Linear Rate Law Research Articles

Fabrication of porous glasses by water vapor corrosion of Y–Al–Si–O–N glass

The effects of exposure conditions on the microstructural changes of the oxynitride Y–Al–Si–O–N glass system were investigated. The oxynitride glass was exposed to dry O2 gas, or water vapor containing either O2 or Ar, at temperatures between 1133 and 1183 K. A porous scale layer was formed by exposure to water vapor, while a non-porous deteriorated scale was obtained only by exposure to dry O2. Formation of the porous layer was promoted by the presence of oxygen in the water vapor. The corrosion rate of the oxynitride glass in humidified O2 near the glass transition temperature followed a linear rate law. The morphology of the porous layer was strongly dependent on the exposure temperature, which may be due to the significant decrease in the viscosity of the glass with increasing temperature. The permeability of the porous layer cut from the exposed glass behaved according to Darcy’s law; therefore, this layer was considered to be composed of three-dimensional continuous pores. The microstructure of the porous layer could be controlled by the exposure temperature, so that a graded porous glass with different morphological characteristics within the layer could be obtained by exposure to humidified gases at different temperatures.

Phase field modeling of defects and deformation

New perspectives on the phase field approach in modeling deformation and fracture at the fundamental defect level are reviewed. When applied at sub-angstrom length scales the phase field crystal (PFC) model is able to describe thermally averaged atomic configurations of defects and defect processes on diffusional timescales. When applied at individual defect levels the microscopic phase field (MPF) model is a superset of the Cahn–Hilliard description of chemical inhomogeneities and the Peierls (cohesive zone) description of displacive inhomogeneities. A unique feature associated with the MPF model is its ability to predict fundamental properties of individual defects such as size, formation energy, saddle point configuration and activation energy of defect nuclei, and the micromechanisms of their mutual interactions, directly using ab initio calculations as model inputs. When applied at the mesoscopic level the coarse grained phase field (CGPF) models have the ability to predict the evolution of microstructures consisting of a large assembly of both chemically and mechanically interacting defects through coupled displacive and diffusional mechanisms. It is noted that the purpose of the MPF model is fundamentally different from that of the CGPF models. The latter have been used primarily to study microstructural evolution with user-supplied linear response rate laws, defect energies and mobilities. Combined phase field simulations hold great promise in modeling deformation and fracture with complex microstructural and chemical interactions.

Cyclic oxidation behavior of TiC/Ti3AlC2 composites at 550–950°C in air

Abstract Bulk TiC/Ti 3 AlC 2 composites containing 5 vol% TiC were fabricated by pressure-assisted self-propagating high-temperature synthesis, and their cyclic oxidation behavior was investigated at 550–950 °C in air for up to 40 cycles. The results demonstrated that at temperatures of 750–950 °C TiC/Ti 3 AlC 2 composites displayed excellent cyclic oxidation resistance. The oxidation kinetics basically followed a parabolic rate law. As revealed by XRD and SEM/EDS, the scales consisted of an outer discontinuous layer of rutile TiO 2 and an inner continuous layer of α-Al 2 O 3 . The scales were dense, adhesive to the substrate and resistant to thermal cycling. However, at lower temperatures of 550 and 650 °C, the oxidation kinetics followed a linear rate law with larger oxidation rates. The cyclic oxidation resistance was deteriorated owing to the formation of microcracks and voids in the scales.

Probability density functions for advective‐reactive transport with uncertain reaction rates

We derive probability density functions for advective transport of a solute that undergoes a heterogeneous chemical reaction involving an aqueous solution reacting with a solid phase. This enables us to quantify uncertainty associated with spatially varying reaction rate constants for both linear and nonlinear kinetic rate laws. While many standard techniques for uncertainty quantification in groundwater hydrology yield only concentration's mean and variance, the proposed approach leads to its full probabilistic description. This allows one to compute so‐called rare events (distribution tails), which are required in modern probabilistic risk analyses. We also compute an effective (apparent and upscaled) kinetic rate constant, a parameter that enters transport equations governing the spatiotemporal evolution of mean concentration. We demonstrate that the effective kinetic rate of nonlinear reactions is time‐dependent. This behavior provides a possible explanation for the observed discrepancy between laboratory‐measured rate constants on uniform grain sizes and measurements in natural systems where the grain size distributions are heterogeneous.

