Nanomechanics of RDX Single Crystals by Force ... - ACS Publications

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Nanomechanics of RDX Single Crystals by Force−Displacement Measurements and Molecular Dynamics Simulations N. Scott Weingarten and Rosario C. Sausa*

Downloaded by MOUNT ROYAL UNIV on August 27, 2015 | http://pubs.acs.org Publication Date (Web): August 25, 2015 | doi: 10.1021/acs.jpca.5b04876

US Army Research Laboratory, ARL-RDRL-WML-B, 4600 Deer Creek Loop, Aberdeen Proving Ground, Maryland 21005, United States ABSTRACT: Nanoenergetic material modifications for enhanced performance and stability require an understanding of the mechanical properties and molecular structure−property relationships of materials. We investigate the mechanical and tribological properties of single-crystal hexahydro-1,3,5-trinitro-s-triazine (RDX) by force−displacement microscopy and molecular dynamics (MD). Our MD simulations reveal the RDX reduced modulus (Er) depends on the particular crystallographic surface. The predicted Er values for the respective (210) and (001) surfaces are 26.8 and 21.0 GPa. Further, our simulations reveal a symmetric and fairly localized deformation occurring on the (001) surface compared to an asymmetric deformation on the (210) surface. The predicted hardness (H) values are nearly equal for both surfaces. The predicted Er and H values are ∼33% and 17% greater than the respective experimental values of 0.798 ± 0.030 GPa and 22.9 ± 0.7 GPa for the (210) surface and even larger than those reported previously. Our experimental H and Er values are ∼19% and 9% greater than those reported previously for the (210) surface. The difference between the experimental values reported here and elsewhere stems in part from an inaccurate determination of the contact area. We employ the parameter √H/Er, which is independent of area, as a means to compare present and past results, and find excellent agreement, within a few percent, between our predicted and experimental results and between our results and those obtained from previous nanoindentation experiments. Also, we performed nanoscratch simulations of the (210) and (001) surfaces and nanoscratch tests on the (210) surface and present values of the dynamic coefficient of deformation friction.

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INTRODUCTION Nanoenergetic materials have fueled a significant scientific and technological interest in recent times because of their use and potential usefulness in many applications, including energy generators for microelectromechanical systems (MEMS), explosive devices, and propellant systems.1−5 Their larger surface-to-volume ratio compared to their bulk counterparts increases the frequency of interfacial chemical and physical interactions, likely influencing their energetic performance, impact sensitivity, and mechanical properties as neat materials or composites. Advances in both nanoscale testing and modeling, along with an increase in computational power and processing speed, provide better opportunity for studying nanoenergetics. Nanomechanic and tribological testing of small-volume samples allows for material characterization and assessment, and the resulting data can be used to test or as input in molecular or meso scale models, aimed at bridging the knowledge base derived from atomic and continuum models. The combination of experimental and modeling efforts provides us with an opportunity to understand the underlying physics of how materials behave during and subsequent to contact, along with key mechanisms governing friction, elastic and plastic deformation, deformation evolution, as well as deriving molecular structure−property−function relations. This understanding is paramount for controlling material behavior © XXXX American Chemical Society

and for design strategies to develop novel structured materials with tailored performance and safety characteristics. Here, we focus on the mechanical and tribological properties of hexahydro-1,3,5-trinitro-s-triazine (RDX) determined by nanoindentation (NI) and molecular dynamics (MD). RDX is a powerful explosive that has been the subject of numerous experimental and modeling studies, including those centering on its crystal structure,6−9 mechanical and tribological properties,10−25 and elastic−plastic behavior under various loading conditions.26−39 Figure 1 shows the molecular and crystal structure of RDX. A molecule of RDX consists of alternating carbon and nitrogen atoms arranged in a six-sided ring. The ring contains three nitro (-NO2) groups, each bonded to one of the nitrogen atoms in the ring, and three pairs of hydrogen atoms, each pair bonded to a carbon atom in the ring. One nitro group is in the equatorial (E) position, and the other two nitro groups are in the axial positions (A), thus forming the EAA conformer in the gas phase. In the condensed phase, RDX exists as several polymorphs with the α-polymorph exhibiting the most thermodynamic stability at ambient pressure and temperature.6,7 X-ray and neutron scattering studies reveal that the α-RDX crystal structure is orthorhombic (space group Received: May 21, 2015 Revised: August 11, 2015

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DOI: 10.1021/acs.jpca.5b04876 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

increasing the probability of hot-spot formation where ignition can occur. MD modeling shows promise for determining the material’s mechanical constants, thus complementing the NI and tribological experiments. Further, the method allows for determining the time evolution of molecular motions and material structural changes with applied forces.47−54 Several representative articles centering on the interaction of an indenter with a film or crystal surface are listed as references. MD studies of RDX are extremely limited however.39 Chen and co-workers investigated NI of the RDX (100) crystal surface as a function of indentation depth using MD.39 Initially, RDX deforms without any increase in thermal energy at depths less than 1.0 nm. However, as the indentation depth increases, the RDX surface temperature increases. They found that the modeled temperature in the damage zone registered at least 200 K higher than outside the deformed zone. Their analysis reveals some RDX molecules displace on the indenter, whereas others decompose near the impact region. Maximum displacement occurred in the (210) surface in the indented region. They reported an H value of 0.391 GPa for small indentation depths, a factor of ∼2 less than reported by Ramos, Hooks, and Bahr. In this paper, we report our combined experimental and modeling study of the α-RDX (210) and (001) crystallographic faces by NI, tribology, and MD simulations. We derive values of hardness, elastic moduli, and dynamic coefficient of friction of deformation (μdef) for these surfaces, and compare them to those published previously. Our results reveal different mechanical behavior for the two surfaces with the (210) surface exhibiting more stiffness than the (001) surface. Further, the (001) surface exhibits isotropic compression during indentation, whereas the (210) surface shows anisotropy during indentation at similar loads. This mechanical behavior depends on the molecular structure of the crystallographic face and the intermolecular interactions occurring during compression.


