Parabolic Rate Law Research Articles

Investigating the kinetics, thermodynamic properties, and mechanisms of high-temperature oxidation in ferrosilicon alloys

Ferrosilicon alloys are widely used as a deoxidizer in steelmaking due to their strong oxygen affinity and high deoxidizing ability. However, compared to other deoxidizers, relatively few studies have been conducted on its kinetics, thermodynamics, and reaction mechanisms. This study aims to investigate the oxidation characteristics of ferrosilicon alloys at different particle sizes, reaction temperatures, and reaction times, and to evaluate their oxidation structure and reaction characteristics. To achieve this, we used the response surface methodology (RSM) to establish a multi-factor model. The results show that reaction time and reaction temperature are the primary factors affecting the oxidation rates, followed by particle size. Wagner’s law was used to verify that the change in oxidation mass follows the parabolic rate law and was discussed in relation to other alloys. Additionally, the application of the volumetric model (VM) and the unreacted core model (URCM) in calculating the activation energy (E) was compared to understand the kinetic characteristics of ferrosilicon alloys more comprehensively. Specifically, when the particle size range increases from 0.075–––0.1 mm to 0.3–––0.5 mm, the estimated E of the VM model increases from 81.82 KJ·mol−1 to 87.84 KJ·mol−1. The URCM model’s result increases from 91.53 KJ·mol−1 to 97.21 KJ·mol−1. Additionally, we evaluated the thermodynamic feasibility of ferrosilicon alloys at temperatures ranging from 273.15 K to 1673.15 K using HSC Chemistry software. This paper describes in detail the oxide layer structure and oxidation reaction process of ferrosilicon alloys and proposes an oxidation reaction mechanism, providing a reliable theoretical basis for the application system of ferrosilicon alloys.

Corrosion kinetics and mechanisms of 15–15Ti steel in flowing liquid lead-bismuth eutectic at 500°C

The application of Liquid Lead-Bismuth Eutectic (LBE) as a coolant in Lead-cooled Fast Reactors (LFRs) presents significant challenges due to its corrosive nature, especially at elevated temperatures. This study investigates the corrosion kinetics and mechanisms of 15–15Ti stainless steel in flowing LBE at 500 °C with oxygen concentrations ranging from 1 to 3 × 10−6 wt% and a flow rate of 1 m s-1. The research highlights the formation and growth of the Fe-Cr spinel oxide layer, which follows a parabolic rate law indicative of a diffusion-controlled process, crucial for long-term material stability predictions. Despite the initial effectiveness of the Fe-Cr spinel layer in mitigating corrosion, its integrity is compromised over time due to spallation and dissolution, allowing penetration of LBE elements and selective dissolution of Fe, Ni, and Cr. The study reveals a complex interplay between direct dissolution of steel components and spallation of the oxide layer, providing critical insights into material loss mechanisms and the degradation of structural materials in LBE-cooled reactors.

High-temperature oxidation behavior and subsurface phase transformation of high-Mn high-Al steel

High-Mn steels are widely used in engineering applications because of their high strength, high hardness, and excellent toughness. In the industrial production of high-Mn steel, the steel is easy to be oxidized during the homogenization process, which may affect the properties of high-Mn steel. In this work, high-Mn high-Al steel with composition of (25–32)wt-%Mn-(8–11)wt-%Al-1wt-%C-Fe was prepared, the oxidation behavior and subsurface phase transformation of steel at 800 °C–1200 °C were investigated by thermogravimetric analysis, scanning electron microscope and X-ray diffraction. The results show that the curve of oxidation weight gain with time is in good agreement with linear equations below 900 °C, which obey the parabolic rate law in the temperature range of 1000 °C–1200 °C. The steel matrix would be covered by the oxide scale earlier at higher temperatures, which decreases the oxidation reaction rate and makes the turning point of the oxidation reaction rate reach faster at higher temperatures. The Mn-depleted zone resulting from the selective oxidation of Mn is formed in the steel matrix epidermis, leading to the subsurface phase transformation, which may deteriorate the steel properties.