Evolution stages of oasis economy and its dependence on natural resources in Tarim River Basin

This paper examines spatio-temporal characteristics of an oasis economy and its relationship with water and mineral resources in the Tarim River Basin from 1965 to 2005. A spatial autocorrelation model, the center of gravity model, and index system of the regional central city are used to probe the evolution laws of spatial structure of oasis economy. The study finds that: 1) The economic centre of gravity, whose variation track during this period follows linear rate law, was moving from headstream to middle reaches of the Tarim River. 2) Positive spatial autocorrelation which showed a waving and ascending trend of regional economy was significant and the neighbor effect of regional economic growth was strengthened continuously. 3) The regional economic centre was located in Hotan City before 1980, moved to Aksu City during the 1980s and to Korla City after 1990. We conclude that above all, during the recent four decades the evolution of the oasis economy in this region has gone through three stages: a traditional agriculture stage (before 1980), oasis agriculture and agricultural product processing stage (1980–1990) and oasis energy industry stage (after 1990). Furthermore, the dependence degree of the oasis economy on natural resources in different stages are studied by using dominance index, regression model, and grey relation method, which shows that an oasis economy highly depends on water resources in the oasis agriculture and agricultural product processing stage while it depends more on mineral resources such as oil and natural gas during the oasis energy industry stage.

Oxidation behavior of novel rail steels at 500°C

Thermo gravimetric analysis (TGA) was used to study isothermal oxidation behavior of four novel rail steels at 500∧C in static air condition. These steels contained different combinations of microalloying elements, Cu, Cr, Ni and Si. The results were compared with the oxidation behavior of three rail steels already in commercial application (C-Mn, Cr-Mn and Cu-Mo). The lowest parabolic rate constant was obtained in case of Cr-Cu-Ni-Si contained rail steel. Spallation of the oxide layer was not observed in any of the rail steels. C-Mn, Cu-Mo and Cu-Si rail steels showed higher values of parabolic rate constants kp. In contrast to others Cu-Si exhibited linear rate law and larger weight gain compared to all other rail steels. X-ray diffraction (XRD) analysis confirmed that the major phase in the oxides was magnetite (Fe3O4). The surface morphology of the oxide scales were correlated with the oxidation rate.

Interaction of Freshly Precipitated Silica Gel with Aqueous Silicic Acid Solutions under Ambient and Near Neutral pH-conditions: A Detailed Analysis of Linear Rate Law

Interaction of freshly precipitated silica gel with aqueous solutions was studied at laboratory batch experiments under ambient and near neutral pH-conditions. The overall process showed excellent reversibility: gel growth could be considered as an opposite process to dissolution and a linear rate law could be applied to experimental data. Depending on the used rate law form, the resulting rate constants were sensitive to errors in parameters/variables such as gel surface area, equilibrium constants, Si-fluxes, and reaction quotients. The application of an Integrated Exponential Model appeared to be the best approach for dissolution data evaluation. It yielded the rate constants k dissol ∼ (4.50 ± 0.68) × 10−12 and k growth ∼ (2.58 ± 0.39) × 10−9 mol m−2 s−1 for zero ionic strength. In contrast, a Differential Model gave best results for growth data modeling. It yielded the rate constants k dissol ∼ (1.14 ± 0.44) × 10−11 and k growth ∼ (6.08 ± 2.37) × 10−9 mol m−2 s−1 for higher ionic strength (I ∼ 0.04 to 0.11 mol L−1). The found silica gel solubility at zero ionic strength was somewhat lower than the generally accepted value. Based on the $${}^{298}K_{\rm SS}^{(I=0)} = 10^{-2.754\pm 0.017}$$ and $$^{298}K_{\rm DBP}^{(I=0)} = 10^{-2.728\pm 0.003},$$ standard Gibbs free energy of silica gel formation was calculated as $$\Updelta{G}_{\rm f}^0(298\,{\rm K}) \sim -\hbox{850,463} \pm 98\hbox{ J mol}^{-1}$$ and −850,318 ± 20 J mol−1, respectively. Activation energies for silica gel dissolution and growth were determined as $$E_{\rm A}^{\rm dissol} \sim 62.0\pm 3.2\,\hbox{kJ mol}^{-1}$$ and $$E_{\rm A}^{\rm growth} \sim 48.8\pm 4.4\,\hbox{ kJ mol}^{-1},$$ respectively. An universal value for growth of any silica polymorph, $$E_{\rm A}^{\rm growth} \sim 37.4 \pm 9.4\,\hbox{kJ mol}^{-1},$$ is not consistent with the value for silica gel growth, which questions the hypothesis about one unique activated complex controlling the silica polymorph growth.

