Effect of phase fraction on the tri-junction in two-phase nanoparticle systems

The equilibrium dihedral angles at the solid-solid-vapor tri-junctions of two-phase Cu-Ag alloy nanoparticles 40-100 nm in diameter were measured as a function of phase fraction using transmission electron microscopy. The {111} solid-solid interface was cusp-oriented while the surface orientations of the Cu-rich and Ag-rich phases at the tri-junction were mostly free to vary. The dihedral angles at the tri-junction were found to vary with the phase fraction, due to the coupling between the relative amounts of each phase and the equilibrium conditions at the tri-junction. This equilibrium condition was used to measure the ratio of the Ag-rich and Cu-rich surface energies to the {111} interfacial energy, which were found as 2.1 and 3.5, respectively.