Oxidation resistance of AlCoFeNiCux high entropy alloys

The oxidation behavior of as-cast AlCoFeNiCux (x = 0.6–3.0) high entropy alloys was studied by isothermal annealing in flowing synthetic air at 1000 °C. A formation of an external protective Al2O3 scale has been found. The oxidation kinetics followed a parabolic rate law. The rate constants were increasing with increasing Cu concentration in the alloys. A scale spallation on the alloys with higher Cu concentration was observed. The spallation facilitated a penetration of oxygen through the scale and promoted the formation of CuO and CuAl2O4. The oxidation mechanism of the AlCoFeNiCux alloys is discussed and compared with previously studied high entropy alloys.

Effect of Heat Treatment Temperature on Isothermal Oxidation of Ni-based Fe-33Ni-19Cr Alloy

This project studies the influence of different grain sizes of Ni-based Fe-33Ni-19Cr alloy obtained from heat treatment procedure on high temperature isothermal oxidation. Heat treatment procedure was carried out at two different temperatures, namely 1000℃ and 1200℃ for 3 hours of soaking time, followed by quenching in the water. These samples are denoted as T1000 and T1200. The heat-treated Ni-based Fe-33Ni-19Cr alloy was subjected to an isothermal oxidation test at 950℃ for 150 hours exposure. Oxidized heat-treated alloys were tested in terms of oxidation kinetics, phase analysis and surface morphology of oxidized samples. Oxidation kinetics were determine based on weight change per surface area as a function of exposure time. Phase analysis was determined using the x-ray diffraction (XRD) technique and surface morphology of oxidized samples was characterized using a scanning electron microscope (SEM). As a result, the heat treatment procedure shows varying grain sizes. The higher the heat treatment temperature, shows an increase in grain size with a decrease in hardness value. The oxidation kinetics for both heat-treated samples showed an increment pattern of weight change and followed a parabolic rate law. The oxidized T1000 sample recorded the lowest parabolic rate constant of 3.12×10–8 mg2cm–4s–1, indicating a low oxidation rate, thus having good oxidation resistance. Phase analysis from the XRD technique recorded several oxide phases consisting of Cr2O3, MnCr2O4, and (Ti0.97Cr0.03)O2 oxide phases. In addition, a uniform oxide layer is formed on the oxidized T1000 sample, indicating good oxide scale adhesion, thereby improving the protective oxide behavior.

The effect of Sn microalloying on the selective oxidation of Fe-(6-10 at.%)Mn alloys

To evaluate the suitability of Sn microalloying as strategy to decrease the selective oxidation kinetics of Mn-alloyed advanced steels, the effects of 0.01 and 0.03 at.% Sn micro-additions on oxide morphology and oxidation kinetics for Fe-6Mn and Fe-10Mn (at.%) alloys were determined under annealing conditions characteristic of the continuous galvanizing process. Selective oxidation followed a parabolic rate law, where activation energy analysis revealed that internal oxidation is rate-determined by the grain boundary diffusion of O in Fe. The 0.01 and 0.03 at.% Sn additions significantly reduced the internal oxidation of alloys with Mn contents of 6 and 10 at.%, which was attributed to interfacial Sn segregation reducing the solubility of O in Fe, the occupation of adsorption sites for water vapour molecules, and the reduction of short-circuit diffusion of O along internal interfaces. Sn microalloying decreased the external oxidation of Fe-6Mn-(0.01,0.03)Sn, but did not significantly alter external oxide thickness of the Fe-10Mn-(0.01,0.03)Sn alloys. In this case, Sn reduced the outward diffusion of Mn along grain boundaries, but also affected the balance between the inward O flux and outward Mn flux. Incorporating the effect of Sn occupying adsorption sites into a selective oxidation model revealed that Sn microalloying is predicted to cause a transition from internal to external oxidation for Fe-10Mn. For Fe-6Mn alloys, however, a Sn micro-addition of 0.01 at.% (∼0.022 wt.%) was sufficient to significantly reduce selective oxidation kinetics and produce beneficial alterations to the external oxide morphology in order to ease reactive wetting in the continuous galvanizing process.

