Crystallographic orientation dependence on nanoscale friction behavior of energetic β-HMX crystal

Tribology behaviors of energetic crystals play critical roles in the friction-induced hotspot in high-energy explosive, however, the binder and energetic crystals are not distinguished properly in previous investigations. In this study, for the first time, the nanoscale friction of β-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (β-HMX) crystal is studied with nanoscratch tests under the ramping load mode. The results show that the nanoscale friction and wear of β-HMX crystal, as a typical energetic material, is highly depended on the applied load. The friction coefficient of β-HMX crystal is initially high when no discernible wear is observed, and then it decreases to a stable value which varies from ∼0.2 to ∼0.7, depending on the applied load, scratch direction, and crystal planes. The β-HMX (011) surfaces show weakly friction and wear anisotropy behavior; in contrast, the β-HMX (110) surfaces show strongly friction and wear anisotropy behavior where the friction coefficient, critical load for the elastic—plastic deformation transition and plastic—cracking deformation transition, and deformation index at higher normal load are highly depended on the scratch directions. Further analyses indicate the slip system and direction of β-HMX surfaces play key roles in determining the nanoscale friction and wear of β-HMX surfaces. The obtained results can provide deeper insight into the friction and wear of energetic crystal materials.


Introduction
Octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) is one of the best energetic materials (EMs) with comprehensive performance, which not only acts as an indispensable component of high-energy explosives in conventional and nuclear warheads, but also an important additive of advanced propellants [1,2]. As an organic material, HMX has four crystalline phases α, β, γ, and δ. Among them, β is the most stable phase at room temperature with the highest density and the lowest mechanical sensitivity, thus β-HMX attracts the most attention in industry and military engineering [3]. β-HMX can decompose violently with large energy release upon external stimuli [4], it has high explosive speed, pressure, and energetic level, which makes it become the main component of many polymer-bonded explosives (PBX) products such as PBX-9011, PBX-9404, PBX-9501, etc. [5]. In the PBX, the explosive powder is bound together in a matrix using, typically, 5%-10% by weight of a synthetic polymer. The particular structure of PBX makes it easier and safer to handle and process compared to other normally used explosive materials, but it tends www.Springer.com/journal/40544 | Friction to absorb shocks, making the PBX very insensitive to accidental detonation offering some immunity to fire and bullet impact, and thus ideal for insensitive munitions under normal conditions [6].
Generally, the ignition of EMs subjected to unexpected stimulation (non-shock ignition) strongly depends on the friction conditions of their interface or surface, which makes the accidental ignition of EMs possible, such as explosive drop and impact [7]. This is because during those accidents, EMs usually encounters the friction process occurring between the energetic crystals or between the energetic crystal and other contact materials, and these friction effects are extremely prone to friction-induced hotspots that may lead to abnormal ignition or even explosion of EMs [8]. Indeed, not only in the unexpected accidents, the friction of EMs also widely exists in the process of granulation, pressing, and cutting [9]. Therefore, it is of critical importance to reveal the friction mechanism of EMs and thus find possible ways to control their friction behavior for process and usage safety.
Up to now, some efforts have been made to understand the friction behavior of EMs. For instance, based on the split Hopkinson press scissor rod (SHPSB) device, the dynamic friction coefficient between steel and PBX tablet increased from ~0.09 to ~0.14 when the sliding interface was in the steady-state friction range, and the growth of friction coefficient was attributed to the structural destruction of the polymer binder and the increase in friction contact area by the shedding of energetic crystals [10]. The counter-surface during the friction process can also affect the dynamic friction coefficient of explosive materials [11]. It was found that when the contact-surface was aluminum alloy, the friction coefficient of PBX is independent of the loading rate, while the friction coefficient at PBX/rubber interface increased with the loading rate [12]. However, although these experimental results provide basic data for quantitatively understanding the friction process of explosives, it should be noted that these tests are performed with PBX tablets, in which the polymer binder and energetic crystals are not properly distinguished, and the obtained tribological information is actually the overall reflection of binder and energetic crystals on the macro-scale [13]. These treatments ignore the "short board effect" of energetic crystals on the friction process of PBX system, that is, the friction sensitivity of energetic crystals is much higher than that of polymer binder, thereby determining the inherent friction safety of PBX system [14]. Therefore, revealing the friction behavior of energetic crystals is still highly required to in-depth understand the evolution mechanism of explosive friction. Moreover, theoretical studies have provided evidences that the friction-induced hotspots locate at the micro sliding interface [15]. Thus, the micro tribological parameters of energetic crystal surface are crucial for establishing a more reasonable friction hotspots model.
