Measurements of the grain boundary energy and anisotropy in tin

The three-dimensional (3-D) geometry of the triple junction formed between two solid Sn-rich particles and a Pb-rich liquid matrix is used to measure the interfacial energy and its anisotropy for individual grain boundaries. The anisotropy is determined using a Cahn-Hoffman capillarity vector analysis of the energy balance at a triple junction. The absolute solid-solid gain boundary energy for each individual boundary is then determined by using the known value for the solid-liquid energy. A total of 136 boundaries are analyzed, with 46 of them forming grain boundaries. The remaining boundaries are found to be wetted boundaries with thin-liquid films formed between the two particles. A correlation between the low interfacial energy and the probability of occurrence for that disorientation is also observed. We also show that the anisotropy, as quantified by the magnitude of the torque term, is a significant portion of the total interfacial energy, especially for low energy boundaries. The degree of twist vs tilt of the boundaries is also analyzed. As expected, there are more tilt boundaries within the system than twist boundaries and most of the low energy boundaries have a mixed tilt-twist character.