Metals 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... 

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... 

In the remainder of this subsection, the goal is to relate these phenomenological rate constants to more fundamental parameters of the growing oxide layer. Table 7.1 lists the parabolic rate constants for a number of metals oxidized in pure oxygen at 1000°C. 

Table 7.1 Parabolic rate constants for various metals oxidized in I atm oxygen at lOOOX...

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. 

On the other hand, refractory-metal sulphides are both very stable and slow growing. This has been addressed by Douglass and coworkers, who demonstrated that the addition of Mo and Mo plus A1 to nickel substantially reduced the parabolic rate constant for sulphidation, by about five orders of magnitude for the composition Ni-30 wt% Mo-8 wt% Al and, in the case of iron alloys, by six orders of magnitude for the composition Fe-30 wt% Mo- 5 wt% Al. In these cases the scales formed were AI0.5M02S4, which gave excellent resistance to sulphidation, but would form molybdenum oxides in oxidizing atmospheres. ... 

If the practical parabolic rate constant has been experimentally determined according to eq. (8-6) from measurements of the thickness of the product layer, then it will frequently be desirable to calculate the weight increase as a function of the product layer thickness. The corresponding rate constant for the weight increase has been named after Pilling and Bed-worth. If q is the area of the metal, and PmcOv density of MeO, then ... 

Parabolic Rate Constants, k, Describing the Rates of Reaction of N2 with Different Samples of Th Metal [1]. 

Chapter 10 deals with high temperature corrosion, in which the thermodynamics and kinetics of metal oxidation are included. The Pilling Bedworth Ratio and Wagner s parabolic rate constant theories are defined as related to formation of metal oxide scales, which are classified as protective or nonprotec-tive. 

Let us make use of Eq. 7.95 to illustrate the temperature and oxygen pressure dependence of the parabolic rate constant. Consider the growth of the metal deficient oxide Ma-yOb on high purity M. Let us assume that the predominant defects throughout the entire... 

In many cases, the layer growth can be described by a parabolic rate law x = kpt, where x is the scale thickness at time t and kp is the parabolic rate constant. This law may be derived from Wagner s theory of metal oxidation. The parabolic rate corrstants contain diffusion coefficients which are related to the concentration of the defects responsible for material transport through the layer. In fact, the higher the deviation from stoichiometry, the larger the diffusion coefficient and, consequently, the faster the oxidation rate of a metal at a given temperature. 

Parabolic Rate Constants kp for Oxidation and Sulfidation of Some Commonly Used Metals in Oj and Sj respectively at 1 atm... 

Order of magnitude of the parabolic rate constant for several oxides as a function of temperature. (From Birks, N. and Meier, G.H., Introduction to High Temperature Oxidation of Metals, Edward Arnold, London, U.K., 1983.)... 

On the other hand, from Wagner s theory of metal oxidation it follows that, if the concentration of predominant defects in the growing scale on a given metal is low enough that their mobility is concentration independent, the self-diffusion coefficient of diffusing species depends in the same way on oxidant pressure as the parabolic rate constant of scale growth. Thus, in the case of molybdenum sulfidation should be the following function of sulfur pressure ... 

Comparison of the parabolic rate constant of Mn sulfidation in pure and Li2S-containing sulfur vapor on the background of the sulfidation (solid lines) and oxidation (dotted lines) rates of several metals. 

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