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Results for “kinetic parameters”
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Predicting encapsulant delamination in photovoltaic modules bridging photochemical reaction kinetics and fracture mechanics
Abstract Photovoltaic (PV) modules are subjected to environmental stressors (UV exposure, temperature, and humidity) that cause degradation within the encapsulant and its interfaces with adjacent glass and cell substrates. To save experimental time and to enable long‐term assessment with intensive degradation only taking place after many years, the development of predictive models is indispensable. Previous works have modeled the delamination of the ethylene vinyl acetate (EVA) encapsulant/glass and encapsulant/cell interfaces under field aging conditions with fundamental photochemical degradation reactions that lead to molecular scission and loss of interfacial adhesion, characterized by the fracture resistance, G c . However, these models were fundamentally limited in that the following aspects were not incorporated: (i) molecular crosslinking in the field, (ii) synergistic autocatalytic interactions of degradation mechanisms, (iii) connection between degraded encapsulant structure and its mechanical properties, and (iv) rigorous treatment of the plasticity contribution to G c with finite element models. Here, we present a time‐dependent multiscale model that addresses these limitations and is applicable to a wide range of encapsulants and interfaces. For the reference EVA encapsulant and its interfaces with the glass and cell, the presented model predicts an initial rise in G c in the first 3 years of field aging from crosslinking, then a subsequent sharp decline from degradation mechanisms. We used nanoindentation to measure the changes in EVA mechanical properties over exposure time to tune the model parameters. The model predictions of G c and mechanical properties match with experimental data and show an improvement compared to previous models. The model can even predict switches in failure interfaces, such as the observed EVA/cell to EVA/glass transition. We also conducted a sensitivity analysis study by varying the degradation and crosslinking kinetic parameters to demonstrate their effects on G c . Model extensions to polyolefin elastomer‐ and silicone‐encapsulants and their interfaces are also demonstrated.
Dynamic Promotion of the Oxygen Evolution Reaction via Programmable Metal Oxides
Hydrogen gas is a promising renewable energy storage medium when produced via water electrolysis, but this process is limited by the sluggish kinetics of the anodic oxygen evolution reaction (OER). Herein, we used a microkinetic model to investigate promoting the OER using programmable oxide catalysts (i.e., forced catalyst dynamics). We found that programmable catalysts could increase current density at a fixed overpotential (100–600× over static rates) or reduce the overpotential required to reach a fixed current density of 10 mA cm –2 (45–140% reduction vs static). In our kinetic parametrization, the key parameters controlling the quality of the catalytic ratchet were the O*-to-OOH* and O*-to-OH* activation barriers. Furthermore, our findings indicate that programmable catalysts may be a viable strategy for accelerating the OER or enabling lower-overpotential operation, but a more accurate kinetic parametrization is required for precise predictions of performance, ratchet quality, and resulting energy efficiency.
