1. Introduction

Energetic materials (EMs) are very important for national security and industrial applications. The pursuit of novel high energetic density materials (HEDMs) with both higher detonation performance and lower sensitivity is a significant topic [1]. To obtain the detonation characterization and intrinsic reaction mechanism of EMs is essential for their studies and actual application. Detonation characteristics, including detonation velocity, detonation pressure, detonation heat, detonation temperature, and enthalpies of formation, always relate to the volume and charged density of EMs. The traditional experimental methods of these characteristics generally require a large doses of samples, for example, hundred grams even kilogram level, which leading to high risks and poor maneuverability. For example, standard measurement methods of detonation velocity by probe [2] and detonation pressure [3] typically consume several hundred grams of the sample for each test since a stable detonation event requires a charge diameter greater than the critical diameter. Furthermore, the detonation reaction process analysis remains a challenge because the instantaneous high pressure and temperature, as well as destructive nature of the explosion. Therefore, direct measurement and analysis is extremely difficult. Theoretically, molecular dynamics simulation [4] from femtosecond (fs) to picosecond (ps) time scales does not accurately guide the actual explosion from nanosecond (ns) to millisecond (ms) time scales. Thus, developing rapid, safe, and intelligent ways with trace dose of consumption is highly desirable.

Laser-induced plasma spectroscopy (LIPS) technology is a good technique choice. Upon ablation by an intense laser pulse (several nanoseconds), a small amount of material (in the range of micrograms to nanograms) is excited and vaporized, and then a laser-induced plasma (LIP) is generated within several picoseconds. The laser-produced plasma expands to hundreds of nanoseconds and then cool with spectral emission. Simultaneously, laser-induced shock waves appear and propagate in the air on the microsecond (µs) time scale, and then generate a laser-induced self-sustaining deflagration (LID) or secondary combustion on the ms time scale for typical EMs. The region of interaction between the pulsed laser and the EMs as well the final expansion in ambient atmosphere range from micrometers to several centimeters. The reactions in laser-induced plasma and following propagation of shock wave and LID is defined as micro-explosion dynamics here. All these LIPS spectra and the time-dependent micro-explosion dynamics imply information about the explosion characteristics.

For the above reasons, the pulsed laser-induced plasma and ignition has been actively studied on various EMs [5–7]. Sustained efforts have been made to further understand the interaction of pulsed laser with explosive, and then figure out the correlation of laboratory-based LIP and real-world detonation event in the past twenty years. In 2003, Lucia et al. [8] firstly proposed that LIPS can act as an effective way to realize explosive detection. Since then, many attempts based on LIPS have been inspired for explosive identification or classification [9–11], trace element detection [12–15] and chemical reaction in LIP [16–18]. Recently, Rao et al. [19,20] found that detonation velocity and pressure had a good correlation with the spectral intensity ratio (CN + C₂)/(C + H+N + O), but a reliable qualitative prediction model was not successfully established. Nagel et al. [21] proposed a single-shot method to determine the detonation energy of laser-induced plasma using the blast model. Gottfried et al. has tried to predict the detonation velocity by measuring laser-induced air shock wave [22] and detonation heat by estimating duration of LID [23] of some typical explosives through schlieren technology. These methods can well derive the detonation velocity of EMs, but can not be used to obtain explosive pressure, detonation temperature and enthalpies of formation, which are also important parameters of EMs.

Herein, we first theoretically illustrate the evolution of LIP towards shock wave formation and LID. Then, seven tetrazole compounds and ten typical secondary explosives are irradiated by ns laser pulse. A statistically spectral method based on the LIPS and micro-explosion dynamics is utilized to establish a linear correlation between the laser generated microscopic explosion characteristics and the macroscopic detonation parameters. The explosive pressure and enthalpy of formation are well determined for the first time as far as we know. Furthermore, the intrinsic natures of micro-explosion dynamics covering ns to ms and their similarity to the detonation reaction in actual macroscale explosion are revealed. These studies make the detonation process further clearer. The results verify that the spectral method can be used as an implementable way for detonation performance diagnosis and reaction mechanism analysis of EMs with the merits of high speed, high accuracy, safety, small dose, and low cost.