Corrosion Properties of Inconel Alloy 600 Coated by Simultaneous Aluminizing-Chromizing Process

In this work Inconel 600 alloy was coated with two different types of coatings, Crmodified aluminide coating and Y- doped chromium modified aluminide coating . Diffusion coating was carried at 1050 oC for 8 hrs under Ar atmosphere by single step aluminizing- chromizing process and by single step aluminizing- chromizing- yttriumizing process. The cyclic hot corrosion tests of IN 600 and its coated systems deposited with 2 mg / cm2 NaCl / Na2SO4 (100/0, 50/50, and 0/100 wt. %) deposits were conducted at 900 oC in air for 105 hrs at 15 hrs cycle. The hot corrosion kinetic of uncoated Inconel 600 alloy follows parabolic rate law when oxidized with 100% Na2SO4 deposits, whereas it follows a linear rate law when oxidized with 100% NaCl deposits and with (50% NaCl + 50% Na2SO4) deposits. In cyclic hot corrosion tests, the parabolic rate constant (kP) values for Cr- modified aluminide coating when oxidized with NaCl / Na2SO4 concentrations (100/0, 50/50, and 0/100 wt. %) deposits are: 2.67x10-6, 2.73x10-6, and 8.34x10-7 (mg2/cm4)/s. respectively. But for Y- doped chromium modified aluminide coating are: 2.10x10-6, 1.51x10-6, and 6.66x10-7 (mg2/cm4)/s. respectively, under the same test conditions. The kP values for both coated systems oxidized with 100% Na2SO4 deposits are one order of magnitude lower than that for 100% NaCl, and for (50% NaCl + 50% Na2SO4) deposits under the same test conditions.

Hot Corrosion Behavior of AlCuFeCr Quasicrystalline Coating on Titanium Alloy with the Mixture of NaCl and Na<sub>2</sub>SO<sub>4</sub> Deposit

The hot corrosion behavior of titanium alloy and AlCuFeCr quasicrystalline coating on titanium alloy in the presence of a solid mixture of NaCl and Na2SO4 deposit at 700°C was studied. The result shows that weight-gain kinetics for titanium alloy exhibited a linear rate law, while the kinetics of AlCuFeCr quasicrystalline coating displayed parabolic growth rate. The corrosion resistance of the titanium alloy was improved by applying the AlCuFeCr quasicrystalline coating. The corrosive oxide morphology formed on titanium alloy was porous. For AlCuFeCr quasicrystalline coating with the mixture of NaCl and Na2SO4 deposit, the scale formed on the coating surface was compact and uniform. Oxide formed on the surfaces of Al-Cu-Fe-Cr quasicrystalline coatings after hot corrosion consisted of Al2O3.

Atmospheric Corrosion of Electroplated Cu Thin Film in Moist Oxygen Environment

Atmospheric corrosion of electrodeposited Cu thin film in water vapour with oxygen was studied using a quartz crystal microbalance. The adsorption of water with N2 carrier gas without oxygen was reversible and roughly proportional to the relative humidity. The corrosion weight gain exhibited an initial linear rate law region followed by a parabolic rate law one. The rate for both regions was influenced by both relative humidity and O2 partial pressure. The electrochemical oxidation process of Cu might occur under an adsorbed water layer. It is considered that the water adsorbed as clusters and corrosion progressed under the water cluster, the thickness and surface coverage of which varied with relative humidity. The rough estimation revealed that the kinetic constants for both first linear rate and parabolic rate laws is proportional to the ratio of surface coverage by water cluster. However, the rate constant is independent of R.H., if normalized by the area of water clusters.

