Al Nanocomposites: Structural Characteristics and

Jan 18, 2017 - It is shown that the effective activation energy (Eef) ranges from 79 to 137 kJ/mol and is directly related to the surface area contact...
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Reactive Ni/Al Nanocomposites: Structural Characteristics and Activation Energy Christopher E. Shuck† and Alexander S. Mukasyan*,†,‡ †

Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, Indiana 46556, United States National University of Science and Technology MISiS, Moscow, 119049, Russia

‡

ABSTRACT: Stochastically structured Ni/Al reactive nanocomposites (RNCs) were prepared using short-term high-energy ball milling. Several milling times were utilized to prepare RNCs with differing internal nanostructures. These internal structures were quantitatively and statistically analyzed by use of serial focused ion beam sectioning coupled with 3D reconstruction techniques. The reaction kinetics were analyzed using the electrothermal explosion technique for each milling condition. It is shown that the effective activation energy (Eef) ranges from 79 to 137 kJ/mol and is directly related to the surface area contact between the reactants. Essentially, the reaction kinetics can be accurately controlled through mechanical processing techniques. Finally, the nature of the reaction is considered; the mechanistic effect of the reactive and three diffusive activation energies on the effective activation energy is examined.

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INTRODUCTION Reactive nanocomposites (RNCs) are a class of high-energy density systems that are safe and can be rapidly converted to usable forms of energy. They are fully dense materials that contain all necessary reactants within individual chemical cells and can be utilized in any environment, including high vacuum, inert atmosphere, and water. RNCs have been proposed for use as solid fuels,1,2 thermo-photovoltaic wave harvesting,3,4 thermo-chemical energy storage,5−7 and secondary energetic carriers,8 among numerous other energetics applications.9−11 Additionally, RNCs are used for synthesis of many advanced and refractory materials through combustion synthesis (CS) approaches. CS has been shown to be a versatile material synthesis method, allowing for production of metals, ceramics, biological materials, and countless other advanced and functional materials.12−15 Understanding chemical reactions is paramount for controlling every productive aspect of RNCs, from energy generation to the synthesis of new materials. Chemical kinetics describe the rate of chemical processes and defines the influence of different conditions on this rate, providing information on the reaction mechanism and sequence of transitions states. Only with statistically proven kinetic data is it possible to model chemical processes in an attempt to effectively control or optimize them. A number of methods have been used to describe the reaction kinetics of gasless reactive systems, including differential scanning calorimetry (DSC) by applying, for example, the Kissinger method for data treatment,16−18 adiabatic electrical thermal explosion (ETE) methods,19,20 and analysis of the temperature time profiles for the combustion wave propagation.21−23 The Ni−Al system is widely used as a model system for gasless high-energy density material. Previous works have been © XXXX American Chemical Society

done to determine the reaction kinetics in this system and their relationship to porosity, particle size, and heating rate, among other factors.17,24−28 Furthermore, it has been shown that highenergy ball milling (HEBM) affects the reaction kinetics of Ni/ Al reactive composites.19,20,29−32 Specifically, it was shown that the activation energy is reduced after HEBM. However, the following questions still remain: (i) Can one precisely control the effective activation energy of the system by changing the HEBM conditions? (ii) What structural parameter is responsible for the enhancement of reaction kinetics? Typically, milling time is used to determine correlations between HEBM and reaction characteristics of the system. This is a problem because milling time is an engineering parameter and is not a fundamental measurement of the system; thus, it does not provide a deep understanding of the phenomenon. The goal of this work is to investigate the reaction kinetics in Ni/Al nanocomposites produced under different HEBM times and to define fundamental correlations between the structural characteristics of the mechanically induced reactive media and measured values of effective activation energy.

