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At least 271 records · Page 15

Oxidative dehydrogenation of propane on the oxygen adsorbed edges of boron nitride nanoribbons

Metal-free boron nitride has recently been reported to exhibit high catalytic activity and selectivity towards oxidative dehydrogenation of propane (ODHP). Despite several experimental studies, the exact nature and function of the active sites in this emerging catalyst are unknown. In the present work, density functional theory calculations are combined with microkinetic modeling to systematically explore the ODHP on oxygen passivated boron nitride nanoribbons (BNNRs). Here, the relative stabilities of different edge structures of BNNR were examined using ab initio thermodynamic analysis, and the most stable oxygen passivated edge structure was used for a mechanistic study. Microkinetic analysis revealed that a N 2 O or NO x -type active site is active and selective for the conversion of propane to propene. In addition to a heterogeneous catalytic cycle, the proposed N 2 O/NO x -type active sites are expected to be able to generate gas phase C 3 H 7 ˙, which in turn can trigger gas phase reactions of ODHP as experimentally speculated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Boron nitride: Novel ceramic reductant for low‐activity waste vitrification

Abstract During vitrification of radioactive wastes, excessive foaming reduces processing rates within melters by hindering heat transfer from the molten glass pool to the reacting melter feed. Formulations of low‐activity waste (LAW) melter feeds, for vitrification at the Waste Treatment and Immobilization Plant at the Hanford Site, conventionally include the addition of sucrose to mitigate excessive foaming by hastening the denitration process. However, incomplete combustion of sucrose produces organics such as acetonitrile (C 2 H 3 N) that may exceed bounding limits of downstream effluent treatment facilities. Using boron nitride (BN) as an alternate reductant to sucrose, in a representative LAW melter feed reduced C 2 H 3 N production by 90% by preventing the low‐temperature sucrose–nitrate reactions. Furthermore, foaming was suppressed due to the higher decomposition temperature of BN than H 3 BO 3 meaning a delayed reaction of a large fraction of boron with the transient glass‐forming melt until above the foam onset temperature, thus reducing the quantity and viscosity of the connected melt and trapping less gas in the foam layer.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Active-to-passive transition in the oxidation of silicon carbide and silicon nitride in air

The active-to-passive transition in the oxidation of SiC and Si3N4 was determined in a flowing air environment as a function of temperature and total pressure. The experimentally observed transition temperatures ranged from a low of 1347 C to a high of 1543 C for partial pressures of oxygen of 2.5 and 123.2 Pa, respectively. The SiC and Si3N4 samples had approximately the same transition point for a given pressure. In general, the higher the flow rate, the higher the transition temperature for a given pressure. The transitions for SiC measured in this study agree with previous data for the transition of SiC measured in pure oxygen at reduced pressures and in oxygen inert gas mixtures.

Vaughn, Wallace L.↗

Environmental Effects on Non-oxide Ceramics

Non-oxide ceramics such as silicon carbide (SiC) and silicon nitride (Si3N4) are promising materials for a wide range of high temperature applications. These include such diverse applications as components for heat engines, high temperature electronics, and re-entry shields for space vehicles. Table I lists a number of selected applications. Most of the emphasis here will be on SiC and Si3N4. Where appropriate, other non-oxide materials such as aluminum nitride (AlN) and boron nitride (BN) will be discussed. Proposed materials include both monolithic ceramics and composites. Composites are treated in more detail elsewhere in this volume, however, many of the oxidation/corrosion reactions discussed here can be extended to composites. In application these materials will be exposed to a wide variety of environments. Table I also lists reactive components of these environments.It is well-known that SiC and Si3N4 retain their strength to high temperatures. Thus these materials have been proposed for a variety of hot-gas-path components in combustion applications. These include heat exchanger tubes, combustor liners, and porous filters for coal combustion products. All combustion gases contain CO2, CO, H2, H2O, O2, and N2. The exact gas composition is dependent on the fuel to air ratio or equivalence ratio. (Equivalence ratio (EQ) is a fuel-to-air ratio, with total hydrocarbon content normalized to the amount of O2 and defined by EQ=1 for complete combustion to CO2 and H2O). Figure 1 is a plot of equilibrium gas composition vs. equivalence ratio. Note that as a general rule, all combustion atmospheres are about 10% water vapor and 10% CO2. The amounts of CO, H2, and O2 are highly dependent on equivalence ratio.

