*Article* **A Novel Understanding of the Thermal Reaction Behavior and Mechanism of Ni/Al Energetic Structural Materials**

**Kunyu Wang, Peng Deng, Rui Liu, Chao Ge, Haifu Wang and Pengwan Chen \***

State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China **\*** Correspondence: pwchen@bit.edu.cn

**Abstract:** Ni/Al energetic structural materials have attracted much attention due to their high energy release, but understanding their thermal reaction behavior and mechanism in order to guide their practical application is still a challenge. We reported a novel understanding of the thermal reaction behavior and mechanism of Ni/Al energetic structural materials in the inert atmosphere. The reaction kinetic model of Ni/Al energetic structural materials with Ni:Al molar ratios was obtained. The effect of the Ni:Al molar ratios on their thermal reactions was discussed based on the products of a Ni/Al thermal reaction. Moreover, depending on the melting point of Al, the thermal reaction stages were divided into two stages: the hard contact stage and soft contact stage. The liquid Al was adsorbed on the surface of Ni with high contact areas, leading in an aggravated thermal reaction of Ni/Al.

**Keywords:** Ni/Al energetic structural materials; thermal reaction; reaction kinetic model; two reaction stages; reaction mechanism

#### **1. Introduction**

All-metal energetic structural materials, such as Al/Ti, Al/Zr, Ni/Al, and so on, have received more and more attention due to their good strength and energy-releasing properties [1–5]. Among them, Ni/Al was considered as a promising material for further application in the defense industry, such as in the fields of fragments and shaped charges, because of its higher energy density (1507.7 J/g at the equal molar ratio), higher strength properties, and faster energy-releasing capacities. Its energy release, which originates from an intermetallic reaction, has received much attention in recent decades. However, its reaction behavior and mechanism have not been explained clearly, which has limited its application.

Currently, for Ni/Al energetic structural materials, a lot of works mainly focused on its macroscopic reaction. For example, Vandersall and Thadhani [6] reported that the shock response of Ni/Al energetic structural material was divided into two categories: shockassisted chemical reaction and shock-induced chemical reaction. Song and Thadhani [7] proposed the thermodynamic calculation model for the shock reaction, based on the effects of the reaction energy release and the formation of products on the equation of state. Bennett and Horie [8] improved the thermodynamic reaction model to reduce the errors and ambiguities of existing Hugoniot calculations. Zhang et al. [9] also built the thermal chemical model of shock-induced chemical reaction. The reaction efficiency was evaluated by combining shock kinetics and chemical reaction kinetics. These works could be used to describe the macroscopic response of the Ni/Al energetic structural material. However, they did not illustrate the microscopic reaction mechanism in detail.

Essentially, the energy release of all-metal energetic structural materials depends on the chemical reaction process [10–12]. The critical parameters of the chemical reaction are determined through the impact-induced energy release test instead of the direct measurement [13]. This method strongly depends on the shock compression theory with the chemical reaction. Due to some assumption, it is difficult to widely use the reaction model for another type of energy release tests.

**Citation:** Wang, K.; Deng, P.; Liu, R.; Ge, C.; Wang, H.; Chen, P. A Novel Understanding of the Thermal Reaction Behavior and Mechanism of Ni/Al Energetic Structural Materials. *Crystals* **2022**, *12*, 1632. https:// doi.org/10.3390/cryst12111632

Academic Editor: Evgeniy N. Mokhov

Received: 24 October 2022 Accepted: 7 November 2022 Published: 13 November 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Generally, the thermal analysis test, referring to the differential scanning calorimeter, has been widely used to understand the chemical reaction of energetic materials [14,15]. To directly determine the activation energy and the pre-exponential factor in the chemical reaction equation of energetic materials, the Kissinger method [16], Flynn–Wall–Ozawa method [17], and Satava–Sestak method [18] were used. Moreover, for a complex chemical reaction, the classical differential methods and kinetic integration methods were built to analyze the thermal decomposition mechanism function and kinetic parameters [19,20]. These works showed a good analysis result, and further revealed that classical thermal analysis methods could be used to analyze the reaction kinetic parameters of energetic structural materials.

A few works on dynamic thermal analysis refer to the basic thermal reaction parameters of all-metal energetic structural materials. It was found that a simple analysis strategy was not used to match the whole thermal reaction process of Al-based energetic structural materials, especially for Ni/Al. According to the Ni–Al binary phase diagram, the Ni–Al eutectic temperature is higher than the melting point of Al. During the thermal reaction process, the state change of Al from solid to a liquid state occurred in a thermal reaction. Resulting from the state change of Al in the Al-based energetic structural materials, the existing reaction model mismatches the kinetic result of thermal reaction. The traditional analysis strategy only considers the solid-solid reaction in the thermal process, but ignores the influence of the state change of Al on the thermal reaction between Al and Ni. This causes the misunderstanding of the thermal reaction process. Therefore, it is urgent and important to study the thermal reaction behavior and mechanism of Ni/Al energetic structural materials depending on the state change of Al.

Herein, we studied the thermal reaction behavior and mechanism of Ni/Al energetic structural materials with the state of Al at two different reaction stages, depending on the melting point of Al. By fitting the differential scanning calorimeter (DSC) curves of Ni/Al energetic structural materials with different Ni:Al molar ratios, the hard contact stage and soft contact stage were distinguished. Their reaction kinetic models were obtained and the thermal reaction parameters, referring to activation energy €, pre-exponential factors (A), and reaction function (f), were calibrated at different reaction stages. Reaction products of Ni/Al thermal reaction was used to analyze the effect of the Ni:Al molar ratios on their thermal reaction. Furthermore, the thermal reaction mechanism of Ni/Al energetic structural material was provided, based on two different reaction stages. This work offered a new way to understand thermal reaction behavior and mechanism of Ni/Al energetic structural materials under the different temperature stages.