2. Experimental and method

2.1 Sample preparation and energetic parameters

Two different types of EMs (particle size < 500 µm, purity > 99.5%) including seven tetrazole ring-based organic high-nitrogen compounds [24] and ten kinds of single-compound explosives, are listed in Table 1. Their typical detonation parameters are obtained by computing methods, including standard enthalpies of formation, detonation velocity, detonation pressure and detonation temperature, as shown in Table 1. The crystal density ρ originates from CCDC (The Cambridge Crystallographic Data Centre). The standard enthalpies of formation at 298.15 K marked as ${\Delta _f}H_m^\Theta $ are calculated by atomization energies method [25]. Moreover, the most important detonation velocity and detonation pressure are calculated by using a semi-empirical formula (Kamlet-Jacobs equation) with crystal density [26]. Oxygen balance (OB) of an explosive (C_xH_yN_wO_z) is calculated using Eq. (1),

Subsequently, each ground powder of 300 mg is pressed into a cylindrical pellet with 1.5 mm thick and 13 mm in diameter at a pressure of 15 MPa for LIPS test. Note that the same volume of various EMs in powder are utilized to ensure the same loading density. 10-15 mg of each sample is evenly pasted on a double-sided tape (18 mm×30 mm) and pressed with a spatula to scrape off excess powders for micro-explosion test.

Table 1. Computational and reaction of energetic properties of EMs.

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2.2 LIPS system

The LIPS spectra are obtained by a home-made setup, as provided in our previous work [27,28]. The spectrometer has been calibrated for their spectral responses using a standard mercury lamp in advance. The spectra are acquired under the excitation of 30 mJ with a time delay (${t_{delay}}$) of 1 µs and acquisition time (${t_{{\mathop{\mathrm int}} }}$) of 30 µs in ambient air and argon flow, respectively. The estimated diameter of the focused laser on the sample is around 250 µm at the ablation site. After each laser shot, the sample is moved to a fresh spot so that the craters do not affect the expansion of shock wave. For each EM, totally 250 optical emission spectra are collected. The LIPS spectra are generally processed with peak averaged intensity and background subtraction. To study the laser-induced plasma chemistry, time-resolved LIPS spectra are collected with the following timing parameters: ${t_{{\mathop{\mathrm int}} }} = 30\mu s$, ${t_{delay}}$ from 0 to 10 µs and $\Delta t = 1\mu s$. 100 spectra are collected at each delay, so that a total of 1100 spectra are acquired for each type of EM.

2.3 High-speed schlieren system

The schlieren system is built up to visually acquire the evolution of the laser-induced shock wave into the surrounding air after laser irradiation on the samples, as the schematic diagram illustrated in Fig. 1(a). A high-speed color camera (MEMRECAM ACS-1 M40, Japan) is utilized to obtain the real-time images of micro-explosion plume. A halogen lamp of 300 W serves as the illumination source, which is focused onto a slit with an aspheric condenser lens and then reflected onto a spherical mirror via the plane mirror. The light deviates when the refractive index changes in the test region which is usually caused by the generation and expansion of plasma plume. Subsequently, the refractive index induced light and shade variation on a knife edge are recorded by the high-speed color camera. The light is collimated between two spherical mirrors (10 cm in diameter, 100 cm in focal length) with a distance of 176 cm. Samples are set on a 2D electric-driven platform for each laser irradiation in a fresh region each time and located at the center between these two spherical mirrors. Laser pulse from a Nd: YAG laser (1064 nm, 7 ns, the maximum energy output ∼ 600 mJ, laser irradiances ∼ 0.77 GW·cm^-2) is focused vertically on the sample surface by the lens with focal length of 75 mm. The plane of the target surface is placed 3 mm above the focus to prevent air breakdown above the sample surface. The focal position (at the edge of the knife) should be optimized to provide the greatest contrast of the visualized images. For all capture images, the high-speed color camera is triggered by the rising edge of a signal from an infrared photodiode (SM05PD4A FGA10) located near the laser exit. Response time from the rising edge of the input trigger signal to the onset of camera exposure is optimized at 740 ns, and the jitter is less than 1 ns. The following camera settings are used for imaging the shock waves: 200000 frames per second (FPS), exposure time of 2 µs, and image size of 480×112 pixels.

