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At least 37 records · Page 2

Isothermal solidification for high-entropy alloy synthesis

Kinetically trapping the high-temperature states through rapid cooling solidification is widely used for the synthesis of high-entropy alloys (HEAs), especially those with intrinsically immiscible elemental combinations. However, strategies need to be developed to overcome the fundamental limitations of rapid cooling solidification in controlling the crystallinity, structure and morphology of HEAs. Here, in this study, we introduce an isothermal solidification strategy for the synthesis of HEAs by rapidly altering the metal alloy composition through liquid–liquid interface reactions at low temperatures, for example, from 25 °C to 80 °C. We use gallium (Ga)-based metal as the sacrificial reagent and mixing medium. By directing the reactions to the interfaces between the Ga-based liquid metal and an aqueous metal ion solution, the foreign metal ions can be reduced at the interfaces and incorporated into the liquid metal quickly. HEAs with various crystallinity (single crystal, mesocrystal, polycrystal and amorphous), morphology (zero, two and three dimensions) and compositions can be achieved through the isothermal solidification. Ga can be completely consumed, resulting in Ga-free HEAs. If desired, Ga can be one of the metal elements in the final products. In situ liquid phase transmission electron microscopy (TEM) studies and theoretical analysis show the isothermal solidification mechanisms. Our direct observations show the enhanced mixing of liquid metal elements and the solidification process with fluctuating nucleation dynamics. The isothermal solidification marks a powerful strategy for HEA synthesis through an unexplored pathway of kinetically trapping the high-entropy states.

Zhang, Qiubo [Lawrence Berkeley National Laborator

Flame kinetics at scramjet-engine-relevant conditions: Role of prompt dissociation of weakly-bound radicals

Combustion in high-speed ram-based propulsion engines occurs under distinct thermodynamic conditions of high reactant temperatures (greater than 1000 K) and relatively low pressures (<5 atm). There is a lack of fundamental flame measurements at such conditions that result in adiabatic flame temperatures (T ad ) exceeding 2500 K. In this work, we have measured laminar flame speeds of oxygen-enriched CH 4 /oxidizer mixtures at sub-atmospheric conditions to probe kinetics at high T ad using the isobaric spherically expanding flame approach. Simulations with recent kinetic models revealed increasing differences between data and model predictions with increasing T ad , reaching up to 25 %. Kinetic analyses reveal that at the thermodynamic conditions in these O 2 -enriched flames, i.e., lower pressures and higher T ad , the effects of HCO prompt dissociation are accentuated. In addition to HCO, the prompt dissociations of CH 2 OH and C 2 H 5 are also considered. Here, the prompt dissociations of all three radicals were evaluated and their effects considered in flame speed simulations. Reaction path analysis for the present flames revealed that approximately half of the reaction flux for HCO formation undergoes prompt dissociation to H + CO. Furthermore, these analyses also revealed that the pathways and sensitive reactions are similar between oxygen-enriched fuel/oxidizer mixtures and preheated fuel/air mixtures, if both have similar T ad . Thus, flames of oxygen-enriched mixtures could be a surrogate to probe the flame chemistry of highly preheated mixtures at relatively low pressures that are often encountered in ram-based propulsion engine combustors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Role of Chemical Disorder in High Temperature Dislocation Glide in Refractory Multi-principal Element Alloys

Refractory multi-principal element alloys (RMPEAs) combine a chemically disordered lattice with a structurally ordered, single‐phase body‐centered cubic (bcc) crystal structure. Chemical fluctuations in these alloys give rise to significant energy barriers that impede dislocation motion. In this study, we use phase field dislocation dynamics to examine how spatial temperature fluctuations compete with randomness in energy barriers to affect the motion of long screw dislocations in three equi-atomic MoNbTa‐based RMPEAs: MoNbTa, MoNbTaW, and MoNbTaVW. Over a wide range of homologous temperatures (T h ≈ 0–0.6), we determined a screw dislocation ‘flow stress’ as the minimum applied stress to sustain continuous motion over a long excursion distance within a fixed timeframe. All three RMPEAs exhibit temperature dependent flow stress with three characteristic glide regimes: at low homologous temperatures, flow stress drops sharply, and screw glide remains planar and rectilinear; at intermediate homologous temperatures, the flow stress levels off as glide becomes planar but wavy; and at high homologous temperatures, flow stress plateaus as screws exhibit nonplanar, three‐dimensional motion. Glide kinetics and transition temperatures are controlled by the chemically induced fluctuations in the energy landscape. The rectilinear to wavy transition temperature is controlled by statistically weakest local barriers in the glide plane, whereas the wavy to 3D transition temperature is governed by statistically strongest local barriers. At low and intermediate homologous temperatures, the relative spread in energy barriers governs glide behavior by controlling the local kinetics of kink pair formation and kink pinning. At high homologous temperatures, the average barrier height governs the glide behavior by controlling the number of out-of-plane excursions during 3D glide. These findings reveal how random chemical fluctuations determine screw‐driven plasticity in RMPEAs, providing critical insight for the design of high temperature structural alloys.