Hot corrosion of AlCuFeCr quasicrystalline coating on titanium alloys with NaCl deposit

The hot corrosion behavior of titanium alloy and AlCuFeCr quasicrystalline coating on titanium alloy in the presence of a solid NaCl deposit at 650, 700 and 750 °C was studied. The result shows that weight-gain kinetics for titanium alloy exhibited a linear rate law, while the kinetics for AlCuFeCr quasicrystalline coating displayed parabolic growth rate. The corrosion resistance of the titanium alloy was improved by applying the AlCuFeCr quasicrystalline coating. The corrosive oxide morphology formed on titanium alloy was porous. For AlCuFeCr quasicrystalline coating with NaCl deposit, the scale formed on the coating surface was compact and uniform. Oxide formed on the surfaces of Al–Cu–Fe–Cr quasicrystalline coatings after hot corrosion consisted of Al 2O 3.

Influence of gas phase composition on the kinetics of chloride melt induced corrosion of pure iron (EU-project OPTICORR)

Heat exchanger tubes in waste-fired boilers are usually attacked by aggressive gases like oxygen, HCl and water vapour as well as by solid and molten salts. Especially if the salt deposit is molten, these compounds cause acceleration of the corrosion process. This study focuses on kinetic investigations on the influence of gas phase composition (O2, HCl and H2O) on the chloride melt induced corrosion of Fe. Thermogravimetric (TG) tests were conducted on Fe covered by a 50 mol.% KCl/50 mol.% ZnCl2-salt mixture at T = 320°C, first in an Ar - O2 - atmosphere. In these experiments the amounts of salt deposit (15 and 30 mg/cm2) and oxygen (4–16 vol.%) were varied to investigate their influences on corrosion kinetics. The TG curves show three kinetic stages, i.e. an incubation phase, a linear stage and a logarithmic/parabolic stage [1]. Further it could be shown that the duration of the incubation phase and the slope of the linear stage depend on the amount of the salt deposit as well as on the oxygen partial pressure (p(O2)). The incubation time increases with increasing amount of salt deposit and decreases with increasing p(O2). Experiments that were carried out in an Ar – O2 – HCl atmosphere (500–2000 vppm HCl, 4–16 vol.% O2) yield enhanced mass gain in comparison to TG tests without HCl. In atmospheres containing at least 1000 vppm HCl corrosion starts immediately without going through an incubation phase following a linear rate law. In the next stage the TG curve follows a rate law that is either parabolic or logarithmic. At higher amounts of HCl (2000 vppm, 8 vol.% O2) the TG curve shows a relative mass loss after about 55 h of corrosion indicating an evaporation of iron chloride. This phenomenon was also observed at 1000 vppm HCl and 16 vol.% O2 but not in the other experiments presented in this study. Experiments carried out in Ar – O2 – H2O are discussed also. In general the TG curves show lower mass gains after some hours of corrosion in comparison to TG tests without H2O but at the beginning a shortened incubation phase is evident.

High Temperature Oxidation of Steels in Air and CO2–O2 Atmosphere

Three kinds of hot rolled steel slabs, viz. high strength steel, bake hardened steel and low carbon steel, were oxidized isothermally between 1100 and 1250 °C for up to 2 hr in 1 atm of air and an 85%N2–10%CO2–5%O2 gas mixture. The steels were oxidized in a similar fashion in both the atmospheres. The oxidation process followed an initial linear rate law, which then gradually transformed to a nearly parabolic rate law. Thick, porous and nonadherent scales formed rapidly, due to the high oxidation temperature. The scales formed consisted of Fe2O3,(Fe2O3+Fe3O4), (Fe3O4+Fe2O3 +FeO) and (FeO+Fe3O4) from the outer surface. The presence of supersaturated oxygen beneath the scale resulted in grain boundary oxidation and the formation of internal oxide precipitates.

