Sintering Kinetics by Stage

Since the introduction of a mathematical model for sintering by Kuczynski [12] numerous other models have been proposed. Reviews of these sintering kinetic models are given in references [13—19]. This description of sintering kinetics is organized into initial, intermediate, and final stage kinetic models. 

FIOUBE 16.B Schematic representation of the contact area between two partically sintered spheres (a) center-to-center distance is constant, (b) decreasing center-to-center distance. The sphere radius is a, x is the radius of the neck, 2h is the decrease in the center-to-center distance, and k is the radius of curvature (negative) for the neck. 

This result is the Kelvin equation. In this approximation, we have further assumed that the particle is essentially a flat particle (with a vapor pressure of Pq) compared to the radius of curvature of the neck. We can calculate the rate at which the neck increases by equating the rate of material transfer to the surface of the lens between the spheres with the increase in its volume. The rate of condensation, m, is proportional to the difference in equilibrium vapor pressure, ZiP, as given by 

For the neck region the area, A, volvune, v, and the radius of curvature, K, have the following definitions  

The reason fi r the limitation ofx/a 0.3 on these definitions of A, V, and K is that a simplified spherical geometry has been used for these calculations. This limits the approach to small simtering times. Substituting these geometric definitions and the condensation rate, m, into the earlier equation, we obtain a relationship for the growth rate of the neck diameter, x, with time  

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