Impact of Grain Boundary Density on Oxide Scaling Revisited

Abstract

A straightforward conceptual tool for discriminating between different oxide scaling processes deviating from the parabolic standard model is formulated. Grain boundary diffusion-controlled oxide scaling is generalized to include lateral grains coarsening. Building on traditional Wagner theory, attenuation of rates of inwards growing oxides owing to the gradual loss of grain boundary density is revisited. Two viable cases are identified. One has the rate of grain boundary density loss to be independent of the rate of oxide growth, while the second case takes the two instantaneous rates to be equal. Simple parabolic-logarithmic and superparabolic-cubic expressions are arrived at for the two cases, respectively. Usefulness is demonstrated by applying the models to published experimental data from 1990 to date. Upon arrival at the superparabolic-cubic behaviour, a generic mathematical form analogous to a 'spring force' attenuating the scale growth was identified. 'Parabolic', 'cubic' and 'logarithmic' scaling emerges as limiting cases.

Reactive Element Effects in High-Temperature Alloys Disentangled

“…At the alloy/oxide interface, elemental RE dopants become oxidized ending up decorating the oxide grain boundaries. This way, inhibition of grains coarsening is achieved, which in turn supports parabolic scale growth, i.e., suppresses the subparabolic kinetics owing to loss of grain boundary density [14,15]. This is…”

“…In [2], bipolaron-mediated redox processes among V O sites were shown to drastically enhance V O mobility and thus to facilitate thermal oxide growth. The change in scaling conditions is captured by the superparabolic-cubic model [15]; see Fig. 6b, Interestingly, Eq.…”

“…Figure 2. The overall change in scale thickness at intermediate temperatures ~ 800-1000 °C was modeled in [15,38], cf. Figure 6a, i.e., early parabolic X ∝ √ t, and late X ∝ √ ln(t) .…”

“…Indeed, in as much as the oxide grain boundaries constitute rapid diffusion paths, the time evolution of grain boundary density change becomes decisive for the rate of scale growth [14,15]. A crucial role of the RE becomes to disallow early grains coarsening-by the Y 3+ decoration of nanograins-the consequence of which is the observed initial high rate of scale growth.…”

Simulations of oxidation of metal nanoparticles with a grain boundary inside

“…[3][4][5][6][7][8][9][10][11]). Nowadays, this area is still open for research (see, e.g., recent experiments [12][13][14][15][16] and models [17][18][19][20][21][22][23][24][25]) due to its complexity related to (i) generation of the electric field between the metal-oxide and oxide-gas interfaces, (ii) stress (or lattice strain) arising due to the lattice expansion during oxide formation, (iii) numerous defects in the oxide structure and their evolution, e.g., via grain growth, and (iv) defects, e.g., grain boundaries and dislocations in the metal phase.…”