High temperature oxidation behavior of MoCoB metallic glass

The oxidation behavior of a Mo51Co34B15 metallic glass was investigated at 873–973 K in dry air. The oxidation kinetics generally followed a parabolic-rate law, which indicated the rate-controlling step in the oxidation process is diffusion, and the parabolic-rate constants increased with increasing temperature, showing the oxidation rate is closely related to temperature. The thinner oxide layer was mainly composed of CoMoO4, MoO3, CoO, B2O3, and MoB, while the CoMoO4 and B2O3 oxides resulted in a lower oxidation rate, and the presence of MoB also suggested that small amounts of crystallization were taking place beneath the inner layer.

Sulfidation behavior of an AlCoCrNiSi high‐entropy alloy

AbstractHigh‐entropy alloys (HEAs) are promising new materials considered for application in high temperature environments. In this work, the sulfidation behavior of an Al–Co–Cr–Ni–Si HEA at different elevated temperatures and various sulfur vapor partial pressures is investigated. Thermogravimetric studies indicate that the sulfidation kinetics are in accordance with the parabolic rate law. The corrosion rate has a strong temperature dependence, whereas the influence of sulfur vapor pressure is practically nonexistent. Changes in temperature also do not seem to affect the sulfidation mechanism as evidenced by the Arrhenius correlation determined between the obtained parabolic rate constants and temperature. Combined SEM–EDS and XRD studies reveal the formation of a thick multilayer scale on the studied alloy, where the outermost relatively compact part is built of Co0.5NiS2 and CrAl2S4 while the inner, rather porous part also contains metallic inclusions, including Si near the scale/substrate interface.

The cyclic oxidation behavior and kinetics of W-Cr-Nb-Y2O3 alloys processed by powder metallurgy route

In the present investigation, yttria (Y2O3) has been added to the W-Cr-Nb alloys to study the cyclic oxidation behavior of on W-Cr-Nb- Y2O3 alloys processed by the powder metallurgy route. The cyclic oxidation tests are performed at 800 °C, 1000 °C, and 1200 °C for 15 h in the air. The oxidation kinetic analysis and implementation of a double Voigt function to calculate the domain size (crystallite size) and microstrain are also investigated. The results show that the cyclic oxidation tests on the sintered W-Cr-Nb-Y2O3 samples have exhibited that [(W0.5Cr0.5)90Nb10]98 - (Y2O3)2 alloy is marginally more oxidation resistant than [(W0.7Cr0.3)90Nb10]98 - (Y2O3)2 alloy at temperatures 800 °C and 1000 °C. In contrast, the [(W0.7Cr0.3)90Nb10]98 - (Y2O3)2 composite shows more oxidation resistance than [(W0.5Cr0.5)90Nb10]98 - (Y2O3)2 composite at temperature 1200 °C, apparently due to the formation of a large number of protective oxides like Cr2WO6, 2NbO5.7WO3 and Y2WO6, and absence of WO3 oxide on the former composite at 1200 °C in air. The values of oxidation exponent n ≈ 2 obtained for the oxidation tests on the [(W0.5Cr0.5)90Nb10]98 - (Y2O3)2 indicate that approximately parabolic rate law is being followed in the range of 800–1200 °C. In the case of [(W0.7Cr0.3)90Nb10]98 -(Y2O3)2 alloy (1 < n < 2) indicates that the rate of oxidation is faster than that predicted by the parabolic rate law but slower than that expected from the linear relationship between mass change per unit area (Δm/S) and time (t).

Revealing the effect of Gd alloying on oxidation resistance and oxide film protection performance of AZ80 alloy

The high-temperature oxidation behaviors and oxide film characteristics as well as corrosion protection of AZ80 and AZ80–0.75Gd (wt%) alloys were investigated to research the effect of Gd addition on oxidation resistance and oxide film corrosion protection performance of AZ80 alloy. The results showed that with 0.75 wt% Gd alloying, Gd2O3 appeared in oxide film, which promoted densification of oxide film and translation of the superlinear rate law oxidation kinetics to approximate parabolic rate law oxidation kinetics of alloy. And after erosion of oxide film containing Gd2O3, the corrosion products were extensively nodulated, resulting in corrosion passivation and showing protection effect.

Exploring the oxidation behavior of undiluted and diluted iron particles for energy storage: Mössbauer spectroscopic analysis and kinetic modeling.

