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At least 73 records · Page 4

Knowledge gaps for neuromorphic ionic computing

BACKGROUND Neuromorphic computing, inspired by the human brain’s ability to process information efficiently, represents a transformative approach to computation. In this Review, we explore the emerging field of neuromorphic ionic computing, which leverages ionic conduction and coupling to mimic neural processes, and identify critical knowledge gaps that must be addressed to realize its full potential. A central theme of the discussion is energy efficiency, a challenge that is both a limitation and an opportunity for this technology. Although complementary metal-oxide semiconductor (CMOS)–based neuromorphic technologies have made strides in scaling to billions of neurons and are increasingly applied in artificial intelligence and numerical computing, they remain orders of magnitude behind the human brain in terms of connectivity and energy efficiency. Neuromorphic ionic computing promises to overcome these limitations by leveraging the distinct architectural and operational principles of the brain. Our brains achieve this energy efficiency by combining several key features: using the same network elements to store and process information; using an incredibly complex and massively interconnected three-dimensional (3D) network of locally active elements that enables sparsity, robustness in the presence of noise, adaptation, and life-long learning; computing at comparatively low voltage and frequency; and last, taking advantage of a plethora of ions and small molecules as information carriers. Here, we propose that ionic computing systems can take advantage of similar features to achieve substantial gains in energy efficiency. ADVANCES Since the first reports of neuromorphic ionic behavior in nanofluidic channels, we have witnessed an explosion of reports that used ionic devices to produce synaptomimetic behaviors. However, achieving the goals of ionic computing requires not only implementation of much more sophisticated device functionality but also overcoming fundamental barriers in materials science, device architecture, and system integration. Current ionic devices, even those incorporating state-of-the-art materials, still suffer from limited functionality and stability, which restrict their performance and increase energy demands. Developing new materials with enhanced ionic properties is essential to overcome these limitations. Similarly, the design of neuromorphic devices must evolve to leverage the particular advantages of ionic processes. Existing architectures often follow a single-information-carrier logic of conventional electronics or are constructed of mesoscale fluidics, failing to capitalize on the energy-efficient mechanisms inherent to ionic systems or implement the multiple-information-carrier paradigm. Current neuromorphic chips focus on large-scale networks of analog memory elements based on mechanisms such as charge trap (flash), filamentary, phase change, or spin, which are built on top of a network of artificial CMOS neurons. Although such prototype networks have achieved impressive performance, it is difficult to envision how they can implement the key features such as massive connectivity, sophisticated plasticity, adaptability, sparsity, and “multichromatic” computing. Although small-scale devices have demonstrated promising results, integrating them, maintaining energy efficiency, and implementing temperature control as systems grow in complexity and size to computationally relevant scale remain major hurdles. Furthermore, interfacing neuromorphic ionic devices with existing computing technologies presents technical and conceptual challenges that will require innovative approaches that combine insights from neuroscience, materials science, and engineering. OUTLOOK Despite these challenges, the potential impact of neuromorphic ionic computing is profound with potential applications ranging from artificial intelligence to robotics and beyond. We also argue that neuromorphic ionic computing systems should not, at least in the beginning, compete with CMOS technologies but rather should focus on applications that require extreme energy efficiency with chemical and/or biological compatibility, such as biomedical applications (for example, brain-computer interfaces), environmental monitoring, and agricultural and food applications. Ultimately, this Review highlights the crucial role of interdisciplinary collaboration in advancing the field. Neuromorphic ionic computing is not merely a technological innovation; it represents a substantial step toward sustainable computation, aligning with the growing demand for energy-conscious solutions in a world that is increasingly reliant on data and computation.

Neuromorphic↗

Effect of advanced component technology on helicopter transmissions

Experimental tests were performed on the NASA/Bell Helicopter Textron (BHT) 500 hp advanced technology transmission (ATT) at the NASA Lewis Research Center. The ATT was a retrofit of the OH-58C helicopter 236 kW (317 hp) main rotor transmission, upgraded to 373 kW (500 hp), with a design goal of retaining long life with a minimum increase in cost, weight, and size. Vibration, strain, efficiency, deflection, and temperature experiments were performed and the results were compared to previous experiments on the OH-58A, OH-58C, and UH-60A transmissions. The high-contact-ratio gears and the cantilevered-mounted, flexible ring gear of the ATT reduced vibration compared to that of the OH-58C. The ATT flexible ring gear improved planetary load sharing compared to that of the rigid ring gear of the UH-60A transmission. The ATT mechanical efficiency was lower than that of the OH-58A transmission, probably due to the high-contact-ratio planetary gears.