#### **2. Experimental**

#### *2.1. Materials*

Different Ni and Al molar ratios will lead to different chemical reactions. Theoretically, when the molar ratio of Ni and Al is 1:1, 1:3, and 3:1, the corresponding apparent reaction is shown in the Equations (1)–(3), respectively [21].

$$\text{Al} + \text{Ni} \rightarrow \text{AlNi} \, - \, 1381.3 \, \text{J/g} \tag{1}$$

$$3\text{Al} + \text{Ni} \rightarrow \text{Al}\_3\text{Ni} \, -1078.24 \, \text{J/g} \tag{2}$$

$$\text{Al} + \text{3Ni} \rightarrow \text{AlNi}\_3 \, -753.4 \, \text{J/g} \tag{3}$$

Three types of samples Ni/Al with different molar ratios were prepared. The molar ratio was set Ni/Al = 1:1, Ni/Al = 1:3, and Ni/Al = 3:1, respectively. The components Ni and Al with the particle size of 20 μm, and 25 μm, respectively, were used. Powders Ni and Al were purchased from Shanghai ST-Nano Sci & Tech., Co., Ltd., Shanghai, China. Alcohol was provided by Chengdu Kelong Chem., Tech., Co., Ltd., Chengdu, China.

The components Ni and Al were mixed with the different molar ratios. Then, the mixed powders were prepared by the milling technique for 5 h in the alcoholic environment. Finally, the powder was obtained with drying treatments.

#### *2.2. Thermal Analysis and Characterization*

The thermal reaction behavior of the mixed powder samples was recorded in an argon atmosphere by a STA449F3 differential scanning calorimeter (Netzsch, Bavaria, Gremany). The mass of each sample tested was 20 mg. The test conditions were alumina crucible with cover, 20 mL/min of protective gas, and 60 mL/min of purging gas. The DSC curves with the range from the room temperature to 1200 K were collected to study their thermal reaction processes under the different heating rates (5 K/min, 10 K/min, 15 K/min, and 20 K/min).

The structure of the reaction products from the thermal reaction of Ni/Al samples were characterized by X-ray diffraction (XRD). XRD patterns from 5–90 degrees were carried out via a D8 Advances XRD apparatus with the voltage of 40 kV and the current of 40 mA.

Generally, the chemical reaction kinetics equation is used to quantify the reaction behavior. According to the DSC test, the parameters of the equation can be obtained [22]. Assume that the reaction of Ni/Al samples follows the Equations (4) and (5), which builds the relation between the reaction degree and the temperature. Actually, the two equations are equivalent as the differential and integral forms of non-isothermal systems for calculating the thermodynamic parameters.

$$\frac{d\alpha}{dT} = \frac{A}{\beta} e^{(-\frac{E}{RT})} f(\alpha) \tag{4}$$

$$\int\_{0}^{\alpha} \frac{d\alpha}{f(\alpha)} = \int\_{0}^{T} \left(\frac{A}{\beta}\right) e^{-\frac{E}{RT}} dT \tag{5}$$

where *α* is the reaction degree, *T* is the absolute temperature with the unit K, *A* is the pre-exponential factor with the unit min-1, *β* is the heating rate with the unit K/min, *E* is the apparent activation energy with the unit J/mol, *R* is the universal gas constant 8.31 J/(mol·K), and *f*(*α*) is the reaction function. According to the DSC curve, the reaction degree *α* means the ratio of the area enclosed by the curve at some temperature to the whole area enclosed by the whole DSC curve.

Considering the results of thermal analysis based on multiple heating rates are more accurate [23], the Ozawa method is used in the current work to determine the parameters in Equation (5). Firstly, define *u* = *<sup>E</sup> RT* , the equation can be rewritten as

$$\int\_{0}^{T} e^{-\frac{E}{RT}} dT = \int\_{-\infty}^{u} -\frac{E}{R} \frac{e^{-u}}{u^2} du \tag{6}$$

Substitute Equation (6)into Equation (5), and define *g*(*α*) = *<sup>α</sup>* 0 *dα <sup>f</sup>*(*α*) and *<sup>P</sup>*(*u*) = *<sup>u</sup>* <sup>−</sup><sup>∞</sup> <sup>−</sup>*e*−*<sup>u</sup> <sup>u</sup>*<sup>2</sup> *du*. Then, Equation (5) can be rewritten as

$$\mathbf{g}(\boldsymbol{\mu}) = \frac{AE}{\beta \mathcal{R}} P(\boldsymbol{\mu}) \tag{7}$$

The Doyle approximation [24] is used to estimate *P*(*u*),

$$
\lg P(u) = 2.315 - 0.4567u \tag{8}
$$

Take the logarithm of Equation (4) combined with Equation (5), and Equation (6) can be rewritten

$$
\log \beta = \left[ \lg \frac{AE}{\mathcal{R} \mathcal{g}(a)} - 2.315 \right] - 0.4567 \frac{E}{RT\_a} \tag{9}
$$

In order to obtain the parameters in the equation, the least square method is used to fit the straight line as Equation (9), where <sup>1</sup> *<sup>T</sup><sup>α</sup>* is the abscissa and *lgβ* is the ordinate. Four DSC curves, under different heating rate conditions, can determine four data points to be fitted. The apparent activation energy can be obtained according to the slope of the fitting line. It should be stressed that in order to obtain *E*, *α* must be chosen to be 1. In addition, the pre-exponential factor *A* and the reaction function *f* are coupled in the vertical intercept.

