastic differences upon phase transition. Furthermore, the Q-resolution achievable in these experiments is sufficiently high for partial phase analysis, despite its low symmetry and large unit cells. For an XFEL source with a bandwidth of 0.1%, reasonable single-crystal diffraction patterns can also be obtained (Figs. 4(e) and (f)) for partial phase analysis.

《Fig. 4》

Fig. 4. Single-crystal XRD measurements on shock-compressed RDX with singlebunch synchrotron and XFEL sources (simulated). (a) Crystal structure of α-RDX [107]. (b) Crystal structure of γ-RDX [102]. 2D XRD patterns for a "pink” synchrotron source (c) and (d) and for an XFEL source (e) and (f) of α-RDX and γ-RDX, respectively. Here, 2θ represents the diffraction angle and χ is the azimuthal angle of the diffraction vector projected on the diffraction pattern. (g) A representative undulator X-ray spectrum, where λ means the wavelength of X-ray. XFEL: 22.68 keV, 0.1% bandwidth (BW).

For polycrystalline diffraction, diffraction rings from a deformed specimen carry information on phase and strain, as well as strength. As we demonstrated recently [51], the Singh theory [111] can be used to deduce volumetric strain and residual strength from diffraction rings obtained with a properly designed diffraction–detection geometry.

The geometry in Fig. 5(a) can be considered as an example of dynamic XRD under shock compression. ψ represents the angle between the diffraction plane normal and the loading direction and can be calculated from the diffraction and azimuthal angles. The distribution of ψ on a 2D diffraction detector is shown in Fig. 5(b). Furthermore, the lattice spacing dm(hkl) extracted from a 2D diffraction pattern with Bragg’s law, is related to ψ via

where, dp(hkl) denotes d-spacing for a specific diffraction plane (hkl) due to equivalent hydrostatic stress and Q depends on strength, residual strength, and single-crystal elastic compliances. The residual strength t is given by t = , where G is the aggregate shear modulus, and parameter f is approximately 1 for all crystal systems.

A polycrystalline α-RDX sample is compressed uniaxially by 5% to mimic plate impact under the loading–diffraction–detection geometry in Fig. 5(a), and the corresponding diffraction patterns before and after shock compression are presented in Figs. 5(c) and (d), respectively. Fitting the diffraction rings at ambient condition yields Q = 0, leading to zero residual strength and volumetric strain, as expected. For the diffraction pattern during shock compression, the residual strength is obtained as t = 0.88 GPa with shear modulus G = 7.83 GPa [112], and the volumetric strain is 5% as preset. Thus, the Singh method can be used to obtain the volumetric strain and residual strength during shock compression, as demonstrated for metals [51].

《Fig. 5》

Fig. 5. XRD measurements on shock-compressed polycrystalline RDX with 25 keV monochromatic X-rays (simulated). (a) Loading and diffraction geometries of ψ, the angle between the shock direction and the normal of a specific diffracting plane ( ). (b) Distribution of ψ on the 2D diffraction detector, set perpendicular to the incident X-ray beam. XRD patterns of (c) uncompressed and (d) 5%-compressed α-RDX.

2.3.2. CDI

Single grains or single particles represent the smallest structural component of EMs, and their size, shape, and internal defects can affect the performance of EMs significantly [113]. For example, the ‘‘grain size effect” on the shock sensitivity of high explosives has been extensively studied [114]. There have been attempts to lower the shock sensitivity by reducing crystal defects [115,116]. Resolving the single-particle structure and dynamics is directly relevant to the synthesis, processing, and performance of EMs [113,117].