Lewicki, David G.↗

Effect of advanced component technology on helicopter transmissions

Experimental tests were performed on the NASA/Bell Helicopter Textron (BHT) 500 hp advanced technology transmission (ATT) at the NASA Lewis Research Center. The ATT was a retrofit of the OH-58C helicopter 236 kW (317 hp) main rotor transmission, upgraded to 373 kW (500 hp), with a design goal of retaining long life with a minimum increase in cost, weight, and size. Vibration, strain, efficiency, deflection, and temperature experiments were performed and the results were compared to previous experiments on the OH-58A, OH-58C, and UH-60A transmissions. The high-contact-ratio gears and the cantilevered-mounted, flexible ring gear of the ATT reduced vibration compared to that of the OH-58C. The ATT flexible ring gear improved planetary load sharing compared to that of the rigid ring gear of the UH-60A transmission. The ATT mechanical efficiency was lower than that of the OH-58A transmission, probably due to the high-contact-ratio planetary gears.

Lewicki, D. G.↗

Influences of chemical sympathectomy and simulated weightlessness on male and female rats

Consideration is given to a study aimed at determining whether the sympathetic nervous system is associated with the changes in maximum oxygen consumption (VO2max), run time, and mechanical efficiency observed during simulated weightlessness in male and female rats. Female and male rats were compared for food consumption, body mass, and body composition in conditions of simulated weightlessness to provide an insight into how these parameters may influence aerobic capacity and exercise performance. It is concluded that chemical sympathectomy and/or a weight-bearing stimulus will attenuate the loss in VO2max associated with simulated weightlessness in rats despite similar changes in body mass and composition. It is noted that the mechanisms remain unclear at this time.

Woodman, Christopher R.↗

Multiscale mechanical design of the lightweight, stiff, and damage-tolerant cuttlebone: A computational study

Cuttlebone, the endoskeleton of cuttlefish, offers an intriguing biological structural model for designing low-density cellular ceramics with high stiffness and damage tolerance. Cuttlebone is highly porous (porosity ~93%) and lightweight (density less than 20% of seawater), constructed mainly by brittle aragonite (95 wt%), but capable of sustaining hydrostatic water pressures over 20 atmospheres and exhibits energy absorption capability under compression comparable to many metallic foams (~4.4 kJ/kg). Here, in this work, we computationally investigate how such remarkable mechanical efficiency is enabled by the multiscale structure of cuttlebone. Using the common cuttlefish, Sepia Officinalis, as a model system, we first conducted high-resolution synchrotron micro-computed tomography (µ-CT) and quantified the cuttlebone's multiscale geometry, including the 3D asymmetric shape of individual walls, the wall assembly patterns, and the long-range structural gradient of walls across the entire cuttlebone (ca. 38 chambers). The acquired 3D structural information enables systematic finite-element simulations, which further reveal the multiscale mechanical design of cuttlebone: at the wall level, wall asymmetry provides optimized energy absorption while maintaining high structural stiffness; at the chamber level, variation of walls (number, pattern, and waviness amplitude) contributes to progressive damage; at the entire skeletal level, the gradient of chamber heights tailors the local mechanical anisotropy of the cuttlebone for reduced stress concentration. Our results provide integrated insights into understanding the cuttlebone's multiscale mechanical design and provide useful knowledge for the designs of lightweight cellular ceramics.