Recent Advancements in Modeling and Simulation of Entry Systems at NASA
This paper describes recent development of modeling and simulation technologies for entry systems in support of NASA's exploration missions. Mission-tailored research and development in modeling of entry systems occurs across the Agency (e.g., within the Orion and Mars 2020 Programs), however the aim of this paper is to discuss the broad, cross-mission research conducted by NASA's Entry Systems Modeling (ESM) Project, which serves as the Agency's only concerted effort toward advancing entry systems across a range of technical disciplines. Technology development in ESM is organized and prioritized from a system-level perspective, resulting in four broad technical areas of investment: (1) Predictive material modeling, (2) Shock layer kinetics and radiation, (3) Computational and experimental aerosciences, and (4) Guidance, navigation, and control. Investments in thermal protection material modeling are geared toward high-fidelity, predictive models capable of handling complex structures, with an eye toward optimizing design performance and quantifying thermal protection system reliability. New computational tools have been developed to characterize material properties and behavior at the microstructural level, and experimental techniques (molecular beam scattering, micro-computed tomography, among others) have been developed to measure material kinetics, morphology, and other parameters needed to inform and validate detailed simulations. Advancements have also been made in macrostructural simulation capability to enable 3-D system-scale calculations of material response with complex topological features, including differential recession of tile gaps. Research and development in the area of shock layer kinetics has focused on air and CO2-based atmospheres. Capacity and capability of the NASA Ames Electric Arc Shock Tube (EAST) have been expanded in recent years and analysis of resulting data has led to several improvements in kinetic models, while simultaneously reducing uncertainties associated with radiative heat transfer predictions. First-principles calculations of fundamental kinetic, thermodynamic, and transport data, along with state-specific models for non-equilibrium flow regimes, have also yielded new insights and have the potential to vastly improve model fidelity. Aerosciences is a very broad area of interest in entry systems, yet a number of important challenges are being addressed: Coupled fluid-structure simulations of parachute inflation and dynamics; Experimental and computational studies of vehicle dynamics; Multi-phase flow with dust particles to simulate entry environments at Mars during dust storms; Studies of roughness-induced heating augmentation relevant to tiled and woven thermal protection systems; and Advanced numerical methods to optimize computational analyses for desired accuracy versus cost. Guidance and control in the context of entry systems has focused on development of methods for multi-axis control (i.e. pitch and yaw, rather than bank angle alone) of spacecraft during entry and descent. With precision landing requirements driven by Mars human exploration goals, recent efforts have yielded 6-DOF models of multi-axis control with propulsive descent of both inflatable and rigid ellipsled-like architectures.
Recent Advancements in Modeling and Simulation of Entry Systems at NASA
This paper describes recent development of modeling and simulation technologies for entry systems in support of NASA’s exploration missions. Mission-tailored research and development in modeling of entry systems occurs across the Agency (e.g., within the Orion and Mars 2020 Programs), however the aim of this paper is to discuss the broad, cross-mission research conducted by NASA’s Entry Systems Modeling (ESM) Project, which serves as the Agency’s only concerted effort toward advancing entry systems across a range of technical disciplines. Technology development in ESM is organized and prioritized from a system-level perspective, resulting in four broad technical areas of investment: (1) Predictive material modeling, (2) Shock layer kinetics and radiation, (3) Computational and experimental aerosciences, and (4) Guidance, navigation, and control. Investments in thermal protection material modeling are geared toward high-fidelity, predictive models capable of handling complex structures, with an eye toward optimizing design performance and quantifying thermal protection system reliability. New computational tools have been developed to characterize material properties and behavior at the microstructural level, and experimental techniques (molecular beam scattering, micro-computed tomography, among others) have been developed to measure material kinetics, morphology, and other parameters needed to inform and validate detailed simulations. Advancements have also been made in macrostructural simulation capability to enable 3-D system-scale calculations of material response with complex topological features, including differential recession of tile gaps. Research and development in the area of shock layer kinetics has focused on air and CO2-based atmospheres. Capacity and capability of the NASA Ames Electric Arc Shock Tube (EAST) have been expanded in recent years and analysis of resulting data has led to several improvements in kinetic models, while simultaneously reducing uncertainties associated with radiative heat transfer predictions. First-principles calculations of fundamental kinetic, thermodynamic, and transport data, along with state-specificmodels for non-equilibrium flow regimes, have also yielded new insights and have the potential to vastly improve model fidelity. Aerosciences is a very broad area of interest in entry systems, yet a number of important challenges are being addressed: Coupled fluid-structure simulations of parachute inflation and dynamics; Experimental and computational studies of vehicle dynamics; Multi-phase flow with dust particles to simulate entry environments at Mars during dust storms; Studies of roughness-induced heating augmentation relevant to tiled and woven thermal protection systems; and Advanced numerical methods to optimize computational analyses for desired accuracy versus cost. Guidance and control in the context of entry systems has focused on development of methods for multi-axis control (i.e. pitch and yaw, rather than bank angle alone) of spacecraft during entry and descent. With precision landing requirements driven by Mars human exploration goals, recent efforts have yielded 6-DOF models of multi-axis control with propulsive descent of both inflatable and rigid ellipsled-like architectures. Results for both configurations have demonstrated the ability to land within the 50-meter precision requirement demanded by Mars human exploration missions, while also reducing propellant requirements by enabling more efficient control through entry and descent. Ongoing research in GN&C is developing mechanical specifications for the systems and establishing engineering feasibility.