Further, in order to determine the reaction function *f* , the master curve method will be used [25–27]. Firstly, to calculate *P*(*u*), the reaction degree value *α* is chosen from 0.1–0.9, and the corresponding temperature *Tα* is obtained based on the DSC curve. Next, to calculate *g*(*α*), the form of *f*(*α*) need to be chosen. Generally, the reaction function has different forms, such as the *n*th-order reaction model, Avrami–Erofeev reaction model, and so on, and it depends on the type of materials. In the current work, the Avrami–Erofeev reaction function was chosen based on the reaction characteristics of Ni/Al energetic structural materials. It can be written as Equation (10), where *n* is the parameter related to the reaction mechanism.

$$f = n(1 - a)[-\ln(1 - a)]^{\frac{n - 1}{n}} \tag{10}$$

Based on Equation (7), the parameter of the reaction function is determined by using the master curve method. Considering the two-stage reaction, taking *α<sup>c</sup>* as the transition point, Equation (7) can be rewritten as,

$$g(u\_c) = \frac{AE}{\beta R} P(u\_c) \tag{11}$$

Divide Equation (7) by Equation (11),

$$P(\mathfrak{u})/P(\mathfrak{u}\_{\mathfrak{c}}) = \mathfrak{g}(\mathfrak{a})/\mathfrak{g}(\mathfrak{a}\_{\mathfrak{c}}) \tag{12}$$

According to the Equation (9), choose an appropriate Avrami–Erofeev reaction function parameter *n* and reaction degree *α* until the two reaction curves (*P*(*u*)/*P*(*uc*) − *T<sup>α</sup>* and *g*(*α*)/*g*(*αc*) − *Tα*) have the highest correlation, and so the best reaction function *f* could be determined. Generally, *P*(*u*)/*P*(*uc*) − *T<sup>α</sup>* should be called the test reaction curve, and *g*(*α*)/*g*(*αc*) − *T<sup>α</sup>* should be called the standard reaction curve. The processing is conducted for the different heating rate conditions.

#### **3. Results and Discussion**

#### *3.1. DSC Analysis*

Figure 1 shows the morphology of the Ni/Al energetic structural material mixed powders with different molar ratios of 1:1, 1:3, and 3:1. It can be seen that by the mixed and ball milling technique, the Ni and Al particles were randomly dispersed, where the bright particle was Ni and the dark particle was Al.

**Figure 1.** SEM images of (**a**) Ni/Al = 1:1, (**b**) Ni/Al = 1:3, and (**c**) Ni/Al = 3:1.

The DSC curves of Ni/Al energetic structural materials with the molar ratios 1:1, 1:3, and 3:1 at different heating rates are shown in Figure 2. For Ni/Al = 1:1, only one exothermic peak occurred during the thermal reaction process from room temperature to 1200 K, which were located at the range from ~870 K to ~950 K. In the DSC curves of Ni/Al = 1:3, two peaks, referring to an exothermic peak at ~900 K and endothermic peak at ~1150 K, appeared in Figure 2b. The exothermic peak represented the thermal reaction of Ni/Al, which was consistent with that of Ni/Al = 1:1 in Figure 2a. The endothermic peak was attributed to the melting process of NiAl3, which was further discussed in XRD results. n addition, the DSC curves of Ni/Al = 3:1 are shown in Figure 2c. The thermal reaction processes between Ni and Al were seen at the exothermic peak.

**Figure 2.** DSC curves of Ni/Al energetic structural materials: (**a**) Ni/Al = 1:1, (**b**) Ni/Al = 1:3, and (**c**) Ni/Al = 3:1.

From the DSC curve in Figure 2, the starting reaction temperature *Ts* and the reaction end temperature *Te* were collected. For the endothermic process of Ni/Al = 1:3 at ~1175 K, the start melting temperature *Ts*<sup>1</sup> and the end melting temperature *Te*<sup>1</sup> were also shown. The value of the heat release H was determined by the integral heat flow over time on the DSC curve. The analysis data is listed in the Table 1.



Based on the thermal reaction characteristics of the Ni/Al samples, it could be found that *Ts* had no obvious changes, but *Te* had increased obviously, as the heating rate increased. With a higher heating rate, the peak value of Ni/Al samples was higher, and the reaction was faster. As the typical DSC curves of Ni/Al = 1:1, *Te* had increased from 912.04 K to 948.17 K. The case of Ni/Al = 3:1 had a similar observation, where *Te* increased from 913.11 K to 942.83 K. However, as the typical DSC curves of Ni/Al = 1:3, *Te* had increased from 925.42 K to 977.31 K. The heat release H with different molar ratios Ni/Al = 1:1, Ni/Al = 1:3, and Ni/Al = 3:1 were about 840 J/g, 764 J/g, and 464 J/g, respectively. For all cases, the heat release *H* was almost constant as the heating rate increased.

#### *3.2. Reaction Products Analysis*

In order to determine the composition of the thermal reaction products of Ni/Al samples, the residue after DSC testing was collected for XRD analysis. The phase structure of the residue is shown in Figure 3. For the sample Ni/Al = 1:1, the main reaction products were Al3Ni2 and AlNi, as shown in Figure 3a. As the Al contents increased, the thermal reaction products of Ni/Al = 1:3 become complicated (shown in Figure 3b), including different Ni/Al intermetallic compounds, such as Al3Ni, Al4Ni3, Al3Ni2, Ni5Al3, AlNi, and so on. As the Al contents decreased, the reaction products of Ni/Al = 3:1 (shown in Figure 3c) led to the XRD peaks of Al4Ni3, AlNi3, Ni5Al3, AlNi and Al3Ni2. It could be found that the actual reaction products of Ni/Al powders with different molar ratios were different from the theoretical products, which indicated that the complex and incomplete reaction processes resulted in the diversity of products.