Defects

Solid-state batteries enabled by ultra-high-frequency self-heating

Solid-state batteries (SSBs) are promising next-generation batteries due to their high energy density and enhanced thermal stability and safety. However, their sluggish kinetics and transport at room temperature result in high internal impedance and critically reduce the attainable discharge energy density. Taking advantage of their strong temperature-dependent ionic conductivity, here we introduce ultra-high-frequency (greater than 105 Hz) self-heating (UHFSH) of SSBs, which can rapidly warm up the batteries from room temperature to operating temperature (∼65°C) in less than a minute. As proof of concept, UHFSH experiments were conducted on symmetric solid-state cells with lithium aluminum germanium phosphate electrolyte in different configurations. Using an experimentally validated model, pack-level simulations predict fast heating (50 K/min) and minimized heating energy consumption (less than 4%). Without any modification of the materials or structure of the batteries, our non-intrusive self-heating strategy potentially enables SSBs to discharge more than 2-fold energy in 25°C ambient.

pulse heating

Enhancing Biopolyester Backbone Rigidity with an Asymmetric Furanic Monomer

Biobased furanic polyesters can exhibit performance advantages over petroleum-derived polyesters, primarily due to their rigid furan-containing backbones. Herein, we develop two strategies to polymerize methyl 5-hydroxymethyl furanoate to poly(5-hydroxymethyl furanoate) (PHMF), a furan-based polyester with even greater backbone rigidity than poly(ethylene furanoate). Thermal, spectroscopic, and computational investigations of PHMF alongside analogous furan-based and phenyl-based polyesters suggest that the high furan content of PHMF leads to its high glass transition temperature, slow crystallization kinetics, and low amorphous mobility. Molecular dynamics simulations suggest that while the backbone of PHMF is exceptionally rigid, its amorphous phase is denser than its phenyl analog due to noncovalent interchain interactions. Together, these results highlight how asymmetric furan-based monomers can modulate key properties in biobased polyesters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Elucidating key reducing species beyond ions in hydrogen plasma smelting reduction of iron ore

Hydrogen plasma smelting reduction (HPSR) of iron ore has attracted significant attention over the past decade due to its high-temperature operation, rapid plasma mediated reduction kinetics, and simpler density-based separation of molten iron product, compared to H2-based solid-state reduction. All of these attributes enable processing of low-grade ores for downstream use in electric-arc furnaces, as virgin iron with low gangue content is required for high quality steel and improved furnace operation. While positive ions exist within the plasma arc, this work demonstrates that near the anodic ore surface, hydrogen radicals and vibrationally excited hydrogen species dominate and their densities correlate well with observed reduction rates. Species concentrations in the transferred plasma arc and at the plasma-ore interface are evaluated using coupled thermal plasma and near-wall non-equilibrium plasma models. The thermal plasma model is validated against experimental voltage data and spectroscopic measurements of plasma temperature and density for varying current inputs. Modeling of the near surface thermochemical non-equilibrium and micrometer scale anode sheath layer reveals, in addition to the expected H + , significant concentrations of ArH + and H$^+_3$ ions, typically not observed in thermal plasmas under thermodynamic equilibrium. Our results show that the inverted sheath structure at the anodic ore surface strongly suppresses reactive positive ion fluxes, while non-equilibrium electron-impact processes generate abundant hydrogen radicals and vibrationally excited species. These findings highlight the critical role of non-equilibrium effects in hydrogen arc-driven iron ore reduction and advance understanding beyond prevailing hypotheses centered on hydrogen ion-driven mechanisms.