A provisional analysis of two-dimensional turbulent mixing with variable density
A predictive method for the titled flows based on the Prandtl energy method was developed and assessed by comparing predicted results with experimental results. For constant-density flows, both gross properties such as spreading rate and maximum turbulent kinetic energy and detailed properties such as mean shear stress distributions are shown to be well predicted. For variable-density flows, considerable attention is devoted to the inclusion in the analysis of the added effect of pressure fluctuations and of the variation in the several extant empirical parameters on the turbulent kinetic energy. It is found that a variation with Mach number of the characteristic Reynolds number for turbulent transport is needed to account for the observed decrease in spreading rate. The predictions which result from these considerations are compared with the limited experimental data presently available for the two crucial cases: compressible adiabatic mixing and low-speed isothermal mixing of two dissimilar gases.
Factors Determining Selectivity of Acid- and Base-Catalyzed Self- and Cross-Condensation of Acetone and Cyclopentanone
In a combined kinetics and density functional theory (DFT) study, we have explored several factors that affect the selectivity of acid- and base-catalyzed self- and cross-aldol condensation of acetone (ACE) and cyclopentanone (CPO). These factors include competitive adsorption, molecular structure, and electron polarization of the two ketones on the catalyst surface. Here, kinetic analysis shows that on MgO, self-condensation of both ACE and CPO is limited by the initial unimolecular enolization step. Accordingly, CPO exhibits a higher self-condensation rate than ACE due to the more favorable α-C–H abstraction by the basic O site. The thermodynamic parameters derived from the kinetic analysis indicate that under cross-condensation reaction conditions, the MgO surface fraction covered by CPO is significantly higher than that covered by ACE. Therefore, the product distribution is dominated by [CPO]-activated products ([CPO]CPO + [CPO]ACE). Also, for a given enolate (indicated as [CPO] or [ACE]), the higher surface coverage of CPO leads to enhanced C–C coupling with CPO as the electrophile ([CPO]CPO > [CPO]ACE; [ACE]CPO > [ACE]ACE). By contrast, for both acid catalysts investigated, the rate-limiting step is the bimolecular C–C coupling, with aspects of this step depending on the density of acid sites. That is, on the high-acid-density MCM-41-SO 3 H catalyst, condensation follows a bimolecular dual-site mechanism (Langmuir–Hinshelwood model). On this catalyst surface, the ACE coverage is higher than that of CPO, which causes a higher selectivity for those products in which ACE is the electrophile ([CPO]ACE > [CPO]CPO; [ACE]ACE > [ACE]CPO). Steric hindrance is another factor that affects selectivity in the same way, favoring products in which the electrophile is ACE since it presents a lower steric hindrance to C–C coupling than CPO. Therefore, the same sequence of products is obtained for the low-acid-density MCM-41-SO 3 H catalyst, which proceeds on a single-acid site with the other molecule in the liquid phase (Eley–Rideal model). In this case, the electrophile coverage is not relevant, but the steric hindrance is, yielding the same trend as above ([CPO]ACE > [CPO]CPO; [ACE]ACE > [ACE]CPO).