**Figure 3.** XRD results: (**a**) Ni/Al = 1:1, (**b**) Ni/Al = 1:3, and (**c**) Ni/Al = 3:1.

Generally speaking, when the heating temperature was lower than the Al melting point temperature, the reaction between Ni and Al took place in a solid–solid contact mode and the main product Al3Ni was first formed [28]. When the heating temperature reached the temperature of the melting point of Al, Al and Al3Ni would form a eutectic liquid phase. The liquid spread to the surface of Ni powders under the action of capillarity, which accelerated the liquid–solid contact with Ni particles. Ni would react with Al3Ni in liquid phase to form Al3Ni2. Further, the formation of Al3Ni2 layer gradually covered the Ni powder and separated Ni from the liquid phase. Moreover, the ongoing formation of Al3Ni2 could only depend on the diffusion of atoms. At the same time, Al3Ni2 would continue to dissolve into the liquid phase side, and gradually form an enrichment layer. When the Al3Ni2 layer increased to a certain thickness, Al3Ni2 and Ni would form AlNi [29]. When the sample was heated to the reverse peritectic reaction temperature around 1130 K, the reverse peritectic reaction of Al3Ni occurred, which corresponded to the endothermic process of Ni/Al = 1:3 in Figure 2b. Considering the low quantity of Al in Ni/Al = 1:1 and Ni/Al = 3:1, the product of Al3Ni was low, which was not found by XRD. In the high content of Ni in Ni/Al = 3:1, AlNi3 formed due to the diffusion reaction between AlNi and Ni [30].

#### *3.3. The Reaction Kinetics Analysis*

The kinetic parameters referring to the apparent activation energy *E* and the preexponential factor *A* were calculated by the Ozawa method described in the Section 2.2. The reaction function *f* was also obtained by the master curve method derived from the temperature integral described in the Section 2.2.

In order to calculate the apparent activation energy *E*, the end reaction temperature *Te* under different heating rates were required. It should be explained that *Te* corresponded to *α* = 1. The temperature data of Ni/Al samples at four different heating rates of 5 K/min, 10 K/min, 15 K/min, and 20 K/min were listed in Table 1. According to the chemical reaction kinetics equations described in Section 2.2, *Te* corresponding to *β* of each sample was taken out to calculate *lgβ* and 1/*Te*. The scatter plot shows the abscissa 1/*Te* and the ordinate *lgβ*. The apparent activation energy *E* was obtained by the least square fitting method. The results of the linear fitting and apparent activation energy *E* are shown in Figure 4.

**Figure 4.** Linear fitting of samples at different heating rates (**a**) Ni/Al = 1:1, (**b**) Ni/Al = 1:3, and (**c**) Ni/Al = 3:1; (**d**) the apparent activation energy E of the samples.

Figure 4d showed that the apparent activation energy *E* of Ni:Al = 1:1, 1:3, and 3:1 are 258.48 kJ/mol, 182.57 kJ/mol, and 318.09 kJ/mol, respectively. When the contents of Al increased, the apparent activation energy *E* of Ni/Al materials reduced, resulting from the higher activity of Al than Ni. Moreover, when the melting of Al occurred, the liquid phase of Al increased the contact surface of Ni particles [31]. The higher quantity of Al would benefit from promoting the thermal reaction.

The Avrami–Erofeev reaction function *f* was generally used for energetic structural materials [6]. However, it was not a single reaction process; the segment fitting method was used here. The parameters in the reaction function were optimized for different segments. According to the theoretical calculation of the master curve method in Section 2.2, *Tα* was defined as the transition temperature of segmented reaction curves. The pre-exponential factor *A* was calculated for the different reaction stages at different heating rates based on Ozawa method.

Figure 5a–c show the fitting results of the test reaction curve at the heating rate 10 K/min. The two reaction curves revealed a good fitting effect. For the other heating rate conditions, it had a similar trend. In order to explore the mechanism on the occurrence of transition temperature, the transition data points of the samples are plotted in Figure 5d. It could be found that the transition temperature points were distributed in the Ni/Al liquid eutectic temperature range, which indicated that the transition from solid state to liquid state of Al was the critical factor, although the discrepancy was presented due to the reaction hysteresis at the high heating rates for Ni/Al = 1:3.

**Figure 5.** The comparison between the reaction curves and the test reaction curve at 10 K/min (**a**) Ni/Al = 1:1; (**b**) Ni/Al = 1:3; (**c**) Ni/Al = 3:1; (**d**) the transition temperature *Tα*.

Table 2 gives the reaction function parameter *n* and pre-exponential factor *A* of all the samples. For the Ni/Al powder samples with the same molar ratio, the different reaction parameters under different heating rates are collected in Table 2. It could be found that as the heating rate increased, both of the parameters n1 and n2 decreased. This is because the increase of the heating rate brought in the temperature accumulation of the sample, which included exothermic reaction. The weakened constraint between lattice atoms originated from the overheating effect, which was good for promoting the reaction process.

The reaction process was described by the Avrami–Erofee reaction function with two sets of parameters and was divided into reaction stage I and II, according to the transition temperature. The schematic diagram of Ni–Al reaction mechanism with the two-stage reaction is shown in Figure 6. In the reaction stage I, both Ni particles and Al particles were solid, and the contact was similar to the point contact. This stage was considered as the hard contact stage. The reaction to generate Al3Ni only occurred at the contact reaction zones. Therefore, the solid phase reaction was limited. Once the reaction temperature had been heated over the melting point, the solid state of Al started to transfer into the liquid state. The reaction entered the reaction stage II, where the liquid Al had a soft contact stage with Ni particles. With a higher reaction temperature, the solid–liquid reaction between Ni and Al occurred at the surface of Ni particles. In this stage, the reaction rate become faster. In addition, the eutectic liquid would also exist at the reaction zones in the reaction stage II, as shown in Figure 6. The soft contact stage was also beneficial for promoting the thermal reaction of Ni/Al materials [32].


