Temperature parabolic rate constants

Provided the mole fraction of A does not fall below N, then the oxide AO will be formed exclusively. The important criterion is the ratio of the oxidation parabolic rate constant to that of the diffusion coefficient of For A1 in Fe, the parabolic rate constant is very low, whilst the diffusion coefficient is relatively high, whereas the diffusion coefficient of Cr is much lower. Hence, the bulk alloy composition of A1 in iron required for the exclusive formation of AI2O3 at any given temperature is lower than the Cr concentration required for the exclusive formation of CrjOj. 

Important features of the selective oxidation process are shown schematically in Figure 1. The slow growth rates of alumina and silica, illustrated in the plot of parabolic rate constants versus temperature at lower right, makes the formation of one of these oxides as a continuous surface layer necessary for long term oxidation protection. This requires that the protective oxide be more stable thermodynamically than the more rapidly growing oxides. The plot of standard free energy of formation as a function of temperature at lower left shows that the Ni-Al system satisfies this condition. Alumina is stable, relative to NiO, even when the activity of aluminum in the alloy is very low. However, when the Al concentration is low the alumina forms as internal oxide precipitates and is non-protective allowing an external layer of NiO to form (illustrated in the cartoon at top). Therefore, a critical concentration of Al exists above which out-... 

Fig. 15. Oxidation kinetics for Ti-22 Al-23Nb orthorhombic alloys in air at temperatures in the range 500-900 °C (left) and the effect of Nb content on the parabolic rate constant for Ti-25 at% Al alloys at 800°C (right).

The influence of temperature on the sulfidation kinetics of Ni36Al at a constant sulfur partial pressure of 6.4X10-7 bar is shown in Fig. 3a. The sulfidation kinetic follows the parabolic rate law over the whole temperature range and the sulfidation rate increases with increasing temperature. From the Arrhenius plot of the parabolic rate constants for sulfidation of Ni36Al in Fig. 3b we calculate an apparent activation energy of 58kJ/mol. 

For the data thicker than L, we can use the linear and parabolic rate constants, k and k, to monitor the effects of changes on the specific process in the L-P model viz. interface and/or transport phenomena. The main perturbations to the rate constants arise from the use of different ambients such as H O or dry 0 , and different oxidation temperatures. 

Equations (3.48) and (3.49) are written in terms of variables that can be measured relatively easily, although it is assumed that the diffusion coefficient is a function of the chemical potential of the species involved. Thus, in order to be able to calculate values of the parabolic rate constant, the relevant diffusion coefficient must be known as a function of the chemical potential of the mobile species. Such data are frequently not available or are incomplete. Furthermore, it is usually easier to measure the parabolic rate constant directly than to carry out experiments to measure the diffusion data. Thus, the real value of Wagner s analysis lies in providing a complete mechanistic understanding of the process of high-temperature oxidation under the conditions set out. 

Figure 3.11 Variation of the parabolic rate constant with oxygen partial pressure and temperature for the oxidation of cobalt, showing the results of Bridges, Bam-, and Fassell ( A T) and Mrowec and Przybylski ( — —...

Since the scale formed on iron above 570 °C is predominantly wustite, growth of this layer controls the overall rate of oxidation. However, since the defect concentrations in wustite at the iron-wustite and wustite-magnetite interfaces are fixed by the equilibria achieved there, for any given temperature, the parabolic rate constant will be relatively unaffected by the external oxygen partial pressure. Increasing the oxygen partial pressure in the gas phase should, theoretically, lead to an increase in the relative thickness of the haematite layer. However, since this layer only accounts for about 1% of the metal-scale thickness, any variation in rate constant with oxygen partial pressure will be difficult to detect. 

Figure 4.7 Parabolic rate constant for the oxidation of cobalt to CoO at various oxygen partial pressures and temperatures, determined by Mrowec and Przybylski. ...

On the basis of Eq.4, parabolic rate constants for each temperature were determined ifom the slope of the straight lines reported in Figure 2 (parabolic rate constants for oxidation at 12(M)°C and 1300°C were determined in the range 10-200h). 

F ure 9.14 Temperature variation of parabolic rate constants for the growth of different oxides [7]. 

Before spallation, oxidation was found to follow parabolic kinetics, consistent with diffusion-limited oxidation as depicted in Figure 3 for a) uncoated AL 441 HP and b) MCO coated AL 441HP at 800, 900, and 1000 °C. Parabolic rate constants, kp calculated from the slope of the line of best fit are summarized in Table 11. Oxidation resistance is significantly improved for coated versus uncoated samples. For all three temperatures, the rate of oxidation is reduced by approximately lOX for MCO coated versus uncoated AL 441HP . It is believed that the improvement in oxidation resistance is derived from the effectiveness of the MCO coating as a barrier to inward oxygen diffusion. 

Oxidation temperature /°C Coated/Uncoated Parabolic rate constant ko / mg cm s ... 

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