Grain-boundary structure modeling

It would appear that the effects of impurities at the grain boundary must be either (a) to increase the diffusion rates or (b) to influence the microstructure and increase the number of short-circuit paths. However, theoretical modelling of the grain boundary structure by Duffy and Tasker and... 

Figure 4.1.7. (a) Model grain boundary structures and the impedance spectra resulting from finite... 

Choice of appropriate model IS is not a technique that can or should be apphed without prior knowledge of the system. Impedance spectra must be interpreted in the context of a model, be this a simple brick-layer model for a ceramic, or an advanced one based on electrode kinetics. When used in conjunction with electron microscopy, IS provides information about structure, and especially grain boundary structure. The microstructural information and the models derived from this are what make the conclusions of IS unequivocal. 

The quasi-continuum (QC) method was first introduced in 1996 by Tadmor et al. for the investigation of deformation in solids. Ever since, this method has been one of the most powerful and widely applied hybrid methodologies. Its primary applications include the study of dislocation nucleation, cracks, interfaces, grain boundary structure and deformation, nanoindentation phenomena, and so on. Various applications are discussed in more detail below. Since its appearance, the model has been improved and expanded, " and these more complete versions are briefly presented here. If additional details are needed, several specialized reviews are available. 

Another type of model electrode uses multilayer electrolytic deposits, which attracted the interest of electrochemists long before physical methods for their structural characterization were introduced. These electrodes were usually characterized by their roughness factors rather than particle size, the former being of the order of 10 -10 (for original references, see the review [Petrii and Tsirhna, 2001]). Multilayer electrolytic deposits have very complex stmctures [Plyasova et al., 2006] consisting of nanometer-sized crystallites joined together via grain boundaries, and hence have very pecuhar electrocatalytic properties [Cherstiouk et al., 2008] they will not be considered further in this chapter. 

Grain boundary models were developed primarily for metals. We can assume that the above mentioned ideas on the structure and energy of grain boundaries also hold, in essence, for ionic, covalent, and van der Waals crystals as well [M. W. Finnis, M. Riihle (1993)]. 

Microstructures are generally too complex for exact models. In a polycrystalline microstructure, grain-boundary tractions will be distributed with respect to an applied load. Microstructures of porous bodies include isolated pores as well as pores attached to grain boundaries and triple junctions. Nevertheless, there are several simple representative geometries that illustrate general coupled phenomena and serve as good models for subsets of more complex structures. 

Fig. 4. A model for the possible relationship between crystalline and disordered regions within a collagen fibril. The cross-sectional model of a 50-nm diameter fibril shows regions of crystallinity interfaced by grain boundaries. The individual crystalline unit cells are shown and the gap region is represented by a darker color. The axial projection of a single microfibrillar unit is also shown. Based on die structures developed by Hulmes et al. (1995) and adapted with permission from Hulmes et al (2002).

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