Oxidation Behavior of Cu60Zr30Ti10 Bulk Metallic Glass

The oxidation kinetics of Cu60Zr30Ti10 bulk metallic glass and its crystalline counterpart were studied in oxygen environment over the temperature range of 573–773 K. The oxidation kinetics, measured with thermogravimetric analysis, of the metallic glass follows a linear rate law between 573 and 653 K and a parabolic rate law between 673 and 733 K. It was also found that the oxidation activation energy of metallic glass is lower than that of its crystalline counterpart. The x-ray diffraction pattern showed that the oxide layer is composed of Cu2O, CuO, ZrO2, and metallic Cu. Cu enrichment on the topmost oxide layer of the metallic glass oxidized at 573 K was revealed by x-ray photoelectron spectroscopy while there was a decrease in Cu content in the innermost oxide layer. The oxide surface morphologies observed from scanning electron microscopy showed that ZrO2 granules formed at low temperatures while whiskerlike copper oxides formed at higher temperatures.

High-temperature OM investigation of the early stage of (TiC+TiB)/Ti oxidation

The initial oxidation behavior of titanium matrix composites (TMCs) was studied in a temperature range 550 to 650∘C in a flow of purified oxygen at atmospheric pressure using thermogravimetry. The oxidation kinetics very initially follows approximately a linear rate law and then a parabolic rate law. The oxidation rate decreases gradually as the oxidation proceeds. The initial in situ oxidation was investigated by high-temperature optical microscopy in air. The oxide layer was examined by X-ray diffraction and scanning electron microscopy combined with an energy dispersive X-ray spectroscopy unit. It was found that the reaction products are predominantly rutile. The reinforcements of TiB and TiC can result in a decrease in the overall oxidation rate at 550, 600, and 650∘C. This is attributed to the interface cohesion and the clean interfacial microstructure between reinforcements and the titanium matrix alloy, which is strong enough such that the reinforcements can act as barriers to solid-state diffusion.

Influence of the microstructure on the formation of alumina scales on near stoichiometric RuAl produced by arc melting

The influence of the microstructure on the oxidation behavior of two-phase near stoichiometric RuAl produced by arc melting was investigated. The oxidation was conducted at 1000 °C. The oxide scale growth and phase formation were studied using scanning electron microscopy, focused ion beam microscopy and in situ X-ray diffraction. The microstructure of the samples consisted of RuAl grains with continuous or isolated intergranular phase composed of Ru(Al) or Ru(Al)–RuAl eutectic. The Ru(Al) intergranular layer is prone to oxidation, which was not observed in samples with intergranular Ru(Al)–RuAl eutectic. Porous, poor-protective α-Al 2O 3 scales were formed. A region with periodic Aluminum oxide/Ruthenium oxide banded layers was developed beneath the external α-Al 2O 3 scale. Scale growth follows a linear rate law.