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EXPERIMENTAL SECTION Material Fabrication. A 35 g equi-atomic mixture of nickel (Alfa Aesar, 3−7 μm) and aluminum (Alfa Aesar, 7−15 μm) powders was subjected to high-energy ball milling (HEBM), specifically high-energy wet grinding (WG), in a PM100 planetary ball mill (Retsch, Germany) in a steel milling jar. A ball to powder ratio of 5:1 was utilized, with 20 mL of hexane as the process control agent. A rotational speed of 650 rpm was Received: December 7, 2016 Revised: January 15, 2017 Published: January 18, 2017 A

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The Journal of Physical Chemistry A used, with the sun-wheel rotation speed being 1300 rpm. The powders were milled for 5 min increments with 60 min rest times in between, for different total milling times of 10, 20, 30, and 40 min. The powders than were sieved for 24 h to isolate the particles 20−53 μm size range. Structural Characterization. A Nanolab 600 Helios Dual SEM/FIB (FEI, USA) was used for structural characterization of the mechanically induced Ni/Al nanocomposite. The composite Ni/Al particles were sectioned utilizing the slice and view (S&V, FEI) software package. This package was used to collect sets of ∼500 images per particle with ∼10 μm width and depth. The images were taken in series, with 10 nm between each frame. A voltage of 30 kV and milling current of 9.7 pA was utilized. This led to a total analyzed volume of ∼500 μm3 per particle and at least ∼2000 μm3 used for the structural analysis. After image acquisition, the raw data required 3D reconstruction for accurate structural characterization of the composite volume. The FIB/SEM image 3D reconstruction was completed using the AvizoFire (FEI) software package. The series of images were first shear corrected (38°) in the “y” direction, contrast normalized, and then aligned using a leastsquares method. After alignment, the edge artifacts (deposited platinum, particles edges, and steel stub) were removed. The two material phases were separated using contrast thresholding, resulting in a binary representation of the two phases (see ref 33 for more information). Using this approach, numerous structural features can be extracted, including distance maps of one phase to the other, diffusive layer thickness, tortuosity, and porosity, among others. For all of these features, the corresponding probability density functions can also be extracted, leading to a more complete understanding of the quantitative structures. A key structural feature that can also be extracted is the surface area contact (SA) between the phases. This was measured through the complete volume of the binary representations of the Ni and Al phases. The total surface area contact between the phases was normalized by the total volume (SA/V). Reaction Kinetics Characterization. The electrothermal explosion (ETE) method was used to study the reaction kinetics by analyzing temperature time profiles observed during extremely rapid adiabatic heating of the investigated reactive media.19,20 Initially, the RNC particles were cold pressed to 70% theoretical maximum density (TMD) into cylindrical shape with 5 mm diameter and 16 mm height. The ETA-100 apparatus (ALOFT, Inc., Berkeley, CA) operates by rapidly Joule heating the sample until the reaction initiation, at which point the external heating is stopped. The device collects a series of 16 channels worth of data using high-speed photodiodes, with a time resolution of 10−5 s and spaced 1 mm apart, with accurate temperature readings from 900 to 3000 K. The time−temperature profiles are stored, leading to a 3D-thermogram, a space-time−temperature map. An example of the data collected from the typical ETE experiment is shown in Figure 1. Joule preheating occurs until approximately 1100 K, at which point thermal explosion takes place and simultaneously the electric current is ceased. It is important to select the appropriate channels where the explosion begins, channels 7−9 in Figure 1, for example, and use this data for further analysis. A set of time−temperature profiles extracted from channels 7−9 and used in later analysis is shown in Figure 2. For each WG time, the measurement was repeated five times

Figure 1. Sample raw data collected from the ETE experiments. Each channel collects a temperature measurement every 100 μs.

to define the standard deviation of the obtained kinetic parameters.

Figure 2. Time−temperature profiles collected from channels 7−9.

To extract kinetic parameters from the ETE method, the following model must be utilized:34 a cylindrical sample with radius r0 and height l, with initial temperature Tin is exposed to the environmental T0. Heat exchange with the environment follows Newton’s law: q = α(T − T0), where α is the thermal diffusivity, and the heat source is a one-step irreversible reaction (Ni + Al → NiAl). The degree of conversion is characterized by η =

(m0 − m) , m0

where m0 and m are the initial and instantaneous amounts of reactive substance, respectively. The rate of chemical reaction is the following: dη = k 0e(−Ea / RT )·ϕ(η) dt

(1)

where ϕ(η) is a kinetic function, which can be described as ϕ(η) = (1 − η)n with n corresponding to the order of the reaction, and Ea is the activation energy. With the kinetic equation and heat transfer conditions, the following equation describes the thermal explosion process: B

