Ni Nanostructured

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C: Physical Processes in Nanomaterials and Nanostructures

Kinetics and Mechanism of Ignition in Reactive Al/Ni Nanostructured Materials Khachatur V. Manukyan, Joshua M Pauls, Christopher E. Shuck, Sergei Rouvimov, Alexander S. Mukasyan, Khachik Nazaretyan, Hakob Chatilyan, and Suren Kharatyan J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b09075 • Publication Date (Web): 30 Oct 2018 Downloaded from http://pubs.acs.org on November 2, 2018

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The Journal of Physical Chemistry

Kinetics and Mechanism of Ignition in Reactive Al/Ni Nanostructured Materials

Khachatur Manukyan1*, Joshua Pauls2, Christopher Shuck2, Sergei Rouvimov3, Alexander Mukasyan2,4 ,Khachik Nazaretyan5, Hakob Chatilyan5, Suren Kharatyan5,6 Nuclear Science Laboratory, Department of Physics1, Department of Chemical & Biomolecular Engineering2, Department of Electrical Engineering3 University of Notre Dame, Notre Dame, Indiana 46556, United States, National University of Science and Technology, “MISIS”, Moscow, Russia4 Laboratory of Kinetics of SHS Processes, Institute of Chemical Physics NAS of Armenia, Yerevan 0014, Armenia5, Department of Chemistry, Yerevan State University, Yerevan 0025, Armenia6

*Phone: +1-574-631-6083, E-mail: [email protected]

Abstract A high-speed electrothermography approach is applied to investigate the mechanism and kinetics for nanostructured Al/Ni foils. Application of the Kolmogorov-Johnson-Mehl-Avrami and adiabatic thermal explosion models reveal that the activation energy for nucleation appears to be much higher than that for reaction. It is shown that formation of intermetallic nuclei is the limiting step that defines the ignition characteristics of the foils at temperatures below 500 K, while the process is reaction limited at higher temperatures. Nucleation is also shown to play an important role during rapid (~10 m/s) propagation of the combustion (reaction) wave along the Al/Ni foils. These findings suggest new approaches for controlling the ignition and combustion processes for nanostructured reactive materials.

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1. Introduction Exothermic reaction in nanostructured Al/Ni materials, such as composite particles and multilayered foils, has been studied extensively1,2,3,4,5,6,7,8,9,10,11,12,13. Localized heating of these materials initiates a self-sustained reaction, which propagates in the form of a reaction wave with high velocity (up to 10 m/s)2,11. The temperature in the combustion front can be as high as 1900 K2,13, with the material reaching its maximum temperature within the span of a millisecond4,14. These unique features make reactive Al/Ni nanostructured materials valuable for the rapid synthesis of intermetallic compounds15,16,17,18,19 and chemical energy storage7,12,20,21,22,23 applications. When joining refractory materials, self-sustaining reactions of sputter deposited Al/Ni foils involving alternating nanoscale metal layers are widely utilized 24,25,26,27. A large number of publications have reported the phase formation mechanism and reaction kinetics in this system12,28,29,30,31,32,33,34,35. The majority of these works utilized differential scanning calorimetry (DSC) coupled with investigation of the reaction product features to identify the phase formation sequence. DSC measurements at different heating rates were also used to extract the activation energies of formation for various intermetallic phases. It was demonstrated that the combustion characteristics and phase formation sequence depends on the microstructure of these reactive materials. For example, the reaction in ball milled Al/Ni nanocomposites can be triggered as low as 500 K12, which is significantly below the reaction onset temperature (912 K; eutectic point) of conventional micrometer-scale Al+Ni mixtures36. Detailed studies have identified two different microstructures for such nanocomposites: coarse (micrometer-size Ni particles embedded in Al matrix) and nano-laminated (altering layers of Al and Ni with the thickness of 30-50 nm)12. DSC analysis of both microstructures showed three exothermic peaks in the temperature range 500-900 K; however, positions and heat release for those peaks were different. The first exothermic peak, observed at ~530 K, was attributed to the dissolution of nickel atoms at the aluminum lattice. 2 ACS Paragon Plus Environment

