Linear Rate Law Research Articles

Hydrothermal Corrosion of Hexagonal Boron Nitride

Corrosion behavior of powdered, hot-pressed, and pyrolytic boron nitride was investigated under hydrothermal conditions at 120°C to 300°C and saturated vapor pressure of water for 1 to 11 days. The reaction kinetics of the corrosion of hexagonal boron nitride (BN) were found to obey linear rate law. Scanning electron microscopic (SEM) observations of the BN powder after hydrothermal corrosion showed that the rate of hydrothermal attack by H2O was determined by anisotropy due to crystallographic orientation. The weight loss of hot-pressed BN specimens was greater than that of pyrolytic BN specimens at each temperature. This result may be explained by the difference in the B2O3 content and the microstructure due to the processing of materials. The corrosion rate of hexagonal BN in hydrothermal corrosion could be expressed by the chemical reaction controlled kinetics with the apparent activation energy around 60kJ/mol.

Rate‐Determining Process of Surface Reaction in the Phosphidation of Silver

A study was undertaken concerning the kinetics and mechanism of the phosphidation of silver at 450°C in phosphorus vapor at 44.0 to 80.0 kPa. X‐ray diffraction patterns and an electron probe microanalysis of the reaction products demonstrated that the films were composed of single layers of . A marker experiment indicated that silver was apparently the component that diffused across these films. In the early stage, the phosphidation obeyed a linear rate law and its rate‐determining process was regarded as the surface reaction; that is, the chemisorption of molecules generated by dissociation of a molecule. When the thickness of a phosphide layer reached a critical value, the reaction kinetics exhibited a gradual transition from the linear to the parabolic rate law as a result of the rate‐determining process changing from adsorption to solid‐state diffusion.

Dissolution kinetics of natural calcite minerals in CO 2-water systems approaching calcite equilibrium

We have measured dissolution rates of various natural calcite samples, e.g marbles, limestones and marine pelagic sediments, in CO 2H 2O solutions of fixed P CO 2 and temperature during their approach to equilibrium with respect to calcite. The runs have been carried out as batch experiments using the free-drift technique ( P CO 2 : 5·10 −3atm; T: 20°C), where size fractioned particles of 100 μm were kept in suspension by turbulently stirring the solution. In each experiment three natural specimens and for reference one of synthetic NBS Calcite (SRM 915) have been investigated. The dissolution rates observed for all natural samples can be represented by an empirical rate law given as R=α 1(1 − C C s ) n1 at Ca 2+ concentrations C< xC s ( n 1 ≈ 1.5−2.3, α 1 ≈ 1.6·10 −7−2.2·10 −7 mmol cm −2 s −1, x ≈ 0.6−0.8). Above this concentration the empirical reaction order switches to a higher value of n 2 ≈ 3–4. In contrast, NBS Calcite exhibits a linear rate law of R=α(1- C C s ) with α ≈ 1.6·10 −7 mmol cm −2s −1, which closely follows the dissolution rates predicted by the mechanistic dissolution model (PWP model) of Plummer et al. (1978). Experiments on NBS Calcite in a solution containing 10 μM KH 2PO 4 exhibited results very similar to natural specimens, displaying inhibited dissolution with respect to synthetic calcite, when approaching equilibrium. Only minor influence of phosphate was observed on the dissolution rates of natural samples. From this observation we suggest a model in which Ca 2+ ions are adsorbed to lattice sites (kinks) active to dissolution, blocking further dissolution there. By an attractive interaction between these ions and impurities (heavy metals or phosphate) on the surface of natural materials their adsorption enthalpy increases with increasing coverage Θ of physisorbed Ca 2+ ions on the surface. From this we derive a rate law: R EMP (C)=(1−θ)R PWP ; C=[ θ (1−θ) ]ƒ exp [ −(U o+U o′θ) K B T ] where R PWP is the rate predicted by the PWP model; and (1 − Θ) gives the amount of surface sites still active to dissolution, which is represented by the Fowler-Frumkin isotherm. Our results show that the binding enthalpy U o is a property of the pure calcite surface, whereas U o′ is dependent on the origin of the materials. Using this rate equation we have examined a variety of calcite dissolution data published in the literature and, in all cases, have found them to obey closely the suggested rate law. Especially the earlier published data on inhibition of calcite dissolution by heavy-metal ions, e.g. Cu 2+ and Sc 3+, fit well into our model. It reconciles with many apparently conflicting results and explains the dissolution rates from the chemical reactions proposed by L.N. Plummer and coworkers and adsorption processes of the solute, both acting simultaneously.