The crystallographic orientation is known to alter the microscopic friction response of crystalline materials. For example, it was reported that the friction and wear of single crystalline silicon on (111) plane was lower than the ose on the (100) plane due to the lower surface energy and higher in-plane strength on (111) plane [16]. Similar friction and wear anisotropy behaviors have also been reported on the other crystalline materials such as single crystalline copper [17], nickel [18], Mg [19], and diamond [20]. During the friction process of HMX, the corresponding friction response can be relied on both the crystalline plane and orientation, and thus the friction-induced hotspot on -HMX surfaces can be varied accordingly. However, to the best of our knowledge, how the crystalline orientation will affect the friction response of HMX has not been addressed yet.
In the present study, the nanoscale friction behavior of β-HMX, as a typical energetic crystal, was systematically studied for the first time. The crystallographic orientation dependent on the elastic-plastic transition, friction coefficient, and deformation behavior on the surface of energetic β-HMX crystal were carefully investigated, and it reveals that the friction behavior of β-HMX crystal exhibits obvious crystal-plane dependence and anisotropy. On this basis, the crystal slip system theory was identified to clarify the internal mechanism of this friction behavior. The obtained findings provide necessary physical information concerning the understanding and controlling the friction and wear of EMs.

Materials and methods
The β-HMX single crystals were provided by Institute of Chemical Materials at China Academy of Engineering Physics. The basic crystal data of -HMX can be found in Table S1 in the Electronic Supplementary Material  (ESM). To obtain the sample for the nanoscratch tests, β-HMX single crystals were mosaicked with cold mounting material (Meijun Technology Inspection Co., Ltd., China) and then polished with a polishing machine (ZYP230, McCord Material Processing Equipment Company, Shenyang) ( Fig. 1(a)). Two typical planes, (011) and (110), of β-HMX crystals were prepared in the present study, because these two planes were the most important planes to affect the crystal morphology [21]. More details about preparing the single crystals can be found in Ref. [22]. Using a 3D contour white light interferometer (MFT3000, Rtec, USA), the surface roughness S a of the (011) and (110) surfaces was estimated to be 20.2 ± 0.8 nm and 18.5 ± 0.3 nm, respectively ( Fig. 1(b)). To characterize the planes of β-HMX crystals, the prepared samples were detected with X-ray diffraction (XRD, X'per MRE, Philips, Netherlands), as shown in Fig. 1(c). It could be seen that the maximum peak intensity of the two samples appeared on the (011) and (110) planes, which represented the crystals growth direction [23].
The nanoscratch tests of β-HMX crystal surfaces were carried out using an Agilent G200 nanoscratch system (Santa Clara, CA) at room temperature (~22 °C) and room humidity (~50% RH) conditions. The indenter tip used for the nanoscratch tests was a conospherical diamond tip with a nominal radius of 2 μm (Fig. 1(d)). The nanoscratch tests were conducted by the ramp loading mode, where the load was linearly increasing the normal load from 0 mN to maximum scratch load (e.g., 3.5 mN) across the lateral displacement of 200 μm. During the nanoscratch process, a pre-scan with a constant normal load of 10 μN was performed to get the initial crystal surface morphology. Then, the tip moved back to the initial position and began to scratch the crystal surface under the given scratch load and speed conditions, then the coefficient of friction (COF, defined as the ratio of friction force to normal load) and penetration (scratch) depth during nanoscratch were recorded simultaneously. The sliding speed of the indenter tip was 5 μm/s. Finally, a post-scratch scan was carried out with the same tip at a normal load of 10 μN to get the residual depth profile of the nanoscratch along the scratch direction ( Fig. 1(e)). Since the β-HMX has a single-oblique crystalline structure, its nanoscratch behavior should www.Springer.com/journal/40544 | Friction depend on the sliding direction, thus two kinds of nanoscratch tests were carried out to study the crystallographic orientation on nanoscratch behaviors ( Fig. 1(f)): (1) scratch directions were set at 0°, 45°, and 90°, respectively; (2) scratch directions were set with 30° per interval in the 360° range. Total four scratch tests were performed at each testing condition to ensure the repeatability of the experiments, and only representative data were shown in this paper. The chemical structures of the wear debris, scratched region, and pristine β-HMX surface were detected by Raman spectroscopy (InVia, Renishaw, England).