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Materials analyzed after the second exothermic peak (690 K) consisted of three phases: Ni, Al3Ni, and Al3Ni2. Finally, material collected after the third peak (~800 K) contained Ni, Al3Ni2, and AlNi phases. The self-sustaining reaction in sputter deposited Al/Ni multilayer foils was also intensively investigated4,9,33,34,35. The reaction front propagation velocity and maximum combustion temperature in these foils depends strongly on the bilayer thickness of the metals and the degree of intermixing at the layer interfaces. The intermixing of reactants, which occurs during deposition, reduces the reaction temperature and propagation velocity of foils with thin bilayers due to the formation of solid solutions. For foils with relatively thick bilayers (greater than 50 nm) intermixing has little effect. Thermal analysis28,29,30, synchrotron time-resolved X-ray diffraction (XRD)35,37, and dynamic transmission electron microscopy (TEM)38,39 were used to understand the phase formation mechanism in Al/Ni multilayer foils. Blobaum and co-authors reported the existence of several exothermic steps at 400 - 980 K using DSC experiments with low heating rates (0.1-2 K/s). They attributed these exothermic processes to the sequential formation of metastable Al9Ni2, and stable Al3Ni, Al3Ni2, AlNi phases28. Unlike DSC experiments, the heating rates during combustion can reach 106 K/s. Therefore, phase formation mechanisms during combustion can be different from that observed in low heating rate experiments. Indeed, synchrotron time-resolved XRD35,37 and dynamic TEM observations38,39 reveal that only the AlNi phase crystalizes from a melt during the self-propagating reaction. Rapid quenching of reaction fronts in Al/Ni foils revealed that the Al melts, then Ni partially dissolves into the melt, where nucleation and growth of the AlNi intermetallic phase occurs33. Recently, a new double-stage mechanism of product formation within combustion wave was also proposed based on quenching experiments and molecular dynamic simulation4. According to this mechanism isolated nanoscale grains of AlNi form between local molten regions. 3 ACS Paragon Plus Environment


Grain coarsening then occurs in the second stage, which is responsible for the heat generation during this stage. Reaction kinetics in nanostructured Al/Ni materials were investigated by thermal analysis techniques such as DSC12,28,36,40, electrothermal explosion41,42, high-temperature scanning calorimetry43, and nanocalorimetry methods44,45. Using DSC measurements at different heating rates (0.1-1 K/s), Manukyan and co-authors extracted the activation energies for Ni dissolution in the Al lattice (93-99 kJ/mol) as well as for intermetallic phases (120-140 kJ/mol) from ball milled Al/Ni composites12. Blobaum et al. also used DSC measurements for multilayer foils at different heating rates to evaluate activation energies for formation of metastable Al9Ni2, as well as stable Al3Ni, and Al3Ni2 phases to be 152.5 ± 5.8; 183.3 ± 9.6; and 165 ± 7.7 kJ/mol, respectively28. Shuck and Mukasyan used an electrothermal explosion method42 to investigate the kinetics of ball milled Al/Ni composites. They showed that increase in the contact surface area/volume ratio of reactants leads to decrease of the apparent activation energy from 137 to 79 kJ/mol. Filimonov et al. also conducted an electrothermal explosion study46 to extract the activation energy for a ball milled nonstoichiometric 3Ni+Al system. They reported an unusually low activation energy of 9.5 ± 2 kJ/mol. Nepapushev et al. studied the kinetics of ball-milled nanostructured Al/Ni composites by electrothermography43 with a heating rate of 4.5-45 K/s. Interestingly, the reaction onset temperature and the temperature of maximum reaction rate decreased with increasing the heating rate. The authors suggested that combustion process proceeds in two stages, the first of which could have a significantly lower activation energy. Liu used47 high-energy synchrotron radiation X-ray reflectivity to determine the activation energy of interdiffusion in Al/Ni foils under indirect heating conditions47. It should be noted that the determined activation energy, 92 ± 7 kJ/mol, of interdiffusion is close to the Ni diffusion into the Al lattice determined by DSC measurements12. Grapes et al. recently used48 high-rate nanocalorimetry to examined the Al3Ni formation reaction at 103 - 105 K/s heating rates. They 4 ACS Paragon Plus Environment

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identified two main steps: solid-stage interdiffusion between reactants without product nucleation and Al3Ni phase formation. The authors estimated the activation energy for interdiffusion at 113 kJ/mol ± 4 kJ/mol, while for the second step an activation energy of 137 kJ/mol ± 4 kJ/mol. Despite significant progress in the study of Al/Ni nanostructured materials, the phase formation mechanism and kinetics during rapid combustion process is not well understood. Most of the results were obtained using indirect heating methods such as DSC or nanocalorimetry. DSC enables study of the kinetics for individual processes at slow heating conditions, while nanocalorimetry provides access to much higher heating rates. Direct resistive heating in thermal explosion type experiments provides heating rate conditions which are realistic for combustion processes. However, there is a significant discrepancy between reported apparent activation energies obtained using electrothermal explosion methods41,42,46. The heating method plays a critical role in the investigation of reaction kinetics in heterogeneous systems. Indirect heating of materials (DSC, nanocalorimetry) involves nonuniform heat transfer through the surface of the material. When heat is supplied through the surface, the heating rate is limited by heat transfer processes, which depend on the sample dimensions and the thermophysical properties of the substance. During direct resistive heating, the matter is heated uniformly by a non-thermal energy dissipation mechanism. The heating mechanism significantly influences the specific reaction times that are available for investigation of kinetic parameters. In this work, we employed the electro-thermography technique to initiate combustion reaction in Al/Ni multilayer foils by direct resistive heating49,50,51. This method allows control of the ignition temperature (Tig.) and delay time (tig.) of foils by changing the electrical parameters. Since these characteristics are directly related to the initiation of combustion reactions, we applied thermal ignition52,53,54,55,56,57 and Kolmogorov-Johnson-Mehl-Avrami58–62 models to extract activation energies that are responsible for initiation of the combustion process. By rapidly 5 ACS Paragon Plus Environment


