Grain Boundary Chemistry and Reactions in Metals
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lites grow, they eventually impinge on one another, and where they do, a grain boundary will form. Subséquent processing of the material may eliminate old boundaries and create new ones, but unless a great effort is made, some boundaries will always be présent. There hâve been many attempts to describe the structure of grain boundaries. The simplest model is one in which discrète dislocations are periodically inserted into the material and produce a misorientation between the two grains. Such a description is valid for a grain boundary in which the misorientation is not too great. But it breaks down for gênerai boundaries in which the orientations of the two grains are random
Figure 1. Optical micrograph shows the grain boundaries in an Fe-P alloy. The grain boundaries were revealed by etching with picric acid.
because the spacing of the dislocations becomes so small that they loose their individual identity. There hâve been attempts to describe grain boundaries in terms of spécifie geometrical lattices, e.g. the coincident site lattice, the Olattice, and the displacement shift complète lattice.1 Thèse models hâve not been very useful in helping to describe the random, high-angle boundaries found in polycrystalline materials. This lack of utility results because thèse models concentrate on grain boundaries that contain a high density of atomic positions that would fit exactly onto the lattices of the two crystals comprising the boundary, a situation not often found in high-angle grain boundaries in engineering materials. Furthermore, thèse studies tend to emphasize the geometrical construct and its manipulations rather than the atomic positions in the grain boundary. They do not yield a gênerai, workable picture of the grain boundary. A far more useful description is the structural unit model,2 where one simply considers the local atomic arrangements in the boundary. One constructs the boundary and then examines the various atomic configurations that are strung together to create it. Studies using this approach hâve found that certain structures are common to many grain boundaries, at least in distorted form. Figures 2a-2d show thèse structures, including the tetrahedron, the pentagonal bi-pyramid, the capped trigonal prism, and the Archimedean antiprism. The frequency with which thèse units occur dépends on the spécifie geometry of the grain boundary under considération. Several important points can be made regarding thèse structural units: (1) One can easily demonstrate that with thèse units a large array of bond lengths and structures can be generated, especially if some distortion of the structures is allowed. (2) The nine-atom capped trigonal prism and the ten-atom Archimedean antiprism allow, when distorted, a transition from one perfect lattice to another, as demonstrated in Figures 2c and 2d. (3) Thèse units provide many atomic arrangements that are not présent in the standard bodycentered-cubic, face-centered-cubic and hexagonal-close-packed structures of metals. It is then not surprising that éléments wi
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