A predictive analytical model is presented for the electrical conductivity of multi-principal-element alloys (MPEAs), including those containing aluminum, transition metals, and refractory metals. Given that the lattice parameter of the Wigner-Seitz cell of an MPEA is similarly variable to a bulk metallic glass, it is postulated that electron scattering can be approximated by a series of two-level systems. The resulting reduced-order model enabled an accurate determination of electrical resistivity and electron thermal conductivity based on the scattering of electrons in a two-level system across a Bloch-potential-based virtual crystal approximation. Model results are compared to experimental four-point probe electrical resistivity measurements between 300 K and 700 K for Al0.3CoCrCuFeNi, CoCrFeMnNi, (CoCrFeMnNi)0.98W0.02, (CoCrFeMnNi)0.95W0.05, and Nb4Ta4V3Ti, for model validation.
The sputter deposition of alternating layers of Ni(V) and Al forms a reactive multilayer known to undergo self-propagating formation reactions when ignited. The sequential deposition process leads to nanometer-scale premixing of reactants at each included interface, which ultimately affects multilayer exothermicity. This work performs the direct measurement of a disordered face-centered cubic (FCC) solid solution premixed phase at the interfaces of Ni(V)/Al multilayers via scanning transmission electron microscopy. The crystallinity of the observed phase differs from previously reported a priori predictions of an amorphous interlayer. The disordered FCC phase retains its symmetry after annealing for 16 h at 135 ± 5 °C, but the lattice parameter shifts consistently with an Al-rich composition. The existence of a crystalline premix in Ni(V)/Al is attributed to the electronic contribution to the entropy of crystallization. The importance of electronic entropy to the phase formation of energetic materials motivates its inclusion when constructing digital twins for atomistic kinetics and ignition sensitivity.
Mesoscale modeling of shock waves in Ni+Al multilayers poses significant challenges that are due, in part, to shock-induced chemical reactions. Current modeling approaches utilize reactive molecular dynamics (MD), but they are limited to resolving domains of only a few hundred nanometers. In contrast, actual multilayer superlattices can be tens of micrometers thick, and they exhibit non-ideal (i.e., wavy) interfaces. The second part of our research builds upon previous work developing physically based, thermodynamically complete equations of state for various Ni and Al intermetallic compositions. Here, we introduce a novel workflow for high-fidelity mesoscale simulations of Ni+Al multilayers using a continuum hydrocode. By increasing the simulation domain size beyond MD limitations (e.g., 2 × 6 μm2) and incorporating explicit interfacial roughness, we investigate the shock response of Ni+Al multilayers at previously unexplored scales. Our experimental design encompasses nine multilayer geometries with varying roughness amplitudes and tilt angles (θ = 15°, 30°, and 45°), alongside 19 flyer impact velocities ranging from 0.3 to 3.0 km/s, resulting in a total of 171 high-fidelity simulations. The bulk shock state from inert 2D mesoscale simulations aligns with the law of mixtures, while temperature and pressure fluctuations strongly correlate with multilayer geometry types. A new metric dubbed the “hot spot probability integral” shows a greater dependence on a tilt angle than interfacial roughness.
Continuum shock mixture models are reviewed and applied to determine the equations of state for five different compositions of Ni xAl y, as well as bulk Ni+Al reactive multilayers, by combining the fundamental property data for elemental nickel and aluminum. From the literature, we down-select and evaluate two analytical models for the mixture Hugoniot, i.e., the well-known method of kinetic energy averaging (KEA) and a recent model proposed by Jordan and Baer [J. Appl. Phys. 111, 083516 (2012)]. Fundamentally, the former method assumes pressure equilibrium, whereas the latter assumes a common particle velocity and mixture sound speed from compressible two-phase cavitating flows. Additionally, we construct thermodynamically complete equations of state by fitting Einstein oscillator series models for the specific heat at constant volume. Finally, the solid solution approximation is invoked for intermetallic compositions, which are not strictly physical mixtures. Overall, the KEA model provides a better fit to the available Ni xAl y and Ni+Al multilayer shock compression data; however, there are combinations of material properties where the performance of these two models is thought to be reversed. Moreover, the results of this work include the first analytical solution of Jordan–Baer that does not require numerical root finding, as well as proposed modifications to the Einstein oscillator series to incorporate some effects of local pressure–temperature equilibrium and reaction–diffusion. Future work is planned that will use these equations of state in mesoscale simulations to study shock-induced reaction in Ni+Al multilayers, and the intended application is illustrated with a brief 2D hydrocode example.