Coherent XRD imaging techniques, especially Bragg CDI (BCDI) and plane-wave CDI (PCDI), are a set of novel X-ray microscopy tools capable of sub-nanometer- and nanometer-level spatial resolutions [118,119]. BCDI is used to investigate the 3D Bragg node of a single-crystal grain via slightly rotating the grain (Fig. 6(a)), and can resolve its 3D structure, 3D strain, and internal defects, including twinning and dislocations [119–122]. Scattering intensity I(q) at a given scattering vector q near a Bragg node can be written as

where is electron density of the lattice, is crystal’s shape function, and represents the displacement field of atoms compared to their ideal lattice sites. PCDI is intended for reconstructing the structure of an isolated crystalline or non-crystalline particle, via detecting coherently scattered X-rays [123–125] (Fig. 6(b)). Unlike BCDI, scattering intensity I(q) for PCDI is determined only by a particle’s electron density distribution function, , and I(q) is given by

Although CDI has rarely been applied to EMs, it does exhibit unique potential. Single grains investigated by BCDI can either be isolated, within a polycrystalline assembly, or embedded in a polymeric matrix (such as PBX). For an isolated grain, the information on 3D structure, 3D strain, and internal defects can be obtained. Moreover, the methodology and experimental instrumentation established for inorganic/metallic nanoparticles [126,127] can be applied directly. For a single grain within a polycrystalline assembly or a polymeric matrix, the aforementioned information can be employed to infer the grain–grain and grain–binder interactions. Grain responses and defect dynamics under external loading can also be derived by in situ BCDI measurements, as presented in Refs. [119,128]. Considering the complexity imposed by the BCDI experiments on EMs, advanced simulation tools, such as GAPD [108] become crucial for experimental design and data interpretation. Fig. 6(b) shows a 3D Bragg node of a Cu nanorod, calculated with GAPD. Its internal twinning defect can be well-reconstructed (Fig. 6(c)). BCDI may not be realistic for high-speed or ultrafast measurements, because of the requirement of sample rotation. Moreover, the brilliance of the incident X-rays is severely limited to mitigate radiation damage to an EM specimen [129].

With intense femtosecond X-ray pulses from an XFEL, singleshot PCDI has been demonstrated to be capable of resolving transient nanoscale dynamics with ~10 fs temporal resolution [125]. Fig. 6(d) presents a PCDI pattern of a bacterium with a single XFEL pulse, and the corresponding reconstructed 2D structure [130]. Explosion dynamics of sucrose nanospheres was studied using single-shot PCDI, and significant sample expansion was observed at 500 fs–1 ps after pump [131]. Given the similarity between sucrose and organic explosives [132], such measurements can be extended to EMs. The pump can either be an optical laser or an X-ray pulse from XFEL. For the X-ray pump and probe with the split-and-delay scheme, the first X-ray pulse can be used for ignition and the simultaneous structural analysis of a particle, while the second X-ray pulse can probe the ignition/explosion dynamics at a certain delay [131]. Such experiments enable us to resolve the growth, combustion or explosion dynamics at the single particle level [113,133–135].

《Fig. 6》

Fig. 6. (a) Schematic diagram of CDI. ki and kf are the incident and diffracted X-ray wavevectors, respectively. q represents the diffraction wavevector. (b) Simulated reciprocal space of a Cu sample with a single twin. qx , qy and qz are three basic vectors of reciprocal space. (c) Reconstruction of (b). (d) Representative diffraction pattern and reconstructed image of Staphylococcus aureus. (d) Reproduced from Ref. [130] with the permission of Springer Nature, ©2016.

2.3.3. SAXS

Inherent structural heterogeneities (Fig. 7(a)) introduced during manufacturing and processing, ranging from nanometer to micrometer length scales, can have significant impacts on the safety and performance of EMs [141–144]. Moreover, nanostructures can be formed as a denotation product. For example, solid carbon is believed to be generated as a major constituent of the detonation products of carbon-rich high explosives (Fig. 7(a)) [145–147]. Characterizing such nanostructures initially or during dynamic loading (their formation and growth dynamics) is essential to establish structure–property relations and understanding the physical and chemical mechanisms in EMs.

