Effects of diffusion barriers on reaction wave stability in Co/Al reactive multilayers

Reactive metal multilayers are materials that store chemical energy in the solid state and then release that energy via deflagrating formation reactions upon an ignition event.^1–4 The reactive metal multilayers are typically fabricated by cold rolling,^1,3 sputter depositing,^1,4 or electrodepositing^1,4 alternating layers of two metals into a nanolaminate superlattice. Constituent materials are selected such that the A–B bond energy is lower than the A–A/B–B bonding condition, making a mixing reaction exothermic. In fact, the reactions are known to self-propagate through the bulk material when ignited at a point. The periodic geometric configuration of vapor-deposited multilayers makes them ideal for implementing a combination of analytical expressions,^5–7 reduced order,^8–10 continuum,^11–13 and molecular dynamics^12,14–16 models used to determine the kinetic properties and mechanisms of rapid mixing and formation reactions. The multilayers contain all reactants internally, which allow them to be used in both underwater¹⁷ and vacuum (i.e., outer space)^18,19 environments. Unlike deflagrating thermite systems,^20–22 the reaction of bimetallic formation reactions typically takes place in the condensed phase. The lack of gas emission has made them ideal for specific applications such as bonding,^1,23–25 alloy synthesis,²⁶ and heat sources for secondary reactions.^1,27–29 In each application space, the chemical composition at a reactive multilayer interface greatly affects the resulting reaction propagation.^2,30

The interfacial chemistry, be it the compositionally graded premixed zone in bimetallic systems or the intermetallics and oxides in vapor deposited thermite multilayers, has motivated the scientific study of tailoring mass transport properties through interfacial diffusion barrier layers.³¹ The specific composition of the interfacial layers in these thermite multilayer systems can have drastic effects on both the reactivity^31–33 and product formation pathway^34–37 during reaction.

The addition of diffusion barriers to the bimetallic reactive multilayers involves the coupled effects of adding an inert thermal mass as well as changing the chemical composition of the interface. A previous work involving the inclusion of inert layers to tune the adiabatic flame temperature of bimetallic reactive multilayers has enabled the determination of underlying reaction mechanisms.³⁸ The inclusion of ternary metals at interfaces can also be used to both enable³⁹ and inhibit^39,40 the multilayer reactivity. Within the Co/Al material system specifically, similar studies were used to explore the mechanisms responsible for instabilities in the reaction front.⁴¹ Here, the reaction instability refers to a time-varying propagation velocity in the radial direction, which may manifest as oscillatory, spinning, or erratic wave behavior.^42–47 The observed instability within the Co/Al system is a bilayer thickness-dependent (i.e., sum of two individual reactant layers) spin-type instability characterized by a reaction wave that spirals in the plane of a film about an axis of rotation normal to a point ignition site.^26,44 Two types of spin modes were identified by Kittell et al.⁴⁸ and will be referred to henceforth as mode I and mode II propagation. Mode I instabilities appear optically as periodic bands at an acute angle to the wavefront normal. Conversely, mode II instabilities appear with band propagation orthogonal to the radially expanding reaction front with well-defined reaction band nucleation sites. They also exhibit a stair-step displacement vs time relationship. These two unstable propagations modes are shown schematically in Fig. 1.

This work explores the self-propagating reactions of Co/Al multilayers with the addition of inert CoAl diffusion barriers. The reaction product phase (B2–CoAl)⁴⁹ was chosen to be the diffusion barrier material in order to avoid changes to reaction activation energy^31,33,38 and isolate the effects of varying mass transport rates. The resulting effects on propagation velocity and stability are then described in terms of material phase within the reaction front.