 

Fig. 1. (a) Schematic diagram of the high-speed schlieren imaging system. (b)The laser-induced shockwave images at different time delay of sample S1. (c) FFT spectra of the sample S1, red circle marked the certain frequency. (d) FFT image.

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2.4 Extraction of time-resolved shock fronts by 1D-FFT

For each sample, a chronological series of images of shock waves are recorded by the high-speed camera. In general, the discrimination of shock front for each image is critical for the velocity estimation, while the raw image always contains a bright saturated spot that originate from the plasma radiation at initial stage. In addition, the shockwave is also perturbed by ambient airflow. All of them greatly impact the extraction of the shock front position. One-dimensional (1D) Fast Fourier Transform (FFT) is usually used for the frequency analysis and denoising of 1D signal. However, in this paper, the FFT is introduced to process the 2D dynamic shock front extraction for the first time.

For convenience, the color images are firstly converted into grayscale for dimension reduction, as shown in Fig. 1(b). In a chronological series of images obtained by high-speed camera, the grayscale values of the same pixel position in each image are extracted as signal variable over time. This time-dependent signal is then processed for 1D-FFT. The relation between the signal amplitude and the frequency is shown in Fig. 1(c). It can be seen that the time-dependent gray value signal contains multiple frequencies. Note that the component with frequency of 0 represents the average brightness of the image, which is independent with noise. Except for that, the frequency with the highest amplitude is marked as a red circle in Fig. 1(c), which just corresponds the frequency of 20000 Hz. This frequency is regarded as the target shock wave signal to finish FFT, and the others are noise. The FFT image in Fig. 1(d) illustrates that the shock wave front propagating outward with time can be discriminated clearly in one diagram. The indistinguishable portion results from the disturbances of the heated air by injected laser beam. All above processes are completed through self-written code.

3. Experimental results and discussion

Theoretically, after laser pulse irradiation on the EMs, the micro-explosion dynamic process experiences different phases covering various time scales:

 

Fig. 2. The schematic micro-explosion dynamic processes in various time scale from ∼ns to ∼ms.

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The phenomena (i) and (ii) are prevalent in the LIPS of most of the materials, while phenomenon (iii) is unique for EMs. Obviously, the physical process and energy conversion mechanism of laser interaction with EMs and non-energetic materials are quite different. In addition to the characteristic LID phenomenon, the plasma radiation of EMs is weaker [29] and the shock wave is stronger compared with that of non-energetic materials. Note that laser-induced micro-explosion is a complex physical process. Laser-induced plasma, shock waves and deflagration are multiply energy conversion processes rather than occurring in strict order. We explore and study dominant process in detail on different time scales under our experimental and observational conditions. Even different kinds of EMs, the occurrence of these three phenomena and the ratio of energy conversion are different because of the different detonation performances. Through a comprehensive analysis on the laser-induced dynamics ranging from time scale of ∼ns to ∼ms, we find that the similarity and consistency of the micro-explosion dynamics with real macroscale chemical detonations. Based on this point, detonation characteristics, such as enthalpy of formation, chemical reaction, detonation velocity, pressure, heat and temperature can be quantitatively predicted by the laser-induced plasma spectroscopy and micro-explosion dynamics.

3.1 LIPS spectra of EMs and the prediction of enthalpy of formation in ns time scale

Figure 3(a) shows the typical LIPS spectrum from sample S1 in air with the broad inverse Bremsstrahlung (IB) band removed. The characteristic peaks including C (247.9 nm), H (656.3 nm), N (742.4 nm, 744.2 nm, 746.8 nm, 868 nm, 870.3 nm, 871.2 nm), O (unresolved triplet at 777.2 nm, 777.4 nm, 777.5 nm and 844.6 nm) as well as three CN bands (358.7 nm, 388.2 nm, 421.6 nm) are involved. Peaks of some impurities, such as Ca, Na and K are also observed. The relatively weak bands of C₂ at 473.6 nm and 516.5 nm are also noticed, as shown in the inset of Fig. 3(a). It derives from the atomic recombination rather than from C₂ native fragmentation. For sample S1, there is no any C-C or C = C bonds. The atomic lines of O should be derived from the air since the samples consists only of C, H and N.

