Diffusive sintering theory

Note y = surface energy, D = volume diffusivity, Ds = surface diffusivity, Db = grain boundary diffusivity, ij = viscosity, b = Burgers vector, k = Boltzman s constant, p = density, S = width of grain boundary diffusion path, P = pressure, M = molecular weight, and 2 = atomic volume. Source From R. M. German, Sintering Theory and Practice (New York Wiley, 1996). Reprinted with permission of John Wiley Sons, Inc. 

Matter transport through diffusion can be described in terms of the flux of atoms or the counterflow of vacancies. The approach based on the counterflow of vacancies driven by a vacancy concentration gradient has been used predominantly in the early development of sintering theory, which is discussed in this subsection first. More general approach based on the flux of atoms driven by a chemical potential gradient will be presented later. The following discussion is started with the mechanism of grain boundary diffusion. 

Tests show values of n from 6 to 15, depending on the type of metal, type of support, and method of catalyst preparation. A theory based on diffusion of tiny crystallites gives = 8 [17]. Sintering can sometimes be retarded by catalyst promoters, but the mechanism of promotion is not clear. 

NMR imaging of gas adsorption/desorption in nanoporous solids, such as Y-AI2O3 and ZnO powders and partially sintered ceramics of these materials, as well as Vycor porous glass was analysed using Brunauer-Emmett-Teller (BET) theory. Visualization of gaseous xenon and methane in the void spaces of aerogels offered unique information and insights into the pore structure and molecular diffusivities of occluded sorbates. ... 

Mass transport processes in ceramics are of interest due to their importance in materials preparation techniques. The phenomenon of sintering by diffusion is reasonably well understood for metallic systems.For 2-component ionic systems two additional features must be considered. (i) In order to produce an overall transfer of material a net flux of each component will occur, the components having in general unequal mobilities. These fluxes are interdependent since, locally, certain concentration ratios must be maintained. (ii) The concentration of defects will vary with distance from the free surface. As an example of the incorporation of these effects we may consider the changes in morphology of a nearly planar surface to which Mullins theory of mass transport may be applied. For the two component case, eg. NaCl, the equation describing the surface evolution by volume diffusion processes may be written as( )... 

Discrepancies between the theory and the experimental results have led to the development of a sintering model, in which diffusion of vacancies from places with a negative surface curvature towards the particle center is the controlling process [449]. Survey of methods was given in [450] and the most known is the Kingery-Berg equation [451], a = Al/lo = mostly... 

Theory of Sintering of Crystalline Materials describes models based on transport by diffusion. The low initial density of gels and the strong tendency toward grain growth make it difficult to sinter to full density. 

The complex behavior described in the preceding section discourages direct tests of sintering models for crystalline materials. Nevertheless, the theory clearly indicates the parameters that must be controlled to get rapid densification. Small particles provide short diffusion paths from the pore to the point... 

Experimental evidence of neck growth was first demonstrated by Kuczynski, who in 1949 sintered large polycrystalline particles onto flat polycrystalline substrates. Theories, based on a two sphere model (each a single crystal), were developed to determine the rate of neck growth and the rate at which particle centres approach one another. These theories conclude that the rate of neck growth is inversely proportional to particle size raised to a power that depends on the mass transport path. Many mass transport paths were subsequently considered, bulk diffusion, surface diffusion, grain boundary diffusion, viscous flow, evaporation-condensation, liquid solution-reprecipitation, and dislocation motion (see reference 8 for a review). 

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