arresting the microstructure of foils before combustion, structural transformation occurring at initial stages of processes were also captured. This approach allows linking the microstructure transformation to the reaction kinetics. 2.1.

Experimental Section

2.2.

Materials Two types of magnetron sputter deposited Al/Ni(V) multilayer foils (NanoFoil®) prepared

by Indium Corp. with bilayer spacings of ∼50 nm were used in this research. The first type of foil consists of Al/Ni multilayers covered at both sides with layers (1 m per side) of brazing alloy (59.0% Ag, 27.3% Cu, 1.3 Ti%, and 12.5). The brazing alloy is designed for joining applications in which Al/Ni(V) is used as an embedded heat source. The second type of custom-made materials consists of only Al/Ni(V) multilayers. The overall thickness of both foils is 0.04 mm. Vanadium is included in the nickel sputter target to make it non-magnetic and thus allows for faster and more stable deposition. The relative thickness of Al and Ni layers in both foils is a 2.5:2 ratio, which corresponds to an average stoichiometry of Al44Ni50V6. 2.3.

Ignition experiments of Al/Ni A reaction chamber equipped with a power source, and a PC-controlled unit (Supporting

Figure 1) was used. The setup allows rapid (up to 4.5 × 105 K/s) and controllable heating of the foils and continuous data acquisition (electrical power, the resistivity, and temperature of the foil) with a frequency of 10 kHz. During ignition experiments, Al/Ni foils (2 x 40 x 0.04 mm) were inserted into the chamber, which was then evacuated to 10−2 kPa, purged with pure argon for 3 cycles, and finally filled with argon to 80 kPa pressure. The foils were heated by direct current (DC). To accomplish the desired well-defined heating schedules for Al/Ni foils and to record DCinduced temperature-time histories (ignition profiles), a set of calibration runs was conducted using three different metals, Pt, Mo, and W, with well-known resistivity-temperature dependences R(T). 6 ACS Paragon Plus Environment

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Two different heating regimes were used for ignition experiments: (i) constant electrical power and (ii) linear increase of power. Constant power ignition: At relatively low temperatures (below 1000 K) one may neglect the radiation component of heat losses and assume that heat transfer from the metallic sample to the inert gas atmosphere takes place by Newton's law. In this case, the equation of thermal balance of DC heated metallic foil can be presented as follows: cpm

dT  P   (T  To ) dt

(1)

where P (Watts or J s-1) is the electrical power used for heating the metallic sample, T0 (K) is the ambient gas temperature, T(K) is the current temperature of the metallic sample, Cp ( J.g-1 K-1) is the specific heat capacity of the metal, m (g) is the mass of the metallic foil, and α (J.K-1 s-1) is the coefficient of heat transfer (heat emission) from the surface of the sample to the ambient atmosphere. The heat transfer coefficient, α, depends only on the sample geometry and not on the metal type. After some time of heating at constant applied electrical power

dT approaches 0, and dt

the foil reaches its stationary temperature (Tst). At this stage the power can be expressed by the following equation:

P   (Tst .  To ) or Tst .  To 

P



(2)

By substitution P from (2) into (1), we can obtain: dT cpm   (Tst .  To )   (T  To )   (Tst .  T ) (3) dt Integrating (3) and assuming that Cp and α are constant in the investigated temperature range, we can obtain: dT   T T T Tst .  T  o c p m dt and ln Tstst..  To   c p m t o T

t

hence: Tst .  T  (Tst .  To ) exp(

 cpm

t)

or 7 ACS Paragon Plus Environment

(5)

(4)


T  Tst .  (Tst .  To ) exp(

 cpm

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(6)

t)

  P t ) (7) 1  exp(   c p m  It should be noted that in the constant power regime, Tst does not depend on metal type if the heat T  To 

exchange with the surrounding gas as well as the geometry of metallic foils are identical. For example, Figure S2 shows that for 2 Watts of applied power, the Tst value for Pt, Mo, or W foils (with the geometry of 2 x 40 x 0.04 mm) is 497 K. Similarly, for 5 Watt power, the corresponding Tst is 793 K. Such good fitting (R2 > 99%) supports all above assumptions. Pure metallic foils were used in this manner to calibrate the power needed for heating the Al/Ni foils to the desired Tst. Using these calibration experiments, we determined the  coefficient for a given geometry of Pt, Mo, and W foils which was then used to determine (via equation (7)) the saturation temperature of the Al/Ni foil upon applying the desired electrical power. Linear power increase: In this heating regime, the temperature of the metallic sample (T) increases linearly according to the following relation: T= To + t where  