Friction coefficient on β-HMX crystal surface under the ramp loading
Figures 2(a) and 2(b) show the COF as a function of normal load during the nanoscratch of (011) and (110) plane of β-HMX surface, respectively. It is clearly that for both planes, the COF is initially high (~1.0), and it decreases with the normal load before reaching a steady-state COF. On the (011) plane, the COF is about the same for various scratch direction tests when the normal load is ≤ 0.2 mN, and it becomes slightly different when the normal load is ≥ 0.2 mN ( Fig. 2(a)).
On the (110) plane, the COF is significantly different when the normal load is ≥ 0.5 mN, depending on the scratch direction ( Fig. 2(b)). Previous studies have shown that when the substrate materials were scratched with a tip in the fully elastic deformation stage [24][25][26], the friction force was mainly governed by the interfacial adhesion, and the corresponding COF could be expressed with the Hertztian contact theory where the COF was a function of F n -1/3 (F n represented the normal load for the nanoscratch tests) [27], thus the COF decreased exponentially with F n in the elastic region. With the further increase in normal load, the substrate material would undergo plastic deformation, in which the ploughing friction began to dominate the friction process and both the adhesion and ploughing friction can contribute to the overall COF [28], as a result, the interfacial COF seemed to be insensitive to the normal load [24][25][26]20]. In the case of β-HMX surface, it is reasonable to speculate that the regardless of various planes, β-HMX surface will show elastic deformation when the normal load is small, and it exhibits plastic deformation after the normal load reaches the critical point, thus the COF of β-HMX surface will decrease with normal load firstly before reaching to a relatively steady-state value. The elastic and plastic deformation of β-HMX surface depends on the surface topography evolution, which will be discussed in the Section 3.2.
On the other hand, the steady-state COF at the second stage is different for two surfaces. On the (011) plane, the steady-state COF is ~0.15, which does not show significantly differences when the scratch direction is 0°, 45°, and 90°, respectively ( Fig. 2(a)). In contrast, the steady-state COF on (110) plane is strongly depended on the scratch direction, where the steady-state COF is ~0.2 and ~0.3 when the scratch direction is 0° and 45°, respectively. Interestingly, the COF at the scratch direction of 90° on (110) plane continues to increases and drastically fluctuates with the increase in normal load, and the maximum value approaches to ~0.7. These results imply that the COF on (110) plane is strongly friction anisotropy, while the COF on the (011) plane is not.

Nanoscratch damage on β-HMX crystal surface under the ramp loading
Besides, the surface damage behavior of β-HMX crystal also shows significant difference between the two planes. It demonstrates that no obvious damage or material removal can be observed at the initial stage of the scratch process ( Fig. 3), indicating only elastic deformation under small normal load. Moreover, the discrepancy between the various scratch directions on (011) plane is negligible ( Fig. 3(a)), in which the characteristic length of the elastic region is almost the same, followed by the stable material removal in plastic region. In contrast, on the (110) plane, neither the characteristic length of elastic region nor the damage morphology of plastic region is similar in different scratch directions, especially substantial cracking and fracture are found in 90° direction ( Fig. 3(b)). It further reveals that surface damage of (110) plane shows strongly wear anisotropy, which is consistent with the results observed in the COF behavior (Fig. 2). The occurrence of cracks and chipping of (110) planes and its consistence with the discontinuities in COF behaviors (Fig. 2) imply the surface deformation of (110) planes at higher load conditions are governed not by purely plastic deformation any more, but by the brittle fracture of crystal and wear debris.
