Kinetics parabolic oxidation

The kinetics of oxidation of mild steel at high temperature are parabolic, with... 

In practice, thermal cycling rather than isothermal conditions more frequently occurs, leading to a deviation from steady state thermodynamic conditions and introducing kinetic modifications. Lattice expansion and contraction, the development of stresses and the production of voids at the alloy-oxide interface, as well as temperature-induced compositional changes, can all give rise to further complications. The resulting loss of scale adhesion and spalling may lead to breakaway oxidation " in which linear oxidation replaces parabolic oxidation (see Section 1.10). 

The oxidation of iron at temperatures between 500 and 700 K was also studied by means of backscattered conversion electron spectroscopy by Simmons et al. (235). An example of these typical upside-down backscatter spectra is shown in Fig. 36. The authors found that the kinetics for oxide formation followed a parabolic rate law and that the resulting oxide formed at these low temperatures was nonstoichiometric Fe304. 

Oxide Thickness Versus Time. Silicon oxidation has been modeled by using the linear-parabolic macroscopic formulation of Deal and Grove (69). As a starting point for the study of this model, the kinetics of oxidation... 

Some of the transition metal-oxide systems have become a subject of intensive research in the last two decades. The relation between the parabolic oxidation kinetics and the predominating point defect in the oxide was verified. To discuss the high-temperature oxidation mechanism of non-noble metals it is appropriate to start with a brief survey of some of the literature on the point defect dependent properties of, for example, nickel oxide. 

Stage 2 also follows logarithmic kinetics, reflecting competition between parabolic oxide growth and short circuit diffusion down preferred channels. Initially, the short circuit paths account for the early observed rapid scale growth. A transition is later observed to parabolic kinetics, which marks the onset of the third stage of scale growth in hot salt accelerated oxidation of -y-TiAl. 

Figure 1. Schematic of film thickness or gain in weight per unit area vs. time for oxidation of a pure metal where diffusion is rate controlling. The kinetics are denoted as parabolic oxidation kinetics.

Figure 2. Schematic of parabolic oxidation kinetics replotted from data of Figure 1...

The oxidation kinetics when liquid oxides are formed often exhibit two stages an initial period of rapid parabolic oxidation followed by linear kinetics. The rapid parabolic period has been modeled by assuming diffusion of metal and/or oxygen through liquid channels, which surround islands of solid oxide. 

Equation (65) demonstrates that decreasing rates are to be expected in the transition from linear to parabolic kinetics. Therefore, the kinetics of oxidation, sulfidation, and so on cannot be exactly linear, even in the start of reaction, but the rate must decrease. This decreasing linear rate often has been misinterpreted, for example, in... 

TiB2 oxidation above 700°C was approximated by the parabolic rate law (9) [190]. Deviations from the parabolic oxidation start at temperatures of 950-1100°C when vaporization of B2O3 becomes noticeable. A cubic law was suggested [191,192], but we assume that a paralinear law (Fig. 7) should better describe the kinetics, similar to the case of BN and B4C. 

The discussion shows that parabolic oxidation kinetics can be explained by different reaction mechanisms. Indeed, the equations (9.50) (9.51), (9.62) and (9.71) each give a theoretical interpretation of the parabolic oxidation constant corresponding to a different mechanism. To distinguish among these it is necessary to complement oxidation experiments by metallographic studies. 

In graphical form, the parabolic oxidation is represented by a horizontal parabola as shown in Fig. 2-7 a. The smaller kp is, the lower is the course of this parabola and the more protective is the situation for oxidation. For the experimental determination of kp, i.e., for the oxidation rate constant, the data measured as oxide scale thickness or mass gain as a function of time are plotted in a parabolic way. That is, the square of the scale thickness or the mass gain measured is plotted on the ordinate while time is plotted in a linear form on the abscissa. Fig. 2-7 b. In such a plot the oxidation kinetics... 

Enhanced parabolic oxidation rates of SiC and Si3N4 due to contamination from furnace tubes used in oxidation experiments have also been observed (Choi et al., 1989 Opila, 1995 Ogbuji and Opila, 1995 Fox, 1998). This enhancement is also attributed to Na impurities from impurities in alumina tubes (Opila, 1995). In one case (Fox, 1998), the oxidation rates of SiC and Si3N4, both very pure CVD materials, were found to follow parabolic kinetics, but at essentially the same rate. It was proposed that impurities from the alumina furnace tubes modified the structure of the silicon oxynitride so much that it no longer offered any additional barrier to oxygen transport than the silica scale. Backhaus-Ricault and Go-gotsi (1995) have also shown that silicon oxynitride is absent in hot isostatically pressed additive-free silicon nitride. This result may also be due to minor amounts of impurities resulting from the HIP process. 

The kinetics of oxidation of tantalum in pure oxygen have been studied at temperatures up to 1400°C and at pressures ranging from less than 1 to over 40 atm (0.10-4.05 MPa). The reaction is initially parabolic, with a transformation to linear rate after a period of time. Increasing the temperature not only increases the rate of oxidation, but also decreases the time before the reaction changes from parabolic to linear behavior. Above about 500°C and pressures from 10 mm Hg to 600 psi (1333 Pa to 4.13 MPa), the transition occurs almost immediately. From 600 to 800°C, the oxidation shows a pronounced increase in rate with pressure above 0.5 atm (0.05 MPa). At 1300°C and 1 atm oxygen pressure, tantalum oxidizes rapidly and catastrophically, but at 1250°C, the metal oxidizes linearly for a short time, then catastrophically. Unlike tantalum-oxygen reactions, however, tantalum-air reactions do not exhibit catastrophic oxidation at temperatures as high as 1400°C. 

Later studies by others [40-44] indicated that the presence of water vapour in air or oxygen had an even more profound effect on the oxidation of steel and Fe-C alloys. It was generally accepted that the presence of water vapour improved the scale adherence and hence increased the oxidation rate or prolonged the period when the parabolic oxidation kinetics were held. 

After the initial linear period, the oxidation kinetics became parabolic if the scale remains adherent. The oxidation rate became independent of the oxygen concentration and concentrations of other gas species at the parabolic oxidation stage. 

The oxidation of a particular metal in air is limited by the outward diffusion of metallic ions through an unbroken surface film of one species of oxide. Assume that the concentration of metallic ions in the film immediately next to the metal is Cj, and that the concentration of ions in the film immediately next to the air is C2, where and C2 are constants. Use Tick s First Law to show that the oxidation of the metal should satisfy parabolic kinetics, with weight gain Am given by... 

The oxidation of another metal is limited by the outward flow of electrons through a uniform, unbroken oxide film. Assume that the electrical potential in the film immediately next to the metal is Vi, and the potential immediately next to the free surface is Vi, where Vj and Vi are constants. Use Ohm s Law to show that parabolic kinetics should apply in this case also. 

The aforementioned inconsistencies between the paralinear model and actual observations point to the possibility that there is a different mechanism altogether. The common feature of these metals, and their distinction from cerium, is their facility for dissolving oxygen. The relationship between this process and an oxidation rate which changes from parabolic to a linear value was first established by Wallwork and Jenkins from work on the oxidation of titanium. These authors were able to determine the oxygen distribution in the metal phase by microhardness traverses across metallographic sections comparison of the results with the oxidation kinetics showed that the rate became linear when the metal surface reached oxygen... 

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