36 MATERIALS SCIENCE↗

Mechanically activated and deactivated ion transport across nanopores with heterogeneous surface charge distributions

To mimic the intricate and adaptive functionalities of biological ion channels, electrohydrodynamic ion transport has been studied extensively, albeit mostly, across uniformly charged nanochannels. Here, we analyze the ion transport under coupled electric field and pressure across heterogeneously charged nanopores with oppositely charged sections on their lateral surface. We only consider such pores with symmetric hourglass-like and cylindrical shapes to focus on the effects of the non-uniform surface charge distribution. Finite-element simulations of a continuum model demonstrate that a pressure applied in either direction of the pore-axis equally suppresses or amplifies the ionic conductance, depending on the electric field polarity, by distorting the quasi-static distribution of ions in the pore. The resulting anomalous mechanical deactivation and activation of ionic current under opposite voltage biases exhibit the functional modularity of our setup, while their intensities are highly tunable, substantially greater than those of analogous behaviors in other nanochannels, and fundamentally correlated to ionic current rectification (ICR) in our pores. A detailed study of ICR subsequently reveals its counterintuitive non-monotonous variations, in the pores, with the magnitude of applied voltage and the pore length, that can help optimize their diode-like behavior. We further illustrate that while the hourglass-shaped nanopores yield the more efficient mechanical suppressors of ion transport, their cylindrical analogs are the superior rectifiers and mechanical amplifiers of ion conduction. Therefore, this article provides a blueprint for the strategic design of nanofluidic circuits to attain a robust, modular, and tunable control of ion transport under external electrical and mechanical stimuli.

Physics↗

Novel High-Voltage, High-Power Piezoelectric Transformer Developed and Demonstrated for Space Communications Applications

Improvements in individual piezoelectric transformer (PT) performance and the combination of these PTs in a unique modular topology under a Phase I contract with the NASA Glenn Research Center have enabled for the first time the simultaneous achievement of both high voltage and high power at much higher levels than previously obtained with any PT. Feasibility was demonstrated by a prototype transformer (called a Tap-Soner), which is shown in the preceding photograph as part of a direct-current to direct-current (dc-dc) converter having two outputs rated at 1.5 kV/5 W and 4.5 kV/20 W. The power density of 3.5 W/cm3 is significantly lower than for magnetic transformers with the same voltage and power output. This development, which is being done under a Small Business Innovation Research (SBIR) contract by Face Electronics, LC (Norfolk, VA), is based on improvements in the materials and design of Face's basic patented Transoner-T3 PT, shown in the left in the following figure. The T3 PT is most simply described as a resonant multilayer transducer where electrical energy at the input section is efficiently mechanically coupled to the output section, which then vibrates in a fundamental longitudinal mode to generate a high gain in voltage. The piezoelectric material used is a modified lead-zirconium-titanate-based ceramic. One of the significant improvements in PT design was the incorporation of a symmetrical double input layer, shown on the right in the following figure, which eliminated the lossy bending vibration modes characteristic of a single input layer. The performance of the improved PT was optimized to 1.5 kV/5 W. The next step was devising a way to combine the individual PTs in a modular circuit topology needed to achieve the desired high voltage and power output. Since the optimum performance of the individual PT occurs at resonance, the most efficient operation of the modular transformer was achieved by using a separate drive circuit for each PT. The output section consists of a separate output rectifier for each PT connected in series.

Carazo, Alfredo V.↗

X-ray and Neutron Reflectivity Studies of Styrene-Maleic Acid Copolymer Interactions with Galactolipid-Containing Monolayers

Styrene-maleic acid (SMA) copolymers have recently gained attention for their ability to facilitate the detergent-free solubilization of membrane protein complexes and their native boundary lipids into polymer-encapsulated, nanosized lipid particles, referred to as SMALPs. However, the interfacial interactions between SMA and lipids, which dictate the mechanism, efficiency, and selectivity of lipid and membrane protein extraction, are barely understood. Our recent finding has shown that SMA 1440, a chemical derivative of the SMA family with a functionalized butoxyethanol group, was most active in galactolipid-rich membranes, as opposed to phospholipid membranes. In the present work, we have performed X-ray reflectometry (XRR) and neutron reflectometry (NR) on the lipid monolayers at the liquid–air interface followed by the SMA copolymer adsorption. XRR and Langmuir Π–A isotherms captured the fluidifying effect of galactolipids, which allowed SMA copolymers to infiltrate easily into the lipid membranes. NR results revealed the detailed structural arrangement of SMA 1440 copolymers within the membranes and highlighted the partition of butoxyethanol group into the lipid tail region. In conclusion, this work allows us to propose a possible mechanism for the membrane solubilization by SMA.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Synthetic Lubricants Derived from Plastic Waste and their Tribological Performance