Figure 1. RDX molecular structure (a) and unit cell structure (b), respectively. The C, H, N, and O atoms are represented by the colors gray, white, blue, and red, respectively. The letters a, b, and c refer to the RDX crystal lengths in the [100], [010], and [001] directions, respectively. The green and pink surfaces correspond to the (001) and (210) planes in Figure 1b.

Pbca) with cell dimensions of a = 1.3182 nm, b = 1.1574 nm, and c = 1.0709 nm. Each unit cell comprises eight RDX molecules.6,8,9 We employ the Miller notation where three integers h, k, and l determine the lattice planes (hkl) and direction [hkl] in the basis of the direct lattice vectors. Nanoindentation is a powerful technique for characterizing a material’s mechanical and tribological properties. Several comprehensive review articles are listed as references.40−45 In this technique, an indenter with loads ranging from nanonewtons to millinewtons penetrates a target material, and its indentation depth is monitored continuously and in situ with nanometer resolution, hence, the term nanoindentation. Nanoindentation allows for material local testing that is not possible using macroscale techniques and, when coupled with in situ scanning microscopy, allows for measuring directly a material’s hardness (H), elastic modulus (E), and coefficient of friction (μ). Although this experimental technique has been applied to many materials, its application to single energetic crystals is extremely limited.11−13,46 Ramos, Hooks, and Bahr reported the direct observation of plastic deformation in RDX crystals by NI.11,12 They performed nanoindents on the RDX (001), (021), and (210) surfaces and determined their values of H, reduced elastic modulus (Er), and maximum shear stress using a conical probe with loads up to 10 mN. Small loads induced elastic-plastic deformation of RDX, whereas large loads caused it to crack. They found the H values to be nearly identical for the surfaces studied, whereas Er depended on the specific crystallographic surface. The (001) surface exhibited the smallest Er value (16.2 GPa), and the (210) surface exhibited the largest Er value (21.0 GPa). Impressions on the (210) and (001) planes showed deformation pile-up features associated with the zone axes of slip planes. More recently, Hudson, Zioupos, and Gill investigated the mechanical properties of different lots of RDX crystals by NI using a Berkovich probe to determine the effects of internal defects on shock sensitivity.13 They found the Er values to depend on specific lot, octahydro-1,3,5,7-tetranitro-1,3,5,7tetrazocine (HMX) impurity, load, and crystal defects. The values ranged from 15.6 to 18.0 GPa at the lowest applied load, 10 mN. Further, they found RDX crystals with many internal defects to have a lower modulus of elasticity than those with few defects. They claim the crystals with lower modulus of elasticity do not dissipate the applied stress as efficiently, thus

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EXPERIMENTAL METHODS We employed the triboindenter (Hysitron TI 950) equipped with a scanning probe microscope for measuring the mechanical and tribological properties of the α-RDX (210) surface. The instrument provides for continuously recording values of applied force, ranging from 100 nN to 10 N with a noise of less than 30 nN, and imposed displacement, down to a few nanometers.55 Further, the instrument allows for in situ imaging and data acquisition and analysis. We performed nanoindents on the RDX surface with a Berkovich diamond probe of ∼100 nm-tip radius using both partial loading indentation and standard nanoindentation. In the former approach, we allowed the indenter to induce a 50 μN force on the RDX surface. Then we withdrew the indenter and subsequently reapplied a higher force. We repeated this cycle 20 times at a force interval of 40 μN to a final force of 1000 μN. The measurement yielded data for determining 20 values of H and Er. In standard NI, we performed 12 individual indents at various RDX surface sites, each at least 10 μm apart from each other and at a peak force of 500 μN. This approach allowed us to obtain a good representation of the surface and avoid any possible effects from nearby indents. We recorded characteristic load− and unload−displacement curves and calculated H and Er values from the unloading portion of the load−displacement curve for both methods. We calibrated and tested the system on B



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MODELING METHODS The MD simulations involve lowering a Berkovich indenter onto the α-RDX (210) and (001) surfaces. Two types of simulations are performed in this study: (1) relatively slow NI, and (2) rapid NI followed by scratch parallel to the surface. Figure 2 shows the initial configuration for the (001) surface

a fused silica quartz standard. Fused silica quartz has a reported H value of ∼9 GPa, an average E value of ∼72 GPa, and a Poisson’s ratio ν of 0.17.56,57 Thus, its Er value should be ∼69.6 GPa using the following expression: 1 = ⌈(1 − ν12)/E1 + (1 − ν2 2)/E2 ⌉ Er

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(1)

where E1 and ν1 represent the Young’s modulus (72 GPa) and Poisson’s ratio (0.170), respectively, of fused quartz, and E2 and ν2 represent those of the diamond probe, E2 = 1141 GPa58 and ν2 = 0.07.59 A series of indents at various contact depths on the quartz surface allowed us to determine the projected indenter area A(hc) as a function of contact depth, h. A best fit of the following equation:55,59,60 A(hc) = C0h2 + C1h + C2h1/2 + C3h1/4 + C4h1/8


+ C5h1/16

(2)

provides the projected area. C0 equals 24.5 for an ideal Berkovich probe, and the fitted parameters C1 through C5 describe deviation from the ideal geometry resulting from tip blunting. We estimated the contact depth employing the following equation: hc = hmax − ε

