Equilibrium shape and interface roughening of small liquid Pb inclusions in solid Al Original Research Article

The shape of liquid Pb inclusions embedded in a solid Al matrix was investigated at temperatures between 300 and 500°C using in-situ electron microscopy. Inclusion shapes in the size range from a few nanometers to about 150 nm were found to depend on size, temperature and thermal history. During isothermal annealing after melting, small inclusions rounded off while larger inclusions remained faceted until the temperature was raised to about 500°C. During subsequent cooling, inclusions refaceted, although less strongly than during heating. The shape hysteresis between heating and cooling cycles was found to be due to the barrier of ledge nucleation necessary to advance the faceted interfaces. It is shown that this kinetic barrier can explain the observed dependence on size and temperature, and that the {1 1 1} interface undergoes a roughening transition at about 550°C. Even under conditions of kinetic limitation it was possible to measure local equilibrium by modeling kinetically limited inclusions as a droplet in a crevice. For this type of measurement, the hysteresis between heating and cooling cycles disappeared, and the true equilibrium shape could be derived. The anisotropy of interfacial energy was shown to be significantly smaller than previously reported, and at about 2%, similar to the anisotropy of the surface energy for fcc metals. From the width of facets on the equilibrium shape, the step energy was determined to be ε=1.9·10−11 J/m at 350°C.