(8)

dT is the heating rate and t is time. By substitution T from (8) into (1), we can obtain: dt

c p m  P(t )   t or P(t) = cpm + at

(9)

Аssuming that Cp and α are constant in the investigated temperature interval, eq. (9) indicates that a linear increase in electrical power corresponds to a linear temperature increase in the metallic sample. Figures S3 and S4 show the calculated T- t and P – T dependencies for three metallic foils Pt, Mo and W with different cpm values at  = 1 and 100 K/s, respectively. These figures indicate that the temperature for all three metallic foils increases linearly for a linear increase in power. 2.4.

Material Characterization


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It was shown that termination of the electrical current through the thin foil led to cooling of the material at a rate of ∼103 K/s. This feature permits arresting and preservation of the intermediate structures. The phases in quenched foils were determined by X-ray diffraction (XRD) analysis with Ni-filtered Cu−Kα radiation (D8 Advance, Bruker) operated at 40 kV and 40 mA. Step-scan data (of step size 0.025° and counting time 30 s) of foils were recorded over the angular range 20−90° (2θ). Atomic-level structure analysis was performed with a Titan-300 (FEI) transmission electron microscope (TEM) with a resolution of 0.136 nm in scanning TEM (STEM) mode and ~0.1 nm information limit in high-resolution TEM mode. The Titan is equipped with an energy dispersive X-ray spectroscopy (EDS, Oxford Inc.) system with a spectral energy resolution of 130 eV. The TEM samples were prepared using a Helios NanoLab 600 system by making crosssectional slices from irradiated foils as described elsewhere63. The Digital Micrograph (Gatan, Inc.) software was used to analyze high-resolution TEM images via a series of functions. The Fast Fourier Transform (FFT) function converts real space images to frequency space images. These images can then be analyzed to identify periodic structures present within the material. Analysis of the resulting images can be completed in a manner directly analogous to that of selected area diffraction images. Furthermore, the twin oval masking function can be used to select d-spacings unique to phases present in the Al/Ni system. By pairing this function with the inverse FFT function, which converts frequency space images back to real space, regions corresponding to the intermediate Al-Ni phases, Al3Ni and Al3Ni2, can be observed distributed throughout the annealed Al-rich layers. Since the material is highly polycrystalline, and many crystallites overlap, this analysis technique was coupled with selected area diffraction in order to verify the presence of the phases of interest. 2.5.

Reactivity Evaluation Annealed and quenched foils (non-reacted) were locally preheated from one side using a

tungsten filament with a surface temperature of 600 K to initiate the self-propagating reaction. A 9 ACS Paragon Plus Environment


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high-speed infrared (IR) camera (FLIR Systems, SC6000) was used to monitor the surface temperature of the reacting foils. The emissivity was calibrated by recording hot-plate heating of sample pieces to 350 K and simultaneously measuring the temperature with a K-type thermocouple 100 μm) attached to the surface of foils. The IR videos were captured over several different temperature ranges, which include temperatures as high as 1900 K and frame rates of 5,000 frames/s. The velocity of front propagation was then calculated using frame-by-frame analysis of the recorded movies. 3. Results 3.1.

Self-ignition of Al/Ni foils Self-ignition of reactive Al/Ni foils was investigated using constant electrical power and

linear heating regimes. Experiments using the constant power regime approximate the scenario in thermal ignition theory when a cold metallic sample (with T0 temperature) is placed into a hot gas environment with Tst temperature. Equation (7) describes the temperature - time history of an initially ambient temperature Al/Ni sample during heating. Constant power resistive heating with different P values allows for determination of a critical value of electrical power, Pcr at which the cr

combustion reaction initiates. Based on Pcr the critical value of ignition temperature ( Tig ) for the Al/Ni foil can be determined using the Eq. 2, i.e. Tigcr  To 

Pcr



. Resistive heating also allows

determination of the ignition delay time (tig), defined as the duration of the period between when power is applied and ignition occurs, for different P values at P>Pcr. The DC-induced ignition profiles for Al/Ni foils without the brazing alloy layer are shown in Figure 1a as a function of electric power. These profiles indicate that to ignite the reaction in these foils the electric power (P) should exceed 0.9 watts. The Tig., sharp inflection point on a profile, of the sample heated with 1.0-watt power, is 434 K. Figure 1a shows that Tig increases 10 ACS Paragon Plus Environment

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Figure 1. DC-induced (a) temperature profiles for the Al/Ni foils heated at a range of constant electrical powers and (b) ignition delay times shown as functions of stationary temperature for both materials.