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Figure 3. SEM images of the typical cross sections of the Ni/Al composite particles after 10 (a) and 40 (b) min of WG, as well as corresponding 3Dreconstracted volumes of the 10 (c) and 40 (d) min of WG.

cρ

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⎡ 1 ∂ ⎛ ∂T ⎞ 1 ∂ 2T ∂T ⎜r · ⎟ + = Qk 0e(−Ea / RT )·ϕ(η) + λ ·⎢ · ∂t ⎣ r ∂r ⎝ ∂r ⎠ r 2 ∂ψ 2 ∂ 2T ⎤ + ⎥ ∂z 2 ⎦ (2)

RESULTS Structural Characterization. It was shown that, as milling time is increased, the structural features of the nanocomposites become increasingly fine. After 10 min of WG, there are numerous large chunks of both Ni and Al; these are formed from entire Ni particles being incorporated via cold-welding into the composite (Figure 3a). As milling is continued, these large chunks are replaced with fine lamellar structures of Ni and Al (Figure 3b). After reconstruction of these data, the internal structural features become clearer, as shown in Figure 3c,d, with the nickel volume being represented by the gray, and the Al phase being represented as the intervening void space. It is seen that the increased milling time leads to a more homogeneous internal structure. The lamellae are stochastically and tortuously oriented in the composite. From these structures, it is readily apparent that the increased milling time leads to both finer lamellae and increased SA contact. To normalize and allow for comparison of data, the SA values are normalized by the analyzed volumes, as shown in Figure 4. The SA/V, after 10 min of WG, is ∼0.0032 nm−1, which corresponds to a particle ∼320 nm in size. This is a significant increase in the SA/V ratio as compared to that of the initial mixture where the Al particle size was 7−15 μm and Ni was 3−7 μm. In either case, this is effectively a 10-fold, or higher, reduction in the particle size, or corresponding increase to the SA/V. At the 20 and 30 min WG cases, the SA/V values are 0.0068 and 0.0070 nm−1, respectively. However, after 40 min of WG, the SA/V is further increased to 0.0120 nm−1, which corresponds to a ∼80 nm particle. Reaction Kinetics Characterization. With the data obtained during ETE experiments, the profiles were collected where an accelerating growth rate of temperature with time profiles was observed. From this data, the activation energy and

with initiation conditions: t=0

T = T0

η=0

and the following boundary conditions: ∂T = α(T − Tin) ∂r

r = r0

−λ

r=0

∂T =0 ∂r

z=±

1 2l

T = Tin

Due to Joule preheating, there is a uniform distribution of the temperature along the entire sample volume, leading to the ability to neglect the heat conduction terms (see refs 19 and 20 for details). To extract the kinetic parameters, the selected time−temperature profile is used where there is a positive ∂T , ∂t or acceleration in the temperature growth rate (Figure 2). Apart from this value, all of the other terms are assumed to be constant. Plotting ln ∂T against the inverse temperature, leads ∂t

−E

to a slope of a . Because of the multiple constants included in R the equation, the exact value of k0 cannot be extracted; however, a composite value that depends on k0 can be determined when T → ∞. C

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0.95 were used for further analysis. This approach was applied to evaluate the activation energy for the reactive nanocomposites prepared under different milling time (Figure 6a). It can be seen that the activation energy for the 10 min milling case is 137 kJ/mol. This drops significantly, to 107 kJ/mol, after ten additional minutes of milling. After this initial drop, the next 10 min of milling decreases the measured activation energy to 103 kJ/mol. Finally, after ten more minutes of milling, Eef has significantly decreased again to 79 kJ/mol. This shows that Eef meaningfully depends on the milling time. However, this does not explain the nonuniform decrease that is observed with increasing milling times. The developed 3D-reconstruction method allows for accurate characterization of the SA/V for each of the nanocomposites, as shown in Figure 4. This allows a real relationship between the reaction characteristics of the fabricated Ni/Al nanocomposites and structural parameters, such as SA/V, to be found. When plotting Eef against the measured SA/V, as shown in Figure 6b, one may see that there is linear relationship between these parameters. This observation, as discussed below, is critical to understand the physical nature of the measured activation energy for the investigated reaction.