Oxidation of TiSi 2 and MoSi 2

Isothermal oxidation experiments were carried out with TiSi 2 and MoSi 2 in air between 1000 and 1400°C. The oxidation rate of TiSi 2 can be approximated at 1100°C by a linear rate law and at 1200 and 1300°C by a parabolic one. The scale formed at 1100°C consists of an outer layer of TiO 2 and an inner layer of a mixture of SiO 2 and TiO 2. Increasing temperature increases the SiO 2 content in the outer layer and at T>1200° C a SiO 2 scale with precipitates of Ti-Si oxides is found. TiSi 2 possesses optimum oxidation resistance between 1200 and 1300°C. The oxidation of MoSi 2 leads to the formation of the volatile oxide MoO 3 which evaporates at T>1200° C. This process favours the formation of a rather pure and very protective SiO 2 layer on the surface. Obviously the evaporation occurs after solid-state diffusion through the SiO 2 at the SiO 2/gas interface.

Low-temperature oxidation of molybdenum disilicide

Cyclic oxidation rates of 95 to 97 pct dense, powder-source molybdenum disilicide (MoSi2) in dry air, wet air, and oxygen have been measured between 400°C and 600°C. Dense MoSi2 does not disintegrate catastrophically (pest) in these atmospheres for exposure times up to 688 hours. Between 400°C and 500°C, Mo and Si oxidize simultaneously to form amorphous SiO2, monoclinic Mo9O26, and vapor-deposited MoO3 plates, and the oxidation rate of MoSi2 in air is influenced by its microstructure, composition, and surface defects. Rapid oxidation obeying a linear rate law occurs over a narrow temperature range near 500°C, where Mo vapor transport by (MoO2) n species is sufficiently rapid to produce large numbers of surface MoO3 plates but simultaneously is slow enough to allow nucleation and growth of solid Mo oxides in conjunction with SiO2. Addition of water vapor to the oxidant stream at 500°C retards nucleation and growth of solid Mo oxides by formation of MoO3·H2O (g), which has a high vapor pressure relative to those of (MoO3) n species. The transition from nonselective oxidation to high-temperature selective oxidation of Si to form a protective SiO2 layer occurs between 500°C and 550°C. Preoxidation of MoSi2 at 1200°C creates a SiO2 barrier layer which prevents further oxidation upon subsequent exposure at 500°C. The oxidation kinetics and microstructural observations support the model of MoSi2 pest in which oxidation in pores and cracks is required for disintegration. Based on these results, low-temperature oxidation phenomena are not expected to restrict the use of MoSi2 as a high-temperature material.

The effect of dodecylammonium chloride on crystal growth of calcium oxalate

The effect of dodecylammonium chloride (DDACl) on the growth of calcium oxalate crystals from high ionic strength solutions has been investigated. At DDACl concentrations below the critical micelle concentration (CMC) adsorption of dodecylammonium ion (DDA +) at the crystal surface was insufficient to affect the crystallization. In the presence of DDACl at a concentration equal to or higher than the CMC a strong inhibition of the crystal growth is observed. It is caused by strong DDA + adsorption on some crystal faces. Furthermore, it was shown that the rate control mechanism changed from exponential rate law (in the control system and at the concentration of DDACl < CMC) to the linear rate law (at DDACl concentrations #62; CMC).

Kinetics of Reaction of Si&lt;sub&gt;3&lt;/sub&gt;N&lt;sub&gt;4&lt;/sub&gt; with Ni

The kinetics and the mechanism of the reaction of Si3N4 with Ni have been investigated. Using a powdered Si3N4-Ni mixture, the reaction rates were measured by means of a thermo-balance in Ar or N2 gas stream. Reaction products were examined by X-ray diffraction. The reaction of Si3N4 with Ni initiated after heating to about 800K. The reaction product layer was a Ni-Si solid solution below 1073K and nickel silicides above 1123K. The reaction rates and the reaction products were independent of the atmosphere. The initial rate was described by the linear rate law. The activation energy was 118kJ/mol. A chemical reaction may be considered as the rate-determining step. When the Ni particles were covered with the reaction product layer, the kinetics obeyed by the parabolic rate law. The formation of nickel silicide increased the rate constant abruptly. The activation energy changed from 171kJ/mol in a regeon of the Ni-Si solid solution to 214kJ/mol in the regeon of nickel silicide. The reaction rates of Si3N4 with Ni are probably controlled by the diffusion through the reaction layer.

