Linear Rate Constants Research Articles

Growth rate of yttria-stabilized zirconia thin films formed by electrochemical vapor-deposition using NiO as an oxygen source

Thin films of yttria-stabilized zirconia (YSZ) were formed onto nickel oxide substrates by an electrochemical vapor deposition process using the substrates as oxygen sources, and ZrCl 4 and YCl 4 as metal sources. After deposition at 1000 °C for 1–6 h, dense films of cubic YSZ were formed. The film thickness increased linearly with deposition time, and the linear growth rate constant was 1.1 × 10 −4 μm s −1. The deposition kinetics were discussed, and it was concluded that the rate-determining step of this process is not the electrochemical transportation of the oxide ions and electrons through the growing film, but the mass transport of oxygen gas, which is dissociated from the NiO substrate, through the substrate pores to the NiO/YSZ interface.

The effect of oxygen concentration on the oxidation of low-carbon steel in the temperature range 1000 to 1250�C

This paper describes the oxidation behavior of low-carbon steel samples in binary gas mixtures of oxygen and nitrogen, at oxygen concentrations ranging between 1% and 15% and temperatures ranging between 1000 and 1250°C. Sample weight gains versus time were analyzed, along with measurements and calculations of sample heating rates due to exothermic heat of reaction at the sample surface. It was found that initial rates of oxidation depended on oxygen content in the gasmixture and that these reaction rates were linear up to oxide thicknesses of 0.4 to 0.5 mm. Calculations of linear oxidation rate constants based on equations for mass transport of oxygen in the gas mixture to the sample surface showed good agreement with those measured experimentally, indicating that the initial period of oxidation is controlled by the mass transport of oxygen to the reaction interface. The linear rate constants showed little dependency on temperature, an activation energy of approximately 17kJ/mole being obtained. Measurements of sample surface temperatures have shown that within this linear-oxidation regime, interfacial temperatures of the samples increase with increasing oxygen contents in the gas mixture, owing to exothermic heats of oxidation. Subsequent oxidation kinetics were found to be parabolic. Measured parabolic rates constants were in good agreement with previous investigations, with activation energy values of approximately 127kJ/mole.

A pharmacokinetic model of anaerobic in vitro carbon tetrachloride metabolism

Carbon tetrachloride (CCl 4) is a potent hepatotoxic agent whose toxicity is mediated through cytochome P450-dependent metabolism. Results from anaerobic in vitro experiments with hepatic microsomes isolated from male F-344 rats indicate that chlorofom (CHCl 3) formation from CCl 4 is nonlinear with dose. Dose is traditionally expressed as the amount of CCl 4 added to the vial. In this study, a pharmacokinetic model has been developed to calculate the concentration of CCl 4 in the microsomal suspension. Hepatic microsomes prepared from fed and fasted animals were incubated with CCl 4 under anaerobic conditions and formation of CHCl 3 over a 5-min incubation period was monitored by headspace gas chromatography. Dose-response curves, based on total amount of CCl 4 added to the microsomes, revealed a nonlinear, biphasic appearance of CHCl 3, with fasting slightly increasing CHCl 3 production in microsomes prepared from fasted rats. Microsomes were also pretreated with the CYP2E1 inhibitor, diallyl sulfone (DAS), before addition of CCl 4. In uninhibited microsomes, there appeared to be a high-affinity saturable phase of metabolism occurring at lower concentrations followed by a linear phase at higher CCl 4 concentrations. Following DAS pretreatment, the saturable portion of the dose-response curve was inhibited more than the linear phase with the biphasic CHCl 3 production becoming more linear. DAS inhibition eliminated the effect of fasting on CHCl 3 formation. The best fit kinetic constants for the saturable phase resulted in an estimate of V max of 0.017 mg/h/mg protein ( V maxc = 7.61 mg/h/kg) and K rmm of 2.3 mg/l (15 μM). The linear phase rate constant ( k f) was determined to be 0.046 h −1 ( k fc = 0.03 h −1). In conclusion, a pharmacokinetic model has been developed for anaerobic in vitro metabolism of CCl 4 to CHCl 3 that estimates metabolic rates based on CHCl 3 formation and actual CCl 4 concentration in the microsomal suspension.

