Experimental evidence for a structural unit model of quasiperiodic grain boundaries in aluminum
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This paper presents a geometrical description of aperiodic grain boundaries within the framework of a quasiperiodic lattice. Experimental evidence is given in support of a structural unit model of quasiperiodic [100]45° twist and [100]45° twist plus tilt grain boundaries in aluminum.
I. INTRODUCTION Grain boundary structures have been the subject of intensive theoretical and experimental investigations, ever since it was realized that they determine many physical properties in polycrystalline materials. The structure of grain boundaries has been described in terms of geometrical models based on the coincident site lattice (CSL),1-2 displacement shift complete lattice,2"4 and 0lattice theories.3 Despite their usefulness in characterizing the global rigid nature of the grain boundary structure, these models still prove to be inadequate for providing a thorough representation of atomic relaxations that may occur at the grain boundary core. Moreover, these geometrical models are applicable only to periodic grain boundaries. Further advances in elucidating the relaxation processes have been achieved with the development of atomistic simulation methods. Methods such as molecular statics and molecular dynamics have been used extensively to model the structure of periodic grain boundaries.5 One significant aspect which emerges from the continued efforts to improve our knowledge of the structure of grain boundaries is the existence of some recurring structural units. The structural unit principle in grain boundaries was originally put forward by Bishop and Chalmers.6 Computer simulations of a large number of periodic grain boundaries in metals have placed the structural unit model on a sound foundation.7 Sutton and Vitek7 have also introduced rules for the determination of the sequence of structural units. This model, which involves structural units (SU), is equivalent to the secondary grain boundary dislocation (SGBD) concept, where a SGBD forms to accommodate the deviation from an "ordered interface".8 The Structural Unit/Grain Boundary Dislocation model (SU/GBD) for grain boundaries in cubic metals proposes the construction of any long period boundary from units of shorter period boundaries. These short period boundaries or "delimiting" boundaries fix the limits on the range of local misorientation. Long period boundaries in a range of misorientation may be J. Mater. Res., Vol. 6, No. 7, Jul 1991
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constructed with a mixture of these delimiting boundary units. High-resolution electron microscopy (HREM) has provided experimental evidence for the structural unit model in periodic interfaces. Symmetrical (110) tilt boundaries,9"11 (001) tilt boundaries,12 and (111) tilt boundaries in gold13 have shown the existence of low energy basic structural units. Despite these advances in the structural characterization of simple periodic interfaces, the structure of complex general grain boundaries remains a challenge. Quasiperiodic interfaces may provide a link between the simp
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