**Table 2.** The reaction function parameter n and pre-exponential factor A of all the samples.

**Figure 6.** Schematic diagram of the reaction mechanism of Ni/Al materials.

#### **4. Conclusions**

In summary, a novel understanding of the thermal reaction behavior and mechanism of Ni/Al energetic structural materials was demonstrated. Depended on the melting point of Al, the thermal reaction stages of Ni/Al were divided into two stages: the hard contact stage and the soft contact stage. The thermal reaction behavior of Ni/Al energetic structural material powder was studied based on the DSC test, XRD characterization, and chemical reaction kinetics analysis. The reaction kinetic parameters and specific reaction mechanism were determined to describe the reaction process for Ni/Al powder. The parameters were used to determine the difficulty and mode of reaction. For the specific kinetic parameters, as the ratio of Al increased, the apparent activation energy of the material significantly reduced. Otherwise, as the ratio of Ni increased, the apparent activation energy increased. It could be found that the exothermic reaction function between Al and Ni was described by Avrami–Erofee segment reaction function. The transition of Al from solid to liquid was the critical factor affecting the establishment of segment reaction function. In addition, the

thermal reaction mechanism of Ni/Al energetic structural material was provided based on the hard contact stage and soft contact stage. This work offered a new idea to understand the thermal reaction behavior and mechanism of Ni/Al energetic structural materials under different temperature stages.

**Author Contributions:** Conceptualization, P.C., H.W. and K.W.; resources, R.L.; writing—original draft preparation, K.W. and C.G.; writing—review and editing, R.L. and P.D.; supervision, P.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the National Natural Science Foundation of China No. 12132003 and 2019-JCJQ-ZD-011-00, State Key Laboratory of Explosion Science and Technology No. QNKT20-07 and Beijing Institute of Technology Research Fund Program for Young Scholars.

**Data Availability Statement:** The data that support the findings of this study are available from the corresponding author upon reasonable request.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**Hai Nan 1,2, Yiju Zhu 2, Guotao Niu 2, Xuanjun Wang 1,\*, Peipei Sun 2, Fan Jiang <sup>2</sup> and Yufan Bu <sup>2</sup>**


**Abstract:** To study the crystal mechanical properties of 3,4-dinitrofurazanofuroxan (DNTF) and hexanitrohexaazaisowurtzitane (CL-20) deeply, the crystals of DNTF and CL-20 were prepared by the solvent evaporation method. The crystal micromechanical loading procedure was characterized by the nanoindentation method, and then obtained the mechanical parameters. In addition, the crystal fracture behaviors were investigated with scanning probe microscopy (SPM). The results show that the hardness for DNTF and CL-20 was 0.57 GPa and 0.84 GPa, and the elastic modulus was 10.34 GPa and 20.30 GPa, respectively. CL-20 obviously exhibits a higher hardness, elastic modulus and local energy-dissipation and a smaller elastic recovery ability of crystals than those of DNTF. CL-20 crystals are more prone to cracking and have a lower fracture toughness value than DNTF. Compared to DNTF crystals, CL-20 is a kind of brittle material with higher modulus, hardness and sensitivity than that of DNTF, making the ignition response more likely to happen.

**Keywords:** DNTF; CL-20; nanoindentation; explosive crystals; micromechanical properties

#### **1. Introduction**

An energetic crystal is a key composition for the explosive formulation designation and its application. In particular, its sensitivity has an important impact on the safety performance of explosive mixtures. Material mechanical performance plays a crucial role on the response behavior of crystals under external mechanical load (such as the impact, friction, impact, etc.), which could result in the formation of "hot spots", and also relate to impact sensitivity. It is reported that for most chemical compounds, sensitivity increases with an energy content rise, although this is not a strict rule [1]. It is of great significance to fully grasp the micromechanical properties of crystals for further understanding the safety properties of materials and analyzing the response mechanism.

The traditional mechanical test method is only suitable for samples with a large size, and struggles to tests smaller ones, especially in the nanometer dimension. Additionally, this problem can be resolved effectively by nanoindentation technology. As a new testing method invented in the early 1990s, nanoindentation technology has been extensively applied to all kinds of materials in the nano/micro dimension, such as ceramics, metals, alloys, energetic materials, etc. [2–6]. Nanoindentation technology uses a computer-controlled load to push a rigid indenter of a specific shape into the surface of the material being tested. At the same time, a high-resolution displacement sensor is used to collect the depth of pressure on the surface of the measured material, and the load–displacement curve of the material surface is obtained. This can effectively measure some mechanical behaviors of materials at the micro/nanoscale, such as hardness, elastic modulus, fracture toughness, strain hardening effect, creep behavior, etc. [7]. Nanoindentation technology is becoming the primary choice for the mechanical property testing of micro/nanoscale materials and structures due to its advantages of simple test operation, high measurement efficiency and wide application range [8]. At present, the research on nanoindentation mainly focuses on

**Citation:** Nan, H.; Zhu, Y.; Niu, G.; Wang, X.; Sun, P.; Jiang, F.; Bu, Y. Characterization and Analysis of Micromechanical Properties on DNTF and CL-20 Explosive Crystals. *Crystals* **2023**, *13*, 35. https:// doi.org/10.3390/cryst13010035

Academic Editors: Rui Liu, Yushi Wen and Weiqiang Pang

Received: 1 December 2022 Revised: 21 December 2022 Accepted: 22 December 2022 Published: 25 December 2022

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

the scale effect of indentation experiments. Early researchers [9,10] found that indentation hardness increased with the decrease in indentation depth through experimental studies. Gerberich [11] studied and found the size effect of indenter shape on indentation hardness. Swadender et al. [12] found that the hardness value decreases with the decrease in the radius of the contact area. Scholars mainly focus on vertical loading and unloading, and study the scale effect of mechanical properties of materials by fitting load–displacement curve and hardness-displacement curve.