 

Fig. 3. LIPS spectra of tetrazole (1H-T, sample S1) in air (a) and in argon (b), respectively. (c) Individual interpretation rate (left, bar graph) and cumulative interpretation rates (right, line) of the first six principal components. (d) PC scores plot of processed LIPS spectra of seventeen kinds of EMs (black oval circles ten kinds of explosives, and red oval circles seven tetrazoles). The well prediction model of ${{\Delta }_f}H_m^\mathrm{\Theta }$ of tetrazole-based high-nitrogen compounds (e) and single-compound military explosives (f). The solid blue line is y equals x.

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To avoid the air interference, the spectral lines in argon are collected, as shown in Fig. 3(b). Strong emission lines of Ar I (696.5 nm,706.7 nm, 714.7 nm, 727.3 nm, 738.4 nm, 750.4 nm, 751.5 nm, 763.5 nm,772.4 nm, 794.8 nm, 800.6 nm, 801.5 nm, 810.4 nm, 811.5 nm, 842.5 nm, 852.1 nm, 866.8 nm) are observed, while the emission intensities of N and O are significantly reduced due to absence of air. Nevertheless, because of larger molar mass and smaller thermal conductivity of argon, the stronger emission of C and H are observed in argon than those in air, and the higher plasma ionization rate and plasma temperature make the spectral line of atoms and ions stronger. Similarly, the intensity of molecular bands also become larger, as more molecules are excited by collisions with the surrounding of argon. All the characteristic peaks from both tetrazole-based high-nitrogen compounds and single-compound explosives are similar, only the intensities vary greatly due to different composition. Among these, O-associated peaks of tetrazole-based compound disappear in the argon atmosphere, because its composition does not contain any oxygen at all. LIPS spectra analysis combined with chemometrics techniques are used to classify different explosives. According to the principal component analysis (PCA) results, the first four principal components (PCs) can account for 94.1% of variance, as shown in Fig. 3(c). A good clustering results in the PCs score plot shows that explosives and tetrazolium energetic compound are well separated and easily distinguished, as shown in Fig. 3(d). Finally, a robust classification model with the average accuracy of 99.0% of training sets and average prediction accuracy of 99.1% of validation sets is successfully established. Consequently, these two types of explosives have to be separated for further analysis of the micro-explosion characteristics.

On the basis of the LIPS spectra, some of macroscopic detonation parameters such as ${\Delta _f}H_m^\Theta $ can be deduced, for they are always tightly correlated with some characteristic emission peaks. It is proven linearly correlated with the intensities of several nitrogen atom lines (742.4 nm, 744.2 nm, 746.8 nm, 868 nm, 870.3 nm, 871.2 nm) at argon atmosphere. The correlation coefficient is beyond 0.9. High-energetic materials with a large amount of chemical energy tend to contain a lot of nitrogen atoms. As a result, stronger atomic emission can be detected in plasma. The intensities of all the peaks of the nitrogen atoms are extracted from LIPS data, then four principal components by PCA are used to establish the multiple liner regression model [30] with R² of 0.9984 for tetrazoles and 0.9967 for single-compound explosives, as shown in Fig. 3(e) and 3(f). To evaluate these models, evaluation parameters such as the maximum relative error (MRE), average relative error (ARE), and root mean square error (RMSE) are calculated for both training set and prediction set, as shown in Table 2. Note that MRE for training set is marked as MRET, and MRE for prediction set is marked as MREP. This rule applies to other parameters as well. These results demonstrate that the ${\Delta _f}H_m^\Theta $ of explosives can be well predicted by LIPS spectra, which never be mentioned in previous reports.

Table 2. Model evaluation parameters.

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3.2 Chemical reaction in plasma

The interaction of ns-laser, plasma with surrounding environment produces plasma shielding, re-heating effects, secondary ionization of the atmospheric molecules and shock waves [31], leading to the diversity of particles in the plasma and the complexity of reactions. The bands of CN molecule observed in the LIPS spectra are particularly important for the analysis of chemical reactions in the plasma of EMs. They can be used to predict the energy release pathways. In addition to CN bond fragments generated by laser ablation, other possible CN formation pathways are listed below,

