Parabolic rate constants

An important aspect of any theory of the oxidation of a pure metal is that it enables us to see how the protective power of the oxide layer can be altered by the introduction of alloying constituents into the metal. According to Wagner s theory, the parabolic rate constant for the system Ni/NiO for example depends upon the concentration of cation vacancies in the oxide in equilibrium with oxygen gas. If this concentration can be reduced, the oxidation rate is reduced. Now this can be done if cations of lower valency than Ni can be got into the oxide (Fig. 1.77). Suppose, for example, that a little Li is added to the Ni. Each Li ion which replaces Ni is a negative... 

The potential influence of shape on the correct design of laboratory test-pieces has been discussed in detail by Romanski. Samples of iron in the form of discs, cylinders, plates or parallelepipeds, and of a wide range of areas, were sulphidised under controlled conditions. The parabolic rate constant could be expressed in terms of the area A of the samples by... 

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. 

Fig. 7.35 Arrhenius plot of the parabolic rate constant for the oxidation of Ni to NiO (after...

Dilute binary alloys of nickel with elements such as aluminium, beryllium and manganese which form more stable sulphides than does nickel, are more resistant to attack by sulphur than nickel itself. Pfeiffer measured the rate of attack in sulphur vapour (13 Pa) at 620°C. Values around 0- 15gm s were reported for Ni and Ni-0-5Fe, compared with about 0-07-0-1 gm s for dilute alloys with 0-05% Be, 0-5% Al or 1-5% Mn. In such alloys a parabolic rate law is obeyed the rate-determining factor is most probably the diffusion of nickel ions, which is impeded by the formation of very thin surface layers of the more stable sulphides of the solute elements. Iron additions have little effect on the resistance to attack of nickel as both metals have similar affinities for sulphur. Alloying with other elements, of which silver is an example, produced decreased resistance to sulphur attack. In the case of dilute chromium additions Mrowec reported that at low levels (<2%) rates of attack were increased, whereas at a level of 4% a reduction in the parabolic rate constant was observed. The increased rates were attributed to Wagner doping effects, while the reduction was believed to result from the... 

Parabolic Rate Constant of Selected Heat Resistant Alloys [5]... 

Before concluding this section, we should briefly explain the averaging procedure which is implicit in the derivation of parabolic rate constants. In order to simplify without loss of generality, we assume that DA>DB. Integration of Eqn. (6.27) yields... 

The factor 4/3 appears since the transport of 6 equivalents leads to the formation of 4 AB204 (see Fig. 6-5). In generalizing Eqn. (6.35), we can calculate the parabolic rate constant as... 

Figure 7-3. Calculated parabolic rate constant k for the oxidation of wustite ( FeO ) to magnetite (Fe304) as a function of the oxygen activity of the surrounding gas. Proportions due to interstitial and vacancy transport are indicated.

By extrapolating Dto 1000 °C, we can calculate the parabolic rate constant kp (see Eqn. (6.30)) and compare it with the experimental value derived from Figure 16-10 b. From this comparison, it seems as if Fe2+ is the rate determining cation for the formation of fayalite by solid state reaction. Since we conclude from Section 15.2.2 that n natural olivines, it is most unlikely (in view of the... 

Because of the appearance of equation 65, B is called the parabolic rate constant. This limiting case is the diffusion-controlled oxidation regime that occurs when oxidant availability at the Si-Si02 interface is limited by transport through the oxide (thick-oxide case). 

The most predominant effect of H20 in the oxidizing ambient is to increase the parabolic rate constant (90). As a result, the effect of the interface reaction as the rate-controlling process increases with increasing H20 content. A relatively small HzO concentration (25 ppm) in 02 is already sufficient to increase the parabolic rate constant by factors of 1.3 and 1.6 for <111>-and <100>-oriented silicon wafers, respectively (99). The linear rate constant increases more gradually over the range of added H20 (0-2000 ppm) (90). 

The parabolic rate constant, B, is affected only slightly. These results show that the doping effect only influences the interface reaction. 

Fig. 33. Parabolic rate constant Kp of different Si3N4 ceramics [455], (SSN Mg/Al [465] SSN-Y/Al [466] HPSN Y/0.2 Al [466] HPSN Mg/Y [467] HPSN Y and HIPSN (no additives)...

Next, we substitute the expressions given by eqns. (202) and (206) into eqn. (190) for the thick-film parabolic rate constant to obtain... 

---