Fmax S

(3)

where hmax represents the maximum penetration depth, Fmax represents the maximum indentation force, S represents the unloading stiffness, S = dFz/dh, determined from the initial slope of the unloading curve, and ε = 0.75 for a Berkovich probe.59 Analysis of the partial load and standard NI data yielded mean values of Er = 69.4 ± 0.6 GPa and H = 9.23 ± 0.15 GPa, as expected. In the case of the partial load indentation, data acquired using loads less than 200 μN yielded values higher than expected for quartz, and we did not use these data. Such a data pattern is normal and is an artifact resulting from an underestimation of contact area for shallow indents at these loads.55 Quantitative force and displacement data allowed for determining the RDX (210) values of μdef. We performed 4 individual scratches at selected RDX (210) surface sites. For each run, we applied a normal force of 50 μN on the surface and scanned the probe at a velocity of 0.20 μm/s for a lateral distance of 10 μm. The calculated μdef value for each scratch represents the average of ∼2000 values over a 6 μm length. The selected length is the center length of the 10 μm scratch (2 to 8 μm). We performed the experiments at 24 °C and ∼40% relative humidity. Overall, the RDX (210) crystals provided by Dr. K. Ramos of the Los Alamos National Laboratory are of high quality. We used an AFM (MFP-3D, Asylum) with Igor Pro 6 software and the trioindenter for topographical imaging of the RDX (210) crystal surface and surface roughness measurements. Our analyses of several 5 μm2 areas recorded using the AFM yield root-mean-square surface roughness values in the range from ∼800 pm to ∼2 nm. We noted some minor crystal imperfections when we scanned the RDX crystals with the AFM and triboindenter, but the in situ imaging and accurate scanning capabilities of the triboindenter allowed us to locate smooth RDX surface sites free of defects. Raman scattering measurements of the RDX surface before indentation and of the indented and surrounding regions did not reveal any RDX decomposition.

Figure 2. Side (a) and top (b) view of the initial simulation configuration for the (001) surface. Cartesian axes and crystallographic directions are indicated.

orientation and the crystallographic directions relative to the Cartesian axes. Dashed lines are added to the indenter to indicate its edges. Periodic boundary conditions are applied in all three dimensions with a vacuum region in the z-direction, as seen in Figure 2a, so both top and bottom surfaces are free. All simulations are performed in the microcanonical ensemble (NVE) using the LAMMPS simulation software.61 We adopted the interatomic potential developed for HMX by Smith and Bharadwaj (SB),62 which has been shown to be transferable for use in MD simulations of RDX.30,63 The substrate crystal is generated from the experimental unit cell for α-RDX,7 rotated such that the normal to the indented surface is in the z-direction and subsequent scratch is in the x-direction. Extra care must be taken to determine the correct dimensions of the simulation cell to ensure that the crystal is consistent across the periodic boundaries, especially for the (210) surface system. We determined the correct simulation cell dimensions by visualizing the molecular centers of mass, and precisely measuring the repeat distance for all three dimensions. The C


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Figure 3. Typical force vs displacement curve for RDX (210). (inset) Energy spent during indentation (A) and unloading energy (B).

unloading data are fitted to a cubic polynomial. This fitted curve is also used to obtain the values of Fz,max and h at the maximum depth of indentation. The depth of the indenter is determined by subtracting the average z-position of a subset of RDX surface atoms that are positioned away from the indenter from the atomic position of the single atom at the tip of the indenter. In the scratch simulations, we directed the Berkovich indenter into the RDX crystal with a speed of 5 × 10−5 nm/ fs to a depth of ∼1.2 nm, a much larger speed than in the NI simulations. Then we immediately changed the indenter velocity to 1 × 10−5 nm/fs in a direction parallel to the surface. For the (001) surface, the indenter moves in the [100] direction, (as seen in Figure 2), while the motion of the indenter for the (210) surface is in the direction perpendicular to [001]. We aligned the flat side of the Berkovich indenter in the intended scratch direction, as also indicated in Figure 2. The simulation runs for a total of 1.4 ns, resulting in a total scratch distance of 12.0 nm. Once again, we utilize the components of the total force on the atoms in the indenter in the analysis. The z-component represents the normal force, and the x-component represents the friction force; the y-component oscillates around zero.

approximate dimensions of the RDX crystals are 26.0 × 23.0 × 21.5 nm for the (001) surface orientation, and 26.5 × 23.5 × 23.0 nm for the (210) surface orientation. The Berkovich indenter comprises rigid carbon atoms that interact with the atoms in the RDX crystal through the same force field. The size of the indenter is 10.0 × 10.0 nm with a depth of 5.0 nm (see Figure 2). These dimensions result in a total simulation size of ∼1.41 million atoms. The RDX crystal is equilibrated for 50 ps with a time step of 1.0 fs. We found it necessary to avoid the use of a thermostat or barostat during equilibration, instead simulating in the microcanonical ensemble, and assigned velocities to the RDX atoms so that the initial temperature is 300 K. As seen in Figure 2, the indenter rests initially far above the surface to ensure its presence does not affect the equilibration process. The structure of the indentation surface remains very similar to the initial configuration during equilibration. The NO2 groups largely define the surface for both the (001) and (210) systems, and upon completion of the equilibration phase, there is some change in the position and orientation of these NO2 groups relative to the central RDX ring. This results in a slight increase in the disorder at the surface, but no reactions occur; the surface after equilibration consists of complete RDX molecules. After equilibration, atoms within 1.0 nm of the lower free surface (opposite the indented surface) are held fixed for NI and scratch simulations. For the NI simulations, the Berkovich indenter is rapidly lowered from its initial position (as seen in Figure 2) to a position directly above the RDX sample at a speed of 0.001 nm/fs. Then we reduce instantaneously the velocity of the indenter to 1 × 10−6 nm/fs and run the simulation to a final depth of ∼1.5 nm. Note that larger depths would require a wider indenter. Once the indenter reaches the maximum depth, we immediately unloaded it at 1 × 10−6 nm/ fs, the same value as the penetration velocity. We used the total force on the indenter atoms to analyze the simulation results and assumed an ideal Berkovich indenter, A(hc) = 24.5h2. To determine the stiffness, Sz = dFz/dh, the

