Structure of Grain Boundaries

An alternative, but to some extent complementaty approach to the structure of grain boundaries notes that as the tilt angle between the crystals forming the grain boundary increases, planes of lower atomic concentrations, the high index planes, such as (221), (331) and (115) in the face-centred strucmre, become parallel to the grain boundary. There is therefore a decrease in the number of metal-metal bonds at the boundary as the tilt angle increases. 

T. Takasugi, Structure of Grain Boundaries , in Intermetallic Compounds Vol.I,... 

Figure 8. Schemes illustrating the dislocation structure of grain boundaries in CP Ti as-processed by HPT (a) and after low temperature annealing (b).

Because of these difficulties associated with systematic grain boundary studies we have at present a very limited understanding of the correlation of grain boundary electric transport properties to the microstructure. Clearly, it is well recognized that detailed information on the structure and composition of grain boundaries is necessary as a basis for an understanding of the correlation between the structure of grain boundaries and their electric properties. 

The atomic level structure of grain boundaries has been an important issue for the past several decades. In cubic materials geometrical constructs of periodic grain boundaries can be obtained for certain misorientation axis-angle combinations that are associated with coincident site lattices (CSLs). The CSLs are formed by the coincident sites of two hypothetically interpenetrating crystal lattices, where S is the reciprocal density of CSL sites. Much of the discussion of grain boundary structure and properties has revolved around the description of grain boundary structures in terms of the CSL, the displacement-shift complete (DSC) and the 0-lattice [10.10, 10.11]. 

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,... 

H. Sautter, H. Gleiter, and G. Baro. Effect of solute atoms on energy and structure of grain-boundaries. Acta. Met., 25 467 73, 1977... 

U. Etb and H. Gleiter. Effect of temperature on the energy and structure of grain-boundaries. Scrip. MetalL, 13 61-64,1979... 

Figure 14.7 Reprinted from Carter, C.B., Fdll, H., Ast, D.G., and Sass, S.L. (1981) Electron diffraction and microscopy studies of the structure of grain boundaries in silicon, Phil. Mag. A 43, 441. With permission from Taylor and Francis, http //www.tandf.co.uk/journals Figure 14.8 Reprinted from Sass, S.L. and Riihle, M. (1984) The detection of the change in mean inner potential at dislocations in grain-boundaries in NiO, Phil. Mag. 49, 759, with permission from Taylor and Francis. http //www.tandf.co.uk/journals...

Us stands for the number of atoms per unit area of the interface, Zj = 3 is the coordination number of atoms in the grain boundary, z = 12 is the coordination number in the grain bulk, and Na is the Avogadro number. To estimate the parameter s, we may use either the expression Uj = taken in the approximation of fee structure of grain boundary, or the expression Wj = derived from the approach [36], where a stands for the interatomic distance. Here WjZj is considered as the number of split interatomic bonds in the grain boundary as compared to the... 

Cahn, J. W. (1982). Transitions and Phase Equilibria Among Grain Boimdaty Structures. Proceedings of Conference on the Structure of Grain Boundaries, Caen, France. Journal de Physique, Vol. 43, pp. C6199-213, ISSN 0449-1947 Chernov, A. A. Mikheev, L. V. (1988). Wetting of Solid Surfaces by a Structured Simple Liquid Effects of Fluctuations. Physical Review Letters, Vol. 60, No 24, p. 2488-2491, ISSN 0031-9007... 

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...

M. Grafoute, Y. Labaye, F. Calvayrac, J.M. Greneche, Structure of grain boundaries in nanostructured powders a Monte-Carlo/EAM numerical investigation. Eur. J. P B 45, 419 24 (2005)... 

The dislocation structures of grain boundaries in B2 (cP2)-type ordered Fe3Al alloys have been observed (Buis etal., 1989,1991). It was shown that a symmetrical low-angle tilt boundary consisted of a regular array of <11 IHypc superdislocations in large areas, accompanied... 

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