Al Composites. Part 2: Shock-Induced

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Shock Loading of Granular Ni/Al Composites. Part 2: Shock Induced Chemistry Mathew J Cherukara, Timothy C. Germann, Edward M. Kober, and Alejandro Strachan J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b11528 • Publication Date (Web): 09 Mar 2016 Downloaded from http://pubs.acs.org on March 14, 2016

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The Journal of Physical Chemistry

Shock Loading of Granular Ni/Al Composites. Part 2: Shock Induced Chemistry

Mathew J. Cherukara1,2,*, Timothy C. Germann2, Edward M. Kober2 and Alejandro Strachan1,†

1School

of Materials Engineering and Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907, USA

2Theoretical

Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA

ABSTRACT We use molecular dynamics simulations to characterize the chemical processes resulting from the shock compaction of a loosely-packed granular reactive composite of Ni and Al. For all of the impact strengths studied (with piston velocities up in the range 0.5–2.5 km/s), we find that reactions initiate in the vicinity of the collapsed pores. For the lowest impact velocities (up≤0.75 km/s), the reactions that initiate at the collapsed pores subsequently slow down as thermal transport dissipates the initial temperature excursion and outpaces the exothermic energy release rate. At intermediate impact velocities (up~1.0 km/s), the localization of thermal kinetic energy is sufficient to establish a reaction rate that is self-sustaining

*

Current address: X-ray Sciences Division, Advanced Photon Source, Argonne National Lab, Lemont, IL 60439, USA

†

Corresponding author: [email protected]

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in exothermic energy release and the sample reacts within a few nanoseconds. At the highest impact velocities (up≥1.5 km/s), the localization of translational kinetic energy as well as thermal energy following pore collapse drives the rapid propagation of the reaction from the collapsed pores. Keywords: condensed phase chemistry, nanostructures, nanomaterials, porous materials, materials at extremes

1. INTRODUCTION Intermetallic reactive composites (IRCs), which include the Ni/Al system studied here, are a class of metastable materials that react exothermically under appropriate mechanical or thermal insult. They are of interest for applications where strong localized sources of heat with limited or no volume expansion are required, such as in primers for explosives1, bio-agent defeat2 and thermal batteries3. The ability to tailor the response of these materials by engineering the nanostructure, either through the process of arrested ball milling4–6 or through thin film deposition7,8, is an added benefit in their application. Ball milled composites of Ni/Al are advantageous both in terms of cost and scalability compared to alternative synthesis techniques. However, ball milling results in a complex nanostructured assembly of particles, wherein each particle contains a fine lamellar structure of alternating Ni and Al layers. The period of this nanolaminate structure can vary from a few nm to hundreds of nm. This complex structure with disparate length scales makes predicting the chemical response of these samples impossible without significant experimental calibration.


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The influence of nanostructure on reaction progression in thermally initiated samples is well understood for simple structures like nanolaminates; and both continuum9–12 and MD simulations13–15 have contributed significantly to this understanding. However, the response of mechanically activated granular compacts is significantly more complex, especially for high velocity shock initiation. Shock loading of granular composites results in complex phenomena, such as those described in Part 1 of this paper,16 including the localization of energy as pores collapse. The latter can occur either via plastic deformation for relatively weak shocks, or via material jetting at high shock strengths17,18. These processes make experimental characterization and predictive modeling of these composites very challenging due to the extremely short length (10-100 nm) and time (1-10 ns) scales involved19,20. Atomistic simulations of shock-induced chemical reactions in reactive granular materials have been handicapped by their computational cost, leading to finite size effects21,22, idealized geometries6, and short simulation time scales . In this work, large scale and long-timescale MD simulations are used to follow the chemistry that occurs during and after the propagation of the shock wave through a granular Ni/Al material. We study the evolution of chemistry under increasingly strong loading conditions so that we can define the transition in the void collapse mechanism, reported in Part 1,16 that changes the mechanism of reaction initiation and propagation. The mechanism of void collapse transitions from a plastic deformation mediated process, to pore filling by molten aluminum, and finally atomistic jetting into the pores. We find that this transition in mechanism also leads to porosity



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having an increasing contribution to the kinetics with increasing shock strength. For weaker shocks, the void collapse localizes thermal kinetic energy, while for stronger shocks, there is an additional contribution of active intermixing through the translational kinetic energy. The remainder of this article is organized as follows: Section 2 describes the simulation conditions and analysis techniques to extract local variables of interest. Section 3 discusses the role of porosity on accelerating the mixing process of Ni/Al and relates the inhomogeneity in the sample to different reaction paths followed by the material during the shock loading process. In section 4, we discuss the long time reaction progression following shock compression. Finally, in section 5, we summarize our results and discuss the implications of our study on understanding the influence of defects on energy transfer at the nanoscale.

