Coincident grain boundary

Coincidence grain boundary in a simple cubic lattice that corresponds to a 36.9° rotation about a <100> direction. One fifth of the atoms (dark circles) in the boundary have common sites. 

The grain boundary energy 7gb should be proportional to . For small values of high coincidence occurs and the number of broken bonds can be minimized. = 1 corresponds to complete coincidence of the ideal crystal. Experimentally it was found that the correlation between 7Gb and is not that simple due to volume expansions or translations at the grain boundaries. A principal problem of the coincident site lattice model is that, even arbitrarily small variations of the lattice orientation lead mathematically to a complete loss of coincidence. This is physically not reasonable because an arbitrarily small deviation should have a small effect. This problem was solved by the O-lattice theory [343], For a comprehensive treatment of solid-solid interfaces and grain boundaries, see Refs. [344,345],... 

V. Randle, The Role of the Coincidence Site Lattice in Grain Boundary Engineering, The Institute of Materials, London, 1996. 

Figure 1.7 View down the [001] direction of a tilt boundary between two crystals (A, B) with a misorientation angle of 36.9° about [001], The grain boundary is perpendicular to the plane of the page. Every fifth atom in the [010] direction in B is a coincidence point (shaded). The area enclosed by the CSL unit cell (bold lines) is five times that of the crystal unit cell, so 2 = 5. (After Lalena and Cleary, 2005. Copyright John Wiley Sons, Inc. Reproduced with permission.)...

Fig. 9.39. Interpenetrating lattices used to consider grain boundary structure (courtesy of D. Pawaskar). Open and filled circles correspond to the two host lattices and filled squares correspond to those atoms that are common to both lattices (i.e. the lattice of coincident sites).

Fig. 9.41. Schematic of several representative grain boundaries with structures described by coincident site lattice model. This set of boundaries corresponds to a (001) rotation axis, and the atomic-level geometries have not been relaxed (courtesy of D. Pawaskar). The filled circles correspond to those sites (coincident sites) that are common to both lattices.

As the main carrier of heat at 300K is considered to be long wave length phonon, which is scattered mainly by grain boundary, the milling time dependence of thermal conductivity is considered to be in good coincidence with the microstructure fonnation shown in Figure 3. 

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]. 

Another possibility for obtaining CSLs exists by approximating the crystal structure by pseudocubic or tetragonal unit cells. This approach of applying the CSL to non-cubic systems has been discussed in the literature by means of the constrained coincident site lattice [10.12] which has, among others, also been applied to YBCO grain boundaries. 

There are also similarities between the YBCO boundaries obtained on Y— Zr02 and SrTiOs bi-crystal substrates. They both exhibit wavy YBCO boimd-ary morphologies with (100), (010) and (110) facets. Their formation mechanism is the same in both systems. It is thus likely that the interaction between the impinging species and the nucleated YBCO is stronger than that with the substrate. Otherwise, the bottom part of the YBCO grain boundary plane would coincide with the position of the substrate boundary. MgO substrates exhibit similar characteristics to Y— Zr02 in terms of the [OOIJybco orientation with respect to the substrate normal. There is, however, no chemical reaction observed at the MgO/YBCO interface. It is thus reasonable to assume that YBCO films grown on MgO bi-crystal substrates will have the same principal... 

Chaudhari, P. and Matthews, J.W. (1971) Coincidence twist boundaries between crystalline smoke particles, J. Appl. Phys. 42, 3063. Original description of the MgO smoke experiment for GBs Zhu, Y. and Granick, S. (2001) Viscosity of interfacial water, Phys. Rev. Lett. 87(9), 096104. The idea is that the viscosity of water can be very different if it is constrained to be a film in a silicate grain boundary. 

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