With the development of nanoindentation technology, it is gradually applied to the characterization of energetic materials. Ramos et al. analyzed the deformation mechanism of brittle material with the nanoindentation test of cyclotetramethylene tetranitramine (HMX) simulative material [13] and the surface testing about monocrystalline Cyclotrimethylene trinitramine (RDX) [14]. Hudson et al. obtained the micromechanical properties of the different crystal RDX, which demonstrated a potential relationship with the degree of crystal internal defects [15]. Mathew and Sewell [16] studied the crystal micromechanical properties of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) and carried out its molecular dynamic simulation. Matthew et al. [17] tested and analyzed the elastic and plastic characteristics for FOX-7, HMX and ADAAF. Zhai et al. explored the yield behavior of PETN and found that the indentation modulus decreases with the increase in indentation depth [18]. According to the investigation on the regular jump phenomenon of RDX (210) [19], Li et al. computed the yield stress and hardness values, and analyzed the elastic modulus of crystal β-HMX [20]. Zhu et al. [21] found that DNAN had worse ability to resist deformation than TNT, but more obvious slow recovery elasticity and stronger impact energy absorption ability. Meanwhile, they found that HATO was harder and more brittle compared with RDX when impacted by external shock [22]. Moreover, Ekaterina et al. found that surface dynamics influence a material's ability to dissipate excess energy, acting as a buffer to mechanical initiation [23]. For the materials with less hardness, such as picric acid and 3,4-dinitropyrazole, the surfaces could be rearranged in response to mechanical deformation. DNTF and CL-20 are typical highly energetic materials with superior crystal density and energy compared to RDX, HMX, TNT, which are crucial parameters to improve the explosive properties. However, few studies have focused on the micromechanical properties of DNTF and CL-20. This paper analyzed parameters such as the elastic modulus and hardness, characterized the break behavior and explored the relationship between crystal properties and sensitivity by means of nanoindentation technology.

#### **2. Materials and Methods**

#### *2.1. Materials*

DNTF and CL-20 crystals were prepared by volatilization using acetone as a solvent at room temperature, where the CL-20 was from Qingyang Special Chemical Industry Co., Ltd. (Qingyang, China), and the DNTF was synthesized by Xi'an Modern Chemistry Research Institute. In addition, the nanomechanical analyzer, TI950, made by the Hysitron company in America, was used to employ the nanoindentation experiments to obtain the mechanical characteristics of crystalline CL-20 and DNTF. The mechanical characteristics included the testing of material hardness, elastic modulus, and fracture toughness, where the indenters were both kinds of Berkovich and the parameters of scanning probe image were 2 μN contact force and 15 μm × 15 μm size, respectively.

#### *2.2. Methods*

In the process of nanoindentation testing, the indenter was pressed into the surface of the samples with a certain load, and when the load reached a designed value, the external force was unloaded.

During the test loading, the indenter displacement (*H*) and load (*P*) were recorded by means of the high-precision load–displacement testing technique. At the contact with the indenter, in the direction of the load, the material had a certain degree of elastic recovery. Figure 1 shows the typical curves of displacement and load in the process of loading and unloading. The key parameters included the maximum load (*P*max), maximum displacement (*h*max), the final indentation depth after complete unloading (*h*f) and the top slope *S* of the unloading curve.

**Figure 1.** Typical crystal load–displacement curve.

In the experiments, the crystalline DNTF and CL-20 explosives were loaded with forces of 500 μN to 5000 μN with the same conditions of 5 s loading, 2 s pressure maintaining and 5 s unloading.

#### **3. Results and Discussion**

#### *3.1. Indentation Curve of Crystalline Material*

According to the nanoindentation testing, the curves of loading and unloading for DNTF and CL-20 were obtained as shown in Figure 2.

**Figure 2.** Quasi-static load–displacement curve for DNTF (**a**) and CL-20 (**b**).

The curves obtained exhibited similarity to the theory curve above. With the increase in loading, the maximum depth of the indenter (*h*max) and the final indentation depth (*h*f) increase continuously gradually. During the loading, the displacement on both crystals showed a sudden increase, which was mainly caused by internal microdefects such as microcracks, micropores, etc. When the contact surface of the indenter is close to the defect, the elasticity and hardness of the local material will decrease sharply, resulting in the sudden increase in the indenter displacement. Therefore, when the existing defects are sensed by the indenter, the indentation displacement increases. In order to clearly compare the loading characteristics of the two kinds of crystal mechanics, three loading–displacement curves at 1000, 3000 and 5000 μN were compared, and the results are shown in Figure 3.

**Figure 3.** DNTF, CL-20 crystal load–displacement comparison curve.

It can be seen from Figure 3 that the two kinds of material showed different mechanical behaviors, in that the indentation depth on the crystal surface was quite different under the same load. Figure 4 shows that the maximum displacement (*h*max) of DNTF was higher than that of CL-20 under the same load. In addition, when the pressure was completely unloaded, the final indentation depth *h*max of the two crystals was basically the same. Therefore, the DNTF was more prone to deformation. Furthermore, the top slope *S* of the unloading curve was also named contact stiffness and increased with the load. The *S*CL-20 was obviously higher than *S*DNTF, which indicated that CL-20 had a harder contact stiffness, as shown in Figure 5.