《Fig. 7》

Fig. 7. Resolving structural inhomogeneities and dynamics of EMs with SAXS measurements. (a) Schematic diagram of a detonation model, and corresponding submicrometer structures of both initial explosives and detonation products. The chemical decomposition of an explosive occurs in the chemical reaction zone (CRZ). PN andPCJ denote the peak pressure and pressure at the Chapman–Jouguet (CJ) plane where the chemical reaction ceases, respectively. (b) Guinier approach and Porod’s law for obtaining the sizes and surface areas of particles/voids, respectively. (c) Particle/void size distribution function (PVDF) derived using scattering profile fitting methods. (d) Typical morphologies of nanoEMs. (e) SAXS curves of different nanostructures. (f) Anisotropic SAXS pattern of a dense system consisting of nanorods with preferred orientations. (c) Reproduced from Ref. [136] with the permission of the International Union of Crystallography, ©2019; (d) reproduced from Refs. [137–140] with the permission of Elsevier, ©2016, ©2020, ©2017, and ©2017, respectively.

SAXS is sensitive to electron density variations or contrast across length scales ranging between a few nanometers to micrometers, and is well-suited for the structural characterization of EMs at these scales. Abundant information can be obtained nondestructively from SAXS measurements, such as particle size distributions (monodisperse or polydisperse) and pore morphologies (open or closed). For monodisperse systems consisting of particles or voids with contrast , the radius of gyration Rg and surface area S can be obtained via the Guinier approach

and the Porod’s law

respectively (Fig. 7(b)). Here, I is scattering intensity and q is the modulus of the scattering vector. For polydisperse systems, particle size distributions can be obtained by curve fitting (Fig. 7(c)).

SAXS has been successfully applied to obtain the surface areas and the internal void and particle size distributions for the powders and pressed pellets of high explosives [148]. For example, synchrotron-based in situ SAXS measurements revealed that thermal cycling leads to a larger void size and higher void concentration in 1,3,5-triamino-2,4,6-trinitrobenzene (TATB)-based PBXs [149], and can be seen as an application in PBX manufacturing. Highly brilliant advanced light sources also enable us to investigate highly transient processes [46,150]. Time-resolved SAXS (TRSAXS), based on synchrotron or XFEL sources is promising to answer certain unresolved questions, especially those that cannot be addressed due to their highly transient nature and the lack of an appropriate diagnostic tool. For instance, synchrotron-based pink-beam TR-SAXS measurements were conducted to explore the mechanism of formation of carbon condensation following detonation [151–153], and the feasibility of pink-beam SAXS was demonstrated [154]. Recent studies indicate that diamond particles form and grow slightly within 300 ns after detonation [155,156], although it is desirable to combine TR-SAXS with simultaneous dynamic XRD to investigate processes discussed above.

Nanoenergetic materials (nanoEMs) represent an interesting group of EMs with high energy density and excellent combustion performance [134,157,158]. NanoEMs can assume various morphologies (Fig. 7(d)), such as nanospheres [159], nanorods/ nanowires [160], networks [161], nanolayers [162], and core– shell structures [163,164]. SAXS is also advantageous in characterizing these nanostructures (Fig. 7(e)), including particle size distribution and nanorod radius. It is worth mentioning that the interpretation of SAXS measurements can benefit greatly from advanced simulation tools, such as SLADS [165] and GAPD, particularly for nanostructures that cannot be simulated or modeled with traditional simulation/analysis methods. These two codes are capable of calculating the scattering of large, anisotropic, and dense nanoparticle systems. Fig. 7(f) illustrates a simulated anisotropic SAXS pattern for a dense system consisting of nanorods with preferred orientations.

《2.4. Simultaneous multiscale measurements》

2.4. Simultaneous multiscale measurements

With many physical and chemical processes in EMs being multiscale in nature, it is highly desirable to obtain information at multiple spatial scales simultaneously during a single shot. In principle, separate "identical” shots can be conducted to acquire data at different spatial scales. However, in reality, no two shots are identical. The approach of simultaneous multiscale measurements is particularly advantageous in experimental rigor, and can bridge measurements at different scales and reveal the physics across different spatial scales.

Three main types of X-ray diagnostics, namely, imaging and diffraction/scattering (Fig. 1(a)), can be implemented simultaneously through a combination of two or three types, such as XRD + PCI and XRD + SAXS, to obtain information at the microand mesoscales. In addition, conventional bulk-scale techniques, such as laser interferometry and strain or stress gauges, can be utilized for macroscale measurements. Therefore, in principle, micro-, meso-, and macroscale measurements can be performed during a single shot. Here, microscale can be broadly defined to include lattice and nanoscale.