08 HYDROGEN

Tailoring Na⁺ Chelation Dynamics for Expedient Sulfur Redox Kinetics in Low‐Temperature Sodium–Sulfur Batteries

Sodium–sulfur (Na–S) batteries have attracted considerable attention due to their high theoretical energy density and the abundant natural availability of sodium and sulfur. However, sluggish kinetics of sulfur conversion, slow Na⁺ transport, and interfacial instability at low temperatures pose significant challenges for their operation and limit their practical application. Herein, three solvents with well-designed molecular configurations are examined. We systematically investigate the impact of chelation effect on the desolvation behavior, sulfur conversion process, ion dynamics, and Na⁺ plating/stripping behavior. Compared with conventional linear ether solvents, the incorporation of methyl groups not only weaken the chelation capability and tailors the inner solvation sheath, but also reduces the energy barrier for Na⁺ transport, thus promoting enhanced sulfur conversion kinetics under low temperature conditions. This work elucidates the relationship among solvent molecules, Na⁺ desolvation behavior, and sulfur reaction kinetics, and offers a strategy for rational design of electrolytes for low-temperature metal–sulfur batteries.

25 ENERGY STORAGE

Mobility assessment of the BCC and carbide phases in the C-Nb, C-U and Nb-U systems

Uranium carbides with refractory metal additions are considered for Gen IV nuclear reactors and nuclear thermal propulsion as fuels for their high-temperature and corrosion resistant properties. Understanding kinetic effects that dictate microstructural evolution during fabrication and operating conditions is essential to advance technological development of these fuels. This work presents the development of an atomic mobility database for C-Nb-U systems based off available experimental data supported with ab-initio methods. The mobility assessments and uncertainty quantification (using Markov chain Monte Carlo) were conducted in the Kawin software. Carbon diffusion is considered dominant, as metal diffusion is much slower, with niobium diffusion being even slower and rate limiting than uranium metal. We provide a comprehensive and self-consistent thermo-kinetic database that is validated by diffusion couple simulations through Kawin. In conclusion, this enables prediction of microstructural and phase evolution critical for the development and lifetime assessment of next generation nuclear fuels.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS

Kinetics of amorphous defect phases measured through ultrafast nanocalorimetry

Recognition of the role of extended defects on local phase transitions has led to the conceptualization of the defect phase, localized thermodynamically stable interfacial states that have since been applied in a myriad of material systems to realize significant enhancements in material properties. Here, we explore the kinetics of grain boundary confined amorphous defect phases, utilizing the high temperature and scanning rates afforded by ultrafast differential scanning calorimetry to apply targeted annealing/quenching treatments at high rates capable of capturing the kinetic behavior. Four Al-based nanocrystalline alloys, including two binary systems, Al–Ni and Al–Y, and two ternary systems, Al–Mg–Y and Al–Ni–Y, are selected to probe the materials design space (enthalpy of mixing, enthalpy of segregation, chemical complexity) for amorphous defect phase formation and stability, with correlative transmission electron microscopy applied to link phase evolution and grain stability to nanocalorimetry signatures. A series of targeted isothermal annealing heat treatments is utilized to construct a Time–Temperature-Transformation curve for the Al–Ni system, from which a critical cooling rate of 2400 °C/s was determined for the grain boundary confined disordered-to-ordered transition. Finally, a thermal profile consisting of 1000 repeated annealing sequences was created to quantify the recovery of the amorphous defect phase following sequential annealing treatments, with results indicating remarkable microstructural stability after annealing at temperatures above 90% of the melting temperature. This work contributes to a deeper understanding of grain boundary localized thermodynamics and kinetics, with potential implications for the design and optimization of advanced materials with enhanced stability and performance.