Figure 4. Dependence of normalized contact surface area between Ni and Al phases as a function of WG time.

pre-exponential factor could be extracted, as explained in Experimental Section. A representative set of raw data is shown in Figure 5. The temperature−time profiles selected from the

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DISCUSSION For purely gas phase reactions, the reactants are completely intermixed and the measured intrinsic activation energy corresponds to the isolated binary collisions of molecules that lead to chemical reaction.35 However, in solid−gas, solid− liquid, solid−solid reactions, it is difficult to obtain the same type of data. For these measurements, different features, such as the structural properties, affect the measured kinetic parameters. Because of this, for gasless reactive systems, the measured and presented activation energies are effective. Figure 6 depicts this phenomenon, showing that within the temperature range 1400−1600 K, Eef is a linear function of the reactant contact surface area. This is a very important conclusion because it suggests that the chemical reaction kinetics can be controlled through processing techniques. For the Ni−Al system, a reaction mechanism was described where an initial solid solution is formed by Ni diffusing into the Al melt, followed by phase formation of solid NiAl grains.36 Considering this, surface diffusion of the Ni atoms along the contact Ni−Al boundary controls the reaction rate. Thus, this reaction is diffusion-limited, which requires that the measured

Figure 5. Arrhenius plot obtained on the basis of a representative set of data collected with the ETE apparatus.

appropriate channels where the explosion reaction was initiated were treated to allow for the effective activation energy (Eef) to be extracted. As explained previously, in this Arrhenius type plot (Figure 5), Eef is related to the negative of the slope divided by the gas constant. For all experiments analyzed, only trials with R2 >

Figure 6. Dependence of effective activation energy of the reaction as a function of milling time (a) and specific contact surface area (b) between Ni and Al phases. D

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Figure 7. Dependence of the pre-exponential factor on the milling time (a) and on the SA/V ratio (b).

however, explains what exactly kef is only that it is highly dependent on the surface area. The opposite scenario does not necessarily imply the opposite case; in the event that there is a dependence of Eef on the SA/V, it does not require that it is a diffusion-limited case, only that diffusion plays a role in Eef. Because kef changes (Figure 7) in all cases, regardless of whether it is reactionlimited, diffusion-limited, or an equal contribution, the only information that can be extracted is from the Eef values. Considering Figure 6, this leads to difficulty in interpreting the results because either scenario, the equal contribution or diffusion-limited, could be applicable. This occurs because, as mentioned above, ED is a composite of the three diffusion activation energies. This means, in the two situations, diffusionlimited and equal contribution, Eef will be functionally dependent on the SA/V. However, there is a way to determine if the conditions are a composite of the two activation energies (ER and ED) or are instead a composite of the three diffusion activation energies (EV, ES, EGB). One would expect that there would be two distinct slopes in Eef against SA/V, the steeper slope would be the composite of the reaction and diffusion, and the shallower slope would be related to the three diffusion activation energies. Because the Eef slope is quite steep over the measured SA/V range, it implies that this case is neither extrema; instead, this is the equal contribution case. This means that kR ≈ kD over the experimental conditions. From Fishbeck’s equation, it is not possible for Ee to exceed either ED or ER, but it gives a lower and upper bound on the possible intrinsic ER and composite ED values. Because diffusion activation energies are typically quite high,39 it is likely that the intrinsic ER value is below 79 kJ/mol and, likewise, the composite ED value is above 137 kJ/mol. The proposed relationship between Eef and SA/V are schematically depicted in Figure 8. Finally, it was shown that reaction initiation in the conventional Ni + Al mixture proceeds once Al melts.38 This effect was explained by a significant increase (2−3 orders of magnitude) in the diffusion rate of Ni into liquid Al compared to standard solid-state volume diffusion. For the same system, as the SA/V is increased, the contributions of surface and grain boundary diffusion, which are again 2−3 orders of magnitude higher than volume diffusion, begin to dramatically increase.39 This means that the solid solution will be able to occur at a significantly reduced temperature, with no requirement of Al melting. This explains why it is possible to initiate the combustion reaction in HEBM materials at a temperature well below the melting point of Al. The increased diffusion rate,

