Absolute interfacial energies of [001] tilt and twist grain boundaries in copper

Abstract

The absolute interfacial energies of [001] tilt and twist boundaries in copper have been determined, by using a Zeiss Interference Microscope to measure the dihedral angles which form during the thermal grooving process. An analysis of the results obtained for small angle, lineage boundaries, in terms of the appropriate dislocation model, shows that the Read-Shockley equation predicts the energy up to misorientations of 5 to 6°, but that for larger misorientations, it gives much too small an energy. It is shown also that van der Merwe's treatment, which avoids some of the limitations present in the Read-Shockley derivation, is capable of predicting the energy up to misorientations of 8 to 9°. Moreover, from the analysis presented herein, it is possible to offer an explanation for the apparent agreement that was obtained, at large misorientations (25 to 30°), between the previous measurements of relative grain boundary energies and the Read-Shockley equation. The large angle grain boundary is characterized by a broad maximum in energy that shows no energy cusps, for either tilt or twist boundaries. Both types of boundaries have nearly the same energy for misorientations less than 18°, but for the range of misorientations, over which there is a maximum in energy, twist boundaries have a lower energy by about 130 ergs/cm 2. An attempt to explain this difference from the results obtained from a calculation made on an atomic basis is discussed.