Diffusion scale growth

Fig. 7.3 Simplified scheme for the diffusion-controlled growth of multilayered scales on pure iron and mild steel above 570° C...

When exposed in air or cathode-side environment, active elements, e.g., Cr, in alloy substrates are preferentially oxidized forming an oxide scale on the alloy surface to protect it from further environment attack. Though the scale growth on an alloy substrate is affected by factors such as scale vaporization and grainboundary diffusion [163-165], it is often approximated by a parabolic relationship with time t ... 

Cylinders, Ellipsoids, and Elliptical Paraboloids. The diffusion-limited growth of particles whose planar intercepts are conic sections can also be analyzed by the scaling method. For example, the scaling function appropriate for a cylinder is T] = r/y/t.4 The solution for the growth of a cylinder is obtained in Exercise 20.5. 

When we consider continuous scale growth, we can expect that the mobile species from the metal (cations diffusing out) will be supplied by alloy grain-boundaries, bulk defects, and dislocations. These diffusivities are quite different from each other D(bulk) D(dislocation) < D(grain boundary) < D(surface). Therefore, we expect the formation of voids around the alloy grain boundaries and dislocations as the scale continues to grow. The chief concerns, here, is How can we prepare an inert state (kinetically and thermodynamically) for the point defects, for the grain boundaries, and especially for the dislocations in the alloy substrate ... 

The aforementioned requirements on surface stability are typical for all exposed areas of the metallic interconnect, as well as other metallic components in a SOFC stack (e.g., some designs use metallic frames to support the ceramic cell). In addition, the protection layer for the interconnect, or in particular the active areas that interface with electrodes and are in the path of electric current, must be electrically conductive. This conductivity requirement differentiates the interconnect protection layer from many traditional surface modifications as well as nonactive areas of interconnects and other components in SOFC stacks, where only surface stability is emphasized. While the electrical conductivity is usually dominated by their electronic conductivity, conductive oxides for protection layer applications often demonstrate a nonnegligible oxygen ion conductivity as well, which leads to scale growth beneath the protection layer. With this in mind, a high electrical conductivity is always desirable for the protection layers, along with low chromium cation and oxygen anion diffusivity. 

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. 

The theory of multi-layered scale growth on pure metals has been treated by Yurek et al The hypothetical system treated is shown in Figure 4.9. It is assumed that the growth of both scales is diffusion controlled with the outward migration of cations large relative to the inward migration of anions. The flux of cations in each oxide is assumed to be independent of distance. Each oxide exhibits predominantly... 

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. 

Fig. 11 Arrhenius-plot relating the parabolic rate constant for the growth ofAl203 scales and data for diffusion in AI2O3, (the scale for the grain boundary diffusion data at the right has been adjusted, so that if 5 = 1 nm, the grain boundary diffusion coefficient corresponds to the bulk diffusion scale) [51].

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