The energy efficiency, mechanical durability, and environmental compatibility of all moving machine components rely heavily on advanced lubricants for smooth and safe operation. Herein an alternative family of high-quality liquid (HQL) lubricants was derived by the catalytic conversion of pre- and post-consumer polyolefin waste. The plastic-derived lubricants performed comparably to synthetic base oils such as polyalphaolefins (PAOs), both with a wear scar volume (WSV) of 7.5×10 -5 mm -3 . HQLs also performed superior to petroleum-based lubricants such as Group III mineral oil with a WSV of 1.7×10 -4 mm -3 , showcasing a 44% reduction in wear. Furthermore, a synergistic reduction in friction and wear was observed when combining the upcycled plastic lubricant with synthetic oils. Additionally, life cycle and techno-economic analyses also showed this process to be energetically efficient and economically feasible. This novel technology offers a cost-effective opportunity to reduce the harmful environmental impact of plastic waste on our planet and to save energy through reduction of friction and wear-related degradations in transportation applications akin to synthetic oils.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Small scales formation via Alfven wave propagation in compressible nonuniform media

In weakly dissipative media governed by the magnetohydrodynamics (MHD) equations, any efficient mechanism of energy dissipation requires the formation of small scales. The possibility to produce small scales has been studied by Malara et al. in the case of MHD disturbances propagating in an incompressible and inhomogeneous medium, for a strictly 2D geometry. We extend the work of Malara et al. to include both compressibility and the third component for vector quantities. Using numerical simulations we show that, when an Alfven wave propagates in a compressible nonuniform medium, the two dynamical effects responsible for the small scales formation in the incompressible case are still at work: energy pinching and phase-mixing. Moreover, the interaction between the initial Alfven wave and the inhomogeneity gives rise to the formation of compressible perturbations (fast and slow waves or a static entropy wave). Some of these compressive fluctuations are subject to the steepening of the wave front and become shock waves, which are extremely efficient in dissipating their energy, their dissipation being independent of the Reynolds number. A rough estimate of the typical times which the various dynamical processes take to produce small scales and then to dissipate the energy show that these times are consistent with those required to dissipate inside the solar corona the energy of Alfven waves of photospheric origin.

Malara, F.↗

Fabrication of pristine 2D heterostructures for scanning probe microscopy

Material-by-design has been a long-standing aspiration that has recently become a reality. Such designer materials have been repeatedly demonstrated using the top-down approach of mechanical exfoliation and stacking, leading to a variety of artificial 2D heterostructures with new properties that are otherwise unattainable. Consequently, tremendous research frontiers in physics, chemistry, engineering, and life science have been created. While thousands of layered crystals exist in nature, only a few dozen of them with manageable chemical-stability have been made into heterostructures using this method. Moreover, experimental investigations of materials that have received limited exploration in the 2D realm, such as cuprates, halides, and perovskites, along with their heterostructures, have been fundamentally hindered by their rapid chemical degradation. Another critical challenge imposed by exfoliating and stacking 2D layers in ambient environment is the absorption of itinerant gas molecules that further contaminate sensitive 2D interfaces in the heterostructures. Such contamination and compromised material properties significantly hinder surface-sensitive local probes—scanning probe microscopy (SPM)—that often require nanometer to atomic scale surface cleanliness. In this article, we aim to provide a technical review of recent development toward 2D materials and heterostructure fabrication in more controlled environments that are suitable for SPM characterizations. These include the development of more efficient mechanical exfoliation and dry-transfer techniques, as well as the incorporation of 2D material exfoliation and transfer in inert gas, low vacuum, and, eventually, ultra-high vacuum environments. Finally, we provide an outlook on the remaining challenges and opportunities in ultra-clean 2D material fabrication techniques.

