A technique is given for finding partial DSC vectors appropriate to crystals with more than one atom per lattice site. The DSC lattice is made up of vectors that represent displacements of one crystal with * Now at Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.respect to the other that leave the boundary structure shifted, but not complete. A new, rapid method for finding the step vectors associated with perfect DSC dislocations is described. Partial DSC vectors and step vectors for perfect DSC dislocations in hexagonal close-packed crystals are determined. The availability of reactions between lattice partial dislocations and grain boundaries in hexagonal closepacked crystals is also assessed.0108-7681/87/050416-07501.50 (~ 1987 International Union of Crystallography
FU-RONG CHEN AND A. H. KING 417
IntroductionGeometrical models of the structures of grain boundaries have received a great deal of attention since the early 1970's, with considerable emphasis being placed upon understanding the principles which govern structure, and the ways in which structure influences the grain-boundary properties (Smith & Pond, 1976;Sutton, 1984). Grain-boundary geometry has been described in terms of the coincidence-site lattice (CSL), and its generalization called the O lattice (which is the lattice of possible origins of the transformation which produces crystal 2 from crystal 1). Also of importance in describing the grain-boundary geometry is the so-called DSC lattice, which is a lattice made up of vectors which represent displacements of one crystal with respect to the other which leave the boundary structure shifted, but complete: DSC vectors thus define the allowable Burgers vectors of perfect grain-boundary dislocations. The existence of DSC dislocations in high-angle grain boundaries, conserving structures of high lattice coincidence through small changes in misorientation, has been confirmed by various transmission electron microscope investigations; most of these observations were made in materials with cubic crystal structures (Bollmann, Michaut & Sainfort, 1972;Clark & Smith, 1978;Sun & Balluffi, 1982). The behavior of grain boundaries, in many cases, has also been linked to the properties of grain-boundary dislocations, although this frequently requires that further geometrical concepts be brought into consideration. Two important geometrical features have been identified beyond the usual CSL, O lattice and DSC lattice: the first of these is the step vector associated with a DSC dislocation, which is used in determining the height of the step in the grain-boundary plane that is associated with the core of a grain-boundary dislocation. The definition of the step vector and an extensive description of its properties was given by King & Smith (1980) and step vectors for grainboundary dislocations in cubic materials were tabulated by King (1982). Quantitative confirmation of the importance of step vectors in determining the behavior of grain b...