To further compare the surface deformation behaviors of the two planes, Figs. 4(a) and 4(c) show the scratch depth during the nanoscratch process and the residual depth at various directions for the (011) and (110) plane, respectively. It is found that the scratch depth and residual depth on the (011) plane are quite smooth and not strongly depended on the scratch directions ( Fig. 4(a)). In contrast, on the (110) plane, the scratch depth and residual depth are relatively smooth when the scratch direction is 0°, while it is relatively rough at the scratch directions of 45° and 90° (Fig. 4(c)). The nanoscratch-induced deformation behavior of the two surfaces is also quantitatively compared. Since both the elastic and plastic deformation as well as cracking and chipping occur, and Figs. 4(b) and 4(d) show the deformation index, defined as the ratio of residual depth to the scratch depth, of (011) and (110) plane, respectively. It demonstrates that for the (011) plane, the deformation index in various scratch directions is zero when the normal load is <0.2 mN, which further supports that (011) plane undergoes elastic deformation under the given sliding contact condition. With the increase in normal load, the deformation index sharply increases to ~35% and continues to increase, which eventually reaches ~75% when the normal load is 3.5 mN (Fig. 4(b)). Based on the scratch depth ( Fig. 4(a)) and optical microscopy image of nanoscratch damage (Fig. 3), it can be roughly estimated that the critical load for the plastic-cracking transition of (011) plane is ~1.7 mN regardless of various scratch directions ( Fig. 4(b)). Nevertheless, on the (011) plane, the deformation index is insensitive to the scratch direction ( Fig. 4(b)), and the deformation index as a function of normal load in different scratch directions is roughly the same.
Different from the (011) plane, the critical load of elastic-plastic deformation on (110) plane varies with the scratch direction (Figs. 4(c) and 4(d)). Specifically, in the scratch direction of 0°, 45°, and 90°, the critical load of elastic-plastic deformation is ~0.15, ~0.2, and ~0.25 mN, respectively. Moreover, when the plastic deformation occurs under higher normal load, the deformation index becomes sensitive to the scratch direction (Figs. 4(c) and 4(d)), and the fluctuation of the deformation index at 90° direction is quite obvious when the normal load is > 2 mN, which is caused by the substantial cracking and fracture (Fig. 3(b)). The fluctuation of the deformation index at 90° direction ( Fig. 4(d)) as well as the formation of substantial www.Springer.com/journal/40544 | Friction cracking and fracture (Fig. 3(d)) are consistent with the fluctuation of COF observed in Fig. 2(b). On the basis of the occurring the radial cracking at β-HMX surface by optical microscopy image (Fig. 3) as well as the in-continues variation in COF (Fig. 2) and scratch depth (Fig. 4), it can be roughly estimated that as the scratch direction on (110) plane of β-HMX surface is 0°, 45°, and 90°, the critical load for the transition from plastic deformation to brittle cracking is ~2.5, ~2, and ~1 mN, respectively. This implies that on the one hand, the initiation of brittle fracture is more feasible as the scratch direction on (110) plane of β-HMX surface is higher, on the other hand, the elastic-plastic deformation and plastic-cracking deformation of (110) plane of β-HMX show more friction-induced anisotropy, which is different from that of (011) plane of β-HMX surface (Figs. 2-4).
Generally, the friction behavior depending on the crystal plane and scratch direction can be closely related to the inherent mechanical properties of the crystal [29]. Thus, Fig. 5 compares the load-depth curves of the two planes recorded by nanoindentation and their corresponding elastic modulus and nanohardness. The nanoindentation tests are performed with a load-control mode where the maximum indentation load is set as 3.0 mN (Fig. 5(a)). 16 individual nanoindentation tests are performed on each surface to ensure the data reproduciablity, and only the representative load-displacement curves are shown in Fig. 5(a). The Poisson's ratio 0.3 of β-HMX is used for the elastic modulus calculation [30]. It is found that the elastic modulus and nanohardness of (011) plane are quite stable, which are ~18.6 and ~0.75 GPa, respectively ( Fig. 5(b)). In the case of (110) plane, the elastic modulus and nanohardness of plane (110) is calculated to be ~19.7 and ~0.63 GPa, respectively, and the error bars are relatively larger than those of (011) plane. The student's t-test show the differences in elastic modulus and hardness in two surfaces are statistically significant (p < 0.01 for N = 10). Since all the nanoindentation tests on various samples are conducted at the same direction, the substantial pop-in during the loading process ( Fig. 5(a)) and the larger error bar of nanohardness of (110) plane ( Fig. 5(b)) imply that it has more obvious damage anisotropy than the (011) plane. Moreover, the nanohardness of  (110) plane is relatively lower than the (011) plane ( Fig. 5(b)), while its steady-state COF is obviously higher (Fig. 2), indicating that the friction behavior of the crystal plane is dominated by the mechanical effect where the surface nanohardness plays important roles [29,31]. Based on the Hertzian contact theory, it is found that the calculated critical contact pressure is higher than the measured nanohardness (Table S2 in the ESM). Previously, it was reported that the