To identify possible reaction pathways, four intensity mappings are generated by the relative emission intensities of different species within the plasma through the time-dependent spectra of sample S1, as shown in Fig. 4(a-d). Each mapping consists of 1100 points extracted from 1100 time-resolved spectra. Note that for better visualization, the X, Y and Z data are all scaled separately, but the trends are not affected. Figure 4(a) and 4(b) demonstrate the emission intensity of CN elevates with the increase of C, but is independent of the content of N and C₂. It means that Eq. (3) may be the dominant pathway for formation of CN rather than Eqs. (2), (4) and (5). To further verify it, the background-corrected emission intensities of atomic and molecular species of tetrazoles in air and argon are shown in Figs. 4(e) and 4(f), respectively. It indicates that the peak intensity of CN is similar to the variation of C, but independent of the intensity of the N and C₂ band in both air and argon. Pearson's correlation coefficient $r$ is used to derive the correlation for paired data sets. The high correlation coefficient of between the total CN emission intensity and the percentage of carbon atoms is 0.99, indicating that the emission of CN can be ascribed to the atomization after laser irradiation. The weak negative correlation (r= -0.4 and -0.3) between the total CN intensity and the percent of C-N bond and C = N bond for various molecules is -0.4 and 0.3, respectively. The structural information of tetrazole compounds is shown in Table 3. These all mean that most of the C atoms are decomposed from the molecules in the plasma by the pulsed laser and then bind with the surrounding N₂ or native N₂ from decomposition reaction to form new C-N molecule. Figure 4(c) shows the intensity of O increases with the increase of N and reduce with the increase of C. This result can be associated with the following reactions

Table 3. % of atom C and % C-N band of tetrazole-based compounds.

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Note that the Eqs. (6) and (7) are important reactions during the decomposition of EMs, since the formation of gaseous products such as CO and CO₂ is highly exothermic and results in the release of large quantities of energy upon detonation [32]. The CO gas is initially detected by an electrochemical sensor after laser irradiation with hundreds of pulses ablation. Our results confirm the similarity and consistency of chemical reactions in plasma with those in macroscopic detonation.

Figure 4(d) shows that the O intensity decreases as the intensity of CN bands increased when the N intensity in a relatively low level. This observation results from the following reaction

The O intensity is quite high and independent of CN content, when N intensity at a high level. This result suggests that the high concentration of O allow the reactions to occur faster and produce more N. Note that the similar reactions are also observed in other tetrazole high-nitrogen compounds and single-compound explosives of sample D1-D10. Our results verify the dominant role of atomic reconstruction for the formation of CN species and the similarity between reactions in plasma of micro-explosion and in macroscale detonation.

 

Fig. 4. Characteristic emission intensities from LIPS data. Contour plots for (a) N, C, CN, (b) C₂, C, CN, (c) N, C, O, (d) CN, N, O emission intensities of sample S1 in air base on time-dependent LIPS spectra. Atomic and molecular peak intensities of different sample in air (e) and argon (f), respectively. Error bars represent 95% confidence intervals.

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3.3 Micro-explosion dynamics and determination of detonation parameters

The interaction between pulse laser and EMs is more complicated than that for non-energetic materials. In addition to the thermal vaporization and non-thermal ablation of the material by the laser, its own chemical reaction of EM and laser-induced secondary excitation on its products are also involved, including ejection of liquid droplet, solid exfoliation and gas formation. In this section, the visual images are used to capture the entire process of pulse laser interaction with microgram EMs on the µs-ms time scale. It facilitates an intuitive understanding of microscopic dynamics and thus it can be used to derive the detonation parameters.

3.3.1 Micro-explosion dynamics in µs range and detonation velocity prediction

The snapshots of the time-dependent evolution of plasma plume and shock wave after laser ablation from sample S1 are shown in Fig. 5(a). The first frame (0 µs) shows a bright plasma spark accompanied by blurred shock front profile from a local point where the laser is ablated. The second frame (5 µs) clearly shows the hemispherical propagation of the shock wave. The distance from the outermost profile of the shock front to the initial point, where the focal laser strikes the sample surface, is defined as the propagation distance R of the laser-induced shock wave, as the arrow marked in the third frame. Shock wave continues to spread outward with the plasma cooling, and the internal shock wave appears behind the first shock front which are readily distinguished as the laser interacts with solid material. In general, there is no secondary shockwaves for the case of laser-induced air plasma plume in contrast to the macroscopic detonation supported by chemical reaction. Thus, it should originate from the reflection from substrate when the first shockwave strikes on the surface. Even though the shock wave remains after 100 µs, it is too weak to distinguish from the background or beyond the range of observable visual range.