Selective Anodic Dissolution of Cu‐Au Alloys: TEM and Current Transient Study

Transmission electron microscopy, selected area diffraction, and current‐time behavior were used to evaluate the mechanism of selective copper dissolution and formation of the Au‐rich protective alloy layer in the low current, , potential region during anodic polarization of Cu‐Au alloys. A planar surface is generally stable below . This stability abruptly disappears at and above . The initially observed parabolic current‐time behavior at with its origin on the alloy side of the metal/solution interface is consistent with a mass‐transfer process normal to the interface but the actual value of the diffusivity (10−12 cm2 s−1) is more indicative of diffusion in the plane of the surface. Alternatively, the diffusion region is grossly defective. At longer times (⪞1 min) in the passive region, the observed departure from the parabolic rate law to an approximately linear rate law coincides with the onset of low density, random pitting over the surface. This local breakdown of the protective Au layer may involve a surface diffusion transport process based on available activation‐energy values.

Surface Effects in Sulfidation Reactions

Pure iron and an Fe–41 wt% Ni alloy are reacted at temperatures in the range 793–1073 K with H2–H2S–N2 atmospheres corresponding to equilibrium P S2 levels from 6.5 × 10−5 to 0.65 Pat The kinetics of iron sulfidation are intermediate in form to linear and parabolic rate laws. The instantaneous parabolic rate constant is found to increase with extent of reaction until a constant value is reached. For fixed equilibrium sulfur pressures, the instantaneous rate increases with hydrogen sulfide partial pressure; for fixed hydrogen sulfide partial pressure, the instantaneous rate decreases as the equilibrium sulfur pressure is increased. It is demonstrated that hydrogen sulfide is the reactant species. A Langmuir-Hinshelwood kinetic model based on the slow dissociation of adsorbed hydrogen sulfide accounts satisfactorily for the unusual gas-phase compositional effects, and also for the rate at which the reacting system approaches steady state. Similar effects are found for the Fe–41%Ni alloy, where nickel sulfide whisker formation results from localized catalysis of the hydrogen sulfide dissociation reaction.

THE MASTER EQUATION FOR LINEAR ADSORPTION AND DESORPTION OF GASES ON SOLID SURFACES

A Markovian model has been derived for a process involving reversible physisorption and irreversible chemical adsorption of simple gaseous molecules on a solid surface, which obey linear rate laws. The model is written in terms of the conditional probability of transition between two populations, physisorbed and chemisorbed molecules. The resultant expression, the master equation of the process, has given rise to the governing differential equations for the mean and variance of the coverage of the solid surface by the gaseous molecules; these equations have been solved analytically. The variance or coefficient of variation, expressing the magnitude of fluctuations, is substantial for a small-size system, e.g., a highly evacuated and/or dilute system. It is not uncommon to find such a system at the commencement and conclusion of any process; these periods are the most critical from the standpoint of operation, monitoring and control.

Kinetics of silicide formation in chromium-amorphous silicon multilayered films

Silicide formation in multilayered thin films of chromium and amorphous silicon was investigated by differential scanning calorimetry (DSC). The DSC traces gave a large main peak that was associated with the growth of the silicide. The growth kinetics followed a linear rate law, with an activation energy of 2.6 eV and a pre-exponential factor of 7.5×107 m/s for the rate constant. An explosive silicide reaction, observed in other metal-silicon multilayered films, could not be induced in this system.

The surface decomposition and extreme-pressure tribological properties of highly chlorinated methanes and ethanes on ferrous surfaces