Jacobson, Nathan S.↗

Radio Frequency Plasma Synthesis of Boron Nitride Nanotubes (BNNTs) for Structural Applications: Part I

It is evident that nanotubes, such as carbon, boron nitride and even silicon, offer great potential for many aerospace applications. The opportunity exists to harness the extremely high strength and stiffness exhibited by high-purity, low-defect nanotubes in structural materials. Even though the technology associated with carbon nanotube (CNT) development is mature, the mechanical property benefits have yet to be fully realized. Boron nitride nanotubes (BNNTs) offer similar structural benefits, but exhibit superior chemical and thermal stability. A broader range of potential structural applications results, particularly as reinforcing agents for metal- and ceramic- based composites. However, synthesis of BNNTs is more challenging than CNTs mainly because of the higher processing temperatures required, and mass production techniques have yet to emerge. A promising technique is radio frequency plasma spray (RFPS), which is an inductively coupled, very high temperature process. The lack of electrodes and the self- contained, inert gas environment lend themselves to an ultraclean product. It is the aim of this White Paper to survey the state of the art with regard to nano-material production by analyzing the pros and cons of existing methods. The intention is to combine the best concepts and apply the NASA Langley Research Center (LaRC) RFPS facility to reliably synthesize large quantities of consistent, high-purity BNNTs.

Hales, Stephen J.↗

Why Boron Nitride is such a Selective Catalyst for the Oxidative Dehydrogenation of Propane

Abstract Boron‐containing materials, and in particular boron nitride, have recently been identified as highly selective catalysts for the oxidative dehydrogenation of alkanes such as propane. To date, no mechanism exists that can explain both the unprecedented selectivity, the observed surface oxyfunctionalization, and the peculiar kinetic features of this reaction. We combine catalytic activity measurements with quantum chemical calculations to put forward a bold new hypothesis. We argue that the remarkable product distribution can be rationalized by a combination of surface‐mediated formation of radicals over metastable sites, and their sequential propagation in the gas phase. Based on known radical propagation steps, we quantitatively describe the oxygen pressure‐dependent relative formation of the main product propylene and by‐product ethylene. Free radical intermediates most likely differentiate this catalytic system from less selective vanadium‐based catalysts.

Venegas, Juan M.↗

Polynomial Expressions for Estimating Elastic Constants From the Resonance of Circular Plates

Two approaches were taken to make convenient spread sheet calculations of elastic constants from resonance data and the tables in ASTM C1259 and E1876: polynomials were fit to the tables; and an automated spread sheet interpolation routine was generated. To compare the approaches, the resonant frequencies of circular plates made of glass, hardened maraging steel, alpha silicon carbide, silicon nitride, tungsten carbide, tape cast NiO-YSZ, and zinc selenide were measured. The elastic constants, as calculated via the polynomials and linear interpolation of the tabular data in ASTM C1259 and E1876, were found comparable for engineering purposes, with the differences typically being less than 0.5 percent. Calculation of additional v values at t/R between 0 and 0.2 would allow better curve fits. This is not necessary for common engineering purposes, however, it might benefit the testing of emerging thin structures such as fuel cell electrolytes, gas conversion membranes, and coatings when Poisson s ratio is less than 0.15 and high precision is needed.

