Size dependent structural stability of Mo, Ru, Y and Sc nanoparticles

The Gibbs free energy model was generalized to predict the phase stability of Mo, Ru, Y and Sc at all size range from nanometer to bulk size. The size-, shape- and temperature-dependent phase diagrams of Mo, Ru, Y and Sc were firstly computed to explain the corresponding experimental observations, including the latest one on Ru nanoparticles. Especially, we re-confirmed and summarized that there exists a general law for the stable phases of metal nanoparticles: for body-centered-cubic (BCC) metals (eg. Mo), there exists face-centered-cubic (FCC) phase at small size; for a kind of hexagonal-close-packed (HCP) metals (eg. Ru), they can transform into FCC at small size; for the other kind of HCP metals (eg. Sc or Y), they can change to BCC at high temperature (Y at 1754 K, and Sc at 1588 K) but to FCC at small size. This work establishes a map of the evolution of the structures from macro to nanoscale.