Convective flow effects on protein crystal growth
A high-resolution microscopic interferometric setup for the monitoring of protein morphologies has been developed. Growth or dissolution of a crystal can be resolved with a long-term depth resolution of 200 A and a lateral resolution of 2 microns. This capability of simultaneously monitoring the interfacial displacement with high local depth resolution has yielded several novel results. We have found with lysozyme that (1) the normal growth rate is oscillatory, and (2) depending on the impurity content of the solution, the growth step density is either greater or lower at the periphery of a facet than in its center. The repartitioning of Na plus and Cl minus ions between lysozyme solutions and crystals was studied for a wide range of crystallization conditions. A nucleation-growth-repartitioning model was developed, to interpret the large body of data in unified way. The results strongly suggest that (1) the ion to lysozyne ratio in the crystal depends mostly on kinetic rather than crystallographic parameters, and (2) lysozyme crystals possess a salt-rich core with a diameter electron microscopy results appear to confirm this finding, which could have far-reaching consequences for x-ray diffraction studies. A computational model for diffusive-convective transport in protein crystallization has been applied to a realistic growth cell geometry, taking into account the findings of the above repartitioning studies and our kinetics data for the growth of lysozyme. The results show that even in the small cell employed, protein concentration nonuniformities and gravity-driven solutal convection can be significant. The calculated convection velocities are of the same order to magnitude as those found in earlier experiments. As expected, convective transport, i.e., at Og, lysozyme crystal growth remains kinetically limited. The salt distribution in the crystal is predicted to be non-uniform at both 1g and 0g, as a consequence of protein depletion in the solution. Static and dynamic light scattering studies in undersaturated and supersaturated solutions have been performed. Diffusivities in undersaturated solutions, were found to vary with lysozyme concentrations. Depending on the salt concentration, the diffusivities either increase or decrease. Interestingly, the corresponding static scattering intensities behave oppositely, Our current analysis indicates that these changes are inconsistent with aggregation in undersaturated solutions. However, the data are compatible with concentration-dependent changes of the interactions between protein and salt.
Phase transformation and growth mechanism of RF sputtered ferroelectric lead scandium tantalate (PbSc 0.5 Ta 0.5 O 3 ) films
Lead scandium tantalate (PbSc 0.5 Ta 0.5 O 3 , PST), an order/disorder ferroelectric, is a potential candidate for electrocaloric cooling and pyroelectric infrared (IR) detector. In this work, we report the phase transformation kinetics from two series of samples containing pure amorphous and mixture of amorphous and pyrochlore to desired perovskite phase using postdeposition rapid thermal processing (RTP) as well as growth mechanism of RF sputtered PST thin films using excess lead target on platinized silicon (Pt/Ti/SiO 2 /Si) substrates. We find that small changes in the temperature ramp have a large effect on the degree of perovskite conversion (ferroelectric phase), orientation (crystallographic texture), and long-range order parameter (< S 111 >). Through isothermal annealing, we obtained optimal perovskite phase at ≥700°C temperature. The phase transformation is characterized by spontaneous formation of center-type in-plane radial rosette-like structures revealed by scanning electron microscopy. The PST perovskite crystallites were found to coexist with pyrochlore in RTP annealed films. The volume fractions for perovskite and pyrochlore phase were obtained from the analysis of “rosettes” and respective X-ray diffraction intensities which helped to determine various parameters associated with phase kinetics (n, k, and activation energy, Ea) and accompanying growth. The effective activation energies of perovskite transition and growth were found to be 332 ± 11 kJ/mol (345 ± 11 kJ/mol) and 114 ± 10 kJ/mol (122 ± 10 kJ/mol), respectively, for pure amorphous only (and mixed amorphous and pyrochlore) phase following nucleation-growth controlled Avrami's equation. A linear growth rate (n~1) for the perovskite phase indicates predominant interface-controlled process and diffusion-limited phenomena thus inhibiting rosette size owing to reactant depletion and soft impingement at the grain boundary. However, the growth behavior is isotropic in two-dimension parallel to the plane of the substrates for both sample series. Furthermore, lead loss was severe for in-situ growth and RTP combined with conventional furnace annealing than those of RTP only films, which were closer to stoichiometric albeit with excess lead and marginal oxygen vacancies (V o ).