Salem, Jonathan A.↗

UZrCN Synthesis via Arc Melting

The next generation of nuclear reactors for both power production and space nuclear propulsion require fuel that is more durable, thermally stable, and more thermally conductive to support rapid heat transfer. High temperature gas reactors (HTGR), advanced gas reactors (AGR), and space-based nuclear thermal propulsion (NTP) are advanced reactor concepts that require a fuel type that can withstand high temperatures (1000-2900K) and flow of corrosive gas coolants such as helium, hydrogen, and carbon dioxide. One fuel with the potential to meet these demanding requirements is uranium-zirconium-carbonitride (UZrCN). UZrCN has many favorable fuel qualities compared to other eligible fuel forms such as uranium dioxide (UO 2 ) and uranium mononitride (UN) that could support the aforementioned reactor concepts. UZrCN has an exceptionally high operating temperature and thermal conductivity which are highly desirable to improve reactor economics and safety. It far exceeds the properties of UO 2 which is the most common fuel form in the United States. UZrCN also surpasses UN in terms of thermal conductivity and operating temperature by eliminating the dissociation problem UN has at 1700K. UZrCN could improve gas reactor performance and enable NTP technologies; however, it is an under-researched fuel that lacks rigorous scientific study. In recent efforts by the Idaho National Laboratory, a variety of novel methods to produce this fuel composition have been explored. One such method is via arc melting of uranium, zirconium, and carbon under a nitrogen atmosphere. Alloy fabrication using arc melting has been utilized for close to 150 years now and is well-understood as a method for rapid alloy prototyping. This process will be used to perform in-situ nitriding to form UZrCN.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Improved Crystal Quality by Detached Solidification in Microgravity

The goals of our work on detached solidification have been to: Develop a complete understanding of all of the phenomena of detached solidification; Make it possible to achieve detached solidification reproducibly; Increase crystallographic perfection through detached solidification. Specifically, we aimed in this project to: Identify a system and develop methods that would allow viewing of the melt surface and convection in the melt during detached solidification in microgravity; Improve understanding of the origination and evolution of detachment through experiments and theoretical treatments; Achieve detachment on earth. The project resulted in 14 publications, 15 presentations, completion of 2 Ph.D. theses, and completion of 2 M.S. theses. Two additional papers are currently being reviewed for publication. Copies of most of the papers are attached as appendices. Among the accomplishments are: Achievement of detached solidification of InSb on earth and determination of the conditions favoring detachment on earth. Development of a new method for coating the interior of silica growth ampoules with transparent boron nitride, which yields the high contact angles for semiconductor melts that favor detachment. Development of a new coating for the interior of Pyrex ampoules yielding very high contact angles for water and molten organic compounds. Development of a material-balance model for steady detached solidification that provides greatly improved insight into the process, both in microgravity and on earth. Dimensionless parameters were found that clarify the role of operating conditions and physical properties. The reason for the occurrence of two steady states was clarified, along with their relative stability. Observation of periodic gas tubes during directional solidification of water and organic compounds. Gas bubbles did not propagate around the periphery to yield full detachment. Failure to obtain detachment is attributed to the ready plastic deformation of these materials, so that the frozen material continues to adhere to the ampoule wall during cooling.

Regel, Liya L.↗

UZrCN Synthesis via Arc Melting - A Novel Synthesis Study

The next generation of nuclear reactors for both power production and space nuclear propulsion require fuel that is more durable, thermally stable, and more thermally conductive to support rapid heat transfer. High temperature gas reactors (HTGR), advanced gas reactors (AGR), and space-based nuclear thermal propulsion (NTP) are advanced reactor concepts that require a fuel type that can withstand high temperatures (1000-2900K) and flow of corrosive gas coolants such as helium, hydrogen, and carbon dioxide. One fuel with the potential to meet these demanding requirements is uranium-zirconium-carbonitride (UZrCN). UZrCN has many favorable fuel qualities compared to other eligible fuel forms such as uranium dioxide (UO2) and uranium mononitride (UN) that could support the aforementioned reactor concepts. UZrCN has an exceptionally high operating temperature and thermal conductivity which are highly desirable to improve reactor economics and safety. It far exceeds the properties of UO2 which is the most common fuel form in the United States. UZrCN also surpasses UN in terms of thermal conductivity and operating temperature by eliminating the dissociation problem UN has at 1700K. UZrCN could improve gas reactor performance and enable NTP technologies; however, it is an under-researched fuel that lacks rigorous scientific study. In recent efforts by the Idaho National Laboratory, a variety of novel methods to produce this fuel composition have been explored. One such method is via arc melting of uranium, zirconium, and carbon under a nitrogen atmosphere. Alloy fabrication using arc melting has been utilized for close to 150 years now and is well-understood as a method for rapid alloy prototyping. This process will be used to perform in-situ nitriding to form UZrCN.