gradually from 434 K to 565 K when electric power applied to the sample increases from 1 to 7 watts. The tig for the same samples exhibits the opposite trend and decreases from 8.96 s to 0.3 s with increasing power. Similar experiments were performed for Al/Ni foils coated with the brazing alloy layer. These results (not shown) indicate that these foils exhibit a trend of Tig and tig vs. electric power similar to the foils without the brazing alloy layer. Figure 1b presents the dependence of tig on Tst for both types of foils. These results indicate that the brazing alloy layer has no significant influence on the ignition delay time within the ~430 – 900 K temperature interval. It should be 11 ACS Paragon Plus Environment


Figure 2. Temperature profiles for the Al/Ni foil without brass layer with (a) different heating rates as well as (b) the effect of heating rate on tig and Tig. noted that tig can be as high as 25 s for foils with the brazing alloy layer when the Tst approaches a critical stationary temperature, 430 K, below which the combustion may not be initiated for both foils. This plot suggests that for coated foils, tig drops from ~25 to 1 s when the stationary temperature increases from 430 to 550 K. Further, increase in Tst within the 550 – 1150 K range results in smaller changes, 1 – 0.3 s in the ignition delay time. For determining the influence of heating rate on ignition parameters, we performed experiments in the linear heating regime for Al/Ni foils with the brazing alloy layer. Those experiments were performed with heating rates in the 0.423 - 42.3 K/s range. The temperature profiles (Figure 2a) show that Tig increases gradually from 435 to 495 K when the heating rate 12 ACS Paragon Plus Environment

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Figure 3. Snapshots of high-speed IR imaging of combustion front propagation in (a) pristine foils and (b) foils annealed to ~425 K at 10.2 K/s, and (c) measured velocity and maximum temperature of foils annealed at different heating rates. A heating rate of 0 indicates the pristine foil. increases to its maximum value. In turn, the tig of samples decreases with increase of heating rate. Figure 2b summarizes the dependances of both ignition parameters on the heating rate. It can be seen that heating rate has a significant impact on the ignition delay time. Indeed, the change of the heating rate from 0.423 - 10.2 K/s results in a decrease of tig over 25 times (346 to 16.8 s). Additional increases in the heating rate from 10.2 to 42.3 K/s results in a moderate drop of tig (16.8 to 4.8 s). The results of ignition experiments indicate that an increase in electrical power or heating rate significantly decreases the ignition delay time of Al/Ni foils, while for both heating regimes, the ignition temperature increases with increase of power or heating rate. 3.2.

Self-propagation reaction in the foils High-speed infrared imaging is utilized to investigate the self-propagating reaction

characteristics, such as front propagation velocity and maximum temperature, of pristine and annealed foils, as a function of heating rate. In these experiments, foils were locally preheated from 13 ACS Paragon Plus Environment


one side using a tungsten filament with a surface temperature of 600 K, and the temperature-time history for the surface of the foil was recorded. The set of snapshots of an IR movie (Figure 3a) for the pristine foil indicates that, after local thermal initiation, the reaction front steadily propagates along the sample. The average combustion velocity for this sample is 9.8±0.5 m/s. The snapshots from IR video recording (Figure 3b) indicate that the combustion front velocity for the annealed foils (heating rate ~10.2 K/s, the maximum temperature of ~425 K) is 12.4±0.4 m/s. The measured velocities for annealed samples as a function of heating rate exhibit a notable feature (Figure 3c). The combustion front propagation velocity for all annealed samples is 26 ± 4 % higher than that of pristine samples. It is important that the measured maximum temperature in the reaction front remains essentially constant (1700 ± 50 K) for all investigated samples.

Figure 4. XRD patterns of the initial (a) and annealed (b-e) foils 3.3.

Structural transformation of foils To establish a relationship between the structural transformation of materials and ignition

parameters, we performed a set of experiments, where the electric power was discontinued 0.05 s before the ignition point and the thin foil was rapidly (~103 K/s) cooled (quenched) to room 14 ACS Paragon Plus Environment

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temperature. Figure 4 illustrates the XRD patterns of the pristine (a) and quenched (b-e) foils. It can be seen that no change in the phase composition of the foils can be detected using XRD analysis. Only the intensities of the Ni and Al diffraction peaks increase for the quenched foils as compared to those of the pristine one. The relative full width at half maximum (fwhm) of the

Figure 5. TEM images of (a) a pristine foil and (b) a foil annealed to ~490 K at 42.3 K/s and image contrast based line profiling results (c) perpendicular and (d) parallel to the direction of the layers. diffraction peaks for all foils remains essentially unchanged. Such increase of peak intensities without change in fwhm value may be attributed to an increase in overall crystallinity (annihilation of defects) within the individual metallic grains without changes in size. Bright-field TEM images of cross-sections from pristine and annealed foils with Ni (dark) and Al (light) layers are presented in Figure S4. These images demonstrate that no significant structural transformations occurred during preheating and grains within individual layers have similar thicknesses before and after annealing. However, STEM images of similar areas (Figures 5a, 5b, and S5) of foils exhibit some differences. The results of image analysis suggest that the 15 ACS Paragon Plus Environment


