Abstract:
We have used density functional perturbation theory to investigate the stiffness of interatomic bonds in small clusters of Si, Sn, and Pb. As the number of atoms in a cluster is decreased, there is a marked shortening and stiffening of bonds. The competing factors of fewer but stiffer bonds in clusters result in softer elastic moduli but higher (average) frequencies as size is decreased, with clear signatures of universal scaling relationships. The stiffness of bonds is found to scale as the inverse tenth power of length. A significant role in understanding trends is played by the coordination number of the bulk structure: The higher this is, the lesser is the relative softening of elastic constants and the greater the relative damping of vibrational amplitudes for clusters compared to the bulk. Our results could provide a framework for understanding recent reports that some clusters remain solid above the bulk melting temperature. Our results suggest that Sn and Pb clusters (but not Si clusters) are more thermally stable than the bulk.