activation energy is effective and should depend on the contact surface area between the reactants. With the experimental methods, along with the previously measured Eef, the pre-exponential factors can be determined. Figure 7a depicts the extracted relative pre-exponential factors for the ETE approach. Similarly to Eef, for the exact same data, Figure 7 shows the effect of surface area on the pre-exponential factor. Understanding that the pre-exponential factor changes, it can be deduced that the measured activation energies are effective, and not truly intrinsic of the reaction. It is possible to understand this through the definition of Eef itself. The following relationship was proposed for solid−gas reactions by Fishbeck but can be extended to solid−solid reactions:37 ⎛ d ln kef ⎞ k E + kDE R ⎟= R D Eef = −R ⎜ ⎝ dT −1 ⎠ kR + kD

(3)

where R denotes reaction and D diffusion. From this, it is possible to see how Eef can be a function of the surface area, even if it is assumed that only the pre-exponential factor can change, and diffusion and reaction activation energies remain constant. With this model, it is possible to see three scenarios: (1) the reaction-limited case, (2) the diffusion-limited case, and (3) the equal contribution case. First, consider a hypothetical case, one where Eef does not appear to change. This would imply that the reaction is at one of the two extrema. However, interestingly enough, this does not imply anything about the relative ER or ED values. The only information we know by the unchanging Eef is that kR ≫ kD or kD ≫ kR, but not specifically which one. However, by considering the fundamental definitions of the two activation energies (ER and ED), it is possible to gain further understanding. ER in that case would be similar to an intrinsic activation energy, one that does not depend on structure but is instead indicative of the required energy to form the new phase. The other case, ED, is actually a composite of three separate activation energies, volume (EV), surface (ES), and grain boundary (EGB) diffusion. In the event that there would be no apparent relationship with Eef and the SA/V, then this would imply that it is not a diffusion-limited case but is instead a reaction-limited case. This must be the case because, as SA increases, the volume diffusion component is reduced compared to both surface and grain boundary diffusion, both of which are orders of magnitude faster than volume diffusion.38 Following the same reasoning, it must follow that kD ≫ kR. Likewise, because of this, it must imply that Eef is essentially ER in this case. None of this reasoning, E

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Competitiveness Program of NUST ‘MISiS’ (No. K2-2016065), implemented by a governmental decree dated 16th of March 2013, N 211. This work was supported by the U.S. Department of State through the Fulbright program.

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Figure 8. Schematic representation of the relationship between the Eef and the SA/V, illustrating the regions where Eef is primarily limited by diffusion, by both diffusion and reaction, and finally by only reaction.

owing to the increased surface contact, leads to the rapid existence of the solid solution, which in turn allows the reaction to proceed.

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CONCLUSION It has been shown that the effective activation energy of the Ni−Al reaction is directly related to its reactant structural properties; for the experimental conditions examined, Eef ranged from 79 to 137 kJ/mol and was linearly related to the SA/V ratio. This means that the reactivity of the system can be directly controlled because it has contributions from the diffusion and intrinsic reaction activation energies. Furthermore, this indicates that previously published activation energies are effective, not truly intrinsic, and are related only to their specific experimental conditions, as such; the structural properties of the reactants must be accurately determined for the measured activation energies to make sense in a broader context. In the diffusion-limited regime, three diffusive rates contribute: volume, surface, and grain boundary diffusion. An increased surface area contact leads to an increase in the contributions of surface and grain boundary diffusion, which are 2−3 orders of magnitude more rapid than volume diffusion. This means the formation of a solid solution can occur at significantly lower temperatures; consequently, this leads to the thermal ignition temperature being lower than the melting point of Al.

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AUTHOR INFORMATION

Corresponding Author

*Alexander Mukasyan. E-mail: [email protected]. ORCID

Christopher E. Shuck: 0000-0002-1274-8484 Alexander S. Mukasyan: 0000-0001-8866-0043 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Department of Energy, National Nuclear Security Administration, under the award number DE-NA0002377 as part of the Predictive Science Academic Alliance Program II. The work was carried out with financial support from the Ministry of Education and Science of the Russian Federation in the framework of Increase F

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