Kinetics internal oxidation

The basic parameters which determine the kinetics of internal oxidation processes are 1) alloy composition (in terms of the mole fraction = (1 NA)), 2) the number and type of compounds or solid solutions (structure, phase field width) which exist in the ternary A-B-0 system, 3) the Gibbs energies of formation and the component chemical potentials of the phases involved, and last but not least, 4) the individual mobilities of the components in both the metal alloy and the product determine the (quasi-steady state) reaction path and thus the kinetics. A complete set of the parameters necessary for the quantitative treatment of internal oxidation kinetics is normally not at hand. Nevertheless, a predictive phenomenological theory will be outlined. 

A more general treatment of the internal oxidation kinetics has been presented by Bdhm and Kahlweit who modified Wagner s analysis to include a finite solubility product of the oxide in the alloy matrix. The key differences in this case are that Nb and No do not go to zero at the reaction front and the concentration of oxygen maintains finite values into the alloy ahead of the front. The case of oxides with large solubility products has been treated by Laflamme and Morral. ... 

The enormous amount of research at the interface between physical and structural chemistry has been expertly reviewed recently by Schmalzried in a book about chemical kinetics of solids (Schmalzried 1995), dealing with matters such as morphology and reactions at evolving interfaces, oxidation specifically, internal reactions (such as internal oxidation), reactions under irradiation, etc. 

Chromium(III) catalyses the cerium(IV) oxidation of primary and secondary alcohols in a mixture of H2SO4 and HC104. Kinetic results have been interpreted in terms of the formation of chromium(IV) in a reversible equilibrium, which forms a complex with the alcohol. Internal oxidation-reduction occurs in a rate-determining step to give aldehyde or ketone and regenerate the catalyst in the +3 state. The oxidation of ethanol under similar conditions has also been studied. ... 

We have discussed the oxidation kinetics of metal alloys and of oxide solutions. These reactions lead to dispersed internal products rather than to external product layers. In the present section, let us pose a different question can the reduction of (nonmetallic) solid solutions e.g., (A,B)2Oa to (A,B)304, (A,B)304, to (A,B)0, or (A, B)0 to (A, B)) similarly lead to internally precipitated particles of the reduced product If so, then do these reactions occur in field III, II, or I of the Gibbs triangle plotted in Figure 9-2 We further note that the reaction (A,B)0->(A,B) is the fundamental process of ore reduction. 

The quantitative discussion of internal reduction kinetics follows the discussion presented in the previous section on internal oxidation. The fundamental kinetic problem to be solved is again the calculation of the rate of advance of the reaction front (Fig. 9-6). To this end we note that... 

Fig. 14. Influence of HjS-content on the kinetic of internal oxidation of Ni36Al at 900°C ...

Fig. 16. Influence of H2S-content on the kinetics of internal oxidation of Ni30Alat900°C ...

Km, but it is too fast to observe at higher concentrations. The T e 1 center has been considered for some time as the initial point at which electrons from substrate enter the laccase molecule 94, 95). In the absence of oxygen, the reduction of the Type 3 Cu-pair is unimolecular at high substrate concentration and is very slow k = 1—2 sec-i). Type 3 reduction is also independent of the nature and concentration of substrate and of enzyme [62, 90, 95). It has been proposed that this slow reduction results from an internal oxidation of Type 1 Cu2+ by Type 3 Cu [90, 95). Fluoride ion strongly inhibits the reduction of Type 3 Cu ( =0.008 sec i) (95), but does not change the qualitative behavior of the reaction. The important fact is that whether fluoride is present or absent the reduction as observed by transient kinetics occurs much too slowly to be a viable step in the catalytic action (62, 90, 94). 

If the Pilling-Bedworth ratio is less than 1 the oxide cannot cover the metal completely and the oxide film has an open or porous structure. Oxidation takes place continuously, and the oxidation kinetics tend to be linear. This type of behaviour is found for the alkali and alkaline earth metals. In the rare cases where the PiUing-Bedworth ratio is equal to 1, a closed layer can form which is stress-firee. When the Pilling-Bedworth ratio is greater than 1, a closed layer forms with a certain amount of internal compressive stress present. 

The rate of internal oxidation will be derived here for a planar specimen geometry using the quasi-steady-state approximation. The results of similar derivations for cylindrical and spherical specimens will be presented. A more rigorous derivation of the kinetics of internal oxidation is presented in Appendix B. 

Alloys of Nb with small additions of Zr exhibit internal oxidation of Zr under an external scale of Nb-rich oxides. This class of alloy is somewhat different from those such as dilute Ni-Cr alloys in that the external Nb-rich scale grows at a linear, rather than parabolic rate. The kinetics of this process have been analyzed by Rapp and Colson. The analysis indicates the process should involve a diffusion-controlled internal oxidation coupled with the linear scale growth, i.e., a paralinear process. At steady state, a limiting value for the penetration of the internal zone below the scale-metal interface is predicted. Rapp and Goldberg have verified these predictions for Nb-Zr alloys. 

Although carburization can enhance the performance of certain components, in cases such as reformer tubes in the treatment of oil and hydrocarbons, carburization of stainless steels is deleterious and life limiting. In this case internal carbides form with kinetics analogous to those for internal oxidation." Consequently, alloys that are resistant to carburization are developed, primarily by alloying with nickel to reduce the diffusion coefficient of carbon, and with silicon and aluminium, which are thought to impart some protection by the formation of impervious silica and alumina surface hlms in the low-oxygen-potential atmospheres. ... 

The following is a treatment of the kinetics of internal oxidation of planar specimens based on an analysis by Wagner. This treatment is more general than that presented in the text in that it considers counter-diffusion of solute. 

Appendix A. Solution to Pick s second law for a semi-infinite solid il i Appendix B. Rigorous derivation of the kinetics of internal oxidation 327... 

Earlier work on the reactions of vinyl halides with tertiary phosphine platinum(0) compounds showed that complexes such as [Pt( y -vinyl halide)(PPh3)2] are formed initially, and the kinetics and mechanism of the oxidative addition (isomerization) were examined. Corresponding work on halogenoalkynes has now been carried out. Thus when c/5 -[PtCl2(PPh3)2] is reduced with hydrazine in the presence of PhC=CX (X =Br or I") the product obtained is [PtX(C= CPhXPPhs). ]. However, with PhC = Cl the intermediate substitution product [Pt(jj -PhC CCl)(PPh3)2] could be isolated and its internal oxidative addition examined mechanistically [see equation (8)]. 

From a kinetic point of view, there is a minimum concentration of oxide former required to ensure that the alloy chromium (or any other oxide former) diffusion flux must be sufficient to outweigh inward oxygen diffusion, thus favouring external scale growth over internal oxide precipitation. The required concentration, NM(Crit), is found from Wagner s analysis [45,110-112] to be ... 

Jox> Cfm coefficients of thermal expansion for oxide and metal parameter indicative of alloy/scale adherence 7 dimensionless kinetic parameter for internal oxidation... 

The kinetics of internal oxidation are generally found to be diffusion-controlled. Accordingly, Wagner (1959) assumed that the depth of the internal oxidation zone, obeys the parabolic expression ... 

Ervin, G. Jr, Nakata, M. M. (1962), Oxidation Kinetics ofZrBe,j and MBe,2, AEC Research and Development Report, NAA-SR-6493. Canoga Park CA Atomics International, pp. 1-26. 

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