Alternating layers of Co and Al were direct current sputter deposited using a cryopumped Unifilm Co. PVD 300 system to produce multilayer films.⁵⁰ Each film was deposited onto either Si (100) wafers with a 4000 Å thick thermal oxide surface coating or a NaCl optical window. Individual sputter targets were utilized for Co, Al, and CoAl. The Co target (VEM, Inc.) was 99.95% pure Co, and the Al target (Sophisticated Alloys, Inc.) was 99.99% pure. The mixed CoAl target (Sophisticated Alloys, Inc.) was of 99.97% purity with an Al fraction of 31.36 wt. %, an impurity of 0.032 wt. % O, and the remainder being Co. The deposition chamber was evacuated to a residual pressure of 1.3 × 10⁻⁵ Pa prior to being backfilled to 1.3 Pa with ultra-high purity Ar, which is used as a sputter gas. In all experiments, approximately 7.5 μm of Co + Al reactants was deposited to maintain a constant caloric potential for the films. Any CoAl deposited as a diffusion barrier was in addition to approximately 7.5 μm of reactants. As a result, the overall thicknesses of the Co/Al + CoAl films varied from film to film, depending on the amount of CoAl necessary for each individual film design.

Deposited films were removed from the substrates to enable the characterization of reaction waves in freestanding foils. Films were removed from the oxidized Si substrates by peeling. Films deposited onto the NaCl crystals were removed by placing the substrate with film into a de-ionized water bath until the multilayer detached. An additional rinse with de-ionized water was performed on the detached foils to remove any residual NaCl.

The inclusion of inert materials as diffusion barriers in the multilayers requires an adjustment to the traditional definition of what constitutes a bilayer. The bilayer thickness in the bimetallic reactive foils is traditionally defined as the period of repeating concentration equal to the combined thickness of one layer of each reactant. The addition of diffusion barriers at each Co/Al interface increases the total thickness of each repeat unit within the foil's concentration profile. To enable comparisons between the multilayers with and without an inert-mediating material,⁴¹ the reactant thickness bilayer (RTBL) is defined, for multilayers containing a diffusion barrier, as the combined thickness of one deposited Co layer plus one Al layer. The RTBL, in the case of multilayers with diffusion barriers, is depicted schematically in Fig. 2(a). Multilayers with RTBL of 33, 50, and 66 nm with diffusion barriers of 1, 2, and 3 nm (plus control studies without barriers) were grown and reacted in this study.

Characterization of deposited diffusion barriers was performed in scanning transmission electron microscopy (STEM). Cross section STEM samples were prepared using focused ion beam lift-out in a FEI Co. Helios scanning electron microscope. The STEM was performed with a 200 kV FEI Co. 80–200 aberration corrected Titan G2 microscope.

The effect of adding diffusion barriers to Co/Al multilayers was investigated using differential scanning calorimetry (DSC). For each experiment, approximately 5 mg of foil was placed into a Cu DSC pan and sealed with a lid. Experiments were performed using a Perkin-Elmer DSC-8500 calorimeter that heated sample foils over a temperature range of 50–725 °C. Samples were tested in a N₂ atmosphere using a flow rate of 20 cc/min. Heating rates of 10, 20, and 40 °C/min were utilized so that activation energies could be calculated by the Kissinger method using a first derivative approach based on the largest negative slope of the exothermic peak near ∼250 °C within each thermogram.⁵¹ This peak was used as it is the most prominent of the multiple exotherms present in the thermogram, and it occurs at the lowest temperature. The quantitative analysis involved choosing the inflection point of the lowest temperature exotherm as the onset of reaction. Total heat release was measured by comparing the first temperature sweep to a baseline created by performing a second temperature cycle of the fully reacted multilayer.

The self-propagating reactions exhibited by the multilayers were imaged in a plan view (i.e., across the longitudinal plane of the foil) with a high-speed Vision Research, Phantom v12.1 camera. Pieces of the Co/Al foil of approximately 10 × 10 mm² were mounted across a washer. Sample ignition was performed by placing a thin strip of a commercially available (Indium Corp. of America) Ni/Al foil in conductive contact with the edge of the suspended Co/Al foil. A capacitive discharge unit provided the spark to ignite the Ni/Al foil, which then served as the heat source to ignite the Co/Al foil. Images were taken at frame rates of ∼10⁻⁵ s/frame with an effective pixel width of 15.5 μm. Wave front morphologies were directly imaged while propagation velocities were calculated by spatially locating the position of the reaction front with respect to time within the videographs.