contact pressure that leads to initiation of plastic deformation of single crystalline silicon (100) was close to the hardness value of silicon (100) [32,33]. In the present study, the higher critical contact pressure than the measured nanohardness value could be originated from the ramp loading mode and its relative higher loading rate at lower load conditions. Moreover, based on the Vickers indentation tests, the indentation fracture toughness of (011) and (110) plane of β-HMX surface are estimated as ~0.097 and ~0.092 MPa·m 0.5 , respectively [34], and the brittle index of (011) and (110) plane of β-HMX surface can be estimated as ~1.42×10 3 and ~1.46×10 3 m -1 , respectively [35]. The slightly lower indentation fracture toughness and slightly higher brittle index of (110) plane of β-HMX surface could be one of the reasons for the occurring cracking and fracture during nanoscratch process compared to that of (011) plane of β-HMX surface (Fig. 3), since the fracture surface energy of (110) plane of β-HMX surface is estimated to be slight lower than that of the (011) plane of β-HMX surface [35]. However, the anisotropy of β-HMX surface is not taken into account during the estimation of hardness, elastic modulus, indentation fracture toughness, brittle index, but the nanoscratch damage of (110) plane of β-HMX surface shows obvious friction and wear anisotropy, which implies that the discrepancy in mechanical property of β-HMX surface alone cannot explain the friction and wear anisotropy of β-HMX surfaces.
According to the results from Figs. 2-5, it can be seen that regardless of the load is applied on the surface normal direction or on the interfacial tangential direction, the (110) plane shows more obvious anisotropy damage behaviors while the (011) plane does not. It is known that as a monoclinic crystal system, there are two main slip directions of β-HMX crystals, namely (001)[100] and (101)  or (101)[010] [36] (Fig. 6(a)). Figures 6(b) and 6(c) present the relative position relationship between the crystal plane and the two slip planes of (001) and (101), and it demonstrates that the angles between (011) plane and the two slip planes are 45° and 60°, respectively ( Fig. 6(b)), while the angles between the (110) crystal plane and the slip planes are 90° and 60°, respectively ( Fig. 6(c)) [36]. Accordingly, when the diamond tip slides on the (011) crystal plane, the stress of the normal load will generate a stress component along the slip plane (001) plane in the 45° direction and the slip plane (101) plane in the 60° direction ( Fig. 6(b)). In contrast, the normal load on (110) surface will cause preferential slippage perpendicular to (001) slip plane, resulting in deformation along the surface normal direction. Therefore, under the same load conditions, the (110) plane will exhibit a deeper penetration depth and lower nanohardness (Figs. 4 and 5). This can also explain the occurrence of the pop-in during the nanoindentation (Fig. 5(a)) and the large error bar on the hardness of (110) plane (Fig. 5(b)), compared with (011) plane.
Based on the slip plane theory, the mechanical www.Springer.com/journal/40544 | Friction differences between different crystal planes of β-HMX are clarified. However, it still unclear that why it shows friction anisotropic behavior. To understand this friction anisotropy behavior, Fig. 7 shows the position relationship between the slip system of β-HMX and the scratch directions, and it indicates that when the diamond tip slides on the (011) crystal plane along the scratch direction of 45° ( ), the angle between the direction of mechanical stress and the sliding surface is < 90° (45° and 60° in Fig. 7(a), respectively), which allows the normal load to slide along the (001)  . When the direction of mechanical stress is consistent with the slip system, dislocation loops will be more likely to occur, which makes the material remove process uniform and stable (Figs. 2-4), with more plastic removal [37]. In contrast, on the (110) plane, the angle difference between (001) and (101) sliding planes is large (the difference is 60°) on the (011) crystal plane, and the (001) sliding plane is perpendicular to the (011) crystal plane, the stress components provided by the horizontal stress generated are in (001) and (100). The 0° ( [1][2][3][4][5][6][7][8][9][10]) scratch direction corresponds to the slip system (001)[100], and the 45° ( [1][2][3][4][5][6][7][8][9][10][11]) scratch direction is close to the slip system (101)  (the difference is 10°). These two scratch directions are close to the corresponding slip systems, so they show uniform and smooth plastic removal (Figs. 2-4). However, in the 90° ([001]) scratch direction, there is no corresponding slip system, and the angles between the scratch direction and the slip directions [100] and  are 90° and 35°, respectively, which may cause complex angle dependence, thus leading to great    (Figs. 2-4). Generally, the mechanical stress required for dislocation generation is much greater than that required for dislocation movement [38]. Therefore, the slip system in the 90° ([001]) scratch direction is difficult to be activated, and the dislocation needs high contact pressure, so the critical load of elastic-plastic damage transformation in the 90° ([001]) scratch direction is the largest (Fig. 4). Once the dislocation is formed, the plastic deformation becomes very easy under the large normal load, and the material will be severely deformed, resulting in serious surface damage (Fig. 4).
