Effects of shape and composition on the Debye temperature and breathing frequency of metal nanoparticles

The vibrational properties of metal nanoparticles with dimensions 1-10 nm are computationally explored at the atomistic level of detail, without resorting to lattice dynamics in the harmonic approximation. Using molecular dynamics simulations, power spectra of the atomic velocities and a measure of the particle volume are obtained, providing estimates for the vibrational density of states (VDOS) and the breathing frequency, respectively. The Debye temperature is inferred directly from the heat capacity resulting from the VDOS. For monometallic particles made of pure gold or iron, the influence of the shape around the cube reference is scrutinized either by varying the sharpness of their edges, or by varying their anisotropy from flat to elongated particles, keeping the number of atoms as approximately constant. The surface fraction of atoms is found as a leading driving force for the breathing frequency, although it cannot explain alone the more subtle variations of the Debye temperature that rely on the entire VDOS. Bimetallic silver-gold particles are also revisited, focusing on the role of chemical ordering (core-shell versus alloy), composition, and size. While the Debye temperature exhibits relatively modest variations throughout all cases investigated, the breathing frequency shows marked differences upon changes in the shape anisotropy or the chemical ordering, especially in core-shell nanoparticles with 20% composition in the core. Competing breathing modes are often found to arise, especially in weakly deformed iron nanoparticles.