In this formulation, the propagation velocity $v x$⁠, is described based on an Arrhenius relationship based on an activation energy $E A$⁠, diffusion coefficient $D 0$⁠, thermal diffusivity $λ$⁠, and set of temperatures $T$⁠. The subscripts of T, 0, f, and ad, correspond to initial, flame, and adiabatic temperatures, respectively. The subscript x is in the propagation direction of a stable front while y denotes the foil cross-plane. The series of eigenvalues $α n$ and Fourier coefficients $κ n$ describe the composition profile within the premixed interlayers, while R is the ideal gas constant. Values for $T f$ are calculated based on the system's enthalpy–temperature diagram and heat of the reaction by the method described in Refs. 52 and 53. Similarly, the phase dependence of $E A$ and $D 0$ is taken from Ref. 53.

Within Eqs. (2) and (3), the subscripts i and j denote the layers surrounding a thermal resistor $ζ$⁠. For the thermal circuit at the premix/diffusion barrier/premix interfaces, the subscripts i and j both refer to a premix at each pure metal interface while $ζ$ is the B2-CoAl product phase. For the complete multilayer stack, i and j are the effective Al and effective Co resistors and $ζ$ is the effective resistor between each metal. The progress variable F is defined as $1 − s / [ γ j 0 w ]$ and w as $1 + γ i / γ j$⁠. The variable $γ$ is the sub-thickness of the denoted layer of the relevant material stack. Input parameters for Eqs. (1)–(3) are provided in Table I.

After deposition of the nanolaminates, cross section STEM images of the films were taken to verify their accuracy with respect to the intended designs. A STEM image of a 2 nm diffusion barrier deposited at a Co/Al interface is provided in Fig. 2(b). The high-angle annular dark field detector used in these STEM produces Z contrast. Therefore, Al appears black, Co is white, and any intermixed material appears gray. A schematic for a prototypical diffusion barrier design is shown in Fig. 2(a) with TEM corresponding to a magnified single interface. Although a barrierless sputter-deposited Co/Al nanolaminate has ∼2 nm of amorphous intermixing,^49,53 the interfacial zone of gray scale contrast is effectively grown to 4 nm with the addition of a 2 nm diffusion barrier. Additional characterization of the interfacial layer involved taking Fast Fourier transforms of the diffusion barrier, which are provided in Fig. 9 within  Appendix A. The material within the diffusion barrier was confirmed crystalline with the symmetry and lattice plane spacing of the B2-CoAl phase, which is consistent with the phase when sputter depositing from CoAl targets as a layer embedded within either Co or Al.⁴¹ The STEM characterization is, thus, consistent with the nominally 2 nm crystalline diffusion barrier being inserted at the interface with some degree of additional mixing at each elemental metal interface.