Amorphous defect phases

AUTOIGNITION DELAY TIMES FOR REFORMATE GAS MIXTURES FROM METHANE GAS ENGINES

Methane slip is a prominent issue in natural gas reciprocating engines that are used in transportation and marine applications. The incomplete combustion that results in methane slip can be resolved with the introduction of hydrogen within the combustion mixture to improve methane oxidation and further enable combustion within the engine crevices where methane has previously remained unreacted. Steam methane reforming (SMR) is a common method used to produce hydrogen and can be used to design an onboard device to reduce methane slip from reciprocating engines. The development of this reformer device requires the validation of high-fidelity chemical kinetic models at the low temperatures of the crevice volumes of these engines. In this work, auto-ignition data is obtained using a shock tube at lean (φ—0.714 or λ—1.4) and stoichiometric (φ, λ = 1) equivalence ratios spanning a temperature range of 1042–1234 K at the 80-bar operating pressure of the test engine. Blends of methane, hydrogen, and reformate products from the SMR reaction are shock-heated in synthetic air, with the ignition delay time measured using an OH* chemiluminescence detector at 310 nm and a CH* detector at 430 nm. The experimental results are compared to several state-of-the-art chemical kinetic mechanisms from the literature. In general, most of the mechanisms show very good agreement with experiments at higher temperatures, with simulation results showing little deviation from experiments at lower temperatures. A sensitivity analysis was conducted, and the results reveal that the reaction H2 + CH3O2 = H + CH3O2H has a very significant role in determining low-temperature ignition delay times (IDTs) of SMR mixtures. These findings provide valuable insights into the chemical kinetics governing methane reformate combustion and contribute to the optimization of onboard reformer designs aimed at mitigating methane slip in natural gas-fueled engines.

Fraze, Matthew

Rapid Oxidation of Uranium Steel Alloys: Combustion Synthesis

This project explored the use of combustion synthesis as a rapid, high-temperature method for oxidizing uranium-bearing steel alloys. Traditional laboratory-scale synthesis methods often fail to replicate the thermal and kinetic conditions experienced by real-world particulates, particularly those formed under rapid quenching or high-temperature scenarios. Combustion synthesis offers a promising alternative by enabling fast, localized heating and flexible precursor selection. A series of targeted experiments were conducted using a U 2 NiCrFe 4 alloy as the precursor. The alloy was oxidized using combustion synthesis reactions fueled by uranyl nitrate and glycine, achieving peak temperatures exceeding 1,200 °C. Postreaction analysis using scanning electron microscopy (SEM), elemental mapping, and Raman spectroscopy revealed the formation of iron-based oxides, with limited but detectable evidence of uranium oxide phases such as UO 2 . The results indicate that under the rapid reaction and cooling conditions of combustion synthesis, iron oxides form preferentially, but uranium oxide formation is kinetically limited. These findings validate combustion synthesis as a viable method for simulating the oxidation behavior of uranium steels in extreme environments and lay the groundwork for future studies aimed at enhancing uranium oxide formation through higher temperatures or modified precursor compositions.

36 MATERIALS SCIENCE

Extreme Speeds and Thermodynamic States in Supersonic Flight

The increasing importance of high-speed flow leads to similar problems in various fields of research which are summarized in what follows. Typical of all cases is the conversion of high kinetic energy into extreme thermodynamic states with temperatures of several thousand degrees, frequently connected with dissociation and ionization of the gas involved. There is also a characteristic small sensitivity to the processes discussed in the case of gases of low molecular weight (light gases). The penetration of meteors into the atmosphere of the earth at astronomical speeds results in temperatures higher than those of the surface of the sun. Such temperatures may be produced in shock tubes, with light gases used as the driving gas. For supersonic fighters the problem of propulsion is less difficult to solve than the problem of large heating, on the surface and in the combustion chamber. Finally, for the space-travel rocket, astronomical speeds have to be reached which require the lightest possible gases as propellants. Here again, dissociation processes in the combustion chamber are of considerable importance.

Oswatitsch, Klaus

First-Principles Insights into the Thermocatalytic Cracking of Ammonia-Hydrogen Blends on Fe(110). 2. Kinetics