The additive manufacture of compositionally graded Al/Cu parts by laser engineered net shaping (LENS) is demonstrated. The use of a blue light build laser enabled deposition on a Cu substrate. The thermal gradient and rapid solidification inherent to selective laser melting enabled mass transport of Cu up to 4 mm from a Cu substrate through a pure Al deposition, providing a means of producing gradients with finer step sizes than the printed layer thicknesses. Divorcing gradient continuity from layer or particle size makes LENS a potentially enabling technology for the manufacture of graded density impactors for ramp compression experiments. Printing graded structures with pure Al, however, was prevented by the growth of Al2Cu3 dendrites and acicular grains amid a matrix of Al2Cu. A combination of adding TiB2 grain refining powder and actively varying print layer composition suppressed the dendritic growth mode and produced an equiaxed microstructure in a compositionally graded part. Material phase was characterized for crystal structure and nanoindentation hardness to enable a discussion of phase evolution in the rapidly solidifying melt pool of a LENS print.
Density-functional theory (DFT) is used to identify phase-equilibria in multi-principal-element and high-entropy alloys (MPEAs/HEAs), including duplex-phase and eutectic microstructures. A combination of composition-dependent formation energy and electronic-structure-based ordering parameters were used to identify a transition from FCC to BCC favoring mixtures, and these predictions experimentally validated in the Al-Co-Cr-Cu-Fe-Ni system. A sharp crossover in lattice structure and dual-phase stability as a function of composition were predicted via DFT and validated experimentally. The impact of solidification kinetics and thermodynamic stability was explored experimentally using a range of techniques, from slow (castings) to rapid (laser remelting), which showed a decoupling of phase fraction from thermal history, i.e., phase fraction was found to be solidification rate-independent, enabling tuning of a multi-modal cell and grain size ranging from nanoscale through macroscale. Strength and ductility tradeoffs for select processing parameters were investigated via uniaxial tension and small-punch testing on specimens manufactured via powder-based additive manufacturing (directed-energy deposition). This work establishes a pathway for design and optimization of next-generation multiphase superalloys via tailoring of structural and chemical ordering in concentrated solid solutions.
A thermally driven, micrometer-scale switch technology has been created that utilizes the ErH3/Er2O3 materials system. The technology is comprised of novel thin film switches, interconnects, on-board micro-scale heaters for passive thermal environment sensing, and on-board micro-scale heaters for individualized switch actuation. Switches undergo a thermodynamically stable reduction/oxidation reaction leading to a multi-decade (>11 orders) change in resistance. The resistance contrast remains after cooling to room temperature, making them suitable as thermal fuses. An activation energy of 290 kJ/mol was calculated for the switch reaction, and a thermos-kinetic model was employed to determine switch times of 120 ms at 560 °C with the potential to scale to 1 ms at 680 °C.
Bimetallic, reactive multilayers are uniformly structured materials composed of alternating sputter-deposited layers that may be ignited to produce self-propagating mixing and formation reactions. These nanolaminates are most commonly used as rapid-release heat sources. The specific chemical composition at each metal/metal interface determines the rate of mass transport in a mixing and formation reaction. The inclusion of engineered diffusion barriers at each interface will not only inhibit solid-state mixing but also may impede the self-propagating reactions by introducing instabilities to wavefront morphology. This work examines the effect of adding diffusion barriers on the propagation of reaction waves in Co/Al multilayers. The Co/Al system has been shown to exhibit a reaction propagation instability that is dependent on the bilayer thickness, which allows for the occurrence of unstable modes in otherwise stable designs from the inclusion of diffusion barriers. Based on the known stability criteria in the Co/Al multilayer system, the way in which the inclusion of diffusion barriers changes a multilayer's heat of reaction, thermal conductivity, and material mixing mechanisms can be determined. These factors, in aggregate, lead to changes in the wavefront velocity and stability.
The propagation of self-sustained formation reactions in sputter-deposited Co/Al multilayers is known to exhibit a design-dependent instability. Multilayers having thin bilayers (<55 nm period) exhibit stable propagating waves, whereas those with a larger period react unstably. The specific two-dimensional (2D) instability observed involves the transverse propagation of a band in front of a stalled front commonly referred to as a “spin band.” Previous finite-element studies have shown that these instabilities are thermodynamically driven by the forward conduction of heat away from the flame front. However, the magnitude of that loss is inherently tied to the bilayer design in traditional bimetallic multilayers, which couples any proposed stability criteria to a varying critical diffusion distance. This work utilizes a recently developed class of materials known as “inert-mediated reactive multilayers” to decouple the thermodynamic and kinetic contributions to propagating wave stability by reducing the stored chemical energy density in normally stable bilayer designs. By depositing an inert product phase (B2-CoAl) within the mid-plane of Co and Al reactant layers, spin instabilities arise as a function of both diluted volume and critical diffusion distance. From there, a stability criterion is determined for Co/Al multilayers based on enthalpy loss from the reaction zone, and its physical significance is explored.
