Parabolic Regime Research Articles

Investigation of surface structuring and oxidation performance of Inconel 718 superalloy by laser remelting with different patterns

The current paper deals with the effect of CO2 laser remelting on the surface structuring and oxidation performance of Inconel 718 superalloy, pointing out different laser-induced surface patterns that make a difference in their oxidation properties vital for high-temperature applications. Surface roughness, microstructure, and oxidation behavior characterization were performed using 3D optical profilometry, SEM, and XRD techniques. The oxidation tests conducted at 1000 °C for 24 h have revealed that remelted surfaces offered better oxidation resistance compared to untreated samples. Notably, the patterned sample showed the lowest weight gain under oxidation, and a parabolic regime in oxidation occurred after 100 min; while in an untreated reference sample, this appears only after 200 min. This improvement in performance results from the formation of a chromium-rich oxide layer on the melt pools, which acts as an effective barrier against further oxidation. The findings show that laser remelting, especially with grid-like surface patterns, results in an improvement in both durability and high-temperature performance of Inconel 718; therefore, it is apparently a very promising technique for lifespan extension of industrially relevant materials.

A thermogravimetric comparative study of the high temperature steam oxidation of bare and pre-oxidized Zircaloy-4, M5Framatome and Optimized ZIRLO™

For Loss of Coolant Accident (LOCA) analysis, high-temperature oxidation kinetics in steam of Zircaloy-4 and the two Nb-bearing alloys used in French Pressurized Water Reactors (PWRs), M5Framatome11M5 and M5Framatome are trademarks or registered trademarks of Framatome or its affiliates, in the USA or other countries. and Optimized ZIRLO™22Optimized ZIRLO is a trademark or registered trademark of Westinghouse Electric Company LLC, its affiliates and/or its subsidiaries in the United States and may be registered in other countries throughout the world. All rights reserved. Unauthorized use is strictly prohibited. Other names may be trademarks of their respective owners., have been studied using Thermo-Gravimetric Analysis (TGA) technique in the temperature range of 900–1200 °C. A specific test procedure allowing the use of a high steam flow rate and good steam supply to the whole specimen surface, as well as fast heating of the specimen, has been developed. Clean kinetic data, not affected by steam starvation, were obtained on the bare, as-received alloys. For as-received claddings, oxidation kinetics are comparable and close to parabolic for the three alloys at 1100 °C and above. Below 1100 °C, a significant deviation from the parabolic kinetic regime was observed, and M5 Framatome oxidizes slower than Zircaloy-4 and Optimized ZIRLO. Thanks to the fast-heating protocol, the influence of pre-oxidation, simulating corrosion in normal reactor operation, could be investigated, avoiding evolution of the pre-oxidation scale during a slow, long heating phase. Pre-oxidized Zircaloy-4 and M5 Framatome were investigated. A strong protective effect is observed below 1200 °C, while at 1200 °C, the pre-oxidation layer appears to be much less protective, possibly due to the monoclinic to tetragonal zirconia phase transformation.

Oxidation behavior of Zr-2.5Nb alloy exposed to steam in the temperature range of 600–1200 °C

Zr-2.5Nb pressure tube material was subjected to isothermal steam exposures in the range 600–1200 °C for different durations to predict its oxidation behavior during hypothetical accident scenarios. The oxidation exponent obtained from power law fitting of the thermogravimetry (TG) curves deviated from parabolic regime. Nevertheless, oxidation kinetics was described by determining the parabolic rate constants (Kp) in two temperature ranges: Kp = 0.029 exp(-111075/RT) (kg/m2)2/sec for 600–900 °C whereas Kp = 77652.6 exp(-254824/RT) (kg/m2)2/sec for 900–1200 °C. In the tested durations, only the 1000 °C sample has shown breakaway transition, after approximately 105 min and has absorbed the highest amount of hydrogen amongst all samples. The trend in hydrogen pickup fraction (HPUF) was verified by two complementary hydrogen determination methods. Clear differences were identified in the α-Zr(O) layer formed on the samples below and above 900 °C. In the α + β range of 600–900 °C, α-Zr(O) consisted of tiny β precipitates. At and above 900 °C in the fully β range, columnar α-Zr(O) grains were observed.