The heat of the reaction for the diffusion barrier foils was characterized in DSC. A series of mass normalized thermograms taken at a 20 °C/min heating rate for various diffusion barrier thicknesses in 33 nm RTBLs are shown in Fig. 3. Thermograms for largest RTBL tested (66 nm) are provided in Fig. 10 within  Appendix B. The phase formation occurring at each detected exotherm in the Co/Al multilayer system has been previously characterized in XRD using rapidly quenched DSC samples in Ref. 46. A previous work has also established that the layers deposited from a CoAl target deposit as B2-CoAl do not contain appreciable stored chemical energy. Furthermore, their inclusion does not cause unique phases to form at heating rates up to 40 °C/min.⁴¹ For the 33 nm RTBL, the peak observed around ∼220–250 °C corresponds to the preferential formation of the Al rich phase Co₂Al₉ with additional intermediate phases (Co₂Al₅ and Co₄Al₁₃) forming at the ∼270–300 °C exotherm.⁴⁶ The exotherm at ∼380 °C corresponds to the formation of the global product phase CoAl from an Al-rich intermediate phase mixture. The effect of adding diffusion barriers to the Co/Al multilayers is to both raise the onset temperature of each exotherm at constant heating rate as well as slightly reduce the total heat released per mole of Co and Al atoms within the multilayer. The former indicates that the diffusion barriers are slowing solid-state mass transport as intended. The latter indicates that the diffusion barriers effectively dilute the multilayer as well. The change in heat release from the addition of diffusion barriers to the smallest (33 nm) and largest (66 nm) RTBLs tested is shown in Table II. Quantification of heat release for each set of samples with the same RTBL was performed with a self-consistent integration baseline. Although the calculated heat release for the baseline control samples from the set of films grown for this study is nominally 5%–15% more exothermic than previously reported values,^41,46,53 the fraction of heat released for samples with diffusion barriers from within the same set of growths is within the measurement error of the volumetric dilution percentage from adding diffusion barriers. Additionally, the stability in solid-state mixing activation energy (Table II) and lack of additional exotherms when compared to a barrierless multilayer indicate that the inert materials added as diffusion barriers are not fundamentally changing the solid-state reaction mechanism in Co/Al. It should be noted that the activation energy calculated from the 10s of °C/min heating rates present in DSC correspond to the slow solid/solid mixing mechanism that traverses through the multiple intermediate intermetallic phases en-route to the B2-product phase. Both $D 0 , ( s / s )$ and $E a , ( s / s )$ for these slow heating rates are substantially different from the kinetic parameters, $D 0 , ( s / l )$⁠, $D 0 , ( l / l )$⁠, $E a , ( s / l )$⁠, and $E a , ( l / l )$⁠, for the solid/liquid dissolution and liquid/liquid mixing responsible for reaction in the self-propagating flame provided in Table I.

Still frames from the high-speed videographs, provided in Fig. 4, show the reaction front morphology for the foils made with and without diffusion barriers. The wavefront morphology for a 33 nm RTBL originates from one of the most reactive and fastest propagating designs in the Co/Al system^44,53 and, thus, should be the most resistant (of the studied multilayers) to instabilities resulting from the addition of inert-mediating layers. Its stable front is shown in Fig. 4(a) for a multilayer having no added barrier. The reaction front maintains its stability for both 1 and 2 nm thick diffusion barrier designs as shown in Figs. 4(b) and 4(c), respectively, but a mode I instability is observed when the diffusion barrier is 3 nm thick in Fig. 4(d).

The reaction front morphologies for the 50 nm RTBL with and without diffusion barriers are shown in Fig. 5. The 50 nm RTBL without a diffusion barrier was chosen because it is known to propagate stably but is at a thickness just below the threshold for the onset of spin (55 nm⁴⁸). A still frame of its stable reaction front is shown in Fig. 5(a). The reaction front morphology of the 50 nm RTBL with a 1 nm diffusion barrier in Fig. 5(b) does not have visible spin bands; however, there is evidence of instability at the marked locations within the image. The reaction front of the 50 nm RTBL with a 1 nm diffusion barrier exhibits optical contrast in the front morphology that is the same as the stable designs, but the reaction wave locally quenches in some areas before reacting the quenched zone later. This behavior can be seen in the time vs position plots beneath the image in Fig. 5(b). The propagating front morphology exhibits local variation, appearing to have a linear time vs displacement relationship in most of the imaged plane, while in some locations, it has stepped behavior akin to the mode II spin band propagation of a 50 nm RTBL with a 2 nm diffusion barrier in Fig. 5(c). Reaction propagation that has these local variations in the characteristics associated with stable and unstable modes will heretofore be referred to as “erratic.” Additional frames of the erratic propagation observed in the 50 nm RTBL with a 1 nm diffusion barrier are provided in Fig. 11 within  Appendix C.

