Vibrational properties and specific heat of core–shell Ag–Au icosahedral nanoparticles

Abstract

The vibrational density of states (VDOS) of metal nanoparticles can be a fingerprint of their geometrical structure and determine their low-temperature thermal properties. Theoretical and experimental methods are available nowadays to calculate and measure it over a size range of 1–4 nm. In this work, we present theoretical results regarding the VDOS of Ag–Au icosahedral nanoparticles with a core–shell structure in that size range (147–923 atoms). The results are obtained by changing the size and type of atoms in the core–shell structure. For all sizes investigated, a smooth and monotonic variation of the VDOSs from Ag to Au is obtained by increasing the number of core Au atoms, and vice versa. Nevertheless, the Ag₅₆₁Au₃₆₂ nanoparticle, with a Ag core, shows an anomalous enhancement at low frequencies. An analysis of the calculated VDOSs indicates that as a general trend the low-frequency region is mainly due to the shell contribution, whereas at high frequencies the core effect would be dominant. A linear variation with size is obtained for the period of quasi-breathing mode (QBM), in agreement with the behaviour obtained for pure Ag and Au nanoparticles. A non-monotonic variation is obtained for the QBM frequency as a function of the Ag concentration for all nanoparticles investigated. The calculated specific heat at low temperatures of the Ag–Au nanoparticles is smaller (larger) than the corresponding one calculated for the pure Au (Ag) nanoparticles of same size. Nevertheless, the enhancement of VDOS at low frequencies of the Ag₅₆₁Au₃₆₂ nanoparticle with a Ag core induced larger values of specific heat than those of the pure Au₉₂₃ nanoparticle in the temperature range of 5–15 K.