(Digital Presentation) Initial High-Temperature Oxidation Behavior of Iron Binary Alloys in Air

High-temperature corrosion is playing a critical role now in many modern industries such as aerospace, gas turbines manufacturing, and steelmaking. For instance, during hot rolling of the steel sheets -as one of the later steps in steel production- before coiling, high-temperature corrosion occurs in the form of oxidation. Such reaction in air is fast and causes the formation of an oxide scale at the surface. This can change the substrate metal in terms of composition and mechanical properties. Therefore, it is essential to study the initial oxidation behavior of steels at high temperatures when exposed to air. There are different mechanisms that can control the oxidation growth rate which lead to either linear or parabolic growth regimes.The goal of this work is to study the initial high-temperature oxidation behavior of binaries with different alloying element contents (<5 wt%). The kinetics, affecting parameters, and oxidation mechanism at different stages of the process were studied. The experiments were conducted in a Thermogravimetric Analyzer (TGA) to obtain continuous mass-gain data while controlling the atmosphere and the temperature. Fe-Mn and Fe-Si samples with different compositions were chosen for isothermal experiments at a range of temperatures (between 950 °C and 1150 °C). The chamber contained gas mixtures, including oxygen, nitrogen, and water vapor, applied with different flow rates. Depending on the alloying element content of the samples or the oxidizing condition such as gas mixture, it is expected to see different oxide phases, oxidation behavior, and growth regimes. Therefore, to find the phases present in the oxide layer and the elemental composition of the oxide layer as well as the metal substrate, X-Ray Diffraction (XRD) and Energy Dispersive Spectroscopy (EDS) measurements were conducted. Since the oxide phases present at room temperature after cooling the oxidized sample can be different with the ones forming at the oxidation temperature, in-situ XRD experiments were conducted. Moreover, both the surface and cross-section of the oxidized samples were characterized via SEM to observe the roughness and thickness of the oxide layer.Linear growth of the oxide layer was observed in the beginning of oxidation for all the samples at different oxidizing conditions, and parabolic growth of the oxide layer was seen only at higher oxygen partial pressures (> 25 kPa). Furthermore, the oxidation mechanism was observed to be gas-phase diffusion within the linear regime, where the linear rate constants agreed with the values calculated via an existing analytical model. The temperature and alloying element content had a negligible effect on the growth rate of the oxide layer. On the other hand, within the parabolic regime, those parameters were much more influential on the kinetics, where the diffusion of species through the oxide layer was the rate-limiting step in oxidation. The result of this work helps in better understanding the initial oxidation behavior of more complex steels at high oxygen partial pressures and determining the surface composition of the steels.

High temperature oxidation behavior of high entropy alloy Al4Co3Cr25Cu10Fe25Ni33 in oxygen-containing atmospheres

High entropy alloys (HEAs) have recently attracted considerable interest and attention due to their novel properties of good corrosion resistance and superior mechanical strength at high temperatures. In this study, we investigated the oxidation behavior of a new high entropy alloy, Al4Co3Cr25Cu10Fe25Ni33, by using thermogravimetric analyzer at temperatures ranging from 800 °C to 950 °C under atmosphere of Ar and O2 for 24 h. The results showed that the oxidation kinetics of Al4Co3Cr25Cu10Fe25Ni33 alloy followed a parabolic regime with its rate constant steadily increased with increasing temperature. The activation energy of Al4Co3Cr25Cu10Fe25Ni33 alloy was found to be 178 kJ/mol. In addition, the bilayer scales and the internal oxidation behavior at the grain boundaries of Al4Co3Cr25Cu10Fe25Ni33 alloy were also examined and discussed.