Materials Science↗

Physics-constrained, low-dimensional models for magnetohydrodynamics: First-principles and data-driven approaches

Plasmas are highly nonlinear and multiscale, motivating a hierarchy of models to understand and describe their behavior. However, there is a scarcity of plasma models of lower fidelity than magnetohydrodynamics (MHD), although these reduced models hold promise for understanding key physical mechanisms, efficient computation, and real-time optimization and control. Galerkin models, obtained by projection of the MHD equations onto a truncated modal basis, and data-driven models, obtained by modern machine learning and system identification, can furnish this gap in the lower levels of the model hierarchy. This work develops a reduced-order modeling framework for compressible plasmas, leveraging decades of progress in projection-based and data-driven modeling of fluids. We begin by formalizing projection-based model reduction for nonlinear MHD systems. To avoid separate modal decompositions for the magnetic, velocity, and pressure fields, we introduce an energy inner product to synthesize all of the fields into a dimensionally consistent, reduced-order basis. Next, we obtain an analytic model by Galerkin projection of the Hall-MHD equations onto these modes. We illustrate how global conservation laws constrain the model parameters, revealing symmetries that can be enforced in data-driven models, directly connecting these models to the underlying physics. We demonstrate the effectiveness of this approach on data from high-fidelity numerical simulations of a three-dimensional spheromak experiment. Finally, this manuscript builds a bridge to the extensive Galerkin literature in fluid mechanics and facilitates future principled development of projection-based and data-driven models for plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Advancements in nanocomposites for enhancing the performance of rechargeable lithium-ion batteries

The benefits of nanotechnology have been realized in almost every component of lithium-ion batteries. From electrodes to electrolytes, the incorporation of nanoparticles as dopants and coatings has shown marked improvements in cell cycle life, efficiency, mechanical and thermal stabilities, and lithium-ion transport. The improvements realized depends on several factors, from processing methods, nanoparticle type, structure, and concentration, to the material into which the nanoparticulate will be incorporated. Regardless of these many factors, nanotechnology has vastly improved the performance of secondary lithium-ion batteries. Here we will highlight some of the works that demonstrate these improvements and the quantitative benefits of nanotechnology.

25 ENERGY STORAGE↗

Unveiling the interaction of nanopatterned void superlattices with irradiation cascades

Nanopatterned microstructures in materials can have a profound impact on materials’ physical and chemical properties. While voids are typically considered as detrimental defects in irradiated materials, the patterning of nanoscale voids causes the formation of void superlattices and provides a highly efficient mechanism for gas storage. Despite the important applications of nanopatterned defect superlattices, how they degrade under irradiation remains unclear. Here we provide direct observation of the evolution of void superlattices under irradiation and elucidate the interaction of void superlattices with irradiation cascades. We reveal that the instability of void superlattices under irradiation is caused by heterogenous void shrinkage and demonstrate the imperative role of mixed 1D/3D diffusion of self-interstitial atoms and injected inert gas atoms on void shrinkage and void superlattice instability. Understanding the degradation mechanisms of nanopatterned microstructures is essential to designing damage-tolerant materials and broadening their applications in extreme environments.

36 MATERIALS SCIENCE↗

Disordering of helium gas bubble superlattices in molybdenum under ion irradiation and thermal annealing

Self-organization of gas bubbles causes the formation of an ordered array of nanoscale gas bubbles (a gas bubble superlattice), a highly efficient mechanism for gas storage under irradiation. Here, the stability of helium (He) gas bubble superlattices in molybdenum (Mo) under krypton (Kr) ion irradiation and thermal annealing has been investigated. The He gas bubble superlattices gradually become disordered under Kr ion irradiation at 300° C, and the order-disorder transformation process completes at 2.5 dpa. Both transmission electron microscopy (TEM) and synchrotron-based small-angle X-ray scattering (SAXS) reveal that the order-disorder transformation of He gas bubble superlattices is associated with a slight increase in the average bubble size. Phase-field modeling indicates that the inhomogeneous growth and coarsening of bubbles/voids cause the disordering of imperfect superlattices under irradiation and implies that highly ordered superlattices could potentially exhibit much stronger resistance to irradiation damage. Under thermal annealing, the He gas bubble superlattices in Mo become unstable and disordered at 1000° C with the bubble size increasing from ~1.1 to ~1.6 nm. The finding in this research provides insights into the disordering mechanisms of defect superlattices as well as guidance for designing stable defect superlattices in harsh environments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