Temperature-responsive smart tracers for field-measurement of inter-well thermal evolution: Heterogeneous kinetics and field demonstration
Temperature-responsive smart tracers enable advanced warning of a “premature thermal breakthrough” and may therefore improve reservoir management and reduce financial risk. A successful calculation of inter-well fluid temperatures requires that temperature-dependent kinetics are known, which typically result from homogeneous batch reactor experiments. However, recent meso-scale field experiments at the Altona Field Laboratory involving fluid flow in a discretely-fractured reservoir suggest that silica-fluid interfaces may accelerate hydrolysis kinetics. Here, the Arrhenius parameters of phenyl acetate hydrolysis are investigated under heterogeneous reaction conditions in packed-bed column experiments. The breakthrough curve of the reaction product is compared to an inert reference tracer (carbon-cored nanoparticles). Temperatures experienced during field testing ranging from 10 to 40 °C were studied using a phosphate buffer solution to maintain a near-neutral pH, as found in the reservoir. The empirically-determined pre-exponential factor and activation energy values are subsequently used in a first-order kinetic model to improve calculations of effective reservoir temperatures for these meso-scale field tests. Here, the results suggest that hydrolysis reactions can directly monitor inter-well reservoir temperatures, but only if the influence of solid-fluid interactions are carefully accounted for.
Mechanistic Study of 1,2-Dichloroethane Hydrodechlorination on Cu-Rich Pt–Cu Alloys: Combining Reaction Kinetics Experiments with DFT Calculations and Microkinetic Modeling
Cu-rich Pt–Cu bimetallic catalysts are among the most promising candidates for actively catalyzing the hydrodechlorination of 1,2-dichloroethane (1,2-DCA) toward ethylene production. Combining reaction kinetics experiments with density functional theory (DFT) calculations and mean-field microkinetic modeling, we present a systematic mechanistic study for 1,2-DCA hydrodechlorination on Cu-rich Pt–Cu alloy catalysts. Our DFT (PBE+(TS+SCS)) results suggest that increasing Cu content in the Pt–Cu alloy destabilizes C 2 -species adsorption while stabilizing the binding of atomic chlorine. The reaction energetics of all the elementary steps in the 1,2-DCA reaction network were calculated on a Pt 1 Cu 3 (111) model surface. The DFT results were then used to construct a microkinetic model, and the model-predicted reaction rates were compared with our reaction kinetics experimental results on a Cu-rich SiO 2 -supported Pt–Cu alloy catalyst through a parameter estimation procedure. Both the reaction kinetics experiments and the microkinetic model after parameter adjustments yielded 100% selectivity to ethylene. The microkinetic model pointed to a reaction pathway involving two sequential chlorine-removal steps on the Pt–Cu alloy catalyst, a mechanism distinct from the one previously identified on pure Pt/SiO 2 catalysts, which involved an initial hydrogen-removal step. Adjustments to the DFT-derived parameters indicate the possible formation of chlorine-induced Cu-enriched surface sites during 1,2-DCA hydrodechlorination conditions, sites that are more active than those encountered in the bulk Pt 1 Cu 3 (111) alloy surface. Furthermore, our study offers valuable initial insights on the 1,2-DCA hydrodechlorination reaction mechanism and the nature of the active sites on PtCu bimetallic catalysts.