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RESULTS AND DISCUSSION Nanoindentation. We employed the techniques partial load indentation and standard indentation to determine the H and Er values of the RDX (210) surface. In the partial load approach, we performed a single indent at a selected location and determined many values of H and Er, each value at a different applied force and indent depth. In contrast, in the standard indentation technique we sampled many regions of the RDX surface and determined many single values of H and Er. The former approach reveals the effects of applied force and imposed indent depth on the H and Er values, whereas the latter approach provides for a better representation of the RDX surface. In both techniques, we determined values of H and Er D


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Figure 4. Typical RDX (210) 3D surface indent impression obtained by in situ scanning probe microscopy imaging. (inset) The 2D impression.

using the methods proposed by Oliver and Pharr.59,60 Although RDX deformation during loading is both elastic and plastic in nature, the initial unloading portion of the force-depth curve represents purely elastic recovery. We computed the values of H by dividing the applied load (Fz,max) by the projected contact area, Ac(h), under maximum load

H=

Fz,max Ac(h)

(4)

and the values of Er by the following equation:

Er =

reported by Ramos and co-workers,11 suggesting their RDX indents resulted in more plastic deformation compared to our indents. Unrecognized experimental artifacts can bias the measured values. Material pileup during the indentation process leads to an overestimation of material properties. This occurrence depends on the experimental conditions. Under our conditions, topographical analyses of our indent impressions reveal RDX pileup of ∼1.5%, as determined from the height of the pileup and indentation depth. Also, we note our topographical images do not reveal any visible surface cracks under the present conditions. The absence of observed cracks is not too surprising because we induced our indents with lower force per crosssectional areas than those used in previous studies. The loading−unloading curve exhibits small discontinuities or “staircases”, particularly near 55 and 65 nm, as shown in Figure 3. These discontinuities result from discrete elastic deformation (regions of positive slope) and plastic deformation (horizontal lines or displacement bursts commonly referred to as “pop-ins”) during indentation.11,45 The small discontinuities occur at loads of ∼125 and 175 μN with a corresponding displacement of ∼5 nm, and reflect single slip processes during indentation. The underlying mechanisms of these processes are the subject of future studies. Figure 5 shows RDX (210) values of H and Er as a function of applied force using partial loading NI. Our applied force ranged from 50 to 1000 μN, and the corresponding indenter penetration depth ranged from ∼18 to 200 nm. The data for forces less than 200 μN are not presented because they are unreliable due to an overestimation of contact area related to the indenter and contact depth. We found a similar behavior with fused silica quartz. On the basis of our partial load results, we used a force of 500 μN for the standard indents. This force allows the indenter to reach depths over 100 nm for accurate determination of the contact area and yields clean indents with minimum perturbation in the surrounding site. Statistical analyses of the partial load data yield mean and standard

π 2β

64

Sz Ac(h)

(5)

where Sz represents the stiffness, and β represents the indenter shape constant, 1.000 for a hemispherical tip and 1.034 for a Berkovich tip.64 The NI of RDX results in both elastic and plastic deformation under our experimental conditions. Figure 3 shows a characteristic loading−unloading curve obtained by monitoring continuously both the applied force and imposed depth of penetration into the (210) surface, and Figure 4 shows the resulting indent impression. During indentation, molecular crystals undergo elastic deformation, plastic deformation, or a combination thereof. The elasticity index, α = Ae/(Ae + Ap), defines RDX’s elastic−plastic behavior during indentation. In the above expression, Ap and Ae refer to the values of the respective force−displacement integrals (areas) of the loading and unloading curves. Their sum represents the total work during indentation, whereas their difference represents the irreversible work. An α value of 1 suggests the material is fully elastic, whereas a value of 0 suggests the material is fully plastic. Our analysis yields a value of α = 0.24 using Ae and Ap values of ∼6.9 × 10−12 J and ∼2.2 × 10−11 J, respectively, suggesting the indentation of the RDX (210) surface is mostly plastic under our experimental conditions. For comparison purposes, we estimate a value of α ≈ 0.15 from the RDX (210) indentation E


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Figure 5. Experimental RDX (210) hardness (upper) and reduced modulus (lower) as a function of probe force.

deviation values of H = 0.810 ± 0.047 (1SD) and Er = 22.8 ± 0.8 (1SD) GPa. Sample surface roughness, microstructural inconsistencies, and interference effects from previous indents may influence the outcome of the NI measurements. Thus, we tested various surface locations as to avoid these potential problems and to obtain a good representation of the RDX surface. We performed 12 indents at various RDX (210) surface locations for standard NI using an applied force of 500 μN, on the basis of our partial load NI results. Statistical analyses of the data yield mean and standard deviation values of H = 0.802 ± 0.022 (1SD) GPa and Er = 23.1 ± 0.4 (1SD) GPa. The median values of H = 0.790 GPa and Er = 23.1 GPa are nearly identical or identical to their respective mean values, indicating the mean values are not influenced by extreme values. Figure 6 presents both box plots and histograms of the H and Er experimental data for both partial load and standard indentation. The figure reveals the H values range from 0.732 to 0.911 GPa, whereas the Er values range from 21.3 to 24.1 GPa. On the basis of Tukey’s method of leveraging the interquartile range, values not in the regions of 0.723 < H < 0.885 and 21.1 < Er < 24.7 are considered extreme values. Thus, we exclude the two values of H = 0.911 and H = 0.903 GPa from subsequent statistical analysis. Unlike the H data, the Er data do not contain any extreme values. Statistical data analyses yield mean and standard deviation values of H = 0.798 ± 30

Figure 6. Box plots and histograms of the RDX (210) hardness (A) and reduced moulus (B) experimental data.