 

Fig. 5. Time dependent shock waves propagation. (a) The evolution of laser-produced shock waves from sample S1. (b) Schlieren images of tetrazoles at 100 µs. (c) The correlation between the laser-induced air shock velocity and the calculated energy of detonation for tetrazole-based explosive.

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In comparison, the plasma plumes with a delay time at 100 µs are extracted, as shown in Fig. 5(b). For samples S1-S7, they are quite different from each other even with the same elements and similar structure, as they are close related to the reaction process and detonation dynamics. The luminescence of sample S2 is obviously weaker than those of other samples, due to a shorter lifetime of plasma. For all single-compound explosives, such as samples D2, D4, D5 and D6, the luminescence is darker than most of low energetic tetrazoles. It illustrates that less luminescence in laser-induced plasma tends to a high detonation performance. In fact, the brightness of plasma can be directly visualized by the senses to estimate the power of explosion.

The R-t relation of shock wave can be expressed by a drag model [33], which is given by

3.3.2 Micro-explosion dynamics in the ms range and detonation temperature prediction

For further exploring the reactions on millisecond time scale, a series of images are captured by removing the knife edge with a frame rate of 10000 FPS and an exposure time of 99.5 µs. All photographs are taken under the same environmental conditions and without interference from external light. The camera is adjusted to white balance before each shoot. After the period of post-plasma, EMs always undergo self-propagating LID event. Figure 6(a) shows the time-dependent fluorescence images of deflagration of sample S1. Toroidal shaped flame core is formed near the sample surface (resembles a two-lobe structure in 2D cross-sectional images), whereafter the shock wave are activated by the laser-created spark [35]. A third lobe-shape flame appears on the incident laser side, then propagates toward the laser source, and dissipates at 0.4 ms delay. With the occurrence of the plasma and shock waves, the air around the sample is heated and even ionized to be hot gas. From the hydrodynamic and gas dynamics aspects, the three lobe-like structure originates from vortex generation during the interaction between rarefaction wave and plasma [36]. The vortex in the tip of plasma causing the third lobe-like structure is composed of high-speed gas with lower density that decay more rapidly [37]. Another vortex at the bottom of the plasma, with a higher density and a lower gas velocity, produces a ring of flame and lasts longer, which involves in unreacted energetic material particles, allowing a larger range of deflagration cloud (several centimeters) being created. As can be seen from the first row of photogragh in Fig. 6(a), there are material exchanges between the deflagration cloud and the sample surface. The hot cloud moves upward with the vortex motion. Then, once the rarefaction wave stop to interact with thermal gas, no vorticity is further produced, and the toroids flame starts to decay. When the fuel is entirely exhausted, the deflagration cloud will disappear. The size of the reaction zone and the reaction rate vary greatly for different samples. Snapshots of the deflagrations at the same time delay (10 ms) are shown in Fig. 6(b). Sample S1 is relatively weak while sample S7 is bright, indicating that the heat release faster for sample S1 than that for sample S7. It can be seen that some hot spots occur for sample S5 and sample S6, which originates from the unreacted carbon particles, since more carbon atoms contained in the molecules lead to a negative oxygen balance. For sample S7, the cloud is too bright to see the hot spots, but it really exists, which also can be seen in later time when the cloud is a bit dark. Note that no deflagration event is observed in sample S2 (5-AT) and D10 (NTO) which is ascribed to the large thermal conductivity or poor crystal quality. There are more heat being transferred and the ignition threshold is not even achieved.

 

Fig. 6. Evolution of laser-induced deflagration and color temperature mapping. (a) The dynamic laser-produced deflagration of sample S1. Snapshots (b) and corresponding color temperature maps (c) of each tetrazole-based explosive at 10 ms. The dark blue background corresponds to room temperature and the maximum scale of 4500 K.