Mechanistic Insights into Molecular Copper Hydride Catalysis: the Kinetic Stability of CuH Monomers toward Aggregation is a Critical Parameter for Catalyst Performance
The activity of molecular copper hydride (CuH) complexes towards the selective insertion of unsaturated hydrocarbons under mild conditions has contributed significantly to versatile methodologies for upgrading these feedstocks. However, these catalysts are particularly susceptible to deleterious aggregation, leading to the depletion of active CuH species. Little is known about the mechanisms of CuH aggregation, how it influences overall catalyst performance, and how it can be controlled. We address these challenges with mechanistic studies on a model reaction of unactivated alkene hydroboration catalyzed by (IPr*CPh 3 )CuH (LCuH). Here, we report a comprehensive mechanistic investigation of this system, identifying an aggregation pathway that continuously depletes catalytically active LCuH to form inactive CuH clusters during turnover. Deactivation of LCuH is controlled primarily by the competition between the kinetics of the initial LCuH dimerization step and that of alkene insertion. We therefore propose that a more comprehensive understanding of CuH catalyst performance must account for the kinetics of the initial LCuH dimerization step, revising a previously explored thermodynamic understanding of CuH aggregation, where the concentration of active species is controlled by equilibria established between CuH dimers and monomers. With a series of (NHC)CuH congeners (NHC = N-heterocyclic carbene), we demonstrate that ostensibly minor structural modifications to the ligand peripheries can drastically affect the LCuH dimerization kinetics, while maintaining reactivity towards on–cycle alkene insertion. We employed a computational approach based on molecular dynamics simulations to provide an in-depth understanding of how specific structural ligand modifications can substantially increase the kinetic stability of monomeric CuH catalysts. Our combined experimental and computational studies suggest strategies for rational ligand design that can be broadly applied to molecular catalyst systems that are susceptible to deactivation via aggregation pathways.
Effect of concentration dependence of the diffusion coefficient on homogenization kinetics in multiphase binary alloy systems
Diffusion calculations were performed to establish the conditions under which concentration dependence of the diffusion coefficient was important in single, two, and three phase binary alloy systems. Finite-difference solutions were obtained for each type of system using diffusion coefficient variations typical of those observed in real alloy systems. Solutions were also obtained using average diffusion coefficients determined by taking a logarithmic average of each diffusion coefficient variation considered. The constant diffusion coefficient solutions were used as reference in assessing diffusion coefficient variation effects. Calculations were performed for planar, cylindrical, and spherical geometries in order to compare the effect of diffusion coefficient variations with the effect of interface geometries. In most of the cases considered, the diffusion coefficient of the major-alloy phase was the key parameter that controlled the kinetics of interdiffusion.
Experimental and computational kinetics study of the liquid-phase hydrogenation of C=C and C=O bonds
Solvent effects on adsorption equilibrium and reaction kinetics are evaluated for hydrogenation reactions catalyzed by Pd/alumina in a series of different solvents. Three reactants – cyclohexene, benzene and benzaldehyde – and three solvents – n-heptane (HEP), methylcyclohexane (MCHA), decalin (DL) – have been investigated. Kinetic analysis of hydrogenation of cyclohexene reveals that hydrogen adsorbs on different sites from those where cyclohexene and the solvents adsorb; however, the presence of hydrogen on these separate sites affects the heats of adsorption of the hydrocarbons. When the solvent is a weakly interacting linear alkane (HEP), the rate determining step of the reaction is the first hydrogenation of adsorbed cyclohexene. Furthermore, this conclusion is supported by DFT calculations that show a higher enthalpy barrier for the first hydrogenation than for the second, while statistical thermodynamics analysis validates the physical significance of the entropy of adsorption parameters derived from the kinetic fitting of experimental data. By contrast, with solvents such as MCHA and DL, which interact more strongly with the metal surface and compete for active sites with the reactant and the surface intermediate, the rate limiting step seems to shift to the second hydrogenation step.