Multiscale Convergence of the Inverse Problem for Chemotaxis in the Bayesian Setting

Chemotaxis describes the movement of an organism, such as single or multi-cellular organisms and bacteria, in response to a chemical stimulus. Two widely used models to describe the phenomenon are the celebrated Keller–Segel equation and a chemotaxis kinetic equation. These two equations describe the organism’s movement at the macro- and mesoscopic level, respectively, and are asymptotically equivalent in the parabolic regime. The way in which the organism responds to a chemical stimulus is embedded in the diffusion/advection coefficients of the Keller–Segel equation or the turning kernel of the chemotaxis kinetic equation. Experiments are conducted to measure the time dynamics of the organisms’ population level movement when reacting to certain stimulation. From this, one infers the chemotaxis response, which constitutes an inverse problem. In this paper, we discuss the relation between both the macro- and mesoscopic inverse problems, each of which is associated with two different forward models. The discussion is presented in the Bayesian framework, where the posterior distribution of the turning kernel of the organism population is sought. We prove the asymptotic equivalence of the two posterior distributions.

Measurement of the Static Structure Factor in a Paraxial Fluid of Light Using Bragg-like Spectroscopy.

We implement Bragg-like spectroscopy in a paraxial fluid of light by imprinting analogues of short Bragg pulses on the photon fluid using wavefront shaping with a spatial light modulator. We report a measurement of the static structure factor, S(k), and we find a quantitative agreement with the prediction of the Feynman relation revealing indirectly the presence of pair-correlated particles in the fluid. Finally, we improve the resolution over previous methods and obtain the dispersion relation including a linear phononic regime for weakly interacting photons and low sound velocity.

A regularized phase-field model for faceting in a kinetically controlled crystal growth.

At equilibrium, the shape of a strongly anisotropic crystal exhibits corners when for some orientations the surface stiffness is negative. In the sharp-interface problem, the surface free energy is traditionally augmented with a curvature-dependent term in order to round the corners and regularize the dynamic equations that describe the motion of such interfaces. In this paper, we adopt a diffuse interface description and present a phase-field model for strongly anisotropic crystals that is regularized using an approximation of the Willmore energy. The Allen-Cahn equation is employed to model kinetically controlled crystal growth. Using the method of matched asymptotic expansions, it is shown that the model converges to the sharp-interface theory proposed by Herring. Then, the stress tensor is used to derive the force acting on the diffuse interface and to examine the properties of a corner at equilibrium. Finally, the coarsening dynamics of the faceting instability during growth is investigated. Phase-field simulations reveal the existence of a parabolic regime, with the mean facet length evolving in , with t the time, as predicted by the sharp-interface theory. A specific coarsening mechanism is observed: a hill disappears as the two neighbouring valleys merge.

Oxidation of ß-SiC at high temperature in Ar/O2, Ar/CO2, Ar/H2O gas mixtures: Kinetic study of the silica growth in the passive regime

The kinetics of silica growth during passive oxidation of SiC was studied using an original interferometric method carried out in a reactor specifically designed for that purpose. The influence of various oxidant species, O2, H2O, CO2 as well as their mixtures was investigated in a high temperature domain ranging from 1550 °C to 1850 °C at atmospheric pressure. This method is an efficient way to measure the various oxidation regimes usually described by the Deal-Grove model. Both the linear and parabolic rate constants are found to be independent of gas phase composition above 1700 °C, and to increase with oxygen partial pressure below 1700 °C for PO2 > 20 kPa. In the parabolic growth regime, we observed a transition from a low temperature interstitial-dominant to a high temperature network-dominant oxygen transport in the silica scale. The present results suggest the existence of a similar transition in the linear growth regime.

Hydrogen Sorption Kinetics in MgH&lt;sub&gt;2&lt;/sub&gt; and TiH&lt;sub&gt;2&lt;/sub&gt; Thin Films

The diffusion mechanism of H in metals and metal hydrides is studied particularly at high H2 pressures. Thin films of Mg and Ti offer a convenient tool to quantify the atomic transport. We show how different parameters of hydrogenation affect the kinetics. At 200°C, the Pd-Mg interface is predominant and a linear regime of hydrogenation is observed, whereas at 300°C a parabolic regime is detected. In Mg, the hydride forms from the surface to the substrate whereas in Ti growth of TiH2 starts from the substrate. A linear kinetics is seen during hydrogenation of Ti films, which is due to the oxide layer on top, measured to be about 10nm thick. In the studied high pressure regime, the hydrogenation is not pressure dependent any more. Quantitative calculation of the growth rate and the diffusion coefficient of H in the hydrides is presented.