Figure 6 High-resolution TEM images of pristine (a,b) and annealed foil to ~490 K with 42.3 K/s heating rate (c,d) area of the light phase (Ni) in quenched samples was reduced by 2.2±0.25% as compared to pristine samples, while EDS analysis revealed that the center of the previously pure Al layers now contains 3-5 at. % Ni. The localized nature of diffusion of Ni into the Al layers is supported by contrasted based line profiling of STEM images (Figure 5d). Coupled with the observation that the average width of Ni layers has decreased after annealing (Figure 5c), we can suggest that the preheating of foils facilitates localized solid-state diffusion of Ni into the Al layer. High-resolution TEM (HRTEM) imaging of the quenched foils confirms that structural transformation at the Al/Ni interface takes place before ignition. Figures 6a and 6b demonstrate the existence of an intermixed amorphous/crystalline interlayer at the Al/Ni interface. These layers have thickness in the range 1-3 nm. Imaging of the Al/Ni interface for quenched foils (Figure 6c, and d) reveals that some ordering takes place in this layer.


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The formation of intermetallic nuclei in these interface regions was demonstrated by applying FFT analysis to the HTEM images obtained for the quenched samples. Figure 7a shows an example of such analysis for a quenched foil preheated at 42.3 K/s. The regions of the image corresponding to Al3Ni and Al3Ni2 lattice fringes identified through FFT analysis are highlighted in purple. FFT analysis of several high-resolution TEM images (Table S1) indicates the presence of ordered structures present that correspond to the intermediate phases Al3Ni and Al3Ni2. These phases were observed to have exclusively formed within the Al-rich layers, which supports the conclusions made using image contrast based analysis of Al-rich layers. The observed formation

Figure 7 FFT analysis of a high-resolution TEM image (a) and selected area diffraction pattern (b) of a foil after annealing at the 42.3 K/s heating rate. of intermediate phases is supported by selected area diffraction analysis (Figure 7b) of the surrounding region, which reveals diffraction spots unique to Al3Ni and Al3Ni2. These results suggest that the kinetics of formation for nuclei of intermediate phases during the initial stages of preheating may play a critical role in the solid-state ignition mechanism for Al/Ni materials.

4. Discussion The results on structural transformation of quenched materials (see section 3.3) just before ignition indicate three notable features. First, XRD (Figure 3) patterns show that the overall 17 ACS Paragon Plus Environment


crystallinity of materials increases during the annealing of the foils. The annihilation of defects in grains and partial crystallization of amorphous regions at the Al/Ni interface could cause such enhancement in crystallinity. Second, based on STEM and high-resolution EDS examinations (Figures, 4 and S5) we can suggest that small amounts of Ni have diffused into the Al phase along the Al/Ni interfaces in annealed sample. Third, FFT analysis of high-resolution TEM images coupled with electron diffraction patterns (Figure 5 and Table S1) indicate that Al3Ni and Al3Ni2 nuclei with 2-5 nm sizes form at the Al/Ni interface. These structural transformations influence the reactivity of annealed materials. The self-sustaining reaction in all annealed foils on average 26% propagates faster than in the pristine material (see Figure 3), due to the existence of preformed nucleation sites. The measured maximum temperature of reaction, however, practically does not change after annealing. In order to link these structural transformations to the kinetics of the considered reactions we used two different approaches. First, we applied an approach based on thermal ignition (sometimes referred as “thermal explosion”) theory which was initially developed for gas phase reactions53,55, and later adopted for solid-state systems56,57. Second, we applied the KolmogorovJohnson-Mehl-Avrami (KJMA) model, which was developed to describe nucleation and growth that occur during recrystallization phenomena.58–62 Thermal ignition theory assumes that the sample is introduced into a preheated furnace with temperature, Tin. The initiation of reaction depends on the balance between the rate of heat release via chemical reaction and the rate of heat loss to the environment. The self-heating of the sample accelerates the heat release rate, and at a specific temperature (ignition temperature, Tig), exothermic reaction rapidly proceeds uniformly through the entire sample. Ignition temperature (Tig) and delay time (tig) are two main parameters used to characterize the thermal explosion conditions. These parameters can be changed either by adjusting the external heating conditions 18 ACS Paragon Plus Environment