For the XRD + PCI measurements, microscale (lattice-level) and mesoscale (in terms of strain field, for instance) information can be acquired with XRD and PCI, respectively. For example, this technique was applied to a textured magnesium alloy AZ31 [57,166]; XRD indicates the presence/absence of deformation twinning, whereas PCI demonstrates strain localization/delocalization, and the stress–strain curves (obtained from stress gauges) exhibit different strain rate hardening features. Such simultaneous multiscale measurements revealed rigorously for the first time that deformation twinning induces strain delocalization, which in turn leads to increased strain rate hardening in magnesium alloy AZ31. The simultaneity allows for sensible cross-scale connections to be made and the underlying physics to be revealed. The XRD + SAXS measurements are helpful in obtaining the phase and size information of nanoparticles simultaneously, and can be used to understand, for instance, the phase, size, and dynamics of postdetonation carbon condensates. Furthermore, the simultaneous multiscale measurements are expected to be applicable to EMs.

《3. Dynamic THz and optical diagnostics》

3. Dynamic THz and optical diagnostics

《3.1. THz and optical spectroscopy》

3.1. THz and optical spectroscopy

The THz regime is located between the microwave and midinfrared regimes on the electromagnetic spectrum [47], spanning 0.3–10 THz (or 10–300 cm-1 ). Certain vibrational modes of EMs can generate unique THz spectral features, thus being useful in the detection and identification of EMs [168]. Additionally, THz spectroscopy can yield the absorption coefficients and refractive indices of EMs [169]. Furthermore, minor changes in the molecular configurations of EMs may result in THz spectral changes. Consequently, THz spectroscopy can reflect the dynamic chemical and physical responses of EMs to external stimuli.

Recently, the THz spectroscopy of EMs has been extended to low temperatures [170,171]. For example, Fig. 8(a) illustrates the temperature-dependent THz absorption spectra of single-crystal RDX measured along the [002] direction using THz time domain spectroscopy (THz-TDS) at 77–300 K. When the temperature increases to approximately 200 K, the absorption peaks of RDX around 0.5 THz disappear, indicating a possible phase change. Melinger et al. [170] measured the THz absorption spectra of RDX films with THz-TDS at 13–293 K. Below 80 K, there are more than 10 THz absorption peaks. At 80–293 K, the spectra show only one distinct peak at approximately 0.84 THz, which becomes relatively weak and broadened as the temperature increases. In Fig. 8(a), the absorption peaks at around 0.5 THz weaken and then disappear for single-crystal RDX along the [002] direction. Damarla et al. [172] reported the THz absorption of RDX powders in a Teflon matrix measured using THz-TDS at 303–573 K. With increasing temperature, the THz absorption peaks of RDX at approximately 0.84 THz broaden at 378 K, indicating thermally initiated decomposition.

《Fig. 8》

Fig. 8. (a) Temperature-dependent THz absorption spectroscopy of RDX along [002]. (b) Spectral radiation in GW·m-3 ·Sr-1 from shocked methane diluted in Ar. (c) Emission spectra of CN molecules from laser-ablated nitromethane in an Ar atmosphere. L denotes the longitudinal position. (c) Reproduced from Ref. [167] with the permission of Elsevier, ©2020.

Although THz absorption spectroscopy has been explored for molecular crystals under static compression [173], it has not been explored under dynamic loading. As a linear absorption spectroscopy technique, the detection sensitivity of THz absorption spectroscopy should be considerably higher than those of nonlinear optical spectroscopy techniques, such as coherent anti-Stokes Raman spectroscopy (CARS) and Raman spectroscopy [174]; thus, THz absorption spectroscopy demonstrates a significant potential in investigating EMs under shock compression.