Aspherical high-speed varifocal mirror for miniature catadioptric objectives.

We present a varifocal mirror based on a piezo-actuated glass membrane that can be used as a secondary mirror in miniature Cassegrain-type mirror- or catadioptric objectives. The mirror section has a diameter of 10 mm on a clear membrane diameter of 23 mm, with a focal range of ±8 m-1 and a response time on the millisecond-scale. The two piezo layers enable an aspherical tuning range that covers the elliptic, parabolic and hyperbolic regime over most of the focal range. We demonstrate the application of the mirror in a simple catadioptric telefocus objective with a focal length of 68 mm at an aperture of 22 mm and a thickness of 16.6 mm.

Oxidation kinetics of Si and SiGe by dry rapid thermal oxidation, in-situ steam generation oxidation and dry furnace oxidation

The fabrication of ultrathin compressively strained SiGe-On-Insulator layers by the condensation technique is likely a key milestone towards low-power and high performances FD-SOI logic devices. However, the SiGe condensation technique still requires challenges to be solved for an optimized use in an industrial environment. SiGe oxidation kinetics, upon which the condensation technique is founded, has still not reached a consensus in spite of various studies which gave insights into the matter. This paper aims to bridge the gaps between these studies by covering various oxidation processes relevant to today's technological needs with a new and quantitative analysis methodology. We thus address oxidation kinetics of SiGe with three Ge concentrations (0%, 10%, and 30%) by means of dry rapid thermal oxidation, in-situ steam generation oxidation, and dry furnace oxidation. Oxide thicknesses in the 50 Å to 150 Å range grown with oxidation temperatures between 850 and 1100 °C were targeted. The present work shows first that for all investigated processes, oxidation follows a parabolic regime even for thin oxides, which indicates a diffusion-limited oxidation regime. We also observe that, for all investigated processes, the SiGe oxidation rate is systematically higher than that of Si. The amplitude of the variation of oxidation kinetics of SiGe with respect to Si is found to be strongly dependent on the process type. Second, a new quantitative analysis methodology of oxidation kinetics is introduced. This methodology allows us to highlight the dependence of oxidation kinetics on the Ge concentration at the oxidation interface, which is modulated by the pile-up mechanism. Our results show that the oxidation rate increases with the Ge concentration at the oxidation interface.

Air oxidation of Zircaloy, Part 2: New model for Zry-4 oxidation

The accident in Fukushima brought up new issues in the area of safety of nuclear reactors. Among others, Spent Fuel Pool accidents gained new focus. The computer codes applicable for safety analyses of Nuclear Power Plants have limited verification and validation in this area and their applicability remains still to be proven. An important phenomenon occurring during loss of water in SFP is air oxidation of Zircaloy cladding material. Mathematical modeling of this phenomenon in computer codes has been under development during the last years. This document presents a review of models for air oxidation of Zircaloy, including: up to date models available in open literature, as well as models available in computer codes: ASTEC, MELCOR, and SPECTRA. The models were tested by performing simulations of a number air oxidation experiments from ANL, KIT, and IRSN.As a result of this work, a recommended set of correlations, applicable for wide range of temperatures, including pre- and post-breakaway reaction, has been selected. For the pre-breakaway (parabolic) regime the correlation of Benjamin et al. (Sandia National Laboratories, Albuquerque, NM, 1979) was selected for the low temperatures and a new correlation has been proposed for the high temperatures. For the post-breakaway (linear) regime, Boase and Vandergraaf (Nucl. Technol., 1977;32:60–71) were selected for the low temperatures and a new correlation has been proposed for the high temperatures. Furthermore, a new model for the breakaway transition has been proposed. The correlation set is applicable for Zircaloy-4, for practically the entire temperature range. The recommended set provides an improved accuracy of results compared to previous models. The current model is applicable to any situation where air oxidation of Zircaloy may occur, for example loss of water in a Spent Fuel Pool.The model recommended in this paper is applicable only for Zircaloy-4. Concerning two other Zr-based alloys, Zirlo™ and M5®, reaction rate coefficients exist in literature, however the existing models are not sufficient to calculate oxidation of these materials with satisfactory accuracy. Breakaway models, specific for these materials, do not exist and should be developed.

