Crystal course-grained

Diffusion in the bulk crystals may sometimes be short circuited by diffusion down grain boundaries or dislocation cores. The boundary acts as a planar channel, about two atoms wide, with a local diffusion rate which can be as much as 10 times greater than in the bulk (Figs. 18.8 and 10.4). The dislocation core, too, can act as a high conductivity wire of cross-section about (2b), where b is the atom size (Fig. 18.9). Of course, their contribution to the total diffusive flux depends also on how many grain boundaries or dislocations there are when grains are small or dislocations numerous, their contribution becomes important. 

Solids appear in one of two forms, either as crystals or powders. The difference is one of size, since many of the powders we use are in reality very fine crystals. This, of course, depends upon the manner in which the solid is prepared. Nevertheless, most solids that we encounter in the real world are in the form of powders. That is, they are in the form of discrete small particles of varying size. Each particle has its own unique diameter and size. Additionally, their physical proportions can vary in shape from spheres to needles. For a given powder, aU grains will be the same shape, but the particle shape and size can be eiltered by the method used to create them in the first place. Methods of particle formation include ... 

It has been observed by some experimenters, but not by the others, that the experimental lattice constant a in crystals of ordinary size was different from that, a + A a, found in extremely small crystals. A recent example72 refers to vacuum-deposited copper grains whose diameter D (they were, of course, not spherical) varied from 24 to 240 angstroms. The lattice constants calculated from the (111) reflexions increased from 3.577 to 3.6143 angstroms when the grain volume decreased, but the particle size had no definite effect on the reflexions from the 220 plane. 

The nature of the material to be studied, which means its degree of crystallinity and perfectness of crystal structure, may have a significant effect on the thermoanalytical behavior. In spite of identical chemical composition of a certain material the variations with respect to structure, imperfections, grain boundaries, etc. are almost infinite. Of course many of these will not show in normal thermogravimetric analysis, with very sensitive apparatus characteristically different TG curves18, 19 may be obtained however. As an example Fig. 26 shows the thermal decomposition of hydrozincite, Zn5(OH)6(003)2, whereby equal amounts of samples from natural origin and synthetic preparations are compared. 

Careful attention has to be given to the purity of the precursors to avoid detrimental effects on conductivity. In a polycrystalline ceramic the conductivities of grain boundaries and bulk contribute to overall conductivity. In the case of polycrystalline YSZ, because of its unusually high intrinsic (bulk) conductivity the grain boundaries are far less conductive than the crystal, typically by a factor of 100. The effect the grain boundaries have on overall conductivity will depend on grain size and, of course, on impurity content (e.g. silica), since impurities tend to concentrate there. It is the effort to understand more of the various contributors to overall conductivity which has led to the application of impedance spectroscopy (see Section 2.7.5). 

We assume in the following discussion that the solid surface under consideration is of the same chemical identity as the bulk, that is, free of any oxide film or passivation layer. Crystallization proceeds at the interfaces between a growing crystal and the surrounding phase(s), which may be solid, liquid, or vapor. Even what we normally refer to as a crystal surface is really an interface between the crystal and its surroundings (e.g., vapor, vacuum, solution). An ideal surface is one that is the perfect termination of the bulk crystal. Ideal crystal surfaces are, of course, highly ordered since the surface and bulk atoms are in coincident positions. In a similar fashion, a coincidence site lattice (CSL), defined as the number of coincident lattice sites, is used to describe the goodness of fit for the crystal-crystal interface between grains in a polycrystal. We ll return to that topic later in this section. 

In the former case, the ions migrate among the interstitial defects, which may be relevant only to small ions such as Li+. This leads to a transference number close to 1 for the cation migration. In the other case, the lattice contains both anionic and cationic holes, and the ions migrate from hole to hole [39], The dominant type of defects in a lattice depends, of course, on its chemical structure as well as its formation pattern [40-43], In any event, it is possible that both types of holes exist simultaneously and contribute to conductance. It should be emphasized that this description is relevant to single crystals. Surface films formed on active metals are much more complicated and may be of a mosaic and multilayer structure. Hence, ion transport along the grain boundaries between different phases in the surface films may also contribute to conductance in these systems. 

Scales Above the Micron Scale. Much can be learned about the workings of a material with little more than an optical microscope and a well-polished sample. One of the first features of a material that will be evident upon inspection via optical means are the type of features shown in fig. 10.2 which reveals a polycrystalline microstructure. Of course, we well know that what we are seeing is evidence of the polycrystallinity of the material. The grain boundaries that separate different grains are clearly evident on the crystal surface. We can also see that depending upon the life history of the material, the grain size can vary considerably. 

---