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By extracting RGB values on each pixel and converting them to chromatic coordinates, the color temperature (Tc) can be derived in terms of International Commission on Illumination (CIE) diagram [38]. The Tc mapping in Fig. 6(c) corresponding to Fig. 6(b) is calculated by self-written code. It reveals that the temperature distribution in the deflagration cloud is stratified and uneven, the same as the brightness distribution. Besides, the incomplete combustion of C particles leads to the appearance of local hot spots, as shown in the case of sample S6. Ten points along the laser incident direction on the snapshot are selected to calculate the average Tc of each EM. Detonation temperature (Td) is calculated by EXPLO 5 with the input of crystal density, standard enthalpies of formation and molecular formula. As shown in Table 4, Tc is 1000∼2000K higher than Td, and no obvious correlation between them is found. It indicates that the Tc at the specific moment of deflagration cloud not directly regarded as criterion to measure the explosion temperature, because the reaction rate, energy distribution and temperature variation are various in detonation dynamics for each EM. The Tc simply describes the transient temperature state of LID plume rather than the average temperature. Figure 7 shows the time-dependent temperature distribution of deflagration fireballs. The internal temperature distribution can be seen clearly and visually with time delay. The results provide a potential approach for a rapid and comprehensive analysis of explosion temperature of deflagration cloud and its evolution over time.

 

Fig. 7. Time-resolved Tc mappings of laser-produced deflagration of sample S1.

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Table 4. Calculated average colour temperature (Tc) and detonation temperature (Td).

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3.3.3 Micro-explosion dynamics in the ms range and deflagration ignition delay, reaction rate, detonation pressure prediction

The integral pixel intensities from chronological snapshots of LID for tetrazoles and single-compound explosives are shown in Fig. 8(a) and 8(b), respectively. In this work, the duration of the deflagration is defined as the time interval from the moment with the lowest summed pixel intensity to the moment, when the radiation intensity approaches the background. The ignition delay time is defined as the time interval from the initial stage of plasma (first frame) to the the lowest summed pixel intensity during the LID process. In fact, the integral pixel intensity is the lowest when the third flame core disappears. In other words, the initiation delay time is approximately the existence time of the third flame core. For each sample, the LID images are captured 8-10 times under the same experimental condition, and the average deflagration duration and ignition delay time extracted from images are all organized in Table 5. All other EMs expect samples S2 and D10 undergo LIP processes and self-sustaining deflagration reaction. The average deflagration durations are linearly correlated to the OB (r=-0.91) and detonation heat (r=-0.65) for sample D1-D10. For melt-cast explosives, such as D4, D6 and D9, the LID can sustain more than 60 ms, even 100 ms for D9. These materials with low OB must consume oxygen in the air or combustion products to fully react, resulting in longer deflagration and slower energy release, thereby, leading to low detonation heat. But the rule can not apply to tetrazole based high-nitrogen compounds, because oxygen is not present in the products. In these EMs, oxygen can only be obtained from ambient environment, which bring about more uncertainty and uncontrollability to interfere with the intrinsic heat release. More differently, the brighter plasma occurred at initial stage means a lower integral emission intensity of deflagration clouds for tetrazole compounds, which illustrates a close correlation between laser-induced plasma and micro-detonation.

 

Fig. 8. Deflagration intensity and its relationship with calculated detonation pressure. Intensity sum of all effective pixels from each frame of the high-speed videos of (a) tetrazoles and (b) single-compound explosives, respectively. The correlations between ignition delay time of LID and detonation pressure of tetrazoles (c) and single-compound explosives (d). (e) Time dependent normalized intensity sum of all effective pixels (|lnI|^1/2) in the Gaussian distribution function. (f) The correlation between effective constant of luminescent intensity rising and detonation pressure.

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Table 5. Reaction parameter of micro-explosion dynamics in ms time scale.