Influence of Binary Polymer Mixtures on the Nonlinear Growth Regimes of Polyelectrolyte Multilayer Films

We report on ellipsometric studies of the nonlinear growth regimes of electrostatically assembled polyelectrolyte multilayer films under in situ conditions. Poly(styrenesulfonate) (PSS) and poly(diallylmethylammonium) (PDADMA) with different molecular weights in 0.1 mol/L NaCl are used. Always, the linear growth is preceded by a parabolic growth regime. For films made from binary PDADMA mixtures, the compositions in the film and the adsorption solution are nearly identical. To explain these findings, a molecular model that describes the parabolic growth quantitatively is introduced. Neutron reflectivity of films prepared from PSS molecular weight above a threshold, >25 kDa, shows that its center of mass is vertically immobile, in both the parabolic and linear growth regimes. Below 25 kDa, the multilayer buildup starts with an exponential growth regime, and pronounced PSS interdiffusion is found with neutron reflectivity. The exponential buildup regime is extended on decrease of PSS molecular weight. For f...

Some qualitative properties for geometric flows and its Euler implicit discretization

We study the geometric flow parabolic equation and its implicit discretization which yield a family of nonlinear elliptic problems. We show that there are important differences in the study of those equations which concerns the propagation of level sets of data. Our study is based on the previous study of radially symmetric solutions of the corresponding equation. Curiously, in radial coordinates both equations reduce to suitable singular Hamilton–Jacobi first order equations. After considering the case of monotone data we point out a new peculiar behavior for non-monotone data with a profile of Batman type (g=min{g1,g2},g1(r) increasing, g2(r) decreasing and g1(rd)=g2(rd) for some rd>0). In the parabolic regime, and when the velocity of the convexity part of the level sets is greater than the velocity of the concavity part, we show that the level set {u=g(rd)} develops a non-empty interior set for any t>0. Nothing similar occurs in the stationary regime. We also present some numerical experiences.

Anomalous Kinetics and Regimes of Growth of Intermetallic Phases during Solid State Reactions in Nanosystems

Two interesting features of formation and growth of intermetallic phases in nanoscale solid state reactions will be discussed:Linear-parabolic “normal” growth: it will be summarized that at the very early stages of the growth of an already existing new phase (i.e. when nucleation problems can be neglected) the linear kinetics can be observed due to the so-called diffusion asymmetry. Indeed, it was shown that if the ratio of the diffusion coefficients differ by orders of magnitude in the parent materials (and so also in the new phase), during the growth of a phase bordered by parallel interfaces from the parent phases (normal growth geometry), the shift of the individual interfaces can be linear at the beginning and a transition to the parabolic regime can take place even after a shift of several tens of nanometres. In addition, an AB compound in contact with the pure A and B phases can be dissolved if the diffusion in B is much faster than in either A and AB. This means that the thickness of this phase should decrease, or even can be fully dissolved, at the beginning and only after some time—when the composition in B will be high enough allowing the re-nucleation of this AB phase—will the AB phase grow further.The common problem of two stages of solid state reactions will be revisited: usually the growth can be divided into two stages: a) the formation (nucleation) and lateral growth of the new phases and b) the “normal” growth of the already continuous phase. It was concluded in different previous reviews that in stage b) in the majority of cases the parabolic growth was observed in accordance with the above i) point: the linear-parabolic transition length was typically below 1 μm, which was the lower limit of detection in many previous investigations. On the other hand recently the application of the linear-parabolic growth law for the analysis of experimental data obtained in nanoscale reactions became very popular, not making a clear distinction between a) and b) stages. It will be emphasized here that care should be taken in all cases when the experimental methods applied provide information only about the increase of the amount of the reaction product and there is no information where and how the new phase (s) grow. We have illustrated in a series of low temperature experiments - where the bulk diffusion processes are frozen - that even in this case a full homogeneous phase can be formed by cold homogenization called Grain Boundary Diffusion Induced Solid State Reaction (GBDIREAC). In this case first the reaction starts by grain-boundary (GB) diffusion and nucleation of the new phase at GBs or their triple junctions, then the growth of the new phase happens by the shift of the new interfaces perpendicular to the original GB. This is a process similar to the diffusion induced grain-boundary motion (DIGM) or diffusion induced recrystallization (DIR) phenomena and in this case the interface shift, at least in the first stage of the reaction until the parent phases have been consumed, can be considered constant. This means that the amount of the phase increases linearly with time, giving a plausible explanation for the linear kinetics frequently observed in stage a).

