Morphological Evolution for Simple Geometries

Both capillarity and stresses contribute to the diffusion potential (Sections 2.2.3 and 3.5.4). When diffusion potential differences exist between interfaces or between internal interfaces and surfaces, an atom flux (and its associated volume flux) will arise. These driving forces were introduced in Chapter 3 and illustrated in Fig. 3.7 (for the case of capillarity-induced surface evolution) and in Fig. 3.10 (for the case of shape changes due to capillary and applied forces). 

For pores within an unstressed body, the diffusion potential at a pore surface will be lower than at nearby grain boundaries if the surface curvature is negative.1 In this case, the material densities as atoms flow from grain boundaries to the pore surfaces. Conversely, macroscopic expansion occurs if the pore surface has average positive curvature. 

An applied stress, as in Fig. 16.1, can reverse the situation by modifying the diffusion potential on interfaces if their inclinations are not perpendicular to the loading direction. With applied stress and capillary forces, the flux equations for crystal diffusion and surface diffusion are given by Eqs. 13.3 and 14.2. For grain-boundary 

As in surface diffusion (Eq. 14.6), flux accumulation during grain-boundary diffusion leads to atom deposition adjacent to the grain boundary. The resulting accumulation causes the adjacent crystals to move apart at the rate2 

Three conditions are required for a complete solution to the problems illustrated in Figs. 3.10 and 16.1. If the grain boundary remains planar, dL/dt in Eq. 16.2 must be spatially uniform—the Laplacian of the normal surface stress under quasisteady-state conditions must then be constant  

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