Triple junction excess energy in polycrystalline metals

The energetics of triple lines are often negligible in polycrystalline systems, but may play a significant role in the finest nanocrystals, and in fact lower the excess defect energies of those polycrystals. This paper develops a methodology to assess polycrystalline average grain boundary and triple junction excess energies for pure fcc metals Ni, Cu, Al, Pd, Pt, Ag and Au using embedded atom method potentials. It is found that there are correlations between the triple line energy and physical quantities such as grain boundary and dislocation line energy, but with a negative sign indicating that triple junctions reduce intergranular excess energy per area on average. The relationship with grain boundary energy is of order ∼−4.5 × 10⁻¹⁰ m, and the triple junction energy is about −1/12 of the dislocation line energy. Despite their low energy, triple junctions can significantly affect total system energy due to their high density in the finest nanocrystals; for example, 6-nm Pd nanocrystals have an effective intergranular energy of ∼0.83 J/m² (compared with the large grain size limit of 0.93 J/m²), translating to a measurable bulk excess enthalpy of ∼6 kJ/mol. Such excess enthalpy is experimentally assessable, and the present framework can be used to measure triple junction energies. For instance, re-analyzing data of Lu and Sun (Phil. Mag., 1997) we obtain grain boundary and triple junction energies of 0.33 J/m² and −3.0 × 10⁻¹⁰ J/m respectively for Selenium nanocrystals, which can be compared with modeled values of 0.76 J/m² and −1.02 × 10⁻¹⁰ J/m by using our method with a published bond-order potential for Se.