**Figure 4.** Load–displacement variation curve.

**Figure 5.** Load-contact stiffness variation curve.

#### *3.2. Crystalline Elastic Modulus and Hardness*

The hardness and elastic modulus of crystalline materials were calculated by the theory of Oliver–Pharr, and the formulas of hardness *H* and elastic modulus *E* are shown below:

$$H = \frac{P\_{\text{max}}}{A} \tag{1}$$

$$\frac{1}{E\_r} = \frac{1 - v^2}{E} + \frac{1 - v\_i^2}{E\_i} \tag{2}$$

$$E\_r = \frac{\sqrt{\pi}}{2\beta} \frac{S}{\sqrt{A}}\tag{3}$$

where *Er* is the equivalent modulus. *Ei* is the modulus of indenter. *A* is the contact area. *β* is a constant related with indenter shape. *ν<sup>i</sup>* is the Poisson ratio of the indenter and *ν* is the Poisson ratio of samples. According to the formulas above, the values of crystalline elastic modulus and hardness were obtained and the variation with load, as can be seen in Figures 6 and 7.

**Figure 6.** Load–crystal modulus of elasticity curve.

**Figure 7.** Load–crystal hardness curve.

As shown in Figures 6 and 7, with the increase in *H*max, the hardness and elastic modulus of DNTF and CL-20 decreased first and then trended toward a fixed value. That is, when the compression depth is small, the mechanical parameters of the material are larger. As the depth of compression increases, the mechanical parameters of the material approach a constant value, which is called the "scale effect", and this effect is related to the plastic strain and the plastic strain gradient of the material [15]. The elastic modulus of the crystal is mainly determined by the strength of the intermolecular binding force. The stronger the intermolecular binding force is, the less easy it is to deform, and the higher the elastic modulus is. With the increase in indentation depth, the elastic modulus changes little but decreases slightly.

The average values of hardness for DNTF and CL-20 is 0.57 GPa and 0.84 GPa, and the elastic modulus is 10.34 GPa and 20.30 GPa, respectively. The average deviations of hardness for DNTF and CL-20 are 0.07 GPa and 0.06 GPa, and those of the elastic modulus are 0.54 GPa and 0.74 GPa, respectively. The elastic modulus and hardness of CL-20 are about 47% and 96% higher than those of DNTF, respectively, which indicates that CL-20 has a high stiffness and is difficult to deform. On the contrary, DNTF experiences easier indentation—namely, CL-20 is "hard" and DNTF is "soft".

In addition, the elastic modulus of a material is not directly proportional to its hardness. The elastic–plastic local deformation in the loading process determines the hardness of the material and the work conducted by external forces, and the elastic recovery in the unloading process reflects the local energy dissipation and elastic modulus of the material. Based on elastic contact theory, the relationship between the elastic modulus and hardness of solid materials depends on the energy dissipation capacity of materials. Additionally, the local energy dissipation *R*<sup>S</sup> of the material is inversely proportional to the ratio of *H/E* [19]. The ratio of CL-20 and DNTF is calculated to be 0.041 and 0.055, respectively, so the local energy dissipation of CL-20 crystals is greater than that of DNTF, which will lead to a lower elastic recovery capacity around the indentation of CL-20 than that of DNTF.

The hardness and elastic modulus of crystals are closely related to the intermolecular binding force. Figures 8 and 9 show the molecular structure of CL-20 and DNTF.

CL-20 is a caged nitroamine explosive with molecular formula C6H6O12N12, and there are van der Waals forces and hydrogen bond interactions between molecules. Pampuram et al. [24] found a novel synthesis method of hexaazaisowurtzitane cages to access CL-20, where CL-20 with a yield of 25% was successfully obtained.

**Figure 8.** Schematic diagram of molecular structure for CL-20.

**Figure 9.** Schematic diagram of molecular structure for DNTF.

By contrast, DNTF is a typical furazan compound, which is composed of an oxidized furazan ring, a furazan ring, a nitro group and other groups. The molecular formula is C6O8N8, and there is no hydrogen element in the molecule, so there is no hydrogen bond between molecules, which is mainly dominated by van der Waals forces. Therefore, the intermolecular binding force of DNTF is weaker than that of CL-20. Due to its strong intermolecular binding force, CL-20 is not easy to deform, resulting in its mechanical properties differing from those of DNTF.

#### *3.3. Crystalline Elastic Property*

In the testing of nanoindentation, pure elastic deformation is almost impossible. Due to the high local stress concentration, local plastic deformation inevitably occurs to some extent, so the variation of crystal depth mainly includes elastic and plastic deformation. In the process of pressing, the total work transforms to the sum of elastic and plastic work of materials. In addition, after unloading, only part of the elastic work is released. From the curve of loading and unloading, the total deformative work *At* and elastic work *Ae* are obtained, and accordingly, the plastic work *Ap* is calculated. The plasticity of crystalline materials can be expressed by dimensionless *δ<sup>A</sup>* as follows [25–27]:

$$
\delta\_A = \frac{A\_p}{A\_t} = \frac{A\_t - A\_c}{A\_t} \tag{4}
$$

$$A\_t = \int\_0^{h\_{\text{max}}} P dh \tag{5}$$

$$A\_{\rm c} = \int\_{h\_{\rm p}}^{h\_{\rm max}} Pdh \tag{6}$$

It can be seen in Table 1 that the total deformation work and elastic deformation work of the two materials increase with the increase in load. Additionally, under the same load, the total deformation work and elastic deformation work of DNTF crystal are significantly greater than that of CL-20. However, the values of *δ<sup>A</sup>* of the two materials are basically the same, which shows that when the crystal is stimulated by external load, the ratio of elastic deformation to plastic deformation of DNTF and CL-20 remains unchanged, and most of the total deformation work is converted into plastic deformation work.


