On the structure of tilt grain boundaries in cubic metals II. Asymmetrical tilt boundaries

Abstract

The results of the study of symmetrical tilt boundaries, reported in the preceding part I, are generalized to asymmetrical tilt boundaries. A classification of tilt boundaries in cubic crystals is developed that reveals which boundaries to choose in order to study equilibrium faceting or intrinsic grain boundary dislocations (g.b.ds) accommodating a misorientation. Two series of atomistic studies of asymmetrical tilt boundary structures are presented based on this classification. The first is a study of long-period (27 ^ 97) [110] asymmetrical tilt boundaries in aluminium. The aims of this study are to investigate whether these boundaries are composed of fundamental structural elements, in the same way as was found in part I for symmetrical tilt boundaries, and to see if localized, distinct stress fields of edge g.b.ds exist throughout the misorientation range. With use of the results of this study, and the principle of continuity of boundary structure enunciated in part I, the boundary unit representation of a 27 — 1193 asymmetrical tilt boundary is derived as an example. It is generally found that the Burgers vectors of intrinsic secondary g.b.ds in tilt boundaries, based on favoured boundary reference structures, are non-primitive d.s.c. vectors. The reason for this is given and a simple formula is presented to derive the Burgers vectors of such dislocations for any favoured tilt boundary reference structure. It is pointed out that, in general, very low angle {0 < 1° say) tilt boundaries cannot be described in terms of units from high angle tilt boundaries, and the transition from the low angle to high angle regimes is discussed. The second atomistic study is an investigation of equilibrium faceting of long-period 27 — 3 [110] tilt boundaries with use of an empirical potential for copper. The limi tations of computer simulation methods using periodic border conditions to study faceting are stated. It is shown, however, that the constraints imposed by the use oi periodic border conditions may be used in a positive sense to carry out the Wultt construction, and thereby deduce equilibrium faceting behaviour.