Nanothermite NiO-Al is a promising material system for low gas emission heat sources; yet, its reactive properties are highly dependent on material processing conditions. In the current study, sputter deposition is used to fabricate highly controlled nanolaminates comprised of alternating NiO and Al layers. Films having an overall stoichiometry of 2Al to 3NiO were produced with different bilayer thicknesses to investigate how ignition and self-sustained, high temperature reactions vary with changes to nanometer-scale periodicity and preheat conditions. Ignition studies were carried out with both hot plate and laser irradiation and compared to slow heating studies in hot-stage x-ray diffraction. Ignition behavior has bilayer thickness and heating rate dependencies. The 2Al/3NiO with λ ≤ 300 nm ignited via solid/solid diffusion mixing (activation energy, Ea = 49 ± 3 kJ/mole). Multilayers having λ≥ 500 nm required a more favorable mixing kinetics of solid/liquid dissolution into molten Al (Ea = 30 ± 4 kJ/mole). This solid/liquid dissolution Ea is a factor of 5 lower than that of the previously reported powder compacts due to the elimination of a passivating Al oxide layer present on the powder. The reactant mixing mechanism between 300 and 500 nm bilayer thicknesses was dependent on the ignition source's heating rate. The self-propagating reaction velocities of 2Al/3NiO multilayers varied from 0.4 to 2.5 m/s. Pre-heating nanolaminates to temperatures below the onset reaction temperatures associated with forming intermediate nickel aluminides at multilayer interfaces led to increased propagation velocities, whereas pre-heating samples above the onset temperatures inhibited subsequent attempts at laser ignition.
Reactive Co/Al multilayers are uniformly structured materials that may be ignited to produce rapid and localized heating. Prior studies varying the bilayer thickness (i.e., sum of two individual layers of Co and Al) have revealed different types of flame morphologies, including: (a) steady/planar, (b) wavy/periodic, and (c) transverse bands, originating in the flame front. These instabilities resemble the “spin waves” first observed in the early studies of solid combustion (i.e., Ti cylinder in a N2 atmosphere), and are likewise thought to be due to the balance of heat released by reaction and heat conduction forward into the unreacted multilayer. However, the multilayer geometry and three-dimensional (3D) edge effects are relatively unexplored. In this work, a new diffusion-limited reaction model for Co/Al multilayers was implemented in large, novel 3D finite element analysis (FEA) simulations, in order to study the origins of these spinlike flames. This reaction model builds upon previous work by introducing three new phase-dependent property models for: (1) the diffusion coefficient, (2) anisotropic thermal conductivity tensor, and (3) bulk heat capacity, as well as one additional model for the bilayer-dependent heat of reaction. These novel 3D simulations are the first to predict both steady and unsteady flames in Co/Al multilayers. Moreover, two unsteady modes of flame propagation are identified, which depend on the enhanced conduction losses with slower flames, as well as flame propagation around notched edges. Future work will consider the generality of the current modeling approach and also seek to define a more generalized set of stability criteria for additional multilayer systems.
Pulsed laser irradiation is used to investigate the local initiation of rapid, self-propagating formation reactions in Al/Pt multilayers. The single pulse direct laser ignition of these 1.6 μm thick freestanding foils was characterized over 10 decades of pulse duration (10 ms to 150 fs). Finite element, reactive heat transport modeling of the near-threshold conditions has identified three distinct ignition pathways. For milli- to microsecond pulses, ignition occurs following sufficient absorption of laser energy to enable diffusion of Al and Pt between layers such that the heat released from the corresponding exothermic reaction overcomes conductive losses outside the laser-irradiated zone. When pulse duration is decreased into the nanosecond regime, heat is concentrated near the surface such that the Al locally melts, and a portion of the top-most bilayers react initially. The favorable kinetics and additional heat enable ignition. Further reducing pulse duration to hundreds of femtoseconds leads to a third ignition pathway. While much of the energy from these pulses is lost to ablation, the remaining heat beneath the crater can be sufficiently concentrated to drive a transverse self-propagating reaction, wherein the heat released from mixing at each interface occurs under kinetic conditions capable of igniting the subsequent layer.
Multilayers composed of aluminum (Al) and platinum (Pt) exhibit a nonmonotonic trend in thermal resistance with bilayer thickness as measured by time domain thermoreflectance. The thermal resistance initially increases with reduced bilayer thickness only to reach a maximum and then decrease with further shrinking of the multilayer period. These observations are attributed to the evolving impact of an intermixed amorphous complexion approximately 10 nm in thickness, which forms at each boundary between Al- and Pt-rich layers. Scanning transmission electron microscopy combined with energy dispersive x-ray spectroscopy find that the elemental composition of the complexion varies based on bilayer periodicity as does the fraction of the multilayer composed of this interlayer. These variations in complexion mitigate boundary scattering within the multilayers as shown by electronic transport calculations employing density-functional theory and nonequilibrium Green's functions on amorphous structures obtained via finite temperature molecular dynamics. The lessening of boundary scattering reduces the total resistance to thermal transport leading to the observed nonmonotonic trend thereby highlighting the central role of complexion on thermal transport within reactive metal multilayers.