Optical spectroscopy has long been used to study dynamic chemical and physical processes in EMs, particularly owing to its high temporal resolutions [175]. Ultrafast optical absorption and Raman spectroscopy, including UV/visible absorption spectroscopy [176], infrared absorption spectroscopy [177], Raman spectroscopy [178], and CARS [179,180], can achieve temporal resolutions up to the probe laser pulse width (the shortest of which can be tens of femtoseconds). In contrast, ultrafast emission spectroscopy, including optical pyrometry and LIBS, can achieve temporal resolution limits of ultrafast detectors, such as streak cameras (1–100 ps) [181,182] and photomultiplier tubes (sub-nanoseconds).

For pyrometry based on photomultiplier tubes, spectral radiation is captured at different wavelengths (channels), and such emission spectra are frequently used to deduce the shock temperature from Planck’s law with temperature or wavelength dependent emissivity [32]. Fig. 8(b) depicts the spectral radiation of shocked gas-phase methane diluted in Ar measured with a 40- channel optical pyrometer; the onset of intense emission at ~4500 ns indicates an ignition event.

Bouyer et al. [183] captured the SDT of nitromethane within a few nanoseconds using a 16-channel pyrometer. Different stages of the SDT, were clearly observed including shock entrance, super-detonation, strong detonation, and steady detonation.

In LIBS, a pulsed laser is focused onto a specimen and ablates it, creating a microplasma for emission spectroscopy. On the basis of molecular and atomic emission lines, LIBS has been mostly utilized in identifying and detecting EMs [184,185]. To improve the sensitivity and selectivity of LIBS, double nanosecond-laser pulses [186] or femtosecond-laser pulses [187] are also used. Time-resolved LIBS has been attempted to understand chemical reaction mechanisms of EMs during laser ablation [185,188,189]. Recently, Zhao et al. [167] investigated atomic and molecular emission of nitromethane in an Ar or N2 buffer gas using fs LIBS. They identified electronic bands of CN, C2, and NH molecules and atomic transition lines of CI, NI, and Hα (Fig. 8(c)). Rotational and vibrational temperatures of CN molecules were determined assuming local thermodynamic equilibrium [191], via fitting with the following equation:

where, I is emission intensity; n, v, and J are principal, vibrational, and rotational quantum numbers, respectively; Ce is the emission constant; h, c, and kB are Planck’s constant, the vacuum light velocity, and Boltzmann constant, respectively; is the transition wavenumber; Trot and Tvib are rotational and vibrational temperatures, respectively; Qrot is the rotational partition function; and are the Franck–Condon coefficient and the Hönl–London factor, respectively; and F' and G' are the rotational and vibrational energy, respectively.

Since LIBS detects only a very small number of atoms and molecules, its capability can be expanded with sensitive trace gas techniques such as mass spectrometry [190]. For example, Civiš et al. [190] studied 1,1-diamino-2,2-dinitroethylene (FOX-7) using a combination of LIBS and selected ion flow tube mass spectrometry (SIFT-MS). Twelve stable gaseous compounds formed in a laserinduced microplasma were identified by SIFT-MS; C, H, and N atoms and CN, OH, and NO molecules were detected via LIBS. The decomposition mechanism in laser-induced breakdown of FOX-7 was then proposed on the basis of the joint measurements.

Rapid expansion of laser-induced microplasma can generate shock waves, which interrupt molecular formation in a microplasma [31]. For example, Harilal et al. [31] investigated the molecular formation mechanism in laser-ablated aluminum with shock wave generated at the plasma front. At the early stage of the plasma expansion, the shock wave inhibited the combustion process by keeping the ambient oxygen away from the microplasma. After the shock wave collapsed, the molecular formation became prevalent. Using a streak camera, Hori et al. [191] obtained time-resolved, single-shot LIBS spectra from a laser induced microplasma in air. Rabasovic et al. [192] tracked the maximum brightness displacement during the rapid plasma expansion of a laserinduced microplasma in air, and a velocity of plasma expansion of 35 km·s-1 was obtained using streaked LIBS. Therefore, LIBS has the potential for investigation of EMs under laser ablation.