2. SIMULATION DETAILS 2.1. Model Nanostructure The initial structure for our simulations (with packing fraction of ~63%), see Figure 1 a), consists of 40 columnar grains of Ni/Al laminate with lamellar spacing of ~7 nm and a ~1:1 atomic ratio. The polygonal grains are oriented with the (1-10) direction along the columnar axial direction (out of the page in Figure 1). As explained in detail in Part 1 of this paper16, the faces are chosen by stochastically assigning probabilities inversely proportional to their surface energies. The simulation cell is periodic in all three directions and has dimensions of 320 nm along X and 320 nm along Z, and is 8.6 nm tall in the out-of-plane Y direction. Following the equilibration procedure outlined in Part 1 of this paper, two shock


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waves are introduced by compressing the boundaries along the X direction as shown in Figure 1. These waves meet approximately at the center of the simulation cell and create two rebounding shock waves, which propagate outwards, meeting again approximately at the periodic boundary23,24. During the shock loading of the material, the total kinetic energy (translational and thermal) increases as the shocked material is accelerated towards the center of the cell and heated. After the collision of the initial waves, the re-shocked material has, on average, no translational kinetic energy while the thermal kinetic energy continues to increase. Thus, a minimum in the global kinetic energy occurs when the shock waves reach the periodic boundaries. When this occurs, these shocked samples are then held at constant volume and energy (NVE ensemble) for the remainder of the simulation to study their chemical reaction following the dynamical loading. This technique allows us to extend the timescales of simulation far beyond the time taken for shock propagation.



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Figure 1: a) Initial simulation structure. B) Final compressed state for the Up=2 km/s case. The two colours within in each grain denote Ni (thin bands) and Al (thick bands). Select grains are highlighted in light blue as a visual guide for the net grain translation and deformation process. Adapted from Cherukara, M. J.; Germann, T. C.; Kober, E. M.; Strachan, A. Shock Loading of Granular Ni/Al Composites. Part 1: Mechanics of Loading. J. Phys. Chem. C 2014, 118 (45), 26377–26386

2.2 Local property calculation To extract local averages of the quantities of interest, the system is binned in a twodimensional (X-Z) grid that extends through the thickness of the simulation cell (8.6 nm), with each bin having dimensions of 5 Å x 5 Å. These bins contain ~150 atoms at the initial density, and ~200 atoms at the maximum density for up = 1.5 km/s. A local reaction coordinate (η) is computed using the nickel fraction in each bin as follows: =

2 ∗ ≤ 0.5 2 ∗ (1 − ) > 0.5

where is the fraction of Ni atoms in the bin. This is defined such that η = 0 for regions that are either 0% or 100% Ni, and η = 1.0 for regions that are 50% Ni and 50% Al. Note that this reaction coordinate does not require that each Ni atom have ~50% Al neighbors; such an identification and counting procedure would be computationally intensive. Rather we rely on the upper-bound estimate that the local region contains ~50% Al and ~50% Ni atoms as indicating a high level of


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reaction progress, a metric that can be evaluated simply and quickly. Local temperatures are computed on this same grid after removing the local translation of the center of mass in the manner described previously.16 All simulations were performed using an embedded-atom potential developed by Purja Pun and Mishin25 and the LAMMPS package26,27. The potential was parameterized using the lattice constants and formation energies of several intermetallics, in addition to those of pure Ni and Al, and accurately captures the melting temperatures of Ni, Al, and several of their intermetallic phases. This potential has been extensively used to study the reaction kinetics of Ni/Al reactive intermetallics under extreme conditions of temperature and pressure9,13,28,29.

3. Chemical reactions during shock loading Pore collapse following the passage of a shock is believed to play a key role in energy localization into hot-spots and, consequently, the initiation of chemical reaction.30–34. The mechanism of pore collapse during the shock loading of this granular composite was observed to depend on shock strength, as described in Part 1.16 At low piston velocities (up≤0.5 km/s), pore closure occurs through the plastic deformation of surrounding grains. At intermediate piston velocities, voids are filled by the flow of solid and molten Al (up=0.75 km/s) or pure molten Al (up=1 km/s). At higher piston velocities (1 < up ≤ 2 km/s) jets of molten Al fill the pore during dynamic compression, and for shock strengths with up≥2.0 km/s a mixture of Ni and Al fill the pore in a spray of atoms. The influx of high-velocity ejecta into pores that



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are oriented such that they can give the incoming mass an angular component of velocity leads to the formation of mass flux vortices. This changing mechanism of pore closure plays a key role in the initiation and sustained chemistry as will be described in the following sub-sections. 3.1 Accelerated mixing The immediate effect of the stronger shocks on the reaction progression is two-fold. First, mechanical shear and multiple shock reflections lead to accelerated mixing at the Ni/Al interfaces within grains, in particular within grains from which material flows into pores, see Figure 2 (b)-(d). Second, the flow of high-energy fluid into the pores leads to accelerated mixing processes, with significant intermixing seen even within the short duration of the shock (tens of ps), Figure 2 (e) and (f).


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Figure 2: Evolution of chemistry during shock loading with up=2 km/s. Snapshots of the local reaction coordinate are shown at a) 5 ps, b) 15 ps, c) 25 ps, d) 35 ps, e) 40 ps and f) 45 ps.