In addition, the regular crack orientation on the (110) crystal plane further provides the evidence of slip systems. Figure 7(b) (right) depicts the scratchinduced cracks expanding along a specific direction, and it reveals that the angle between the crack and the scratch direction is ~55°, with the Miller index identified as [ ] and [010], respecttively. It is worth noting that the cracks in the 0° scratch direction are tiny, while substantial cracks can be found in the 90° scratch direction. This is because there is no corresponding sliding system in the 90° scratch direction, thus a large number of cracks will appear when plastic deformation begins to occur (Fig. 4).

Crystal orientation dependence of nanoscratch on β-HMX (110) surface
To further reveal the friction and wear anisotropy of (110) plane of β-HMX, we've conducted the nanoscratch tests over the 360° directions with 30° differences, as shown in Fig. 8. It can be seen that regardless of the sliding speed, the (110) plane of β-HMX show clearly wear anisotropy under the given applied load conditions. To quantitatively analyze the effect of crystalline orientation on the nanoscratch on (110) crystal plane, the critical loads corresponding to the elastic-plastic deformation transition are estimated from the residual depth after nanoscratch tests (Figs. S1-S3 in the ESM). As shown in Fig. 9(a), the critical load for the elastic-plastic transition of (110) plane shows weak dependence on the scratch direction when the sliding speed is 1 and 10 μm/s, and it shows strong scratch direction dependence when the sliding speed is 100 μm/s, where it is the largest when the scratch direction is 180°. The deformation index at the maximum load shows more scratch direction dependence, where the deformation index is the largest when the scratch direction is 0° and 180°, and it is the smallest when the scratch direction is 120° ( Fig. 9(b)). The COF, fitted at the plastic stage shown in Fig. S4 in the ESM, shows strong dependence on the scratch direction, where the COF is the largest (approaches to ~0.7) when the scratch direction is 0° and 180°, and it is the smallest (~0.2) when the scratch direction is 90° and 270° (Fig. 9(c)). This is because when the scratch direction is 0° and 180°, the corresponding sliding directions is [001] and [1 _ 10], respectively. There is no corresponding slip system at these scratch directions, thus the deformation index at the maximum load and the COF is the largest (Figs. 9(b) and 9(c)). In contrast, when the scratch direction is 90° and 270°, the corresponding sliding directions is [001 _ ] and [11 _ 0], respectively, the scratch direction at the slip direction can cause the smallest deformation  Figure 9(d) summarizes the relationship between the COF, scratch direction, and slip system based on polar coordinates, clearly showing that the COF along the slip direction is small, while the COF deviating from the slip direction is large. Besides, note that since the slip systems on the (110) crystal plane is asymmetric, the distribution of COF in the 360° direction is also asymmetric.
To reveal the friction mechanism of (110) plane of β-HMX, the Raman spectra of wear debris, scratched area, and the pristine β-HMX are compared in Fig. 10. Clearly, there are four main Raman features at ~834, ~882, ~951, and ~1,312 cm -1 , which can be assigned to the C-N bond, N-N bond, HMX ring, and -NO 2 bond in β-HMX crystal, respectively [39,40]. Moreover, no significantly structure change among the pristine β-HMX surface, wear debris, and scratched region is found, regardless of various scratch directions (Fig. 10). This implies that no chemical reaction occurs during the nanoscratch process, and the govern mechanism during the nanoscratch process should be the mechanical interactions (such as interfacial friction and ploughing) between the diamond tip and β-HMX surfaces.

