Concave oxide surfaces

On the planar surface of silicon, the increase in the volume of the oxide is aeeommodated via free expansion of the film in the direction perpendicular to the Si/Si02 interface. Residual stresses due to the mismatch between the thermal expansion coefficients are concentrated in the oxide and directed in parallel to the plane (biaxial compressive stress). Their magnitude is estimated at —0.3 GPa for a 1-pm-thick film (Jaccodine and Schlegel 1966). In oxidation of a profiled Si surface, there appear additional stresses directed perpendicular to the silicon/oxide interface. These stresses strongly affect the oxidation kinetics of 2D structures (macropores, piUars, trenches, etc.) (Uematsu et al. 2002 Liu et al. 1992). The results obtained in studies of oxidation of nonplanar surfaces are also applicable to macroporous silicon. One fundamental feature of 2D oxidation (Kao et al. 1987, 1988) is that the oxidation rate of convex and concave silicon surfaces decreases. This retardation is more pronounced for concave surfaces. The oxide thickness strongly depends on the radius of... 

Concave surfaces are of industrial importance, in relation to the internal surface of bores, holes and pipes, but are not found on typical solid testpieces and have received much less discussion. The stress patterns will tend to be the opposite of those found on convex surfaces for example, an oxide growing by cation diffusion should be in tension at the metal interface. Bruce and Hancock have discussed the oxidation of curved surfaces and show how the time to adhesive failure of the oxide can be predicted if its mechanical properties are known. 

The reduced oxidation near sample corners is related to these stress effects, either by retarded diffusion or modified interfacial reactionsManning described these stresses in terms of the conformational strain and distinguished between anion and cation diffusion, and concave and convex surfaces. He defined a radial vector M, describing the direction and extent of displacement of the oxide layer in order to remain in contact with the retreating metal surface, where ... 

The reversible Type I isotherm (Type I isotherms are sometimes referred to as Langmuir isotherms, but this nomenclature is not recommended) is concave to the p/pa axis and na approaches a limiting value as p/p° — 1. Type I isotherms are given by microporous solids having relatively small external surfaces (e.g. activated carbons, molecular sieve zeolites and certain porous oxides), the limiting uptake being governed by the accessible microporc volume rather than by the internal surface area. 

The open hearth proeess (Fig. 21.37) uses a dishlike container that holds 100 to 200 tons of molten iron. An external heat source is required to keep the iron molten, and a concave roof over the container reflects heat back toward the iron surface. A blast of air or oxygen is passed over the surface of the iron to react with impurities. Silicon and manganese are oxidized first and enter the slag, followed by oxidation of carbon to carbon monoxide, which causes agitation and foaming of the molten bath. The exothermic oxidation of carbon raises the temperature of the bath, causing the limestone flux to calcine ... 

George, C., Dorfs, D., Bertoni, G., Falqui, A., Genovese, A., Pellegrino, T., Roig, A., Quarta, A., Comparelli, R., Curri, M. L., Cingolani, R., and Maima, L. A cast-mold approach to iron oxide and Pt/iron oxide nanocontainers and nanoparticles with a reactive concave surface. Journal ofAmerican Chemical Society, 133(7), 2205-2217 (2011). 

The anisotropy of the oxide formation rate was used to convert the cross-sectional shape of macropores in (lOO)-oriented Si wafers from rounded square to circular upon an increase in their diameter via removal of the sacrificial Si02 layers (Trifonov et al. 2007). Figure 2 presents the results for a sample subjected to 11 cycles of oxidation in dry oxygen at 1,100 °C for 1 h. Note that the tendency toward pore rounding due to the oxidation rate anisotropy is enhanced by the oxidation retardation on the concave surface at square comers. 

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