GPa and Er = 22.9 ± 0.7 GPa. Using the standard error of the H or Er mean, we calculated 95% confidence intervals, which contain the “true” sample mean. These intervals are (0.786− 0.811 GPa) for H and (22.6−23.2 GPa) for Er. We list our RDX (210) H and Er values in Table 1. These values agree well with the H = 0.672 ± 0.035 GPa and Er = 21.0 ± 0.6 GPa values reported by Ramos, Hooks, and Bahr.11 Previous reported H and Er values of RDX crystals with randomly oriented crystallographic faces range from ∼0.235 to 0.700 GPa and from ∼13 to 21 GPa, respectively.10−14 The discrepancies in the H and Er values determined among research groups stem in part from the inaccurate determination of indent area. We eliminate this parameter from eqs 4 and 5 by considering the ratio δ = √H/Er and compare our results to F


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The Journal of Physical Chemistry A Table 1. Experimental and Modeled Hardness and Reduced Modulus of the RDX (210) and (001) Surfacesa experiment

model previous resultsb

present results RDX

H

Er

√H/Er × 10−2

H

(210) (001) RDX

798 ± 30

22.9 ± 0.7

3.91

672 ± 35 615 ± 35

Er 21.0 ± 0.6 16.2 ± 1.0 previous resultsc 16.6−18.0

440−543

present results √H/Er × 10−2 3.90 4.84

H

Er

√H/Er × 10−2

1.060 1.050

26.8 21.0

3.84 4.88

4.00−4.09

The symbols H and Er are expressed in GPa, and √H/Er is expressed in (GPa)−1/2. bResults reported in ref 11 and in ref 13. cResults reported in ref 13. The authors obtained the RDX from Dyno Nobel, now Chemring Nobel AS, and characterized it as having “low internal defects” with an HMX impurity of 0.02%. The effects of NI on the crystallographic faces are not reported. We calculated the H values from their reported indentation stiffness data. The authors obtained the low H and Er values using 10 mN loads and the high values using 200 mN loads.


a

those published previously. The physical meaning of this parameter relates to the resistance to plastic indentation.65,66 The values of δ, along with the H and Er values, are listed in Table 1. The table reveals that our RDX (210) value of δ = 3.91 × 10−2 compares remarkably well to the value of 3.90 × 10−2, which we calculate for the same crystallographic surface from the results of Ramos and co-workers,11 and differs only by 2 to 5% with the values we calculate using the NI results of Hudson and co-workers.13 This excellent agreement is noteworthy considering the experimental uncertainties and the Er dependence on crystallographic surface, as we will discuss below and in the Modeling Section. We calculated the Er value for a specific [hkl] direction for RDX from the following expression:67 1 = l14S11 + l 2 4S22 + l3 4S33 + l12l 2 2(2S12 + S66) E[hkl] + l 2 2l32(2S23 + S44) + l12l32(2S13 + S55)

(6)

where l1, l2, and l3 represent the direction cosines between [hkl] and the unit vectors [100], [010], and [001], and Sij represent the elastic compliance constants of RDX, which we compute from reported isothermal second-order elastic constants converted from ambient isentropic values by Clayton and Becker.29 The constants comprise two data sets reflecting the softest and stiffest reported experimental values, obtained by resonant ultrasonic (RUS) and Brillouin scattering methods, respectively.15,16 The RUS values are in reasonable agreement with the more recent RUS values reported previously by Schwarz and co-workers, and they are in line with those obtained by Sun and co-workers using impulsive stimulated thermal scattering.17,18 We note recent Brillouin measurements by Bolmer and Ramos show agreement with previous experimental results, except those from the previous Brillouin scattering measurements.19 Hooks and co-workers compare the reported experimental elastic constants of RDX and evaluate the sources of errors in a critical and comprehensive review published recently.68 Our experimental Er value of the RDX (210) surface is consistent with the value we calculate using the compliance constants of RDX determined from RUS and Brillouin scattering data. Figure 7 reveals RDX’s three-dimensional (3D) dependence of E with crystallographic direction obtained with eq 6 using the Sij values listed in Table 2. The elastic anisotropy in RDX is clearly visible from Figure 7, as the degree of deviation from a spherical geometry indicates the degree of anisotropy. Our calculations for the (001) surface yield respective E values of 15.4 and 18.0 GPa (Er = 15.7 GPa and Er = 18.3 GPa) using RUS and Brillouin data, whereas those for

Figure 7. Directional dependence of Young’s modulus of RDX calculated using compliance constants derived from RUS data (upper) and Brillouin data (lower).

the (210) surface yield respective E values of 19.2 GPa and 23.3 GPA (Er = 20.6 GPa and Er = 24.9 GPa) using RUS and Brillouin data. These values are listed in Table 3. Our experimental Er = 22.9 GPa value for the (210) surface lies G


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The Journal of Physical Chemistry A Table 2. Elastic and Compliance Constants of RDX RUS


Brillouin

elastic constants

valuesa (GPa)

compliance constants

C11 C22 C33 C12 C13 C23 C44 C55 C66

24.56 18.85 17.33 7.61 5.30 5.24 5.15 4.06 6.90

S11 S22 S33 S12 S13 S23 S44 S55 S66

valuesb ( × 10−3 (GPa−1)

elastic constants

values (GPa)a

compliance constants

47.96 63.72 64.93 −16.7 −9.62 −14.2 194 246 145 valuesb ( × 10−3 (GPa−1)

C11 C22 C33 C12 C13 C23 C44 C55 C66

36.48 24.49 20.78 0.90 1.26 8.16 11.99 2.72 7.68

S11 S22 S33 S12 S13 S23 S44 S55 S66

27.48 46.99 55.45 −0.52 −1.46 −18.42 83.40 368 130

a

Isothermal, second-order elastic constants of RDX converted from ambient isentropic values reported in reference by Clayton and Becker,29 computed from previous reported values obtained from RUS15 and Brillouin scattering data.16 bCompliance values calculated from elastic constants by matrix inversion.

