Anisotropy grain boundaries

The essential difference between treatments of chemical processes in the solid state and those in the fluid state is (aside from periodicity and anisotropy) the influence of the unique mechanical properties of a solid (such as elasticity, plasticity, creep, and fracture) on the process kinetics. The key to the understanding of most of these properties is the concept of the dislocation which is defined and extensively discussed in Chapter 3. In addition, other important structural defects such as grain boundaries, which are of still higher dimension, exist and are unknown in the fluid state. 

From the data listed in Table 3, it may be noted that the polarization values of the ceramics are lower than that of the single crystal [7,8] whereas the coercive field is higher. This may be attributed to the existence of the non-ferroelectric layers at the metal-ferroelectric interfaces and grain boundaries. In other way, when the anisotropy of the crystal get stronger, the displacement of ions, which is demanded by polarization inversion, get larger, the coercive field will be stronger. 

In equilibrium, the morphology of a surface is determined by the anisotropy of the surface energy. While the surface morphologies that we observe in most practical situations are not in global equilibrium, local equilibrium can be achieved at the intersection of two facets or at the point were a grain boundary intersects the surface. Observations of surfaces in local equilibrium give us the... 

If the anisotropy is small enough that the differential term can be ignored, then the ratio of the surface energies is simply related to the cosine of the angle at which they meet. Note that one criterion for the application of Eq. 3 is that the facets are in local equilibrium. For this to be true, there must be no net growth or evaporation. If this is true, then thermal grooves at surface-grain boundary intersections should maintain a quasistatic profile and increase in width with the one quarter power of time [45]. 

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