Thermal oxidation kinetics of (100) and (111) silicon in nitrous oxide

Thermal oxidation of (100) and (111) silicon (Si) in a nitrous oxide (N2O) ambient has been studied. The oxidation rate follows a parabolic to linear behavior. The activation energies in the parabolic regime were found to be 2.02 and 1.54 eV/molecule for (100) and (111) Si, respectively. The activation energy for the linear rate constant is estimated to be 1.61 and 1.37 eV/molecule for (100) and (111) Si, respectively. The limiting mechanism for the parabolic regime is attributed to the diffusion of oxidant through a surface oxynitride layer. The gradual shift to linear behavior is unusual and is in direct contrast with the Grove–Deal model [J. Appl. Phys. 36, 3770 (1965)]. Finally, secondary ion mass spectrometry shows a temperature dependent distribution and concentration of nitrogen at the interface.

Effects of crystallinity and thickness of silicide layer and substrate orientation on the oxidation of NiSi2 on silicon

Oxidation kinetics for both dry and wet oxidation of epitaxial NiSi2 (200 nm)/(001)Si samples as well as dry oxidation of polycrystalline NiSi2 (200 nm)/(111)Si and epitaxial NiSi2 (600 nm)/(111)Si samples have been studied by transmission electron microscopy. Comparing oxidation kinetics data of 200-nm-thick epitaxial NiSi2 on (001) and (111)Si, activation energies of the parabolic rate constants are rather close, whereas those for linear rate constants are substantially different. The orientation dependence of the linear activation energies is explained in terms of the total number of available Si atoms for oxidation as a function of the substrate orientation. Oxide growth rate was found to be higher in polycrystalline NiSi2/(111)Si samples than that in epitaxial NiSi2/(111)Si samples. Strong influence of the grain boundaries of NiSi2 on oxidation kinetics was observed with the grain boundaries serving as fast paths for oxidation. For dry oxidation of epitaxial NiSi2 (600 nm)/(111)Si samples, both parabolic and linear activation energies are higher than those of Ni(200 nm)/(111)Si samples.

Ultrathin Gate Dielectrics grown in Mixtures of N2O and O2 Using Rapid Thermal Oxidation

ABSTRACTA study comparing the oxide growth and electrical properties of 60Å oxides grown in different mixtures of O2 and N2O was performed. The oxide growth for all mixtures examined, as well as that of the pure O2 and N2O cases, fit a Deal-Grove oxidation model modified for Rapid Thermal Oxidation (RTO). Linear growth rate constants found for both a simple linear model and the modified Deal-Grove model are significantly greater for mixtures containing only 35% O2 than for pure N2O oxidation. The uniformity of the oxide growth across the wafer for the gas mixtures resembles that seen in pure N2O oxidation rather than pure O2 oxidation. The electrical properties were measured using Surface Photo-Voltage (SPV) techniques along with conventional Capacitance-Voltage (C-V) and Current-Voltage (I-V) techniques. Oxides grown in 100% N2O showed significantly higher oxide charge when compared to oxides grown in 100% O2. An in-situ anneal in an Ar ambient reduces the oxide charge for all gas mixtures examined. The higher oxide charge accompanies an increase in the interface trap density for the oxides grown in 100% N2O. The in-situ anneal reduces the interface trap density for oxide grown in 100% O2 but has little effect for oxides grown in 100% N2O. The interface trap density is reduced by the in-situ annealing for oxides grown in mixtures of O2 and N2O.

Hydrolysis of Lanthanide Dicarbides: Rates of Reaction of Cubic and Tetragonal Solid Solutions with Water

Two series of solid solutions, Ho 1- x La x C 2 and Nd 1- x LaC 2, have been made and their X-ray unit cell parameters measured. The Ho 1- x La x C 2 series contains two tetragonal phases and a cubic solid solution series which has enabled the reaction rate constants for the water hydrolysis reaction of a cubic dicarbide phase to be determined for the first time. By comparing the linear rate constants and the activation energies across the two series the nature of bonding in general and the structure of the cubic phase are elucidated. A comparison with microhardness data is made and the change in M -C 2 bonding as a function of composition is considered.

The hydrolysis reaction of some cubic and tetragonal lanthanide dicarbide solid solutions

Two series of solid solution dicarbides made from a light and a heavy dicarbide, Er 1- x Ce x C 2 and Lu 1- x La x C 2, have been made and the change in X-ray lattice parameters across the series of tetragonal and cubic phases determined. Deviations from Vegard's law behaviour are discussed. Both series have been hydrolysed in water vapour at 11.0 × 10 2Nm −2 pressure and 14.5 °C and the rate constants for the linear reaction determined. The reaction rates for the Lu 1- x La x C 2 samples with water have been measured together with four cubic phases, Lu 0.5La 0.5C 2, Lu 0.5Ce 0.5C 2, Lu 0.5Pr 0.5C 2 and Lu 0.5Nd 0.5C 2. The changes in linear reaction rate constants for these samples, together with those of CeC 2 and LuC 2, are discussed in terms of CC bond lengths and f character of the metal band electrons which contribute to the MC 2 covalent bond. The reactivity sequence CeC 2 > Ce 0.5 Lu 0.5 C 2 ⪢ LuC 2 is explained.

