Structural materials polycrystalline modeling

The bulk and grain boundary behaviour of a polycrystalline electroceramic material can be described by a Voigt structure consisting of two RC circuits. This simple Voigt structure is shown in Figure 4.24a. The parameters of this model all have direct physical meanings Rl =Rh, ci = R2 = Rgb, and C2 = Cgb, where b refers to bulk and gb refers to grain boundary. 

There are many ways to build a model of the crystal structure of a polycrystalline material without first using the intensities of individual Bragg reflections, which are hidden in powder diffraction due to partial or complete overlapping. Most of the direct space approaches are, in effect, trial-and-error methods and they include some or all of the following components ... 

Frequently, polycrystalline specimens exhibit a preferred orientation of the crystallites or polycrystalline texture. In addition, many manufacturing processes of technological materials can induce texture. In comparison with specimens having randomly oriented crystallites, the relative intensities of the diffraction lines of textured samples are modified. As a consequence the structural and quantitative phase analysis of polycrystalline samples becomes impossible without proper modeling of the texture. 

The most frequently used technique for the determination of crystal structures is single crystal analysis. However, if no single crystals of suitable size and quality are available, powder diffraction is the nearest alternative. Furthermore, single crystal analysis does not provide information on the bulk material and is not a routinely used technique for the determination of microstructural properties. Neither is it often used to characterize disorder in materials. Studies of macroscopic stresses in components, both residual from processing and in situ under load, are studied by powder diffraction, as is the texture of polycrystalline samples. Powder diffraction remains to this day a crucial tool in the characterization of materials, with increasing importance and breadth of application as instrumentation, methods, data analysis and modeling become more powerful and quantitative. 

For some cases, it is possible to use refinement techniques (6) to obtain very accurate structural data. This is especially true for the well understood diffraction techniques and, therefore, for characterizations of polycrystalline material. With an increasing level of physical understanding the number of techniques which are suitable for use in refinement is bound to grow. Because of the local minimum problem, the starting model should already be close to reality for single-technique refinements. We expect that the... 

A feature that arises from our consideration of the analytical models is the difference in complexity between the sintering phenomena in polycrystalline materials and amorphous materials. The analysis of viscous sintering on the basis of Frenkel s energy balance concept appears relatively simple in principle. The idealization of the structure of amorphous materials leads to analytical solutions that describe the sintering behavior in a very satisfactory manner. 

For polycrystalline materials, the sintering phenomena are considerably more dependent on the structural details of the powder system. Because of the drastic simplifications made in the models, they do not provide an adequate quantitative representation of the sintering behavior of real powder systems. The models do, however, provide a good qualitative understanding of the different sintering mechanisms and the dependence of the sintering kinetics on key processing parameters such as particle size, temperature, and, as we shall see later, applied pressure. 

The transport of ions through the SEI, which consists mainly of polycrystalline material, takes place by mobile point (Schottky or Frenkel) defects. As a result, the contribution of the grain boundaries must be taken into account. In the first models describing the SEI, its structure was represented as comprising two or more separate layers of different composition and properties. The first (the SEI itself), is thin and compact, while the second one (if it exists) on top of the SEI... 

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