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More importantly, a primary observation is that there is a good correlation between ignition delay time and the calculated detonation pressure for tetrazoles (r=-0.97) and single-compound explosives (r=-0.91), as shown in Fig. 8(c) and 8(d). It is a valuable evidence of linking LID and macroscale detonation event in a general way. To our knowledge, it has never been reported before. The probable reason for the connection between LID and detonation pressure is that LIP which is similar to real world detonation provides the initial pressure for the deflagration reaction. The shorter the initiation delay, the faster the third blade flame core disappears, the greater the initial pressure provided by plasma, and thus the greater the detonation pressure. As we know, the deflagration reaction rate can be indicated by the rising rate of the leading edges of the measured luminescence curve. Normalized to the peak intensity of $I(t )$ then is well fitted to a Gaussian distribution function ${e^{ - {k^2}{{({t - b} )}^2}}}$ with the goodness up to 0.99 for D1-D9, where k and b are fitting indexes. The relationship between t and $\textrm{|}\ln (I ){|^{1/2}}$ is almost linear for single-compound explosives, which can be seen from time dependent normalized intensity sum of all effective pixels ($\textrm{|}\ln (I ){|^{1/2}}$) in the Gaussian distribution function, as shown in Fig. 8(e). The fitting coefficient k is defined as the effective constant of luminescent intensity rising rate, which can be derived from the slope of each line of different explosives in Fig. 8(e), and represents the deflagration reaction rate. The effective constants for each explosive are summarized in Table 5. A good correlation between the effective constant and calculated detonation pressure with r = 0.98 is proven for the traditional single-compound explosives for the first time, as shown in Fig. 8(f). For tetrazoles, the correlation index reduces to r = 0.82, which results from the initial rising edge of deflagration luminescent curve in Fig. 8(a) is irregular even two peaks is hard to determine. The constant is also closely correlated to the pressure sensitivity of combustion, namely, the higher the pressure, the higher the burning rate. Our results reveal an intrinsic nature of micro-explosion dynamics and the close relation between micro-detonation induced by a pulsed laser and a macroscopic detonation. For explosives with excellent detonation performance, more energy transfers from plasma to micro-explosion process, resulting in a darker, shorter-lived plasma than non-energetic or low-energetic materials. Then, on the µs time scale, the energy and pressure sustained on the shock wave fronts usually leads to a hotter ionized air zone on the sample surface. And then the energetic fragments, gaseous production and oxygen will react easily, thus shorter ignition delay time and accelerate the combustion rate of the deflagration cloud on the ms time scale.

In comprehensive studies of micro-explosion dynamics on microgram-milligram EMs over ns-ms time period, our results prove that the laser-induced micro-explosion related LIPS spectra, shock wave and deflagration can be adapted for the performance prediction of tetrazole-based organic compounds as raw material for HEDMs synthesis and common explosives. Thus, laser-induced luminescence, acts as a micro-zone explosive simulator combined with statistically spectral method to complete the prediction and evaluation of macroscale explosion parameters according to the following definite rules,

4. Conclusion

The results in this paper reveal the feasibility of exploring macro-scale parameters of explosives by using laser-induced plasma spectra and micro-explosion dynamics by small-dose EMs. We have successfully evaluated some parameters of tetrazole-based high nitrogen energetic compounds and conventional single-compound explosive via multi-dimensional detection means. Spectroscopic results show that the correlation coefficient between the intensity of CN molecular radiation and the proportion of C atoms is as high as 0.99. This indicates that the CN emission mechanism is occupied by chemical reactions of atomic recombination. Moreover, the correlation between ${\Delta _f}H_m^\mathrm{\Theta }$ and the intensity of nitrogen atom is greater than 0.9. Then, a multiple liner regression model based on PCA is first proposed to well predict the enthalpy of formation with ARE <3%. Time-resolved spectra prove the consistency of macroscopic detonation reaction with micro-plasma chemical reaction. In addition, the evolution of the shock front and deflagration from high-speed images indicate a good linear relationship between the measured velocity of shock wave and calculated detonation velocity (r = 0.96), the obtained ignition delay and calculated pressure (r=-0.97 for tetrazoles and r=-0.91 for military explosives) as well as the effective constant of the luminescence intensity and the calculated pressure (r = 0.98 and 0.82, respectively).

For explosives with better detonation performance under laser ablation, more energy is transferred from plasma to micro-explosion processes, thus resulting in a darker plasma than non-energetic or low-energetic materials. Then the energy and pressure loaded on the shock wave fronts on the µs time scale usually leads to a hotter ionized air zone above the sample surface, so the energetic fragments, gaseous production and oxygen are easily to be reacted, thus shorter ignition delay time and faster combustion rate of deflagration clouds on the ms time scale. The proposed method will provide a simple, safe, low-cost and effective way for the measurement and evaluation of explosion performance to meet the requirements of future explosive parameter test.