The influence of preexisting host rock damage on fault network localization

The transition from stable to unstable fracture propagation occurs when fractures begin to interact and link. Thus, fracture network coalescence controls how rocks and engineered structures fail. Here, to constrain the factors that influence localization in shear zones under brittle conditions, we build discrete element method models with a rough fault embedded in a shear zone. We add varying numbers of diffuse, randomly-placed weaknesses to examine the influence of diffuse damage on fracture network localization. The number of weaknesses controls the localization behavior of the fault network and the final fault geometry. We quantify localization using the Gini coefficient of the fracture volume, which measures the nonuniformity in a population. Each model generally increases in localization toward failure. However, models with more diffuse damage experience delocalization phases that are superimposed on the overall trend of increasing localization. The observed link between delocalization and host rock damage may help explain the varying localization of low magnitude seismicity in southern California. Models with more diffuse damage produce more complex fault geometries comprised of several parallel strands of wing cracks. The propagation of these wing cracks reduces the shear stress acting on the model boundaries, indicating that this fracture development increases the mechanical efficiency of the system.

58 GEOSCIENCES↗

Relativistic non-thermal particle acceleration in two-dimensional collisionless magnetic reconnection

Magnetic reconnection, especially in the relativistic regime, provides an efficient mechanism for accelerating relativistic particles and thus offers an attractive physical explanation for non-thermal high-energy emission from various astrophysical sources. I present a simple analytical model that elucidates key physical processes responsible for reconnection-driven relativistic non-thermal particle acceleration in the large-system, plasmoid-dominated regime in two dimensions. The model aims to explain the numerically observed dependencies of the power-law index $p$ and high-energy cutoff $\gamma _c$ of the resulting non-thermal particle energy spectrum $f(\gamma )$ on the ambient plasma magnetization $\sigma$ , and (for $\gamma _c$ ) on the system size $L$ . In this self-similar model, energetic particles are continuously accelerated by the out-of-plane reconnection electric field $E_{\rm rec}$ until they become magnetized by the reconnected magnetic field and eventually trapped in plasmoids large enough to confine them. The model also includes diffusive Fermi acceleration by particle bouncing off rapidly moving plasmoids. I argue that the balance between electric acceleration and magnetization controls the power-law index, while trapping in plasmoids governs the cutoff, thus tying the particle energy spectrum to the plasmoid distribution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Plasmon-Driven Ammonia Decomposition on Pd(111): Hole Transfer’s Role in Changing Rate-Limiting Steps

Here, ammonia (NH 3 ) has the potential to be a hydrogen carrier because it can be transported and stored with ease, but only if it also can be decomposed easily when needed. Understanding how to control the frequently rate-limiting N–H bond breaking and N–N bond forming on catalytic surfaces may help design efficient means for NH 3 decomposition. Yuan et al. recently demonstrated photocatalytically selective N–H bond breaking in NH 3 on plasmon-driven aluminum–palladium (Al–Pd) antenna–reactor heterostructures. Using embedded correlated wavefunction (ECW) theory, we predict that the rate-determining step (RDS) for NH 3 decomposition on Pd(111) via thermocatalysis (dissociating the first N–H bond, *NH 3 → *NH 2 + *H, in the ground state, where * means adsorbed) differs from that via photocatalysis (dissociating the second N–H bond, *NH 2 → *NH + *H, in the excited state). This result is consistent with the measured catalytic efficiency and selectivity of NH 3 -deuterium (D 2 ) exchange reactions (an indirect way to measure N–H bond breaking) on Al–Pd heterodimers. We also determine the origin of the observed selectivity of thermocatalysis and photocatalysis on Pd(111) toward doubly deuterated (NHD 2 ) and monodeuterated (NH 2 D) products, respectively, and explore viability of the full NH 3 decomposition path, also via ECW theory. Additionally, we predict that the associative desorption of *N as N 2 from Pd(111) is extremely difficult in thermocatalysis at least at low surface coverages; metal-to-adsorbate hole transfer in photocatalysis stabilizes the transition state for the first N–H bond dissociation, shifting the RDS to the second N–H bond breaking. Furthermore, the redistribution of electrons around *N upon excitation reduces the electron density in the Pd–N bonds, which may lower the barrier for N 2 associative desorption in photocatalysis. Thus, light-induced, plasmon-mediated, excited-state hole transfer may provide an efficient mechanism to accelerate NH 3 decomposition.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