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or by altering the microstructure of the reactive material. If the tig is relatively small, which occurs when Tin is sufficiently high, the heat losses from the reacting sample can be neglected and the process proceeds under adiabatic or near adiabatic conditions. According to thermal ignition theory, under adiabatic condition the ignition delay time (tad) depends only on the initial temperature of the furnace (Tin) where the reaction takes place53,56, and the following expression approximates their relation:

tad



c RTin2 exp( E RT

Qk0 E

in

)

(10)

where c is the heat capacity of reactants, Q is the heat of reaction, R is universal gas constant, k0 is the pre-exponential factor and E is the activation energy for reaction. The method of reaction initiation in Al/Ni foils used in the present research contains several essential features of the thermal explosion phenomena. The Al/Ni specimen is uniformly heated to some stationary temperature (Tst) by electrical current and then self-ignites after some ignition delay time (tig) when the rate of heat release by chemical means exceeds the rate of heat loss. During DC-induced ignition of Al/Ni foil, the Tin term in equation (10) can be replaced by Tst, which represents the maximum temperature that the foil would reach during heating of an inert foil with identical dimensions at constant power. In near-adiabatic conditions (rapid heating of samples) the tig  tad and the logarithm of equation (10) results in the following expression:  

ln  

   2  st 

tig T

 







c R   E  1         Qk E   R  T  0    st 

 ln

(11)

The Arrhenius-type plots of ln(tig/Tst2) against 1/Tst for both types of reactive foils across the entire range of powers studied in this work are shown in Figure S6. These plots indicate the existence of a linear relationship between the two parameters across a wide temperature range (500-1000 K). Linear fitting of the data points in this interval permitted us to extract activation energies of 24±1.1 and 28±1.1 kJ/mol for foils without and with a brazing alloy layer, respectively



(Figure 8). The small difference between these two activation energies suggests that the alloy layer does not have a significant effect on the ignition kinetics of Al/Ni foils.

Figure 8. Linear fitting of the ln (tig/Tst2 ) against 1/Tst for Al/Ni foils (a) without and (b)with brazing alloy. As discussed in the Introduction section, previous works have reported a broad range of activation energies for individual intermetallic phases in Al/Ni nanoscale materials using DSC, nanocalorimetry, high-speed scanning calorimetry, etc. We compare the values obtained in the present study to the electrothermal explosion, laser, and hot plate initiation experiments because that data can be attributed to the initiation of rapid combustion reactions. Table 1 displays the activation energies of both ball-milled materials and sputter-deposited foils. Our reported 20 ACS Paragon Plus Environment

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activation energies (for 500 – 1000 K) do fall within the broad range of values for initiation of the self-sustaining reaction. These results indicate that the activation energies reported in present work and by previous researchers can be categorized into two groups: ~75 – 105 and ~10-30 kJ/mol. The first range of activation energy values was prevously atributed to solid-state dissolution of Ni onto the Al lattice12 or an intermixing6,47 process. Table 1 A List of Activation Energies Calculated for Ni/Al Nanoscale Materials and Method of Initiation of Combustion Process from Literature and This Work # 1

2

3

4

5

6

7

8

Initiation method

Activation energy, kJ/mol

Temperature range, K

Refs.

Hotplate ignition

77.3 ± 1.3

500-1000

6

Al layer: 50-100 Ni layer: 50-100

Electrothermal explosion

79 ± 10

500-1500

42

Compressed pellets, 75-85% TMD

Not reported


105 ± 13

500-1400

41

Ball-milled material

Compressed pellets, unknown TMD

Not reported


9.5 ± 2

500–1300

46

Al/Ni nanoparticles mixture

Compressed pellets, 55-60% TMD

Al particle: 80 Ni particle: 800

Laser ignition

21.2 ± 2.5

800-1500

7

Al/Ni foil, without brazing alloy layer

Sputter deposited foil, ~100% TMD

bilayer thicknesses ~50 nm

Electro thermography

24± 1.1

500-1000

This work

Al/Ni foil, braze alloy layer




28 ± 1.0

500-1000

This work




57 (n*=0.5) 113 (n*=1) 226 (n*=1) 340 (n*=3) 453 (n*=4)

430-500

This work

Material

Sample

Al/Ni foils without brazing alloy layer



Compressed pellets, 70% TMD


Al/Ni foil, braze alloy layer

Particle/layer size/thickness, nm Bilayer thicknesses range from 20 200 nm

(* n is the Avrami exponent). The Kolmogorov-Johnson-Mehl-Avrami (KJMA) model was used to analyze the data obtained at low (430 - 500 K) stationary temperatures with the “long” incubation periods and for 21 ACS Paragon Plus Environment


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which the thermal explosion theory is not valid. In general, the KJMA model accounts for both nucleation and growth stages that occur at constant temperature58–60. The measurable isotherms observed for Tst500 K as well as formation of intermetallic nuclei in the quenched foils suggest that we should account for both of these stages. The equation used is of the form: 𝑛