The effects of adding diffusion barriers to 66 nm RTBL multilayers on wavefront morphology are shown in Fig. 6. The 66 nm RTBL without a diffusion barrier propagates with mode I spin bands in Fig. 6(a). Counter to the trends observed in the 33 and 50 nm RTBL, adding a 1 nm diffusion barrier to a 66 nm RTBL induces stability in the reaction front as shown in Fig. 6(b). Increasing the diffusion barrier thickness to 2 nm results in an erratic propagation mode, a single frame of which is shown in Fig. 6(c) for comparison to the other 66 nm RTBL designs. Additionally, a series of eight frames showing the mixture of multiple propagation modes for the 66 nm RTBL with a 2 nm diffusion barrier are provided in Fig. 7. The reaction front starts as a stable front until 2.47 ms after ignition (defined as the time of first light emission in the high-speed camera). The front then quenches much like mode II propagation, and then a single band nucleates at the film edge at 2.80 ms after ignition and begins propagating transverse to the ignition site. Unlike mode II propagation, the band simultaneously propagates in a radial direction with a mixture of uniform optical contrast and regions that resemble mode I spin bands. Local quenching of this mixed front is also observed at 4.13 ms before the quenched region begins reacting 0.33 ms later.

The reaction front of a 66 nm RTBL with a 3 nm thick diffusion barrier in Fig. 6(d) also contains distinct characteristics not previously observed in barrierless Co/Al multilayers of any bilayer thickness.^44,46 While there is optically visible structure at the reaction front indicating an instability, the optical contrast of ∼100 μm behind the front becomes uniform. The observed optical contrast in Fig. 6(d) differs from the quenched in spin band morphology in the reacted product visible in Fig. 6(a) where the periodic ridges persist behind the front to the edge of the image. Of three samples tested, two maintained the described morphology across the full centimeter of the foil while one locally quenched before reigniting and continuing propagation like other erratically propagating designs. Videography frames showing the erratic mode are provided in Fig. 12 within  Appendix D.

The measured velocities are plotted alongside model predictions for each of the tested RTBL designs both with and without diffusion barriers in Fig. 8. The reported error bars on the experimental data points represent the minimum and maximum velocities measured over three ignited foils. The modified Mann model⁶ predicts that the product phase conductivity embedded within the premix zone change both reduces $k lon$ and increases $k trans$ of the overall foils, which then reduces $λ x$ and increases $λ y$ in Eq. (1), respectively. These changes to the thermal circuit lead to a decline in average velocity of the propagating reaction. Additionally, the reduction in stored chemical energy per unit mass in multilayers with diffusion barriers can reduce the net forward propagation velocity by lowering $T f$ in Eq. (1). Values for $T f$ are determined from the enthalpy–temperature diagram based on the method described in Refs. 48 and 53. Given the 15% spread in measured heats of reaction between this work and previous studies, model velocity bands are plotted in Fig. 8 corresponding to a propagation of the maximum uncertainty in formation enthalpy to calculated $T f$ and $v x$⁠. Because $T f$ is constrained by the product melt isotherm (1947 K) for all three barrierless designs, $v x$ is not affected by the uncertainty in average heat release. In fact, the uncertainty in average heat release from calorimetry does not change the predicted velocity for each of the diffusion barrier designs tested for the 50 and 66 nm RTBLs due to this isotherm. However, $T f$ falls below the product melt isotherm between a 1 and 2 nm thick diffusion barrier in the 33 nm RTBL. Here, the uncertainty in average heat release leads to the velocity band plotted in Fig. 8, depicting the range of possible rates at which predicted $T f$ falls off the product melt isotherm and its effect on propagation velocity. The model predictions in Fig. 8 consider a case where $D 0$ remains unchanged. Due to the nature of the methodology developed in Ref. 7 to calculate the values for $E A$ and $D 0$ in Ref. 53, a unique pair is chosen that best fits the measured velocities in the barrierless foils. Shifts from uncertainty in the one variable will produce a concomitant change in the other to maintain a velocity equal to the empirical value of the barrierless foils. The inclusion of diffusion barriers, therefore, changes $T f$ and $λ$ in Eq. (1) at constant $E A$ and $D 0$ to produce the prediction bands in Fig. 8.