Oxidation of U-20 at% Zr alloy in air at 423–1063 K

The oxidation behavior of U 0.80Zr 0.20 alloy (two-phase mixture of U and UZr 2 below 878 K and single solid solution above 1008 K) was studied by thermogravimetry in the temperature range from 423 to 1063 K in air. During oxidation in the low temperature region (423–503 K), the sample kept its initial shape (a rectangular rod) and the surface of the sample was covered by a black thin adherent UO 2 + x oxide layer. On the other hand, by oxidation in the middle temperature region, the sample broke to several pieces of thin plates and blocks, and fine powder at 643–723 K and entirely to fine powder at 775–878 K, all of which were analyzed to be a mixture of U 3O 8 and ZrO 2. By oxidation in the high temperature region (1008–1063 K) the sample broke to very fine powder, which consisted of U 3O 8 and ZrO 2. Based on the sample shape, the oxide phase identified after oxidation and the slope value of the bilogarithmic plots of the weight gain against time, the oxidation kinetics was analyzed with a paralinear equation in the low temperature region below 503 K and a linear equation in the middle and high temperature regions above 643 K. Oxidation rates of U 0.80Zr 0.20 (two-phase mixture) in the low and middle temperature regions were smaller than those of uranium metal. A discontinuity in the plot of the linear oxidation rate constant versus reciprocal temperature was found to be present between 723 and 838 K, similarly to the case of uranium metal previously reported. The linear rate constants of single-phase solid solution in the high temperature region above 1008 K seemed to be a little smaller than those estimated by the extrapolation of the values in the middle temperature region.

Transformation temperatures and hydrolysis rates of three series of dicarbide solid solutions: YC2-HoC2, YC2-LuC2 and GdC2-ErC2

Abstract Three series of tetragonal substitutional solid solutions have been prepared for the systems Ho1−xYxC2, Lu1−xYxC2 and Er1−xGdxC2 and the kinetics of their reaction with water have been studied. A linear reaction rate constant was observed for all samples. The reaction rate for YC2 at 1.93 cm cm−2 min−1 is anomalously fast from ionic size considerations; YC2 is shown to be closer to GdC2 in its hydrolysis and hardness behaviour than to HoC2 with which it is closely related in size. The results are discussed in terms of CC bond length distances and f character of the bonding electrons in the covalent component of the MC2 bond.

Wet oxidation of GeSi at 700 °C

About 500-nm-thick films of Ge0.36Si0.64 and Ge0.28Si0.72 grown epitaxially on (100)Si have been oxidized at 700 °C in wet ambient. A uniform GexSi1−xO2 oxide layer forms with a smooth interface between it and the unoxidized GexSi1−x layer below. The composition and structure of that layer remains unchanged as monitored by backscattering spectrometry or cross-sectional transmission electronic microscopy. The oxide of both samples grows as square root of oxidation duration. The parabolic rate constant increases with the Ge content and is larger than that for wet oxidation of pure Si at the same temperature. The absence of a regime of linear growth at this relatively low temperature indicates a much enhanced linear rate constant.

Hydrolysis of lanthanide dicarbides: rates of reaction with water vapour

The kinetics of the reaction between water vapour and nine of the lanthanide dicarbides, YC 2 and UC 2 have been investigated by gravimetric and gas evolution techniques. Mild conditions were used with water vapour pressures in the range 5.8–16.6 × 10 2 N m −2 and temperatures from 4.0–48 °C. Over 90% of the reactions studied showed linear kinetics with the remainder following parabolic rates. Linear reaction rate constants lie in the range0.34–18.1 × 10 −2 mg cm −2 min −1 depending on the carbide, temperature and pressure. For any given temperature and water vapour pressure the rate constant increased in the series from LaC 2 to DyC 2 and then decreased in the series DyC 2 to LuC 2, suggesting that the light lanthanides are least reactive. YC 2 had rate constants close to those of GdC 2, whilst UC 2 reacted some 50 times more slowly. In general, at any given water vapour pressure, in the range studied, the rate constant decreased with increasing temperature — a behaviour leading to negative values for the activation energy. From the activation energies a mechanism controlled by water adsorption on the product layers is postulated which suggests that the data do not give a true picture of LaC 2 + H 2O reactions. Increasing the water vapour pressure always increases the reaction rate constants. The results are discussed in the light of data from UC 2 and CaC 2.