Observation and Modeling of the Thermal Runaway of High-Capacity Pouch Cells Due to an Internal Short Induced by an Indenter
Owing to the complexity of coupling mechanical and electrical solvers for finite element analysis (FEA) of mechanical abuse of a battery, the simulation should be performed by incorporating a local short circuit model activated based on the status of battery elements. However, the approach should also consider various other conditions of the battery simulated, such as the initial state of charge (SOC), for precise simulations of the internal short. This study proposes an approach developed with a mechanical model and single-particle battery model, along with a reaction kinetics model for thermal abuse using LS-DYNA. Several key parameters were selected, such as the activation criteria, kinetic abuse and element integration points during the internal short circuit induced by the indenter. The impact of these key parameters in the FEA on thermal runaway response for various initial SOCs from 25 to 100 % were analyzed. The FEA results obtained were compared against experimental results with various parameters such as activation criterion of internal short, kinetic abuse based on accelerating rate calorimetry (ARC) data. Finally, the root causes of the discrepancy between the FEA and experimental results are discussed regarding integration point what solver can make difference during calculation.
Impact force as a scaling parameter
The Federal Aviation Administration (FAR PART 25) requires that a structure carry ultimate load with nonvisible impact damage and carry 70 percent of limit flight loads with discrete damage. The Air Force has similar criteria (MIL-STD-1530A). Both civilian and military structures are designed by a building block approach. First, critical areas of the structure are determined, and potential failure modes are identified. Then, a series of representative specimens are tested that will fail in those modes. The series begins with tests of simple coupons, progresses through larger and more complex subcomponents, and ends with a test on a full-scale component, hence the term 'building block.' In order to minimize testing, analytical models are needed to scale impact damage and residual strength from the simple coupons to the full-scale component. Using experiments and analysis, the present paper illustrates that impact damage can be better understood and scaled using impact force than just kinetic energy. The plate parameters considered are size and thickness, boundary conditions, and material, and the impact parameters are mass, shape, and velocity.
Model of ASTM Flammability Test in Microgravity: Iron Rods
There is extensive qualitative results from burning metallic materials in a NASA/ASTM flammability test system in normal gravity. However, this data was shown to be inconclusive for applications involving oxygen-enriched atmospheres under microgravity conditions by conducting tests using the 2.2-second Lewis Research Center (LeRC) Drop Tower. Data from neither type of test has been reduced to fundamental kinetic and dynamic systems parameters. This paper reports the initial model analysis for burning iron rods under microgravity conditions using data obtained at the LERC tower and modeling the burning system after ignition. Under the conditions of the test the burning mass regresses up the rod to be detached upon deceleration at the end of the drop. The model describes the burning system as a semi-batch, well-mixed reactor with product accumulation only. This model is consistent with the 2.0-second duration of the test. Transient temperature and pressure measurements are made on the chamber volume. The rod solid-liquid interface melting rate is obtained from film records. The model consists of a set of 17 non-linear, first-order differential equations which are solved using MATLAB. This analysis confirms that a first-order rate, in oxygen concentration, is consistent for the iron-oxygen kinetic reaction. An apparent activation energy of 246.8 kJ/mol is consistent for this model.
Early stage growth of amorphous thin film: Average kinetics, nanoscale dynamics, and pressure dependence
We used the coherent grazing incidence small angle x-ray scattering technique to study the average kinetics and nanoscale dynamics during early-stage a-WSi 2 sputter deposition. The kinetic and dynamic properties are examined as a function of pressure, which is known to be a critical factor in determining final surface roughness. Surface growth kinetics and dynamics are characterized by time parameters extracted from the height-height structure factor and correlation functions. The roughness at a given length scale reaches a maximum before relaxing down to a steady state. The lateral length scale dependence and pressure dependence are then compared among the measured kinetics and dynamics time parameters. Surfaces grown at lower pressures are smoother, leading to longer correlation times. The time parameters to reach a dynamic steady state and a kinetic steady state show contrasting pressure dependence. A dynamic steady state is reached earlier than the kinetic steady state at high pressure. A more random deposition direction and lower kinetic energy at higher pressures can explain these phenomena, along with the hypothesis that larger nanoclusters form in vapor before arriving at the surface. Here, a continuum model is applied to simulate the overall behavior with mixed success.