《3.2. Ultrafast imaging interferometry》

3.2. Ultrafast imaging interferometry

Ultrafast imaging interferometry allows for temporally and spatially resolved (1D or 2D) measurements of displacement/velocity fields under dynamic loading and is advantageous for making connections between structural inhomogeneity and wave front roughening, and likely, hot spots. Such interferometric diagnostics include 1D line-VISAR [193], 2D-VISAR [194], and TIDI [195]. TIDI/2D-VISAR maps out-of-plane surface (or interface) displacement/velocity field, and their highest temporal resolution can reach the width of a probe laser pulse or the temporal resolution limit of a detector (femtoseconds to nanoseconds) [196,197]. The spatial resolution is normally 1–10 μm. The displacement sensitivity of TIDI and velocity sensitivity of VISAR are approximately 10 nm and 10 ms-1 , respectively.

The probe and reference light paths (two arms) are built in a TIDI system, and the phase of the probe light evolves dynamically as a specimen responds to an external stimulus. The interference of these two arms is recorded by a 2D detector as

where I is light intensity, r is the reflection coefficient, f0 is the initial frequency of fringes, and Φ is the phase shift induced by the loading. The displacement field can be obtained via solving Φ, as follows:

where is the wavelength of the probe light and θ is tilt angle in the incident light. For 2D-VISAR, both paths collect lights from the same target, and an etalon is placed in the reference path to induce a time delay.

TIDI and 2D-VISAR have been used in dynamic loading of metals, and these successful applications spell their potential for EMs. Fig. 9(a) shows a TIDI fringe image and corresponding displacement field of polycrystalline materials under shock loading [198]. The out-of-plane displacement field shows displacement gradients and thus wave field heterogeneity, as a result of slight bowing in loading (the general tendency) and local grain structure (the local fluctuations). TIDI is a promising tool for studying the effect of structural inhomogeneity on shock response of EMs, in particular, thermomechanical processes related to hot spots.

With a streak camera, line-VISAR is capable of measuring velocity field across a line by recording Doppler shift in the frequency of a probe laser. The interferometer consists of two light paths, and an etalon is placed in one of the paths. The time delay induced by the etalon creates phase shift between the two paths. Typical temporal, spatial, and velocity resolutions of line-VISAR are 1 ns, 10 lm, and 20 ms-1 , respectively. An example of line-VISAR measurement for laser-shocked aluminum [199] is shown in Fig. 9(b). Here, line-VISAR measures the free surface velocity field (1D) and shock front roughening. Although the roughening is minor in this case, the high spatial and temporal resolutions offered by line-VISAR allow for ultrafast measurements on wave front inhomogeneity in EMs (such as PBX) with inherent structural inhomogeneity at different spatial scales.

《Fig. 9》

Fig. 9. Dynamic imaging interferometry. (a) TIDI: fringe pattern of shocked copper and (b) corresponding out-of-plane displacement map. (c) Line-imaging VISAR: streak camera record of laser-shocked aluminum and (d) corresponding velocity history. (a, b) Reproduced from Ref. [198] with the permission of AIP Publishing, ©2007; (c, d) reproduced from Ref. [199] with the permission of Spring Nature, ©2019.

《4. Summary》

4. Summary

We briefly review X-ray, THz, and optical diagnostics for investigating EMs at multiple temporal and spatial scales, including 2D and 3D X-ray imaging, X-ray diffraction, coherent XRD imaging, SAXS, THz and optical absorption/emission spectroscopy, and 1D and 2D velocity/displacement interferometry, with emphasis on their capabilities for temporally and/or spatially resolved measurements. Basic principles of measurement and data analysis and illustrative examples are presented. In general, the discussed techniques have great potential for application in investigation of EMs, and there is a requirement for concerted efforts in defining scientific questions and engineering problems, experimental design, data analysis and interpretation, and multiscale modeling.

《Acknowledgements》

Acknowledgements

We are grateful for contributions from the PIMS X-ray Group. This work was supported by National Natural Science Foundation of China (11627901 and 11802252).

《Compliance with ethics guidelines》

Compliance with ethics guidelines

Yiyang Zhang, Sen Chen, Yang Cai, Lei Lu, Duan Fan, Jinchun Shi, Junyu. Huang, and Sheng-Nian Luo declare that they have no conflict of interest or financial conflicts to disclose.