Energetic Description of Grain Boundaries

As with our previous treatments of interfacial energy, the fundamental idea is to make a comparison between an A-atom state in which all of the atoms are in their ideal bulk positions and an A-atom state in which the interface of interest is present. 

As an example of the type of supercell that can be used in this analysis, fig. 9.44 shows a scheme in which the grain boimdary is at the interior of a cell whose outer boundaries perpendicular to the boundary are treated as rigid slabs. In this case, the forces on the atoms in the region being relaxed are computed in exactly the 

Semiempirical determination of grain boundary structure and energetics. 

Simple grain boundaries in metals have been exhaustively considered from the standpoint of empirical descriptions of the total energy. The logic of much of this work is founded on the contention that prior to understanding the susceptibility of boundaries to segregation and fracture or their role as short-circuit paths for diffusion, it is necessary to first understand the structures themselves. The majority of this work has emphasized bicrystals. 

A series of studies in Ni have been made for tilt boundaries that elucidate the role of misorientation in boundary structure. The case study of interest to our present discussion (Rittner and Seidman 1996) involved the use of a pair functional description of the total energy to investigate 21 distinct symmetric tilt boundaries with a (110) tilt axis. Representative examples of the relaxed structures are shown in fig. 9.45 and the corresponding grain boundary energies are shown in fig. 9.46. 

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