Implications of friction on EMs
The results reported in the current study reveal an important aspect that has not been recognized in previous studies. During the nanoscale friction and wear of β-HMX crystal surface, the COF is not a fixed value and it is varied with applied load and the scratch direction on the crystal surfaces (Figs. 2 and 9). In the friction-induced hotspot model [8], the COF is an extremely important parameter to determine the frictional work. In the temperature calculation process using the classic crack friction hotspot model, a fixed COF value of 0.1-0.2 is usually used [41][42][43], which is not consistent with the obtained results by experiments (Figs. 2 and 9). This means that a more accurate value of COF should be considered under various dynamic sliding contact conditions during the friction-induced hotspot calculation process. On the other hand, the COF value of 0.1-0.2 is obtained with sleeveless SHPSB measurements, where the polymer bonding materials and EMs are not well distinguished [10][11][12]. Given that the COF is strongly depended on the substrate materials [44], thus, more deeper insights into the friction and wear of polymer bonding materials and its comparison with EMs are needed to fully reveal the tribology behavior of EMs, which will be one of the research topics in future studies.
It is known that the COF is strongly depended on not only the loading parameter, but also the materials that are used as the counter-surface [45,46]. Previously, it was reported that dynamic COF of explosive materials (GO-924) depended on both the loading rate and counter-surface materials [12]. Thus, to completely reveal the tribology behavior of EMs surface during the manufacturing and in-service process, the effect of counter-surface materials on the friction behavior, especially the friction behavior between two β-HMX crystal surfaces, should also be considered, which will be one of the research topics in future studies. This is because the friction-induced hotspot of EMs can be facilitated when the friction occurs at the cracking area at nanoscale [47,48], thus, the nanoscale friction behaviors between two EMs surfaces are of great importance to complement the understanding the tribology behaviors of EMs surfaces. It should be noted that the decomposition temperature for triggering the explosion of β-HMX is 200-300 °C [49]. This means the temperature rise at β-HMX interface by frictional heating must be close or even higher than this temperature to trigger the explosion. How the temperature rise at β-HMX interface under the given sliding contact conditions has not been obtained by experiments or simulations at this moment, but it will be one of future studies to address the critical frictional conditions for possible explosion of β-HMX.
Previously, numerous studies have demonstrated that in humid air, the adsorbed water impinging for the gas phase can participate in the friction process and contribute to the tribological behavior of crystalline materials (such as silicon and copper), especially when the water-enhanced adhesion force at nanoscale is comparable with the normal load [50][51][52]. In the present study, the soft (110) plane show wider damage than the harder (011) plane (Fig. 5) and no evolution of chemical structure of wear debris and scratched area is found (Fig. 10), indicating that it is the mechanical effect, not the water-induced mechanochemical effect, that governs the friction process of β-HMX surface. Although the mechanochemical effect on nanoscale friction of β-HMX surface can be ruled out, how the environment-induced mechanical effect will affect the nanoscale friction of β-HMX surface remains elusive. This is because not only the water-induced adhesion force can affect the applied normal load to some extents, the nanomechanical properties of β-HMX surface can also be varied with ambient temperature [27], both the two factors can result in the variation of friction-induced hotspot on β-HMX surface. This can lead to further investigations of the environment effects (such as humidity and temperature) on nanoscale friction of β-HMX surface.

Conclusions
In this study, nanoscale friction behavior of β-HMX crystal is studied with nanoscratch tests under the ramping load mode. The friction coefficient of β-HMX crystal is initially high when no discernible wear is observed, and then it decreases to a stable value which varies from ~0.2 to ~0.7, depending on the applied load, scratch direction, and crystal planes. The β-HMX (011) surfaces show weakly friction and wear anisotropy behavior, which is because the scratch direction of β-HMX (011) surfaces under the given conditions is closed to the slip system and directions. In contrast, the β-HMX (110) surfaces show strongly friction and wear anisotropy behavior where the friction coefficient, critical load for the elastic-plastic deformation transition and plastic-cracking deformation transition, www.Springer.com/journal/40544 | Friction and deformation index at higher normal load are highly depended on the scratch directions. This is because on β-HMX (110) surfaces, either no corresponding slip system at these scratch directions or large difference between the scratch direction and slip direction can cause the substantial plastic and cracking deformation. the Ministry of Education, Southwest University of Science and Technology. He is a candidate for academic and technical leaders in Sichuan Province. His current research interests include nanotribology, ultraprecision machining, surface, and interface technology, and tribology of metal-based composite coatings. He has published more than 70 papers in professional journals. As a group leader, he has undertaken more than 20 research projects.