Grain boundary diffusion

Figure C2.11.6. The classic two-particle sintering model illustrating material transport and neck growtli at tire particle contacts resulting in coarsening (left) and densification (right) during sintering. Surface diffusion (a), evaporation-condensation (b), and volume diffusion (c) contribute to coarsening, while volume diffusion (d), grain boundary diffusion (e), solution-precipitation (f), and dislocation motion (g) contribute to densification.

It can be seen drat the major difference lies in die activation energy being lower in the grain boundary. Data for a number of metals show that the activation energy for grain boundary diffusion is about one-half of that for volume diffusion. 

Figure 19.2 shows, at a microscopic level, what is going on. Atoms diffuse from the grain boundary which must form at each neck (since the particles which meet there have different orientations), and deposit in the pore, tending to fill it up. The atoms move by grain boundary diffusion (helped a little by lattice diffusion, which tends to be slower). The reduction in surface area drives the process, and the rate of diffusion controls its rate. This immediately tells us the two most important things we need to know about solid state sintering ... 

Here p is the density, a is the particle size, C and n are constants, Q is the activation energy for sintering, R is the gas constant and T is the absolute temperature, n is typically about 3, and Q is usually equal to the activation energy for grain boundary diffusion. 

Several alkali chlorates and perchlorates undergo fusion during the onset of decomposition, the autocatalytic character of reaction then being attributable to the greater rate of reaction in the melt. Khorunzhii and II in [849], from work on the reactions of Na+ and K+ salts of chloric and perchloric acids, conclude that surface and grain boundary diffusion exert an essential role in decomposition rate control. 

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