The plotted lines in Fig. 8 also assume that the diffusion barrier resides at the center of the intermixed zone, which enables the use of the EDS profile from Ref. 53 when calculating the Fourier coefficients and eigenvalues in Eq. (1). While there is some evidence that premixing following the inclusion of co-deposited B2-CoAl favors wider intermixed zones at Co interfaces (up to ∼3:1 ratio),⁴¹ the distribution around a diffusion barrier will not necessarily be the same as a layer embedded within a reactant due to the difference in the chemical potential at an A–B interface compared to an A–A interface. Additionally, the gray scale contrast in Fig. 2(b) cannot resolve the ∼2-unit cell⁵⁷ difference between a symmetric and a ∼3:1 Co-rich ratio configuration. The effect on k (and proportionally $λ$⁠), $α n$⁠, and $κ n$ from offsetting the diffusion barrier location within the premixed zone toward a wider Co-rich side all individually increases $v x$ in Eq. (1).

The velocity predictions match experimental values both from this work and in literature^44,53 for each of the multilayer designs without diffusion barriers. Of interest is that the time-independent Mann model accurately predicts the average velocity of the barrierless 66 nm RTBL that propagates with a time-dependent mode I spin instability. The convergence of mode I spin instability net-average propagation velocities onto time-independent solutions in Co/Al originates from the fact that for the specific bimetallic system the spin band nucleation rate is fast enough to produce linear time vs position behavior during self-propagation.⁴¹ Furthermore, the Mann model calculates a velocity proportional to a $T f$ determined by the thermodynamic state of the foil, and it has been previously demonstrated that time-dependent phenomena, such as radiative loss,⁵³ can be incorporated into the analytical solution by solving for the enthalpy within the flame width. This $T f$ represents an “effective temperature” averaged over time-dependent events, such as instabilities, that locally exhibit an oscillatory temperature profile.⁴⁶ In the case of mode I spin, losses from net-forward heat conduction are not losses from the thermodynamic system, and so the time-averaged heat within the flame becomes quantitatively equivalent to a time-independent solution for $T f$⁠. The Mann model, therefore, provides the central velocity within the radial direction about which the instability oscillates.

For the designs that propagated stably (i.e., 33 nm RTBL with a 1 or 2 nm diffusion barrier and the 66 nm RTBL with a 1 nm diffusion barrier), the drop in net forward propagation velocity is within the measurement error of model predictions. However, the unstable reaction waves arising from 3 nm thick diffusion barriers in 33 nm RTBL designs, 1 and 2 nm thick diffusion barriers in 50 nm RTBL designs, and 2 nm thick diffusion barriers in 66 nm RTBL designs all fall below predicted values. The unstable mode propagating at 1.4 ± 0.2 m/s for the 66 nm RTBL design with a 3 nm thick diffusion barrier is difficult to interpret because the samples that did not locally quench propagate at the expected value when only considering the loss in stored chemical energy from inserting an inert material, while the one sample that did locally quench had a slower velocity of 1.2 m/s.