Ammonia (NH 3 ) is an energy-rich molecule that is routinely synthesized from nitrogen (N 2 ) and hydrogen (H 2 ). NH 3 ’s more favorable physical properties compared to H 2 suggests it may offer a way to more conveniently store, transport, and, when needed, extract H 2 via thermal decomposition. However, the high kinetic barrier and endoergicity to decompose to H 2 and N 2 require high temperatures. The standard reaction free energy indicates nearly 100% thermodynamic conversion to the diatomic molecules only at ~673 K and higher. However, even at these temperatures, a catalyst, e.g., iron (Fe), is needed for favorable kinetic conversion. Here, in this study, we explore via density functional theory the kinetics of NH 3 decomposition on the most stable facet of body-centered cubic Fe, namely, (110), under typical high-temperature and finite-pressure operando conditions. We predict coverage-dependent energetics of elementary surface reactions, often neglected in atomic-scale modeling. From these models, we find the recombinative desorption of adsorbed N as N 2 is rate-determining at 573.15–773.15 K and even at an extreme case of 1173.15 K. From microkinetic modeling, we find that the steady-state turnover frequencies (TOFs) for N 2 and H 2 generation rates (r$_{H_2}$) depend exponentially on temperature. The catalyst achieves a steady-state TOF of 36.4 s –1 and an r$_{H_2}$ of 0.107 μmol cm –2 s –1 for a feed of 1.8 bar NH 3 with 0.2 bar H 2 at 1173.15 K. However, at 773.15 K, with the same feed composition and velocity, the steady-state TOF and r$_{H_2}$ decrease to 0.14 s –1 and 4.10 × 10 –4 μmol cm –2 s –1 , respectively, as the process is significantly hindered by slow N 2 desorption. Although at first glance counterintuitive, our simulations suggest that surface modifications that reduce Fe’s reactivity toward NH x species should enhance its overall NH 3 decomposition activity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Metastable formation and disordering kinetics of body-centered orthorhombic CrNi 2 laths in a Cr-Ni binary alloy

Chromium (Cr) alloys combine low density with high-temperature strength but suffer from brittleness and rapid softening. Body-centered orthorhombic (BCO) CrNi 2 laths have been shown to improve Cr-alloy high-temperature strength retention, yet their thermal stability and transformation behavior remain unclear. CrNi 2 conventionally forms through long-range ordering from a face-centered cubic (FCC) phase. Using multiscale microscopy and neutron diffraction, we show that CrNi 2 instead nucleates from a body-centered cubic (BCC) matrix, in a binary Cr 85 Ni 15 alloy. Despite aging above the equilibrium ordering temperature, CrNi 2 persists for ∼220 h at 760 °C before fully disordering, indicating sluggish transformation kinetics. The formation and decomposition follow differing transformation pathways (BCC → CrNi 2 → FCC), revealing kinetic asymmetry not captured by equilibrium Cr-Ni phase diagrams. In conclusion, these findings redefine the transformation behavior of CrNi 2 , establish its metastable kinetic window, and suggest alloying strategies to stabilize CrNi 2 for precipitation strengthening of high-temperature Cr-alloys.

CrNi2 transformation kinetics

Solar Decarbonization of Paraffin Dehydrogenation Through Particle Heat Carriers (Final Technical Report)

This project focuses on solutions to decarbonize high-temperature catalytic processes using solar thermal heat. The primary project goal is to show the validity of a moving packed bed reactor for propane dehydrogenation using catalyst particles as the heat carrier for the reaction, which can be heated by concentrated solar energy in a particle receiver. This concept, if further developed, may provide a cost-effective pathway for converting lower value gases to important chemical precursors for industrial materials using only renewable energy. The project was divided into six tasks. In Task 1, DFT calculations were performed to understand the role of Pt and Sn in the catalytic dehydrogenation reaction. In Task 2 chemical kinetics measurements were made for several catalyst formulations at high temperatures. In Task 3, the solar absorptance of catalyst particles was compared to the absorptance of commonly used materials in particle receivers. In Task 4, numerical models were developed which could predict performance of the complete system and predict specific temperatures in the system. In Task 5, a prototype system was designed, fabricated, and tested to show the validity of the concept. Task 6 concerned project management activities. Experiments with the prototype showed repeatable thermal performance at temperatures targeted for the reaction. A limited set of tests were done with active catalyst and propane dehydrogenation, showing conversion of propane to propylene with a range of conversions and selectivities. The results are promising, and the prototype designed was reliable during testing, and the team expects that further development of the prototype would yield improved results. A numerical model framework based on coupled fluid and particle mechanics was developed with high computational efficiency using GPU calculations. The model may prove highly useful for evaluating other high-temperature particle systems. However, it was determined that simpler porous media models were good fits for the needs of the current moving packed bed concept. Data showing strong solar absorption of the particles validates the plan of using existing solar particle receivers with only a change in the particle type. Catalyst investigation showed that Pt 1 Sn 3 is the most viable candidate for developing PtSn catalysts for high temperature propane dehydrogenation, considering the balance of activity, selectivity, and deactivation. This project completed an initial study of various factors needed to incorporate a moving bed catalytic reactor for propane dehydrogenation into a concentrated solar thermal particle system. Future developments may allow this technology to be scaled up and help to use solar thermal energy to decarbonize not only the propane dehydrogenation reaction, but other gas-solid catalytic reactions at similar temperatures.

