The further geometry of grain boundaries in hexagonal close-packed metals

Abstract

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...

Review: grain boundary faceting–roughening phenomena

“…Therefore, the exact CSL exists in Zn only for GBs with rotation around [0001] axis. In all other cases, the so-called constrained CSL approach should be used (CCSL) [105][106][107][108][109][110][111]115]. The parallel elongated sides of the twin plate are formed by the coherent symmetric twin ð1102Þ 1 || ð1102Þ 2 grain boundary (STGB) facets [112].…”

Atomic Structures of $$ [0\bar{1}10] $$ Symmetric Tilt Grain Boundaries in Hexagonal Close-Packed (hcp) Crystals

“…STGBs are simple grain boundaries that are fully described crystallographically by a tilt axis and tilt angle 2h. For this class of boundaries, prior studies have investigated, for instance, the effect of GB defect structure on the propensity for sliding, [4,10] partial transmission and absorption, [4][5][6][7][8][9]11] and vacancy migration energies and entropies. [12,13] Most atomic-scale structural models for STGBs have been developed for high-symmetry face-centered-cubic and body-centered-cubic crystals.…”

“…Generally, as h tilts off coherency, intrinsic GBDs should form to accommodate the deviation, an expectation that has been confirmed experimentally. [41][42][43] Prior studies involving extensions of theories based on CSLs and structure unit models (SUMs) postulate that the STGBs that deviate from a nearby coherent (''favored'' [18] ) boundary in orientation space should contain some fundamental units or resemble that of the favored boundary, [11,[37][38][39][42][43][44][45][46][47] apart from the distortions that result from the GBDs. Recently, we carried out a systematic study of STGB structure spanning the entire range of misorientations: 0 deg < 2 h < 180 deg in Reference 3.…”

Crystallographic Considerations

“…The lower symmetry of the other crystal classes necessitates the more sophisticated formalism known as the constrained coincidence site lattice, or CCSL (Chen and King, 1988). The value of S also gives the ratio between the areas enclosed by the CSL unit cell and crystal unit cell.…”