Abstract

A framework for the discussion of grain boundary properties is established in terms of discrete elements such as dislocations or boundary coincidence units, more complex sets of interacting elements, or no discernible structure. Examples of models which fall wholly within a single class are discussed but favor is given to dislocations for small misorientations and to structureless grain boundary regions based on random close packing (rcp) and the change of atomic radii with coordination number for large. The free volume of a grain boundary V_F (cm ³/cm ²), defined as a special version of the excess volume (cm ³) attributable to any crystal defect, is then explicitly calculated for dislocation boundaries and for the rcp structure. We argue that a combination of these two structures yields the minimum possible V_F over the entire angular range of misorientation. When various existing grain boundary models are appraised we are then led to conclude that free volume is the best single criterion currently available for evaluation.