Two distinct types of extreme pressure lubricant additive behavior using chlorinated hydrocarbons have been identified using a pin and v-block apparatus. The first, which has been observed previously (and referred to as Type I) and exhibited by 1,4-dichloro-butane, CHCl 3, and CH 2Cl 2, shows an initial increase of seizure load as a function of additive concentration, but reaches a plateau at higher concentrations. In contrast, the seizure load continues to increase with concentration when CCl 4 is used as an additive. This behavior is designated Type II. Both C 2Cl 6 and C 2HCl 5 exhibit both types of behavior, being Type I at lower concentrations, converting to Type II at higher concentrations. The rate of film growth on an iron foil measured with a microbalance is shown to be significantly faster for a Type II additive (CCl 4) and a Type I additive (CH 2Cl 2, CHCl 3). CCl 4 is also shown to grow according to an essentially linear rate law with an activation energy of about 38 kJ mol −1. Two possible seizure mechanisms are postulated. First, seizure is considered to occur when film removal by abrasion exceeds the growth rate, thereby leading to complete removal of the protective film. Secondly, measurements of the temperature close to the interface indicate that seizure can occur at some critical temperature T c . Measurements of the seizure load as a function of bath temperature corroborate this view and T c appears to be about 950 K. X-ray photoelectron spectroscopy analysis of the films formed by CH 2Cl 2 decomposition shows substantial carbon depletion in the film at higher growth temperatures. Surface analysis of chemisorbed carbon and chlorine formed by CCl 4 decomposition shows that carbon is removed from the surface in this temperature range. FeCl 2 also thermally decomposes and melts at about 950 K and provides a possible alternative explanation for the onset of seizure at T c .

Surface oxidation kinetics of Si3N4-4%Y2O3 powders studied by Bremsstrahlung-excited Auger spectroscopy

Samples of silicon nitride powder containing 4.0% Y2O3 in weight were heated in air at temperatures between 900 and 1000 °C. The average SiO2 layer thickness on the Si3N4 powder particles, as a function of time at a particular temperature, was measured by Bremsstrahlung-excited Auger electron spectroscopy. Oxidation was found to follow a linear rate law with an activation energy of 56±1.5 kcal mol−1. The yttrium level measured by X-ray photoelectron spectroscopy was also found to decrease as a function of the oxide layer thickness. This suggests that there is a reaction between the Si3N4 and Y2O3 particles which results in the formation of an yttrium-rich phase at the interface between the surface SiO2 layer and the underlying Si3N4 particle.

Surface Oxidation Kinetics of an a-Si3 N4 and an Amorphous Si3 N4 Powder

ABSTRACTSurface oxidation kinetics of an a-Si3 N4 submicron size and an amorphous nano-size powder have been studied using x-ray photoelectron spectroscopy (XPS) and Bremsstrahlung-excited Auger electron spectroscopy (AES). The samples were oxidized by heating in air at temperatures between 850°C and 1000°C. The oxide thickness for each heating time and temperature was determined both from the relative 0 Is and N Is XPS peak intensities and from the Si02 and Si3 N4 Si KLL peak intensities. In each case, there was a good agreement between the oxide thickness value calculated from the XPS data and that obtained from the AES data. At these temperatures, oxidation followed a linear rate law. Activation energies of 15±1 kcal/mole and 27±1 kcal/mole were measured for the a-powder and the amorphous powder, respectively.

Determination Of Intermetallic Formation Mechanism Using Differential Scanning Calorimetry Of Multilayered Thin Films

ABSTRACTThe ability to determine which growth mechanism (interface-reaction-rate-limited vs. diffusion-limited) of intermetallic formation by interfacial reactions using differential scanning calorimetry (DSC) is demonstrated. Suicide formation in multilayered thin films of chromium and amorphous silicon was chosen as a model system. It is shown that suicide formation in this system followed a linear rate law corresponding to an interface-reaction-rate-limited growth mechanism. An activation energy and pre-exponential for the rate constant were determined.

Oxidation Behavior of TiAl at High Temperatures in Purified Oxygen

Oxidation behavior of a TiAl coupon was studied in a temperature range 1100 to 1400 K in a flow of purified oxygen at atmospheric pressure using thermogravimetry and standard metallographic techniques. The oxidation kinetics initially follows approximately a linear rate law. The oxidation rate decreases gradually as the oxidation proceeds. However, they never follow the parabolic rate law. This is attributable to the crack formation near the scale/substrate interface. The oxide scale has two layers: an outer layer consisting mainly of rutile and an inner porous layer consisting of a mixture of rutile and α-alumina. The preferential growth of rutile is responsible for the initial kinetics. Large voids are developed near the interface between the outer and inner oxide layers. Thin alumina platelets grow almost normal to the substrate surface as an internal oxide near the scale/substrate interface. The lamellar structure thus developed is maintained in the scale near the interface.