36 MATERIALS SCIENCE↗

UZrCN Formation via Arc Melting – A Novel Synthesis Study

The next generation of nuclear reactors for both power production and space nuclear propulsion require fuel that is more durable, thermally stable, and more thermally conductive to support rapid heat transfer. High temperature gas reactors (HTGR), advanced gas reactors (AGR), and space-based nuclear thermal propulsion (NTP) are advanced reactor concepts that require a fuel type that can withstand high temperatures (1000-2900K) and flow of corrosive gas coolants such as helium, hydrogen, and carbon dioxide. One fuel with the potential to meet these demanding requirements is uranium-zirconium-carbonitride (UZrCN). UZrCN has many favorable fuel qualities compared to other eligible fuel forms such as uranium dioxide (UO2) and uranium mononitride (UN) that could support the aforementioned reactor concepts. UZrCN has an exceptionally high operating temperature and thermal conductivity which are highly desirable to improve reactor economics and safety. It far exceeds the properties of UO2 which is the most common fuel form in the United States. UZrCN also surpasses UN in terms of thermal conductivity and operating temperature by eliminating the dissociation problem UN has at 1700K. UZrCN could improve gas reactor performance and enable NTP technologies; however, it is an under-researched fuel that lacks rigorous scientific study. In recent efforts by the Idaho National Laboratory, a variety of novel methods to produce this fuel composition have been explored. One such method is via arc melting of uranium, zirconium, and carbon under a nitrogen atmosphere. Alloy fabrication using arc melting has been utilized for close to 150 years now and is well-understood as a method for rapid alloy prototyping. This process will be used to perform in-situ nitriding to form UZrCN.

36 MATERIALS SCIENCE↗

Technology Maturation of Wireless Harsh Environment Sensors For Improved Condition Based Monitoring Of Coal Fired Power Generation

The overall goal of this project was to demonstrate and develop the usage of high-temperature (HT) harsh-environment (HE) wireless surface acoustic wave resonator (SAWR) sensor technology to promote reliable maintenance through condition-based maintenance (CBM) for field applications in harsh service conditions associated with power plant environments. The project aimed to advance the HT HE wireless SAWR sensor technology from TRL 5 to TRL 7. In addition to HT HE wireless temperature sensing, efforts were dedicated during this project to investigate, develop and increase the TRL from 3 to 5 for the following technologies: (a) HT HE strain sensors to address additional CBM monitoring needs, such as boiler tube mechanical / thermal stresses, which can provide early indications for boiler tube cracking and failure; and (b) HT aluminum nitride (AlN) and scandium aluminum nitride (ScAlN) based piezoelectric thin film fabrication and implementation of SAW sensors, with the goal of releasing the need to use single crystal piezoelectric materials for SAWRs and thus broaden possible technology applications to non-planar and harder to modify surfaces. To achieve the goals mentioned above, UMaine and its partner, Environetix Technologies Corporation, established partnerships with the following power plants: Longview Power (Maidsville, WV), a coal-fired power plant; Penobscot Energy Recovery Corp (PERC, Orrington, ME), a waste-to-energy power plant; and the UMaine Steam Plant (Orono, ME), an oil / natural gas power plant. To realize wireless HT HE SAWR sensor systems in these harsh service conditions, the University of Maine research team worked with Environetix and these power plants to define, design, fabricate, test and validate a mature prototype wireless temperature SAWR sensor system for boiler tube applications within the HT HE of the reheater pass damper chamber to directly and wirelessly monitor the temperature at eighteen independent boiler tube locations. The system included three levels, or “tiers”, of wireless communication to enable remote monitoring: Tier 1, the wireless link in the reheater pass damper chamber directly accessing the sensors on the boilers; Tier 2, the wireless local area network link, transmitting processed sensor information within the power plant to the Tier 3, a commercial wireless signal carrier company for secure remote data monitoring outside of the power plant. Regarding the wireless sensor system installed at Longview Power, temperature information from the boilers was continuously transmitted from the Longview boilers at Maidsville, WV, to Environetix headquarters, Orono, ME, over a 34 month period, when the system was finally decommissioned. Strain sensors and piezoelectric ScAlN thin film sensors were successfully installed on the exhaust duct at the UMaine Steam Power plant. The advances in wireless strain sensors and thin film piezoelectric film fabrication and testing were performed mostly in UMaine laboratories and field tested at the UMaine Steam Plant, due to its close proximity to UMaine/Environetix, access to the plant facility, and due to difficulties in accessing the other power plants during the COVID shut-down period. The project accomplished the TRL level increase of the targeted CBM technologies through the successful fabrication, installation, test, and validation of dedicated and commercial wireless sensor systems, utilizing the three different power plants. The outcomes of this project, including the wireless sensor data capability, are expected to yield an advance for CBM in harsh power plant environments. The reduction of maintenance costs, improved safety during plant operation, and increased power plant efficiency will lead to increased revenues (i.e., fewer forced outages) due to better process monitoring enabled by the wireless HT HE SAWR temperature sensor technology.