Rates of weathering rind formation on Costa Rican basalt

Weathering rind thicknesses were measured on ∼ 200 basaltic clasts collected from three regionally extensive alluvial fill terraces (Qt 1, Qt 2, and Qt 3) preserved along the Pacific coast of Costa Rica. Mass balance calculations suggest that conversion of unweathered basaltic core minerals (plagioclase and augite) to authigenic minerals in the porous rind (kaolinite, allophane, gibbsite, Fe oxyhydroxides) is iso-volumetric and Ti and Zr are relatively immobile. The hierarchy of cation mobility (Ca ≈ Na > K ≈ Mg > Si > Al > Fe ≈ P) is similar to other tropical weathering profiles and is indicative of differential rates of mineral weathering (anorthite > albite ≈ hypersthene > orthoclase ⪢ apatite). Alteration profiles across the cm-thick rinds document dissolution of plagioclase and augite and the growth of kaolinite, with subsequent dissolution of kaolinite and precipitation of gibbsite as weathering rinds age. The rate of weathering rind advance is evaluated using a diffusion-limited model which predicts a parabolic rate law for weathering rind thickness, rr, as a function of time, t(rr =κt), and an interface-limited model which predicts a linear rate law for weathering rind thickness as a function of time (rr = kappt). In these rate laws, κ is a diffusion parameter and kapp is an apparent rate constant. The rate of advance is best fit by the interface model.Terrace exposures are confined to the lower reaches of streams draining the Pacific slope near the coast where the stream gradient is less than ∼3 m/km, and terrace deposition is influenced by eustatic sea level fluctuations. Geomorphological evidence is consistent with terrace deposition coincident with sea level maxima when the stream gradient would be lowest. Assigning the most weathered regionally extensive terrace Qt 1 (mean rind thickness 6.9 ± 0. 6cm) to oxygen isotope stage (OIS) 7 (ca. 240 ka), and assuming that at time = 0 rind thickness = 0, it is inferred that terrace Qt 2 (rr = 2.9 ± 0.1 cm) is coincident with stage 5e (ca. 125 ka) and that Qt 3 (rr = 0.9 ± 0.1 cm) is consistent with OIS 3 (ca. 37 ka). These assignments yield a value of kapp of 8.6 × 10−13 cm s−1 (R2 = 0.99). Only this value satisfies both the existing age controls and yields ages coincident with sea level maxima. Using this value, elemental weathering release fluxes across a weathering rind from Qt 2 range from 6.0 × 10−9 mol Si m−2 s−1 to 2.5 × 10−11 mol K m−2 s−1. The rate of rind advance for the Costa Rican terraces is 2.8 × 10−7 m yr−1. Basalt rind formation rates in lower temperature settings described in the literature are also consistent with interface-controlled weathering with an apparent activation energy of about 50 kJ mol−1. Rates of rind formation in Costa Rica are an order of magnitude slower than reported for global averages of soil formation rates.

Corrosion of nickel in molten LiCl–Li 2O at 750 °C

Corrosion of the reduction vessel induced by molten LiCl–Li 2O is an important problem in the lithium reduction technique for the spent nuclear fuel management. This study investigates the corrosion of nickel in molten LiCl–10 wt% Li 2O at 750 °C by immersion experiments, with the aim of unraveling the corrosion behavior. Nickel corrodes very fast in the melt, forming a layer of NiO, which is converted to Li 2Ni 8O 10 and then to LiNiO 2. The weight loss curve shows a linear rate law, which is owing to the harmful reaction between oxides and melt at the melt/scale boundary with the formation of the porous corrosion scale. The corrosion mechanism of nickel is also discussed.

Stochastic analysis of effective rate constant for heterogeneous reactions

A probability density function (pdf) formulation is applied to a heterogeneous chemical reaction involving an aqueous solution reacting with a solid phase in a batch. This system is described by a stochastic differential equation with multiplicative noise. Both linear and nonlinear kinetic rate laws are considered. An effective rate constant for the mean field approximation describing the change in mean concentration with time is derived. The effective rate constant decreases with increasing time eventually approaching zero as the system approaches equilibrium. This behavior suggests that a possible explanation for the observed discrepancy between laboratory measured rate constants on uniform grain sizes and field measurements may in part be caused by the heterogeneous distribution of grain sizes in natural systems.

Kinetics of chemical vapor deposition of Si on Ni substrates from a SiCl 4–H 2 gas precursor mixture

The kinetics of chemical vapor deposition (CVD) of Si on the Ni substrate at deposition temperatures between 850 and 1050 °C using hot-wall reactor and SiCl 4–H 2 gas mixture was investigated. The deposition rate of Si on the Ni substrate obeyed a linear rate law. The activation energy for Si deposition was approximately 117 kJ/mol at low temperatures, indicating that the rate-limiting step for deposition of Si was the chemical reaction step to deposit Si on the surface of substrate. At high temperatures above 975 °C, activation energy was approximately 29 kJ/mol, indicating that that was the mass transport step of reactant gas species through a gas boundary layer from the main gas stream to the surface of Ni substrate. Under CVD conditions of Si limited by the mass transport step, there was a limit in the increase of the Cl/H input ratio to increase the deposition rate of Si on Ni substrate due to etching effect of Si.