almost midpoint between the values we calculated from RUS and Brillouin data. Our analysis suggests the original Brillouin data reflects an RDX reduced modulus that is most likely too high, whereas the RUS data reflects one that is probably too low. We performed MD simulations of NI of both the RDX (001) and (210) surfaces. Data points corresponding to instantaneous calculations of force and indent depth are plotted in Figure 8 for both surface systems. Data points for depths less than 0.3 and 0.5 nm for the (100) and (210) surfaces, respectively, are not shown because the force on the indenter is negative, indicating an attractive force with the substrate. The loading and unloading portions of the data are fit separately to cubic polynomials, and values of α, H and Er are determined similar to the experimental procedure. Our MD simulations predict respective elastic and plastic energies of ∼1.2 × 10−17 and 2.8 × 10−17 J for (001) surface and ∼1.0 × 10−17 and 2.3 × 10−17 J for the (210) surface. These energies yield an α value of ∼0.30 for both surfaces, 25% greater than the experimental value, suggesting the indentation process is somewhat more elastic under the modeled conditions compared to the experimental

Figure 8. Modeled loading and unloading curves for the (a) (001) surface and the (b) (210) surface. Data points represent instantaneous calculations of force and depth. Cubic polynomial curves are shown, which were fitted separately to the loading and unloading portions of the data set.

conditions. We also did not observe a temperature increase, most likely because of the shallow indentation depth. The resulting H values are 1.050 GPa for the (001) surface and 1.060 GPa for the (210) surface. Both values are statistically equivalent because of the modeled uncertainty, suggesting H is independent of crystallographic surface. Our calculations yield Er values of 21.0 and 26.8 GPa for the respective RDX (001) and (210) surfaces. We list the predicted H and Er values, along with experimental values in Table 1. Unlike our predicted H values, our predicted Er values compare well with the experimental values. Further, they agree reasonably well with the values we calculate using RUS and Brillouin data. Our

Table 3. RDX Er Values (GPa) Oriented for Indentation on (001) and (210) Surfacesa experiment c

(001) (210)c

RUS

Brillouin

present

previousb

model

15.7 (E = 15.4) 20.6 (E = 19.2)

18.3 (E = 18.0) 24.9 (E = 23.3)

22.9 ± 0.7

16.2 ± 0.6 21.0 ± 1.0

21.0 26.8

a

Obtained by NI and MD simulations and by using eqs 6 and 1. bResults reported in ref 11. cCalculated Er values using indenter values of Ei = 1141 GPa and νi = 0.07 and RDX E values derived from eq 6 and calculated RDX Poisson values of 0.18 and 0.29 for the (001) and (210) surfaces, respectively. H


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profiles show a region of nearly zero displacement near the bottom of the simulation region, indicating that the sample is sufficiently large, and the effect of the bottom fixed atoms on the results are negligible. The displacement of atoms below the indenter in the (001) system is fairly localized, and the response is symmetric. In contrast, the displacement is asymmetric for the (210) surface, with those atoms to the left of the indenter having been displaced more than those to the right. Atoms that are not directly under the indenter have a larger displacement for the (210) system, indicating that the angled lattice planes in the (210) system allow the horizontal loading force of the indenter to be transmitted vertically. Figure 9c,d shows the atomic positions of the nitrogen and carbon atoms for the same configuration, oxygen and hydrogen atoms having been removed from the image for clarity. It is clear from the figures that rearrangement of the molecules directly under the indenter in the (210) system occurs at greater depths than for the (001) system. This accounts for the higher reduced elastic modulus observed for this surface system. In both systems, we did not observe plastic slip, which would occur at larger indentation depths, as observed in prior simulation studies of RDX NI.39 The RDX molecular configuration of the crystallographic surface determines to a large extent the Er value of RDX and the rearrangement and deformation of RDX molecules with applied force. Figure 10 shows the molecular configuration of

simulations captured the larger reduced elastic modulus for the (210) system compared to the (001) system. Indentation depth and contact area are two key differences between the MD simulations and the experiment and thus require care in making direct comparisons between the two. The tip angle of a Berkovich indenter is relatively large (total included angle of 142.3°), which results in shallow indentation depths in the MD simulations. Hardness is expected to decrease at larger indentation depths, which could account for some of the discrepancy in those results. In addition, the estimation of the experimental area contributes to the experimental uncertainty. Once again, we use the ratio √H/Er, which is independent of area, to compare the predicted values to the present and past experimental values. As seen in Table 1, our predicted √H/Er value of 3.84 for the (210) surface is nearly the same as those we derive from the experimental data. Similarly, our predicted √H/Er value of 4.88 for the (001) surface compares favorably to the (001) value of 4.84 we calculate from published data. Our MD simulations show unequivocally that the Er value of RDX depends on crystallographic surface. The simulations are performed such that the final depth of the indenter is the same in both the (001) and (210) systems (∼1.5 nm), allowing for the direct comparison of forces between the two systems. The indenter very rapidly reaches the final depth, and fluctuations in the depth measurement dissipate as the simulation progresses. The predicted Er (210) value is ∼27% greater than the Er (001) value, in excellent agreement with experiment (∼23%). Further, the predicted RDX (210) and (001) results are in line with those we derive using RUS and Brillouin scattering data (see Table 3). Er (210) > Er (001) for both data sets, and the percent difference ranges from ∼24 to 28%. Figure 9a,b shows a cross section of the two simulations at an indentation depth of 1.5 nm, with atoms colored according to the magnitude of the displacement from their initial position (the direction of the x-axis is also indicated). The displacement

Figure 10. Molecular structure of RDX (001) surface oriented for indentation (a), (210) surface oriented for indentation (b), side view of (001) surface before indent (c), and side view of (210) surface before indent (d).