Thin thermal oxides of silicon and the orientation effect: An empirical approach

Within a linear-parabolic model of oxide growth on silicon in dry oxygen a set of linear and of parabolic rate constants has been constructed. Data from multiple sources have been collected and correlated with some general concepts. One activation energy for the linear rate constants was found to apply to all silicon orientations. The activation energies for the parabolic rate constants for the several silicon orientations are different. In the fitting of data it is found that the oxygen pressure dependence of oxidation is sublinear and the coefficient for 〈100〉 silicon is not the same as for 〈111〉 silicon. Numerical values for these temperature- independent coefficients are chosen. An initial rapid oxidation appears essentially as a small, limited, growth step. Comparisons of calculated oxidation curves are made with reported orientation effect data.

The Oxidation Kinetics of Thin Polycrystalline Silicon Films

The oxidation dynamics and morphology of undoped and heavily phosphorus‐doped polycrystalline silicon films oxidized at a wide temperature and time range in dry and wet atmosphere have been investigated. It is shown that the oxidation rates of polycrystalline silicon films are different from that of single‐crystal silicon when the oxidation temperature is below 1000°C. There is a characteristic oxidation time, , under which the undoped polysilicon oxide is not only thicker than that of (100)‐oriented single‐crystal silicon, but also thicker than that of (111)‐oriented single‐crystal silicon. For phosphorus‐doped polycrystalline silicon films, the oxide thickness is thinner not only than that of (111)‐oriented, single‐crystal silicon, but also thinner than that of (100)‐oriented, single‐crystal silicon. According to TEM cross‐sectional studies, these characteristics are due to the enhanced oxidation at grain boundaries of polycrystalline silicon films. A stress‐enhanced oxidation model has been proposed and used to explain successfully the enhanced oxidation at grain boundaries of polycrystalline silicon films. Using this model, the oxidation linear rate constant of polysilicon has been calculated and used in the modeling of the oxidation dynamics. The model results are in good agreement with the experimental data over the entire temperature and time ranges studied.

High‐Temperature Oxidation of Chemically Vapor‐Deposited Silicon Carbide in Wet Oxygen at 1823 to 1923 K

The oxidation of chemically vapor‐deposited SiC in wet O2 (water vapor partial pressure = 0.01 MPa, total pressure = 0.1 MPa) was examined using a thermogravimetric technique in the temperature range of 1823 to 1923 K. The oxidation kinetics follow a linear‐parabolic relationship over the entire temperature range. The activation energies of linear and parabolic rate constants were 428 and 397 kJ · mol−1, respectively. The results suggested that the rate‐controlling step is a chemical reaction at an SiC/SiO2 interface in the linear oxidation regime, and the rate‐controlling step is an oxygen diffusion process through the oxide film (cristobalite) in the parabolic oxidation regime.

Oxidation of Plasma‐Deposited α ‐ Six C 1 − x : H Films

The thermal oxidation characteristics of films were studied for compositions from and varying hydrogen concentrations. The carbide films were plasma‐deposited onto oxidized Si substrates, using two differently configured deposition systems; silane, methane, and argon gas mixtures; and, temperatures from 200° to 600°C. The films were oxidized in either dry oxygen or air (with approx. 1 volume percent water) for times between 1 and 270h and temperatures from 500° to 900°C. The resulting oxide surface layers were characterized by etch rate, profilometry, XPS, and RBS techniques and were determined to consist of virtually stoichiometric at the outermost surface with perhaps small islands of unreacted carbide remaining near the inner interface. Oxidation rates were found to increase rapidly with increasing C and H concentrations and were always much larger than those of sintered, sputtered films of stoichiometric. The oxidation results were found to fit reasonably well to a mixed linear‐parabolic time dependence. This kinetic analysis suggested that the large observed increases in the linear and parabolic rate constants with decreasing could be attributed to preferential attack on C‒H bonds which are more prevalent in the graphitic, C‐rich films than in the tetrahedrally coordinated, Si‐rich ones.