Iron is an abundant and non-toxic element that holds great potential as energy carrier for large-scale and long-term energy storage. While from a general viewpoint iron oxidation is well-known, the detailed kinetics of oxidation for micrometer sized particles are missing, but required to enable large-scale utilization for energy production. In this work, iron particles are subjected to temperature-programmed oxidation. By dilution with boron nitride a sintering of the particles is prevented enabling to follow single particle effects. The mass fractions of iron and its oxides are determined for different oxidation times using Mössbauer spectroscopy. On the basis of the extracted phase compositions obtained at different times and temperatures (600-700 °C), it can be concluded that also for particles the oxidation follows a parabolic rate law. The parabolic rate constants are determined in this transition region. Knowledge of the particle size distribution and its consideration in modeling the oxidation kinetics of iron powder has proven to be crucial.

Numerical studies on the propagation of iron dust flames in confinement

Iron powder is a promising alternative fuel owing to its high energy density, non-volatile combustion, and recyclability using green hydrogen. For the safe storage, transportation, and use of iron powder as a reactive energy source, the physical mechanisms behind pressurising dust flames in explosions must be understood. Here, we study the propagation of one-dimensional iron dust flames in confinement using an Euler–Lagrange framework with reflective adiabatic boundary conditions. The gas phase is described by the compressible Navier–Stokes equations, and heterogeneously burning iron particles follow the parabolic rate law for solid-phase oxidation, and diffusion-limited combustion during liquid-phase combustion. We demonstrate that the pressurisation in a closed vessel leads to an increase in unburnt gas density, decelerating flame propagation via a decrease in thermal diffusivity. Flames through dust suspensions at concentrations above the thermodynamic limit are quenched, while for concentrations near the quenching limit, flames are quenched before re-ignition. The trajectories of particles and gas parcels demonstrate that particles are strongly entrained in the gas streams, causing fluctuations in local dust concentrations. The transient evolution of flame speeds in confinement is used to inform a pressure-rise model, which predicts the time to peak pressure in a 20-L vessel with good agreement to experimental measurements. Our insights provide mechanistic understandings about dust flame propagation under pressurising conditions, particularly relevant to the informed design of explosion protection measures.

The response of 316 L steel manufactured by selective laser melting route to high-temperature oxidation behaviour: The role of microstructure modification

The current work examines the effect of 316 L steel's microstructure, which is modified through varying scanning angles with the sample surface (HNS (0°), INS (45°), and VNS (90°)) in the selective laser melting (SLM) method and through surface mechanical attrition treatment (SMAT), on its high-temperature oxidation behaviour (at 600–800 °C) is investigated. We have obtained a deeper understanding of the steel's oxidation behaviour by applying various characterisation techniques. The SMATed steel has a ∼ 1000 μm thick deformed layer containing a gradient microstructure, and its topmost layer contains fine twins and nanograins (∼30 nm). The hardness of this surface is ∼1.65 times the non-treated steel's hardness. All samples follow a parabolic rate law during oxidation. The VNS sample unveils the slowest oxidation rate amid the non-treated samples. SMAT increases the activation energy of oxidation. The distribution of elements across the oxidised samples' cross-section shows discontinuous Cr spreading within the oxide layer on the non-treated samples; however, the deformed samples show uniform distribution. Unlike non-SMATed samples, a minute decline in Cr and Mn content is observed underneath the oxide layer on the SMATed samples, confirming their enhanced outward diffusion. The oxide layer on SMATed samples has more Cr- and Mn-rich oxides. These oxides occupy the grain boundaries of the oxidised non-SMATed surfaces, where the micro-pores and cracks are present. Conversely, oxidised SMATed surfaces display uniform, defect-free Cr- and Mn-rich oxides with finer grains. Moreover, the SMATed layer remains reasonably stable during high-temperature oxidation (hardness drop ranges between ∼9 and ∼ 30%).