the RDX (001) and (210) surfaces oriented for indentation. The RDX molecules form a zipperlike pattern with intertwining NO2 groups between the RDX rings. The NO2 groups are oriented axially in the (001) configuration. As the indenter applies a force on the (001) surface, the rings relieve the stress by absorbing most of the energy. The NO2 groups bound to the rings move or deform more readily than the rest of the molecule. The repulsive NO2 interactions with other NO2 groups stymie the motion and deformation of the RDX molecules. This restricted motion, along with limited

Figure 9. Final predicted configuration of RDX indentation of the (001) surface (a) and (210) surface (b) with atoms colored according to the displacement from their equilibrated position. (c, d) The final RDX indentation of the (001) and (210) surfaces, respectively, at 1.5 nm. The oxygen and hydrogen atoms are excluded from the images for clarity. I


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Figure 11. A representative RDX (210) scratch image recorded by in situ scanning microscopy. (inset) The corresponding scratch depth profile along the scratch direction near 2 μm.

and the coefficient of deformation or “ploughing” friction (μdef) equals the lateral force (Fx) divided by the normal force (Fz).

deformation of the rings, assists the crystal back to its original configuration once the applied force is removed. The induced stress is isotropic and propagates in the direction of the applied force in the (001) configuration. In contrast, the RDX rings with CH2 groups are angled with respect to the indenter in the (210) configuration, as shown in Figure 10b. The NO2 groups are not as rotationally restricted as in the (001) configuration, and thus the RDX molecules experience more skewed ring motion and deformation, accounting for the higher Er (210) value compared to the Er (001) value. The induced stress propagates along the angled rings, causing asymmetric displacement of the deformed molecules in the (210) configuration, unlike the (001) configuration. Nanoscratches. We performed nanoscratch tests on the RDX (210) surface to determine the dynamic coefficient of friction due to deformation, μdef. Figure 11 shows a typical image produced by scratching the (210) surface at a rate of ∼0.2 μm/s for a length of 10 μm. Bowden and Tabor showed that adhesion and deformation contribute to the friction between two surfaces in contact moving tangentially to the contact plane.69 The coefficient of friction may be expressed as μ = μadh + μdef

μdef =

(9)

We monitored the normal force, normal displacement, lateral force, and lateral displacement as a function of time and present a plot μdef as a function of lateral distance in Figure 12. An average of 2000 measurements over a length of 6 μm yields a μdef value of 0.293 ± 0.012, statistically equivalent to the values obtained from our analyses of 3 other RDX scratches. The coefficient of deformation friction between the RDX (210) surface and diamond has not been reported previously. We note the coefficient of friction of RDX sliding on various materials, including another RDX surface, has been reported.25,70 Amuzu and co-workers reported the coefficient of friction of RDX sliding against glass depends on the load and whether the sliding causes elastic or plastic contact.70 They measured a value of ∼0.35 for loads >50 mN and a sliding velocity of ∼0.2 mm/s. Under these experimental conditions, they characterized the contact as plastic. In contrast, they found the RDX coefficient of friction to decrease with load for loads 1 at loads 1.0 for both surface systems, much larger than the experimental values. The indenter in the simulations is a rigid structure, which may result in larger forces in the direction opposite to the indenter’s motion. Also, the discrepancy between simulation and experiment may be a result of the small force applied and large velocity of the indenter (∼10 m/s). We note Chang and co-workers reported a velocity effect on the coefficient of friction of alkanethiol chemisorbed on a gold surface in their MD nanoscratch simulations.71 Their calculations revealed the coefficient of friction increased from ∼0.92 at 100 m/s to ∼1.3

Figure 14. Final snapshots of the (a) (001) surface and (b) (210) surface systems.

along the top surface. Both systems show a large number of molecules that have climbed up the sides of the indenter, similar to that predicted for the RDX (100) by Chen and coworkers.39 We note this effect is less pronounced in the (210) surface compared to the (001) surface. This accounts for the slightly lower friction coefficient for the (001) surface, as it is easier to drive the molecules that have climbed the indenter than if they had remained near the surface. Figure 15 shows a cross section of the final snapshot; hence, the indenter can be seen in full (as compared to Figure 14). Only carbon atoms are shown, and they are colored by displacement from their original positions. Just as in the indentation simulations, in both cases we do not observe plastic slip, and the crystal remains intact far from the scratched surface. Although not clear from the figure, there is no trench left behind the indenter. There is some disorder in the molecules that fill in behind the indenter, and that disorder penetrates to greater depths in the (210) system.

Figure 13. x-component (a) and z-component (b) of the force on the indenter as a function of time for the (001) surface system in red and (210) surface system in blue. K


