Behavior of Grain Boundaries Near the Melting Point

The absolute grain boundary energies of {011} tilt boundaries in bismuth at a temperature very near the melting point were measured over the range of misorientations 0.5° to 14.5°. A study of the structure of these boundaries was extended as far as 27°. The results at small tilt angles (θ≤6°) can be described accurately in terms of a heterophase dislocation model. This model also correctly predicts the grain boundary energies of [001] tilt boundaries in copper near the melting point, again for tilt angles less than about 6°. The heterophase dislocation model is unique, inasmuch as it permits the calculation of absolute grain boundary energies in terms of usually available thermodynamic and elastic quantities and a simple macroscopic parameter related to the boundary structure. In addition, the theory provides a basis for interpreting the structural transition observed in bismuth tilt boundaries at intermediate misorientations (θ=15°). Finally, the failure of current theories to predict the correct energy-misorientation dependence over a wide range of misorientations is ascribed to linear and nonlinear interactions among the misfit dislocations—interactions which increase rapidly in importance for misorientations above about 5°. For a quantitative description of the energetic behavior of higher angle grain boundaries than are treated at present, a theory which accounts for such interactions appears to be required.