Effects of Mo and Nb on the microstructure and high temperature oxidation behaviors of CoCrFeNi-based high entropy alloys

A series of CoCrFeNi(Mo, Nb) high entropy alloys (HEAs) were prepared using vacuum arc-melting. The effect of Nb and Mo on the microstructure and high temperature anti-oxidation properties of HEAs was investigated. The addition of only Mo was found to not cause formation of new phase, but did increase the lattice distortion. After the addition of Nb, as-prepared CoCrFeNiMo0.2Nb0.1 and CoCrFeNiMo0.2Nb0.2 alloys are characteristic of duplex-phase structures of FCC and Laves, in which the Laves phase is semi-coherent with FCC matrix. Our studies also revealed that the oxidation kinetics of the alloys followed parabolic rate law and the corresponding oxidation rate constants were calculated. Due to the synergistic effects of Mo and Nb, the anti-oxidation properties of HEAs improved significantly. It was also discovered that the new Laves phase containing Mo and Nb at the inner oxidation layer hindered the outward diffusion of active metal cations, ergo improving the oxidation resistance of HEAs. With increase of Nb content, it was further recognized that the layered structure of Laves phase was thinner and denser. Therefore, the oxygen ion diffusion process in the CoCrFeNiMo0.2Nb0.2 alloy can be inhibited effectively by the new formation of duplex-phase structures with undulated Laves phase and FCC matrix.

Comparative studies on oxidation behaviour of cobalt-based D-gun coatings on boiler steel

The protection system against material degradation at elevated temperatures is gaining technological importance. Three cobalt-based coatings were developed on SAE213-T91 boiler steel using the detonation gun method. The oxidation performance of all the specimens was examined for 50 cycles of 1 h heating at 900 °C in a thermal cyclic furnace and 20 min cooling at 25 °C outside the furnace. All the oxidised samples were investigated through SEM/X-ray mapping and an X-ray diffraction analyser. All the specimens obeyed the parabolic rate law of oxidation approximately. The oxidation resistance of Stellite 6 coating was found to be superior among all coated and uncoated specimens due to the growth of protective oxide Cr2O3 and CoCr2O4 spinel in it. The development of Ni, Cr and Co oxides in Stellite 21 coating resulted into its slow oxidation rate, whereas the growth of the non-protective WO3 and CoWO4 phases in WC-Co coating caused its rapid oxidation.

Kinetics of intermetallic compound layers between AISI 321 stainless steel and molten aluminum

The interfacial reaction between liquid aluminum and solid steel is critical to understanding the evolution of intermetallic compounds (IMCs) in the brazing and weld brazing processes of aluminum-to-steel dissimilar alloys. In this study, hot dip aluminizing of AISI 321 stainless steel at different temperatures was conducted to reveal the influence of reaction temperature and time on interfacial IMCs. Electron microscopy analyses were employed to investigate the interfacial microstructures. A single layer of θ-Fe4Al13 was observed at 700°C. In contrast, the IMCs of interfaces dipped at 800–1000°C consisted of a thin inner layer of η-Fe2Al5 + ζ-FeAl2 next to the steel and a thick layer of θ-Fe4Al13 close to the aluminum. For the inner layer, the thickness increased with increasing dipping temperature and time. Its growth was described by a parabolic rate law, which suggested a diffusion-controlled mechanism at the interface. An activation energy of 66.5 kJ mol−1 was obtained. For the Fe4Al13 layer, the thickness evolution at different temperatures was different from that of the inner layer, with a thick IMC layer at 700°C, a thinner IMC layer at intermediate temperatures (from 800 to 900°C), and a slightly thicker IMC layer from 950 to 1000°C. The growth kinetics of Fe4Al13 at 700°C were controlled by diffusion, interfacial reactions, and dissolution mechanisms. The evolution of Fe4Al13 between 800 and 1000°C was governed by diffusion and dissolution mechanisms. The appearance of the inner layer and the evolution kinetics of Fe4Al13 accounted for the decrease in thickness with increasing temperature between 700 and 900°C.

Microstructure evolution formed during early liquefaction stage between pre-oxidized Zircaloy 4 with SUS316 stainless steel at 1573 K