𝑦 = 1 ― 𝑒𝑥𝑝( ― 𝑘𝑡𝑖𝑠𝑜𝑡ℎ𝑒𝑟𝑚)

(12)

where y is the fractional volume conversion, k is a rate function dependent on temperature, tisotherm is the duration of the isotherm/stationary temperature, and n is the Avrami exponent typically associated with the number of growth nuclei present during early stages of transformation and the geometry of grain growth (1-, 2-, or 3-dimensional). The duration of the isotherm, tisotherm, was measured from the results of constant power experiments in the range 1.00 – 2.50 W (see Figure 1) and is shown as a function of Tst in Figure S7. The temperature dependence of the rate variable, k(T), may be obtained using equation (12) for specific degrees of conversion, y, and different values of n. It is assumed that the degree of conversion is relatively low during the nucleation stage. The data presented in Table S2 were obtained for y = 0.01 (1% of conversion). It can be seen that regardless of the value chosen for n, k rapidly increases with increasing temperature. Table S2 suggest that k, which represents the nucleation and growth rate, is on the order of 10-3-10-5 for T=434 K and varies from 10-1 -102 for T=500 K. The rate function, k, may be assumed to follow an Arrhenius-type dependence on temperature: 𝐸

(𝑅𝑇 )

𝑘(𝑇𝑠𝑡) = 𝑘0𝑒𝑥𝑝

𝑠𝑡

(13)

where k0 is a temperature-independent rate constant, R is the gas constant, and E is the sum of activation energies of nucleation and growth. A log plot of k with inverse temperature is shown in Figure 9 for different n values. Analysis of these results shows that the activation energy 22 ACS Paragon Plus Environment

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Figure 9. Linear fitting of the ln(k) against 1/Tst for Al/Ni foils with brazing alloy. calculated does not depend on the assumed degree of conversion, but is strongly dependent on the assumed Avrami exponent (n) and increases from 57 for n=0.5 to 453 kJ/mol for n=4 (see also Table 1, row #8). The slope analyzed for 434-453 K, used to calculate activation energy, fit the measured results with R2 = 0.93. It is interesting that these values of activation energy (57-453 kJ/mol) are much larger than those (22-30 kJ/mol) obtained for higher temperatures (500-1000 K) using the thermal explosion approach. This effect can be explained by the fact that the nucleation process (generation of nuclei for the intermediate phases, e.g. Al3Ni) is extremely temperature sensitive, as is confirmed by its high activation energy. Preheating at a higher power allows the foil to rapidly reach a relatively high temperature at which nucleation rate becomes comparable with the reaction (growth) rate and the process switches from a nucleation-limited regime to a reaction-limited regime. Data obtained in this work and by others (see Table 1) suggests that after the nuclei have formed, the followed reaction has a much lower energy barrier. This fact is further supported by the observation that combustion front propagation velocity increases as compared to the pristine foils for the preliminary annealed specimen (Figure 3). Further analysis showed that during the annealing 23 ACS Paragon Plus Environment


stage, nucleation processes have already begun to occur, which significantly lowers the energy barrier of the reaction. 5. Conclusions Investigation of kinetics for chemical reactions in nanostructured Al/Ni foils using the electrothermography revealed that the formation of intermetallic nuclei is a limiting step, which defines the ignition characteristics of the material at temperatures below 500 K. The estimated value for the activation energy of nucleation is much higher than that of the reaction, implying that the nucleation rate increases quickly with increased temperature. Moreover, it is shown that nucleation plays an important role in enhancing the reaction propagation velocity through the Al/Ni foils. These findings suggest new approaches to control ignition and combustion processes for such reactive media. Finally, the nucleation stage should be accounted for in future theoretical models that attempt to describe the ignition and combustion phenomena in reactive systems. Supporting Information A table for FFT analysis of high-resolution TEM images of the annealed foil. A table for calculated k values for different n at different temperatures. Photos of experimental setup for DC-induced ignition of Al/Ni foils. DC heating with constant electrical power and linear heating regimes. Cross-sectional bright-field TEM and scanning TEM images of pristine and annealed foil with EDS spectra. Arrhenius-type plots. Dependence of duration of the isotherm on stationary and reciprocal temperature. Acknowledgements This work was partially supported by the Department of Energy, National Nuclear Security Administration, under the Award No. DE-NA0002377 as part of the Predictive Science Academic Alliance Program II. This work was also partially supported by a joint grant (AR 13RF 057//13 03 90604) of State Committee of Science of Armenia and Russian Foundation for Basic Research 24 ACS Paragon Plus Environment

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(RFBR). One of the co-authors (AM) was working on this paper during his summer visit to National University of Science and Technology (Moscow) supported by a grant in the framework of Increase Competitiveness Program of NUST ‘MISiS’ (No. K2-2017-083), implemented by a governmental decree dated March 16, 2013, N 211.

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