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(3) Siegert, B.; Comet, M.; Spitzer, D. Safer Energetic Materials by a Nanotechnological Approach. Nanoscale 2011, 3, 3534−3544. (4) Ghoniem, N. M.; Busso, E.; Kioussis, N.; Huang, H. Multiscale Modeling of Nanomechanics and Micromechanics: an Overview. Philos. Mag. 2003, 83, 3475−3528. (5) Martirosyan, K. Nanoenergetic Gas-Generators: Principles and Applications. J. Mater. Chem. 2011, 21, 9400−9405. (6) McCrone, W. C. Crystallographic Data. 32. RDX (Cyclotrimethylenetrinitramine). Anal. Chem. 1950, 22, 954−955. (7) Hunter, S.; Sutinen, T.; Parker, S.; Morrison, C.; Williamson, D.; Thompson, S.; Gould, P.; Pulham, C. Experimental and DFT-D Studies of the Molecular Organic Energetic Material RDX. J. Phys. Chem. C 2013, 117, 8062−8071. (8) Choi, C.; Prince, E. The Crystal Structure of Cyclotrimethylenetrinitramine. Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. 1972, B28, 2857−2862. (9) Singh, M.; Kaur, S. Crystal Structure of Cyclonite. Curr. Sci. 2000, 78, 1184−1185. (10) Elban, W. L.; Armstrong, R. W.; Yoo, K. C.; Rosemeier, R. G.; Yee, R. Y. X-ray Reflection Topographic Study of Growth Defect and Microindentation Strain Fields in an RDX Explosive Crystal. J. Mater. Sci. 1989, 24, 1273−1280. (11) Ramos, K.; Hooks, D.; Bahr, D. Direct Observation of Plasticity and Quantitative Hardness Measurements in Single Crystal Cyclotrimethylene Trinitramine by Nanoindentation. Philos. Mag. 2009, 89, 2381−2402. (12) Ramos, K. J.; Bahr, D. F.; Hooks, D. E. Defect and Surface Asperity Dependent Yield During Contact Loading of an Organic Molecular Single Crystal. Philos. Mag. 2011, 91, 1276−1285. (13) Hudson, R.; Zioupos, P.; Gill, P. Investigating the Mechanical Properties of RDX Crystals Using Nono-Indentaion. Propellants, Explos., Pyrotech. 2012, 37, 191−197. (14) Elban, W. L.; Hoffsommer, J. C.; Armstrong, R. W. X-Ray Orientation and Hardness Experiments on RDX Explosive Crystals. J. Mater. Sci. 1984, 19, 552−566. (15) Haussühl, S. Elastic and Thermoelastic Properties of Selected Organic Crystals: Acenaphthene, Trans-Azobenzene, Benzophenone, Tolane, Trans-Stilbene, Dibenzyl, Diphenyl Sulfone, 2,2′-Biphenol, Urea, Melamine, Hexogen, Succinimide, Pentaerythritol, Urotropine, Malonic Acid, Dimethyl Malonic Acid, Maleic Acid, Hippuric Acid, Aluminium Acetylacetonate, Iron Acetylacetonate, and Tetraphenyl Silicon. Z. Kristallogr. 2001, 216, 339−353. (16) Haycraft, J.; Stevens, L.; Eckhardt, C. The Elastic Constants and Related Properties of the Energetic Material Cyclotrimethylene Trinitramine (RDX) Determined by Brillouin Scattering. J. Chem. Phys. 2006, 124, 024712. (17) Schwarz, R. B.; Hooks, D. E.; Dick, J. J.; Archuleta, J. I.; Martinez, A. R. Resonant Ultrasound Spectroscopy Measurement of the Elastic Constants of Cyclotrimethylene Trinitramine. J. Appl. Phys. 2005, 98, 056106. (18) Sun, B.; Winey, J.; Hemmi, N.; Dreger, Z.; Zimmerman, K.; Gupta, Y.; Torchinsky, D.; Nelson, K. Second-Order Elastic Constants of Pentaerythritol Tetranitrate and Cyclotrimethylene Trinitramine Using Impulsive Stimulated Thermal Scattering. J. Appl. Phys. 2008, 104, 073517. (19) Bolme, C.; Ramos, K. The Elastic Tensor of Single Crystal RDX Determined by Determined by Brillouin Scattering. J. Appl. Phys. 2014, 116, 183503. (20) Ye, S.; Tonokura, K.; Koshi, M. Theoretical Calculations of Lattice Properties of Secondary Explosives. J. Japan Explos. Soc. 2002, 63, 104−115. (21) Gallagher, H. G.; Halfpenny, P. J.; Miller, J. C.; Sherwood, J. N.; Tabor, D. Dislocation Slip Systems in Pentaerythritol Tetranitrate (PETN) and Cyclotrimethylene Trinitramine (RDX) [and Discussion]. Philos. Trans. R. Soc., A 1992, 339, 293−303. (22) Halfpenny, P. J.; Roberts, K. J.; Sherwood, J. N. Dislocations in. Energetic Materials. J. Mater. Sci. 1984, 19, 1629−1637.

Figure 15. Cross section of the final snapshot with only carbon atoms shown, colored by displacement from original positions. (a) (001) and (b) (210) surface systems.


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CONCLUSION We have performed a combined experimental and modeling study of the nanomechanics and tribology of the RDX (001) and (210) surfaces by indentation and scratch tests and by molecular dynamics simulations. The respective experimental H and Er values of the RDX (210) surface are ∼0.800 and 22.9 GPa, which agree well with values reported previously. Our predicted H and Er values from the MD simulations for the (001) surface are 1.050 and 21.0 GPa, respectively, and those for the (210) surface are 1.160 and 26.8 GPa, respectively. We have used the parameter √H/Er, which is independent of contact area, for data comparison, and found a difference of only a few percent among predicted and experimental values reported herein and previously. Our simulations reveal the H values of the (210) and (001) surfaces are the same statistically, whereas the Er value of the (210) surface is ∼27% greater than that of the (001) surface. Snapshots of the simulations at the maximum depth of indentation show the (001) surface compresses symmetrically, predominantly normal to the horizontal planes, compared to the (210), which compresses asymmetrically along the angled planes. The origin of this phenomenon relates to the differences in molecular configuration of the two surfaces. MD simulations of nanoscratching the (210) and (001) surfaces yield μdef values of 1.3 and 1.1, respectively, in contrast to our experimental value of 0.29 for the (210) surface. This discrepancy may result from the large velocity of the indenter compared to the experiment.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Drs. D. Taylor and K. Strawhecker of the Army Research Laboratory (ARL) for many helpful discussions, and Dr. K. Ramos of the Los Alamos National Laboratory for providing us with the RDX crystals. Computer support was provided by the DOD Supercomputing Resource Centers at ARL and AFRL. Support from the ARL Multiscale Response of Energetic Materials Program is also gratefully acknowledged.

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REFERENCES

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