ABSTRACT The reaction between Zircaloy and stainless steel is a key interaction in the core degradation process during a severe accident in a light water reactor because this combination leads to eutectic liquefaction. In this study, the reaction mechanism and rate-limiting process were experimentally investigated at 1573 K where the eutectic liquefaction was observed dominantly. The diffusion couple of pre-oxidized Zircaloy4 and SUS316 stainless steel were annealed for various holding times, and the interface microstructure was metallographically examined. The reaction layer consisted of five phases: the α-(Fe,Cr,Ni) phase, the metastable (Fe,Cr,Ni)23Zr6 phase, the Laves Zr(Fe,Cr,Ni)2, α-Zr(O), and the liquid phase. The reaction layer thickness in the Fe-rich side consisting of α-(Fe,Cr,Ni) and (Fe,Cr,Ni)23Zr6 obeyed the time parabolic rate law, while the ones involving the liquid phase formation followed the saturation-type convection-controlled function. A formula in a combination of diffusion and convection process was introduced for estimation of reacted volume, which showed good agreement with the experimental results. It was newly realized that a model to provide the mass transfer coefficient regarding the convection-controlled process would be required for improvement of the core degradation model.

High-temperature oxidation behavior of Inconel 693 alloy at 900 °C–1200 °C

Inconel 693 alloy is a potential nuclear waste vitrification electrode material. The resistance to oxidation at high temperatures can affect the service life of the vitrification process equipment. The high-temperature oxidation behavior of Inconel 693 alloy has been investigated at temperatures of 900 °C, 1050 °C, and 1200 °C. The results show that the kinetic curves obeyed the parabolic-rate law at different oxidation temperatures without abnormal turning points. The oxide film showed a multilayer structure and the oxidation products were similar at different temperatures. Differently, a new product of AlN was generated at 1050 °C and 1200 °C compared with that at 900 °C. At 900 °C, the surface of the alloy was covered with relatively dense and complete oxide films. As the temperature increased, the oxide films were flaked seriously. The oxidation provided effective oxidation protection after 50 h at 1200 °C. In addition, part of the internal oxidation products Al2O3 acted as an effect of pegging Cr2O3 films.

Evolution of intermetallics between solid Fe-Cr/Fe-Ni alloys and molten aluminium

Investigations of the evolution of intermetallic compounds (IMCs) at the interface between iron-based alloys and molten aluminium have important technical and scientific significance in many key areas. Most previous studies of IMCs formed at molten aluminium/solid steel interfaces have been focused on relatively long reaction times, but less research has been performed on the evolution of IMCs at the aluminizing interfaces of Fe-Cr and Fe-Ni alloys within a few seconds. In this study, hot-dip aluminizing experiments under natural convection conditions were employed to study the evolution of two interfacial IMCs (Fe-15Cr alloy and Fe-35Ni alloy with molten aluminium) at 700–900°C within 30 s. The IMCs for Fe-15Cr consisted of an Fe4Al13 layer next to the aluminium and an Fe2Al5 layer adjacent to the steel. In contrast, only one layer of Fe4Al13 was detected at the interface between the Fe-35Ni alloy and molten aluminium. The growth of Fe2Al5 was described by a parabolic rate law. An activation energy of 7.53 kJ/mol was determined for the temperature range of 700–900°C. The evolution of Fe4Al13 for the two alloys was similar: their thicknesses decreased anomalously with increasing dipping temperature, and their kinetics were controlled by both diffusion and dissolution. In this study, based on reaction-diffusion theory, growth and dissolution equations of the IMCs were established, and the diffusion coefficients of Al atoms in Fe2Al5 and Fe4Al13 were obtained for the first time. The similarities and differences in the IMCs for the two alloys were explained mainly by the different diffusion coefficients.

High-temperature oxidation behavior of Cu64Zr36 metallic glass powders

Cu64Zr36 metallic glass powders were prepared via gas atomization. The high-temperature oxidation behavior of Cu64Zr36 metallic glass powders under the influence of internal factors (powder particle size) and external factors (oxidation temperature and oxidation time) was experimentally investigated by using XRD, DSC, TGA, SEM and TEM. The oxidation kinetics, oxide phase, surface morphology and microstructure of metallic glass powders were analyzed. The results show that Cu64Zr36 metallic glass powders form multiple layers of surface oxides after oxidation and the major components of the surface oxides are t-ZrO2, m-ZrO2, Cu2O and CuO. The oxidation kinetics follows a double-stage parabolic rate law. The oxidation process is dominated by the inward diffusion of O anions and the outward diffusion of Cu cations. Thermodynamic analysis shows that the Gibbs free energy change of the oxidation reaction increases with the decrease of particle size, leading to a more rapid and thorough oxidation of the powder with a smaller particle size.