On the disclination-structural unit model of grain boundaries

The relation between two elastic continuum approaches to grain boundary structure, the dislocation and disclination models, is discussed. It is shown that the disclination model has two advantages: a well-behaved expression for the elastic energy of disclination dipole walls, which describes the elastic energy over a wide interval of misorientations, and a continuous misorientation angle dependence of the elastic energy of grain boundaries in an interval between two delimiting boundaries. The elastic energy of the most general, faceted disclination wall is calculated. For cases in which both the energies of delimiting boundaries and elastic constants are available from atomic simulations (〈001〉 and 〈111〉 tilt boundaries in copper and 〈001〉 and 〈011〉 tilt boundaries in diamond) quantitative agreement between the disclination model and simulation results is obtained.