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First published in 1997. Routledge is an imprint of Taylor & Francis, an informa company.
Faceting of high angle grain boundaries in SIGMA = 3 and SIGMA = 5 coincidence lattices of the fcc structure was studied using thinfilm bicrystal specimens of controlled geometry. A number of relatively high index boundaries in the coincidence lattices (containing relatively low planar densities of coincidence sites) was found to break up into low energy facets corresponding to low index planes of the coincidence lattices (containing high densities of coincidence lattice sites). These results are consistent with a general expectation that the grain boundary energy decreases as the planar density of coincidence sites increases, i.e., the two-dimensional periodicity of the boundary becomes shorter, and long-ranged distortions are reduced. (auth).
As the selection of material for particular engineering properties becomes increasingly important in keeping costs down, methods for evaluating material properties also become more relevant. One such method examines the geometry of grain boundaries, which reveals much about the properties of the material. Studying material properties from their geometrical measurements, The Measurement of Grain Boundary Geometry provides a framework for a specialized application of electron microscopy for metals and alloys and, by extension, for ceramics, minerals, and semiconductors. The book presents an overview of the developments in the theory of grain boundary geometry and its practical applications in material engineering. It also covers the tunneling electron microscope (TEM), experimental aspects of data collection, data processing, and examples from actual investigations. Each step of the analysis process is clearly described, from data collection through processing, analysis, representation, and display to applications. The book also includes a glossary of terms. Exploring both the experimental and analytical aspects of the subject, this practical reference guide is essential for researchers and students involved in material properties, whether in physics, materials science, metallurgy, or physical chemistry.
It is proposed that, to a good approximation, the construction of a boundary can be described in terms of three basic steps: (1) a rigid body joining of two perfect crystals along the boundary plane (Step I); (2) a primary relaxation (Step II) consisting of relaxations in the boundary centered on O-Lattice elements which act to improve lattice matching in these regions; and (3) a possible secondary relaxation (Step III) which produces the final structure composed of patches of a low .sigma. boundary and secondary grain boundary dislocations. The energy after Step I is obtained by summing pairwise interactions across the boundary and is found to be relatively low for a number of low .sigma. boundaries and to approach a larger constant value for all large .sigma. boundaries. The energy decrease due to Step II varies monotonically with crystal misorientation according to a Read-Shockley function, and the energy decrease associated with Step III produces cusps in the energy versus misorientation curve at misorientations corresponding to low .sigma. boundaries. The model appears to be consistent with the present knowledge of boundary structure and energy, and its general applicability is discussed.
This work is intended to be a mathematical underpinning for the field of grain boundary engineering and its relatives. The interrelationships within the set of rotations producing coincident site lattices in cubic crystals are examined in detail. Besides combining previously established but widely scattered results into a unified context, the present work details newly developed representations of the group structure in terms of strings of generators (based on quaternionic number theory, and including uniqueness proofs and rules for algebraic manipulation) as well as an easily visualized topological network model. Important results that were previously obscure or not universally understood (e.g. the [Sigma] combination rule governing triple junctions) are clarified in these frameworks. The methods also facilitate several general observations, including the very different natures of twin-limited structures in two and three dimensions, the inadequacy of the [Sigma] combination rule to determine valid quadruple nodes, and a curious link between allowable grain boundary assignments and the four-color map theorem. This kind of understanding is essential to the generation of realistic statistical models of grain boundary networks (particularly in twin-dominated systems) and is especially applicable to the field of grain boundary engineering.