Idealized two dimensional sintering by interface diffusion

Abstract

The authors consider an idealized two-dimensional model of the sintering of a close packed array of cylindrical grains with equivalent planar grain boundaries (GB) midway between each pair of cylinders. The scale and temperature are assumed to be such that material transport is completely dominated by diffusion along the GB's and on the pore surfaces; lattice diffusion is therefore neglected. This requires the condition D[sub gb]a[sub 0]/D[sub L]L >> 1, where D[sub gb] and D[sub L] are respectively the grain boundary and the lattice diffusion coefficients, a[sub 0] is an atomic dimension and L is the order of the cylinder radius. For particles sizes of 1 micrometer or less, of interest in the sintering of very fine powders, this condition is satisfied except possibly very near the melting point. The treatment takes into account an applied hydrostatic pressure during sintering but assumes that it is insufficient to cause plastic flow. Further, they ignore complications such as grain growth and the concomitant dragging and/or abandonment of pores by GB's, as well as the coarsening of pores. Possible extensions of the model to estimate the effect of these complications are discussed in the last section. As material moves from the GB's intomore » the pores, thereby permitting the movement of the cylinders together, it will tend to alter the shape of the pores. They shall show, however, that it is reasonable to assume that surface diffusion is sufficiently rapid to redistribute the material and maintain the pore in the shape it would have in static equilibrium.« less