14 SOLAR ENERGY

Rapid, efficient reduction of iron oxide with ammonia

Reducing iron oxide to iron metal with fossil fuels produces circa 4% of annual anthropogenic CO 2 , ca. 2 Gt/a, as direct chemical emissions from the process. Using ammonia instead of coke—releasing only water and nitrogen as byproducts—could be a widely deployable method of decarbonizing industrial ironmaking, because ammonia carries hydrogen and can be transported easily worldwide. However, initial reports suggest that the reaction of ammonia with iron oxide is slow and inefficient, completed only in hours and using only a few percent of the ammonia supplied. Drawing on thermodynamic and kinetic analysis of the reaction, we explored high-temperature, high-flow reaction conditions designed to increase the reaction rate and the ammonia utilization. We report the reduction of iron oxide in 1 min while using 64% of the ammonia supplied. We show that these insights translate to the gram scale and the reduction of pelletized ore, a common form used industrially.

36 MATERIALS SCIENCE

Gas-Cooled High-Temperature Pebble-Bed Reactor Reference Plant Model Updates

This work presents the latest improvements to, and investigations performed with, the pebble-bed high-temperature gas-cooled reactor (PB-HTGR) reference plant models for the United States Nuclear Regulatory Commission. These models serve as the foundation for the future development of detailed design evaluation models based on license applications. The reference plant models have been developed with the Comprehensive Reactor Analysis Bundle, or BlueCRAB, which is the code suite proposed for non-light-water reactor systems safety analysis. It incorporates various simulation tools developed by the Nuclear Energy Advanced Modeling and Simulation program, including the Griffin code for reactor physics, the Pronghorn and SAM codes for core thermal fluids, the BISON code for solid conduction and fuel performance, and the SAM code for system analysis. The primary objective of the work that was performed was to assess BlueCRAB’s level of readiness for modeling a PB-HTGR. To do so, we first developed numerical models in BlueCRAB that include the key physics for this technology to ensure an adequate level of fidelity for modeling PB-HTGR core performance and for performing multiphysics simulations for equilibrium core conditions and different accident scenarios. Then we simulated transient scenarios, including depressurized and pressurized loss of forced cooling accidents, over-cooling, and control rod withdrawal events with delayed and prompt supercritical reactivity insertions. The analysis in this report includes comparisons of the 2D thermal fluid porous media models in Pronghorn and SAM, and comparisons of coupled SAM/Griffin/SAM and coupled Pronghorn/Griffin for depressurized and pressurized loss of forced cooling, over-cooling, and control rod withdrawal events. In addition, we compare 3D, 2D, and 0D/PKE neutronic models for the two control rod withdrawal scenarios with coupled Pronghorn/Griffin. The comparisons show that the BlueCRAB models lead to physically intuitive solutions for the scenarios examined. The changes in the various scalar and vector fields, such as neutron flux, power, temperature, density, pressure, and velocity, are within the expected ranges, and their distributions can be explained by the system response of the transients and the geometric and material variations. Several comparisons suggest that the porous media models in Pronghorn and SAM can lead to similar solutions, even though they are based on different methodologies. This work further highlights the need for flexible tools with various levels of fidelity to cover the breadth and depth of needs that may arise in future technical evaluations of the PB-HTGR. We believe that the BlueCRAB capabilities will be a significant asset for confirmatory analyses in order to resolve important safety questions.

22 GENERAL STUDIES OF NUCLEAR REACTORS

Association of CN in an expansion wave.

Kinetics of CN radicals association generated by shocking cyanogen-argon mixtures at high temperatures in reflected shock region of expansion wave

GAS MIXTURE