Influence of Polymer Molecular Weight on the Parabolic and Linear Growth Regime of PDADMAC/PSS Multilayers

The buildup of polyelectrolyte multilayers is investigated in solution with multiple angle null-ellipsometry. Polyanion poly(styrenesulfonate) (PSS) and polycation poly(diallyldimethylammonium) (PDADMAC) are adsorbed sequentially from 0.1 M NaCl solution. First the films grow parabolically. After Ntrans deposited PDADMAC/PSS layer pairs a transition from a parabolic to a linear growth occurs. For molecular weights above a threshold (Mw(PSS) > 25 kDa and Mw(PDADMAC) > 80 kDa), Ntrans is 15, the thickness per layer pair in the linear growth regime is 12.3 nm. If either the PDADMAC or the PSS molecular weight is decreased below the threshold value, Ntrans either falls (for PDADMAC, lowest value observed is 8) or rises (for PSS, highest value observed is 33), respectively. Simultaneously, in the linear growth regime, the thickness per layer pair decreases (down to 4.3 nm) or rises (up to 25 nm). Furthermore, for low molecular weight PSS, three growth regimes are observed: exponential, parabolic, and linear. T...

A New Experimental Apparatus for In-Situ Characterization of Silica Growth During Passive Corrosion of SiC at Very High Temperatures

A new experimental method based on Joule-heating and interferometry was developed in order to gather in situ quantitative information on the kinetics of silica growth during passive corrosion of SiC under CO2-containing environments at very high temperatures. This method proved efficient in studying the thin-oxide regime and the initial linear regime as well as the parabolic regime described in the Deal–Grove rate law. Linear rate constants followed an Arrhenius law with a very high activation energy of 593 kJ mol−1 and were independent of gas composition, suggesting the chemical reaction at the SiC/SiO2 interface involved a vacancy mechanism.

Effect of Phosphoric Acid Treatment on Isothermal High Temperature Oxidation Behaviour of AISI 304 Stainless Steel at 800°C

Phosphoric acid treatment is used as a way to improve the high temperature oxidation resistance of a chromia-forming AISI 304 steel. Chromia-forming steels are excellent candidates to resist to high temperature oxidizing atmospheres because of the formation of protective oxide scales. The oxide scale growth mechanisms are studied by exposing phosphoric acid-treated and untreated 304 steel samples to high temperature conditions in air. The analyses were carried out by means of thermogravimetry, and in situ X-ray diffraction (XRD). The experimental results show that the phosphoric acid treatment does not have a beneficial effect on cyclic high temperature oxidation (up to 70h of the oxidation test) of AISI 304 steel because of growth of a layer mainly formed by external cation diffusion which grows very quickly. The isothermal high temperature oxidation of this steel at 800°C in air shows a very fast initial iron oxidation towards the external interface, allowing to chromium element to be more available to the internal interface to form a continuous chromia layer, thus causing the establishment of a parabolic oxidation regime and leading to a beneficial reduction of the oxidation rate (after 70h of the oxidation test).

Chemical interdiffusion in binary systems; interface barriers and phase competition

The problem of simultaneous growth and competition of intermediate phases during reactive diffusion is formulated and solved. In this paper, we compare existing models of steady state reaction diffusion and introduce the new one basing on the bi-velocity method. We extend old problem and propose method based on material (lattice) fixed frame of reference. It allows computing the material velocity in the reacting system in which reactions at several moving interfaces occur. All reactions lead to the lattice shift due to the difference of intrinsic diffusivities and different molar volumes. The following peculiarities are taken into account: (1) the deviation from local equilibrium at all interfaces; (2) the mobilities of the components in the bulk and interphase zone; and (3) the molar volumes of the components. We show the kinetic of the reactions, the non parabolic regime, the multiphase scale growth and present the practical application of the method.