Modeling of Grain-Boundary Structures

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... 

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)]. 

This work clearly demonstrated that it is important to establish direct correlations between microstructure and transport properties of grain boundary junctions. At this point, both the complex and varied structures of grain boundaries that have been found and the extremely complicated transport behavior, present considerable challenges concerning the development of models for the connection between structure and transport properties. However, it is clear that progress in this field is directly dependent on our ability to develop such models. 

The structural unit model has been used successfully to predict the structures of grain boundaries in perovskite structured SrTiOs bicrystals [11.31-11.34]. The structural units observed for symmetric SrTiOs [001] tilt boundaries are shown in Fig. 11.8. In a similar manner to the isolated dislocation cores in YBCO, the structural units also appear to contain atomic positions where the cations are too close together. Again, depending on the structural unit, the close separation of the atomic columns can occur for either of the sub-lattice sites,... 

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. 

A further insight in this rather simple nanostructure was given by a numeric approach based on the Embedded Atom Method this new route was developed to model the structure of grain boundaries in metallic nanostructured powders. Numeric aspects are detailed in [160]. As it is illustrated in Fig. 4.20, realistic atomic structures of twisted and tilted double and triple grain boundaries as a function of the relative disorientation of the grains were successfully modelled by... 

Fig. 4.20 Computer modelled atomic structure of grain boundaries in nanostructured metallic powders...

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. 

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