Given that each source of error for the values in Eq. (1) would lead the calculated velocity prediction to underestimate propagation velocity in Co/Al with diffusion barriers, it becomes apparent that the barrier itself is inhibiting net forward propagation for mode I spin bands in the 33 nm RTBL with 3 nm thick diffusion barrier design. The reduction in propagation velocity can be described by a reduction in $D 0$ that occurs for unstable modes but not stable ones, describing that behavior requires knowledge of the material heat transport and phase conditions at which spin bands form. It has been previously determined that instabilities in Co/Al first arise when thermal conduction in the net forward direction reduces the enthalpy in the flame below the Co melt isotherm.⁴¹ Instead of mixing within a co-melt, the reaction involves dissolution of Co atoms into liquid Al.⁵³ The forward conducted heat is then able to grow a pre-reacted layer at the interface between solid Co and liquid Al, which impedes self-propagation of the flame. While the location of CoAl diffusion barriers changes the thermal conductivity locally at the reaction nucleation site and prevents a simple analytical quantification of the enthalpy loss in a given multilayer design like in Ref. 53, the description of present phases for both stable and spin band propagation can be used to interpret the convergent and divergent velocities to a modified Mann model when diffusion barriers are added to the Co/Al multilayers. Namely, the observation that the diffusion barriers do not reduce $D 0$ so long as the wavefront maintains stability occurs because the thin layer cannot remain intact to inhibit mixing when the reactants co-melt. The only drop in velocity comes from the additional inert mass within the bimetallic liquid. However, if the Co reactant remains solid, the diffusion barrier of higher melting temperature (1640 vs 1495 °C)⁵⁸ remains at the interface, and the liquid Al and Co atoms must pass through the CoAl before they can react. The additional barrier to mass transport (i.e., lower $D 0$⁠) is consistent with the observed drop in propagation velocity beyond a direct removal of energy per unit mass for multilayers with diffusion barriers once a spin mode is activated. Calculations of the reduced $D 0$ based on the velocity of the unstably propagating foils were not performed because an underlying assumption of the Mann model is that forward heat conduction is small enough to not change $T f$⁠. Given that the mechanism for the onset of instabilities in Co/Al is the net forward conduction of heat sufficient to reduce the flame temperature below the Co melt isotherm, such a calculation would produce a nonphysical $D 0$⁠.

A closer look at the local velocity within the steadily propagating regions of the erratically propagating reaction in the 66 nm RTBL with a 2 nm diffusion barrier provides further insight into a phase-based explanation of diffusion barrier effects. The linear portion of the position–time plot in Fig. 7 is propagating at a velocity of 1.7 ± 0.1 m/s, which would fall above the lower bound of the model line for that multilayer design in Fig. 8, meaning that the propagation is erratic because co-melting of reactants is only sometimes achieved. Similarly, for other erratically propagating designs, the steady zones have propagation velocities of 2.6 ± 0.1 m/s for the 50 nm RTBL with a 1 nm diffusion barrier and 1.6 ± 0.1 m/s for the 66 nm RTBL with a 3 nm diffusion barrier. Both of these values fall above the lower bound for velocity predicted by the Mann model. Essentially, erratic propagation is occurring because there exists a stochastic component of melting in confined thin films where the phase change nucleates preferentially at grain boundaries and film edges.⁵⁹ Local variations in foil topology or edge effects can affect the melt nucleation and lead to the observed local variation in propagation behavior.

The reversal of trend, in which the addition of a 1 nm thick diffusion barrier to the 66 nm RTBL design made propagation more stable, has interesting implications for designing reactive metal multilayers that are more resilient to aging effects. While the thin CoAl layer reduced the stored chemical energy by ∼5% compared to a 66 nm RTBL without any barrier, it also increased the full-foil transverse thermal conductivity from 39 to 51 ± 3 W/m K while reducing the longitudinal thermal conductivity from 154 to 152 ± 1 W/m K. The change in thermal conductivity occurs because the crystalline deposit from the CoAl targets⁴¹ is almost a factor of 5 more conductive than the amorphous premix layer.^53,60 The result is that the ratio between the rate of heat release into the flame and conduction away from the front increases, which, in turn, promotes stability even if the average velocity decreases. Notably, the window where the induced stability was observed is very narrow given that it required an initial RTBL design near the stability threshold and a 30% increase in transverse thermal conductivity with only a 5% decrease in stored chemical energy. Meanwhile, the transition to an erratic propagation with an additional nanometer in diffusion barrier thickness in spite of it only representing a 7% loss in stored chemical energy with a 70% increase in transverse thermal conductivity suggests that there also exists a kinetic limitation on dissolving the barrier itself into the melt.