Oxidation kinetics of silicon carbide whiskers studied by X-ray photoelectron spectroscopy

Silicon carbide whisker surfaces were characterized by X-ray photoelectron spectroscopy (XPS) to determine changes in the surface oxide film which occurred as a result of heating in air at temperatures from 600 to 800 °C. Equations were derived for the calculation of surface oxide film thickness from the SiC to SiO2 2p intensity ratios. Oxidation was found to follow a linear rate law in this temperature range for the first 10 nm of oxide growth. An activation energy of 17.2 ± 2.8 kcal mol−1 (72 ± 12 kJ mol−1) was measured.

Corrosion of Iron by Li2 CO 3 Melt at 1073 K

The corrosion of iron has been studied gravimetrically in the presence of melt in atmosphere at 1073 K in order to examine the effect of the amount of the melt on the metal on the corrosion process. When the surface of Fe was covered with a thin film of melt, the total weight of the specimen increased, the corrosion reaction followed a linear rate law, and the major product was iron oxide. At that time the weight gain was proportional to the metal loss. When the metal was fully immersed in the melt the weight of the cell decreased. The corrosion reaction of Fe was relatively slow in this case and the major product was while a small amount of could also be formed.

4825162 Nuclear magnetic resonance (NMR) imaging with multiple surface coils

Extension of reactive transport modeling to predict the coupled thermal, hydrological, and chemical evolution of complex geological systems is predicated on successful application of the approach to simulate well-constrained physical experiments. In this study, steady-state effluent concentrations and dissolution/precipitation features associated with crushed quartz and tuff dissolution at 240°C have been determined experimentally using a plug-flow reactor (PFR) and scanning electron microscopy (SEM) techniques, then modeled with the reactive transport simulator GIMRT (Steefel and Yabusaki, 1996) using a linear rate law from transition state theory (TST) . For quartz dissolution, interdependence of the specific surface area (Am) and reaction rate constant (km) predicted from the modeling agrees closely with that obtained from an analytical solution to the reaction–transport equation without diffusion/dispersion, verifying the advection-dominant nature of the PFR experiments. Independently-determined Aqtz and kqtz from the literature are shown to be internally consistent with respect to the model and analytical interdependence, implying appropriateness of the linear TST rate law and adequacy of BET-determined Am for use in modeling PFR experiments. Applications of this integrated approach for monomineralic dissolution include assessment of internal consistency among independent Am and km data, estimation of km from BET-determined Am, and rapid evaluation of alternative rate laws. For tuff dissolution, accurate simulation of the experimental steady-state effluent concentrations (to within 3% for Na, Al and K; to within 15% for Si and Ca) and dearth of alteration phases (<1 vol.% in the model) defines minimum supersaturation thresholds for nucleation of primary minerals (to suppress their secondary precipitation) and the (non-unique) relative km of hydrous aluminosilicates. For such multicomponent, multiphase experiments, reactive transport simulators provide the only practical means of estimating and constraining these kinetic parameters. Despite the approximations and uncertainties inherent in present-day models, close agreement between the experimental and simulation results reported herein provides an important measure of confidence for extending the modeling approach to address increasingly complex systems for which development of experimental analogs is impractical or impossible.

Hot corrosion behaviour of Nimonic‐105 in NaCl and Na2SO4

AbstractThe hot corrosion behaviour of Nimonic‐105 alloy was investigated in the presence of NaCl and Na2SO4 by employing the crucible test. The experiments were carried out in the temperature range 700°–800°C for periods of 2 to 20 hours. The end reaction products were characterised by the XRD, XRF, SEM, EPMA and chemical analysis techniques. Weight loss plots obtained in pure salts followed a linear rate law. However, the weight loss results obtained in salt mixtures indicated two zones of severe corrosion. The first zone occured in the presence of low concentrations of NaCl (1–5%) when the salt mixture was maintained in the solid + liquid (S + L) state and the other in the molten state, containing higher concentrations of NaCl (15–30%). Blisters and cracks were observed on the immersed surface of the corroded sample in the first zone and on the exposed top surface in the second zone. Both zones were occurred in the temperature range 700°–800°C, i.e., above the eutectic temperature (635°C) of the corrodent mixture and around the m.p. of NaCl (800°C). The heavy corrosion in the second zone was associated predominantly with voluminous formation of nickel coated Ni3S2 globules, and Na2MoO4. Denudation of alloying elements was observed due to preferential removal by the corrodents. The degradation of the alloy in the presence of corrodents is discussed.