Figure 3 shows the state of reaction at the end of the shock compression process for different piston velocities. We find that increasing the piston velocity leads to an increase in the amount of reaction occurring during the passage of the shock; this is despite the net shorter timescales for shock loading with increasing piston velocities. These accelerated mixing processes are driven by the increasingly strong jetting phenomena at higher piston velocities and the subsequent development of flow vortices in the collapsing pores16.



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Figure 3: Extent of reaction at the end of the shock loading process for different piston velocities. a) Up=0.5 km/s, t = 146 ps; b) Up=0.75 km/s, t = 103 ps; c) Up=1.0 km/s, t = 82 ps; d) Up=1.5 km/s, t = 61 ps; e) Up=2.0 km/s, t = 49 ps; and f) Up=2.5 km/s, t = 41 ps. 3.2 Alternate reaction paths We now explore whether the change in mechanism of pore collapse with increasing shock strength affects the subsequent chemical response of the samples. Specifically, we investigate the effect of the development of fluid vorticity on the convective mixing of Al and Ni and on the chemical reaction path. To do this, we first spatially bin the sample and extract local temperatures and reaction coordinates as described in the methods section of this paper and in Part 1. We then examine the


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distribution of states of temperature and reaction coordinate occupied by the sample. Figure 4 shows heat maps of the distribution of temperature-reaction coordinates following shock compression for samples loaded at different piston velocities. The color for each temperature-reaction coordinate pair represents the population of that state with the scales shown at the right. The temperature axis has been scaled by the average temperature in the simulation cell for normalization. Also shown in the top panels for each case are the distributions of the scaled temperature alone (after binning).

Figure 4: Temperature-reaction coordinate phase space maps at the end of the shockloading process for different piston velocities. Also shown are the binned local temperature distributions (top panels). The temperature axis is scaled to the average



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temperature in the sample. With increasing piston velocity, the heterogeneity in the sample increases. The times are the same as given in Figure 3. We note that during the adiabatic reaction of nanolaminates previously studied, a uniform temperature distribution is observed throughout the sample, as thermal diffusivity is faster than the mass transport that governs chemical kinetics35–37. This would appear as a distribution of local temperatures independent of reaction coordinate in the heat maps in Figure 4. This is essentially what we observe at low piston velocities (up≤0.5 km/s) where pore closure is primarily through plastic deformation of surrounding grains or through the extrusion of Al into the pore. In this case, the temperature distribution remains largely uniform with the exception of a few outliers, see Figure 4 (a). These points correspond to regions along the surfaces of grains that heat up due to friction against neighboring grains. Interestingly, increasing the piston velocities to 0.75 km/s and 1 km/s, where pore filling occurs through fluid flow16, shows high-temperature tails in the distributions with increasing reaction coordinate. This indicates that faster, mechanicallyinduced, chemistry leads to locally increased temperatures that heat transport is unable to homogenize within the timescales of the shock loading. For even higher piston velocities (up≥1.5 km/s), the simulations reveal new mechanisms for reaction, indicated by changes in the distribution of temperaturereaction coordinate states shown in Figures 4 (d)-(f). These should be attributable to the increasing influence of how the pores collapse. Figure 5 maps the spatial regions in the sample that correspond to the different sections on the reaction


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coordinate-temperature space plots for the sample shocked at 2 km/s, Figure 4 (e). To gain insight into the physical processes corresponding to the reaction states of the system, we divide the reaction coordinate-temperature plot into three regions, as shown in Figure 5. Region B is at relatively low and uniform temperature and is slowly reacting as a thermally-ignited sample would. Figure 5 (b) shows that these slowly reacting regions are quite distinct from the collapsed pores. Region C, shown in Figure 5 (c) shows regions in the sample that experience faster chemical reactions accelerated by mechanical mixing. These regions correspond to the outer extremities of the vortices, where rapid fluid flow erodes the material in the grains surrounding the material, leading to rapid mixing. A yellow arrow shows the suggested reaction path followed by these regions. Finally, region D (all points to the right of the oblique white line) denotes regions in the reaction coordinatetemperature maps that deviate from the conventional processes discussed above and that tend to have high temperatures and low reaction coordinates. Figure 5 (d) shows that these regions correspond to material in the core of the vortices. This material follows a different reaction path, as shown by green arrows in Figure 5(a). The material first heats up rapidly due to mechanical impact and incoming ejecta, but then transfers that heat to, and mixes with, the surrounding grains as it cools down.



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Figure 5: Alternate reaction paths c) and d) possible through porosity inherent in the sample in contrast to the bulk state b). Up was 2.0 km/s for this case. Local temperatures are shown in e).

4. Chemistry following shock loading We now turn our attention to the chemical processes following the passage of the shock waves in the reactive sample. As described in the methods section, after the passage of the reshock, we follow the subsequent evolution of the samples using NVE simulations. This allows us to follow the evolution of chemistry over time with minimal changes in the mechanical state. The simulations indicate three distinct


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regimes of reaction propagation as a function of impact strength, an observation we attribute to the increasing influence of porosity on the reaction propagation through the localization of kinetic energy as described previously16. For the lowest piston velocities (

Al Composites. Part 2: Shock-Induced

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