Bond Stiffening in Nanoclusters and its Consequences

TL;DR

This study uses density functional perturbation theory to analyze how bond stiffening in small Si, Sn, and Pb clusters affects their elastic and vibrational properties, revealing universal scaling and implications for melting behavior.

Contribution

It provides new insights into bond stiffening effects in nanoclusters and their impact on elastic and vibrational properties, highlighting the role of coordination number.

Findings

Bond shortening and stiffening occur as cluster size decreases.

Smaller clusters have softer elastic moduli but higher vibrational frequencies.

Clusters can remain solid above bulk melting temperature due to these effects.

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. 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.