20 FOSSIL-FUELED POWER PLANTS↗

Formation of uranium nitride nanoparticles via mechanical alloying of uranium-molybdenum alloy fuels in gaseous nitrogen

Uranium-molybdenum (U-Mo) alloys show promise as a nuclear fuel system due to their high thermal conductivity and fuel loading capability. However, U-Mo systems are susceptible to irradiation induced swelling ultimately affecting the cladding via mechanical and chemical interactions. To address these shortcomings, this research investigated the formation of uranium mononitride (UN) nanoparticles within a 90 wt% U/10 wt% Mo (U-10Mo) matrix to act as a prospective defect sink for fission products at nanometric hetero-interfaces. To promote the formation of UN, U-10Mo powders were mechanically alloyed under a high purity nitrogen atmosphere. Variations of the milling process investigated included media size, duration of milling, and number of times the milling jar was re-aerated with nitrogen gas. Characterization of the fuel microstructure was completed using light element analysis, X-ray diffraction, scanning and transmission-electron microscopy, electron energy loss spectroscopy, and atom probe tomography. UN nanoparticles measuring 1–5 nm in radius were observed in the U-Mo matrix as early as 1 h into the mechanical alloying process. Milling time in excess of 10 h was found to lead to deleterious effects induced by the stainless-steel milling media.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Ceramic applications in turbine engines

In the past the potential of vehicular gas engines could not be realized because component materials served to limit the turbine operating temperature, thereby restricting fuel economy and initial cost. It was, therefore, not possible for the vehicular gas turbine to compete with more conventional engines. The emergence of low-cost, high-temperature ceramic components has the potential to reverse this situation. For example, the Allison GT404 engine, operating with ceramic components at turbine inlet temperatures up to 2350 F to 2500 F, has the potential of a fuel economy which is better than that of current Diesel engines. The Allison AGT100 engine operating with ceramic components offers the possibility of a 30% improvement in fuel economy over 1985 spark ignition engines. The materials considered for an employment in the ceramic components include silicon carbide, silicon nitride, aluminum silicate, and lithium aluminum silicate.

Byrd, J. A.↗

Laser-Induced Thermal Decomposition of Uranium Coordination Compounds with Non-oxidic Ligands to Produce Nitride and Carbide Materials

The production of ceramics from uranium coordination compounds can be achieved through thermal processing if an excess amount of the desired atoms (i.e., C or N), or reactive gaseous products (e.g., methane or nitrogen oxide) is made available to the reactive uranium metal core via decomposition/fragmentation of the surrounding ligand groups. Here, computational thermodynamic approaches were utilized to identify the temperatures necessary to produce uranium metal from some starting compounds—UI 4 (TMEDA) 2 , UCl 4 (TMEDA) 2 , UCl 3 (pyridine) x , and UI 3 (pyridine) 4 . Experimentally, precursors were irradiated by a laser under various gaseous environments (argon, nitrogen, and methane) creating extreme reaction conditions (i.e., fast heating, high temperature profile >2000 °C, and rapid cooling). Despite the fast dynamics associated with laser irradiation, the central uranium atom reacted with the thermal decomposition products of the ligands yielding uranium ceramics. Residual gas analysis identified vaporized products from the laser irradiation, and the final ceramic products were characterized by powder X-ray diffraction. The composition of the uranium precursor as well as the gaseous environment had a direct impact on the production of the final phases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