Effects of metabolic inhibitors and incubation temperature on the saturable uptake of propranolol by isolated rat lung tissue

The effects of several metabolic inhibitors (50 microM) on the initial uptake rate of propranolol (0.5 to 500 micrograms mL-1) by the minced lungs (0.4 g) isolated from 7-week-old rats has been investigated in oxygenated, pH 7.4 Krebs-Ringer bicarbonate buffer solution (20 mL) containing 3% BSA at 37 degrees C for 5 min. The effect of the incubation temperature was also examined. Metabolism of propranolol was almost insignificant (i.e. less than 1.3% of the initial load). The overall initial uptake rate was considered to be a combination of apparent linear transport and saturable processes. For the control uptake rate, the linear transport rate constant was 1.26 +/- 0.16 g-1 mL-1 min-1, while Vmax and Km' of the capacity limited uptake process were estimated as 0.727 +/- 0.074 mg g-1 min-1 and 24.8 +/- 2.71 micrograms mL-1, respectively. No metabolic inhibitor tested had an effect on the linear transport rate of propranolol but 2,4-dinitrophenol and potassium cyanide inhibited saturable uptake rate (i.e. Vmax) of propranolol significantly (P less than 0.01) while ouabain, phloridine and iodoacetic acid did not do so significantly. Reduction of the incubation temperature to 15 degrees C decreased and at 25 degrees C tended to decrease, both linear transport and saturable uptake rates.

The kinetics and mechanism of titanium hydride formation

The kinetics and mechanism of titanium hydride formation were studied by measurements of overall reaction rates combined with metallographic examinations of partially hydrided samples. The main part of the reaction involves the formation of a continuous protective hydride layer which progresses into the sample. Paralinear rate equations fit the kinetic behaviour over a pressure range of 30–450 Torr H 2 and temperatures of 100–250 °C. The reaction rate is controlled by the diffusion of hydrogen through the protective thickening product layer which finally reaches an apparently constant thickness for diffusion as a result of cracking on the outer surface. This maximum thickness is temperature dependent and increases abruptly above approximately 150 °C. A corresponding apparent deviation from Arrhenius dependence is observed in the linear rate constants. Morphological aspects of hydride development are described. The effect of the metal microstructure on the hydriding kinetics is discussed.

Kinetics of dry oxidation of silicon. I. Space-charge-limited growth

Recent studies of the kinetics of dry oxidation of silicon have shown that the time dependence is more precisely described by a power-of-time law than by a linear-parabolic expression. This study shows the power law to be correct. This follows from the interdependence of the experimental linear and parabolic rate constants. The linear-parabolic expression appears to be equivalent to the first terms of a series expansion of the power-of-time law. The omission of higher-order terms gives systematic deviations known as the ‘‘anomalous’’ initial regime. An ionic space-charge-limited growth model is introduced, based on the classical oxidation theory of Wagner and accounting for the effect of internal fields on conduction. First, it is shown that both the magnitude of ionic and electronic conduction are sufficiently high, which is illustrated for an oxide layer of 300 Å growing at 870 °C. It is made plausible that the oxide-fixed charge density, Qf, is sufficiently large at high temperatures to cause large internal fields. An expression is derived which accounts for the mutual Coulomb repulsion of charges in very dense space-charge layers. The excellent fit of the derived expression and its application will be discussed in part II.

シリコン基板の熱酸化に及ぼす臭素の影響

Silicon substrates were oxidized in an O2/Br2 ambient. In the initial stage of the oxidation, the rate was slower than that of the conventional oxidation. In the course of the O2/Br2 oxidation, however, the rate was gradually accelerated.The oxidation reaction was analyzed on the basis of the mixed control model of the diffusion of oxygen in the SiO2 film and the chemical reaction at the SiO2/Si interface. The linear rate constant, kL was smaller and the parabolic rate constant, kP was larger in comparison with those of the conventional oxidation, respectively. But the activation energies were almost the same as the conventional ones.SIMS (Secondary ion mass spectroscopy) and FT-IR (Fourier transform infrared spectroscopy) were employed. The bromine in the SiO2 films existed near the oxide films as Si-Br bonds.The above results led to the following conclusion. In the initial stage, the Si-Br bonds formed at the SiO2/Si interface reduced the number of the SiO2 production sites, which retarded the oxidation rate. On the other hand, the Si-Br bonds in the SiO2 films increased the numbers of the solubility- and the diffusion-sites of oxygen in the SiO2 films, resulting in the acceleration of the oxidation rate, in the course of the process.