**Table 1.** Calculated elastic–plastic work of DNTF and CL-20.

Since the *δ<sup>A</sup>* average value of DNTF (0.64) is smaller than that of CL-20 (0.73), it can be concluded that CL-20 crystals have a higher plastic deformation and transformation ability. However, the elastic transformation ability of DNTF crystal is stronger, and the elastic recovery ability of DNTF is higher than that of CL-20, which further reflects the characteristics of the large local energy dissipation of CL-20. This also means that under the same loading conditions, the structural integrity of CL-20 crystals is weaker than that of DNTF crystals, so it is more likely to be damaged under impact.

#### *3.4. Fracture Toughness Property*

Crack formation is an important form of crystal mechanics, and the fracture toughness (*K*IC) parameter is generally used to quantify and measure the nanoindentation. *K*IC reflects the energy required for crystal fracture, which means the ability of crystals to prevent crack propagation. In general, the higher the fracture toughness value of the material, the higher the critical stress required for crack instability propagation and the stronger the crack resistance. According to the theory of fracture mechanics and the analysis of the angular radial crack traces in the nanoindentation test, the mathematical relationship between the fracture toughness value and the indentation crack length is as follows:

$$K\_{IC} = \alpha \sqrt{\frac{E}{H}} \left(\frac{P\_m}{C^{3/2}}\right) \tag{7}$$

where *P*<sup>m</sup> is the load, *C* is the radial crack length, and *α* is the empirical parameter related to the indenter (*α* of the cubic angle indenter is 0.036).

A cubic angle indenter was used to test the radial crack on the surface of DNTF and CL-20 crystals at 3000 μN, and the results are shown in Figure 10. It can be seen that obvious cracks appear in CL-20, while no cracks appear in DNTF. The radial cracks of DNTF and CL-20 and the average radial crack lengths were obtained under 4000 μN and 5000 μN loads by means of the same loading method. The elastic modulus and hardness obtained were substituted into Equation (7) to obtain the fracture toughness values under different loads, as shown in Table 2.

With the increase in loading from 3000 to 5000 μN, the crack length on the surface of the two crystals shows an increasing trend, and the crack length of CL-20 is more significant. With the increase in loading, the fracture toughness value of CL-20 decreases continuously, showing a typical material brittle fracture behavior. In addition, the fracture toughness value of CL-20 crystals is lower than that of DNTF crystals, and it is more prone to cracking than DNTF crystals. The experimental results show that CL-20 exhibits brittleness. Although the compressive strength is high under quasi-static conditions, the impact resistance is weak. In contrast, DNTF shows toughness—that is, under the same

impact load, it will absorb more energy and undergo large deformation without sudden failure, and DNTF crystal has strong anti-failure ability.

**Figure 10.** Crystal indentation crack at 3000 μN for (**a**) DNTF and (**b**) CL-20.


**Table 2.** Crack length and fracture toughness values at different loads.

#### *3.5. Crystal Mechanics and Crystal Sensitivity*

Under impact conditions, when materials with different elastic moduli deform, the higher the elastic modulus is, the higher the strain rate will be, and the greater the impact stress will be [28]. Therefore, under the dual action of stress and strain rate, stress concentration is more likely to lead to crystal fracture and the formation of "hot spots" for the high elastic modulus material. From the perspective of the mechanical properties of materials, by comparing the mechanical properties of CL-20 and DNTF crystals, it can be seen that CL-20 crystal has a high elastic modulus and hardness, and CL-20 is brittle and prone to cracking. Consequently, CL-20 is more likely to lead to an ignition response than DNTF. In addition, DNTF crystal is a typical high-energy melting and casting carrier. In addition to low modulus and hardness, it also has the property of endothermic melting, which is beneficial to inhibit the formation of "hot spots". Understandably, DNTF is less likely to react than CL-20.

As the typical high energy density materials, both DNTF and CL-20 have high energy and high sensitivity. According to the mechanical sensitivity test method of GJB772A-97, the impact sensitivity of CL-20 and DNTF is 100% and 88%, respectively [29,30], and the friction sensitivity is 100% and 84% [31,32], which means that DNTF mechanical sensitivity explosion probability is lower than CL-20. It can be concluded that although DNTF and CL-20 are both highly sensitive materials, DNTF is relatively safer than CL-20 according to the crystal mechanical properties and sensitivity performance data.

#### **4. Conclusions**

The average hardness of DNTF and CL-20 is 0.57 GPa and 0.84 GPa, and the average elastic modulus is 10.34 GPa and 20.30 GPa. The hardness, elastic modulus and local energy dissipation of CL-20 are significantly higher than those of DNTF.

Most of the pressing work of CL-20 crystal is converted to plastic work, and its elastic recovery ability is less than that of DNTF. The indentation morphology shows that CL-20 crystal is more prone to cracking than DNTF crystals, and the fracture toughness value is lower than that of DNTF crystals. Compared with DNTF crystals, CL-20 is a brittle crystal material with high modulus and high hardness.

Based on crystal micromechanics, CL-20 crystals have a lower sensitivity than DNTF and are more prone to an ignition response.

**Author Contributions:** Conceptualization, H.N., Y.Z. and X.W.; methodology, H.N., G.N. and Y.B.; formal analysis, H.N., Y.Z. and G.N.; investigation, G.N., P.S. and F.J.; writing—original draft preparation, H.N., G.N. and Y.B.; writing—review and editing, G.N. and Y.B.; supervision, H.N. and X.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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