One-Dimensional (1D) Nanostructured Materials for Energy Applications

At present, the world is at the peak of production of traditional fossil fuels. Much of the resources that humanity has been consuming (oil, coal, and natural gas) are coming to an end. The human being faces a future that must necessarily go through a paradigm shift, which includes a progressive movement towards increasingly less polluting and energetically viable resources. In this sense, nanotechnology has a transcendental role in this change. For decades, new materials capable of being used in energy processes have been synthesized, which undoubtedly will be the cornerstone of the future development of the planet. In this review, we report on the current progress in the synthesis and use of one-dimensional (1D) nanostructured materials (specifically nanowires, nanofibers, nanotubes, and nanorods), with compositions based on oxides, nitrides, or metals, for applications related to energy. Due to its extraordinary surface–volume relationship, tunable thermal and transport properties, and its high surface area, these 1D nanostructures have become fundamental elements for the development of energy processes. The most relevant 1D nanomaterials, their different synthesis procedures, and useful methods for assembling 1D nanostructures in functional devices will be presented. Applications in relevant topics such as optoelectronic and photochemical devices, hydrogen production, or energy storage, among others, will be discussed. The present review concludes with a forecast on the directions towards which future research could be directed on this class of nanostructured materials.

Machín, Abniel (ORCID:0000000341343344)↗

Evaluation of an innovative high temperature ceramic wafer seal for hypersonic engine applications

A critical mechanical system in advanced hypersonic engines is the panel-edge seal system that seals gaps between the articulating engine panels and the adjacent engine splitter walls. Significant advancements in seal technology are required to meet the extreme demands placed on the seals, including the simultaneous requirements of low leakage, conformable, high temperature, high pressure, sliding operation. In this investigation, the design, development, analytical and experimental evaluation of a new ceramic wafer seal that shows promise of meeting these demands will be addressed. A high temperature seal test fixture was designed and fabricated to measure static seal leakage performance under engine simulated conditions. Ceramic wafer seal leakage rates are presented for engine-simulated air pressure differentials (up to 100 psi), and temperature (up to 1350 F), sealing both flat and distorted wall conditions, where distortions can be as large as 0.15 inches in only an 18 inch span. Seal leakage rates are low, meeting an industry-established tentative leakage limit for all combinations of temperature, pressure and wall conditions considered. A seal leakage model developed from externally-pressurized gas film bearing theory is also presented. Predicted leakage rates agree favorably with the measured data for nearly all conditions of temperature and pressure. Discrepancies noted at high engine pressure and temperature are attributed to thermally-induced, non-uniform changes in the size and shape of the leakage gap condition. The challenging thermal environment the seal must operate in places considerable demands on the seal concept and material selection. Of the many high temperature materials considered in the design, ceramics were the only materials that met the many challenging seal material design requirements. Of the aluminum oxide, silicon carbide, and silicon nitride ceramics considered in the material ranking scheme developed herein, the silicon nitride class of ceramics ranked the highest because of their high temperature strength; resistance to the intense heating rates; resistance to hydrogen damage; and good structural properties. Baseline seal feasibility has been established through the research conducted in this investigation. Recommendations for future work are also discussed.

Steinetz, Bruce M.↗

Modeling and Real-Time Process Monitoring of Organometallic Chemical Vapor Deposition of III-V Phosphides and Nitrides at Low and High Pressure

The purpose of this paper is to review modeling and real-time monitoring by robust methods of reflectance spectroscopy of organometallic chemical vapor deposition (OMCVD) processes in extreme regimes of pressure. The merits of p-polarized reflectance spectroscopy under the conditions of chemical beam epitaxy (CBE) and of internal transmission spectroscopy and principal angle spectroscopy at high pressure are assessed. In order to extend OMCVD to materials that exhibit large thermal decomposition pressure at their optimum growth temperature we have designed and built a differentially-pressure-controlled (DCP) OMCVD reactor for use at pressures greater than or equal to 6 atm. We also describe a compact hard-shell (CHS) reactor for extending the pressure range to 100 atm. At such very high pressure the decomposition of source vapors occurs in the vapor phase, and is coupled to flow dynamics and transport. Rate constants for homogeneous gas phase reactions can be predicted based on a combination of first principles and semi-empirical calculations. The pressure dependence of unimolecular rate constants is described by RRKM theory, but requires variational and anharmonicity corrections not included in presently available calculations with the exception of ammonia decomposition. Commercial codes that include chemical reactions and transport exist, but do not adequately cover at present the kinetics of heteroepitaxial crystal growth.

Bachmann, K. J.↗