From a design perspective, only materials’ systems that have highly thermally insulating amorphous premixed layers and have a potential spin instability, such as Co/Al, Sc/Ag,⁵² and Al/Pt₄,⁷ may benefit from using their order of magnitude more conductive product phase^56,61 as a diffusion barrier to improve stability. Within the common Ni/Al multilayer system, the intermixed zone has been suggested by some to have the B2 phase,⁶² a disordered solid solution,^63,64 or an amorphous.^63–65 Without a substantial difference in thermal conductivity between the diffusion barrier layer and pre-existing interlayer that exists between the localized d-states of amorphous transition metal alloys⁶⁶ and the ordered intermetallic bonding of their stoichiometric compounds, the loss in stored chemical energy will overwhelm changes to the effective conductivity of the interlayer thermal resistor. Should a materials’ system not have a substantial difference in thermal conductivity between its as-deposited interlayer and reaction product phase, an inert metallic ternary may provide a suitable alternative. Also, while models have predicted the possibility for a spin instability in Ni/Al,⁵⁴ only 1D oscillatory instabilities have been experimentally observed in the Ni/Al materials’ system, which are not fundamentally tied to overcoming the latent heat of melting for either reactant⁴² and, thus, could not be suppressed by using diffusion barriers to increase thermal conductivity of the interlayers.

The Co/Al multilayer system with CoAl diffusion barriers has been grown and characterized, in terms of the deposited microstructure, stored chemical energy, and reaction behavior. The diffusion barriers act as inert-mediating layers by reducing the internal energy per unit atom/mass/volume and change the macro-scale thermal conductivity of each design. The loss in stored chemical energy and anticipated effects lead to lower propagation velocities for a given RTBL, albeit to a lesser degree than substantially increasing bilayer thickness or using a less reactive material system. However, for most multilayer designs, the addition of diffusion barriers reduces the likelihood of stable propagation. The introduction of either spin instabilities or outright erratic propagation represents a potential failure mode if a diffusion barrier naturally grows within a multilayer as a result of material aging. It is also possible to intentionally design a reactive multilayer such that the diffusion barrier changes the thermal circuit to reduce conduction away from the flame front enough so that it overwhelms the thermodynamic reduction in stored chemical energy. These designs will involve using large bilayer thicknesses with minimal thickness diffusion barriers possessing a higher thermal conductivity than the naturally occurring premix layer.

The authors thank M. Rye and J. Michael for FIB sample preparation and M. Rodriguez for XRD. The authors also thank D. Kittell for his internal peer review. This work was supported by the Sandia National Laboratory Directed Research and Development (LDRD) program. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under Contract No. DE-NA0003525. This work describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the U.S. Government.

The authors have no conflicts to disclose.

Michael J. Abere: Formal analysis (lead); Methodology (equal); Writing – original draft (lead). Robert V. Reeves: Conceptualization (supporting); Investigation (lead); Methodology (equal). Catherine Sobczak: Investigation (supporting). Hyein Choi: Formal analysis (supporting); Visualization (lead). Paul G. Kotula: Formal analysis (supporting); Investigation (supporting). David P. Adams: Conceptualization (lead); Formal analysis (supporting); Funding acquisition (lead); Project administration (lead); Resources (lead); Supervision (lead); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Fast Fourier transforms taken from a STEM image of a diffusion barrier co-deposited from a CoAl target between a Co and a Al layer are shown in Fig. 9. The structure was confirmed crystalline with the symmetry and lattice plane spacing of the B2-CoAl phase.

Thermograms of the 66 nm RTBL Co/Al foils are provided in Fig. 10. The thermograms at differing diffusion barrier thicknesses were taken at a heating rate of 20 °C/min. Exotherms are represented with a negative heat flow.

A sequence of still frames from high-speed videography of 50 nm RTBL with a 1 nm diffusion barrier at 0.125 ms timesteps are shown in Fig. 11.

A sequence of still images from high-speed videography of 66 nm RTBL with a 3 nm diffusion barrier at 0.25 ms timesteps are shown in Fig. 12.