Structure-dependent vibrational properties of metallic nanoclusters

Abstract

The thermally vibrational properties of icosahedral (ICH) and face-center-cubic (FCC) copper nanoclusters have been compared by carrying out molecular dynamics simulations with a local-environment-dependent tight-binding potential. Although both ICH and FCC copper nanoclusters exhibit a low-and high-energy enhancement of vibrational density of states (VDOS) in comparison with the bulk copper, the vibrational properties of nanoclusters show a strong structure-dependent feature. The different structure is revealed to result in the different atom package, the different lattice shrinkage, the different local pressure, and thus the different VDOS. The different atom package at the surfaces of clusters is responsible for the different lowenergy VDOS in a different power-law behavior between the FCC and ICH clusters. The lattice contraction and the internal pressure in the sense of the bulk are unified to explain the enhanced high-energy tail in the VDOS of FCC clusters, but not in the case of ICH clusters.

Surface specific heats of metal nanocrystals at low temperatures

“…Therefore, the phonon specific heat can be theoretically obtained if g(ω) is known. The previous studies have shown that the surface VDOS is scaled as g(ω)∼ω 1.5 and the core VDOS as g(ω)∼ω 2 at low frequencies [9][10][11]24]. This implies the spatial dimension n=2.5 for surfaces and n=3 for the core.…”

“…This is different from the pure 2D system. In this sense, the spatial dimension of surfaces should be between 2D and 3D [9][10][11].…”

“…(1), (7), and (8) agrees with the experimental measurements. As a matter of fact, the surface effect has been revealed to be responsible for the enhanced low-frequency vibration mode and thus the enhanced specific heat of nanocrystals at low temperatures [3][4][5][6][7][8][9][10][11][12][13][14]. With increasing the grain size in nanocrystals, the fraction of atoms at the surfaces decreases and result in a less contribution of surface phonons to the total specific heat as indicated in Eq.(1).…”

“…Although it is qualitatively successful for the nanocrystals, the Debye's T 3 law cannot be self-consistent in quantitatively explaining both the enhanced low-frequency vibrational density of states (VDOS) of nanocrystals and the variation of their specific heat with temperature [1][2][3][4][5][6][7][8]. It always gives the phonon specific heat as ∼T 3 at low temperatures while the VDOS of nanomaterials at low frequencies is a power law of frequency with an exponent below 2 due to the existence of the surfaces, interfaces, or grain boundaries [8][9][10][11][12][13][14]. The fit of the low-temperature specific heat of nanocrystals on the basis of the Debye's T 3 law results in a much smaller surface Debye temperature than the experimental data [8].…”

On the forbidden graphene's ZO (out-of-plane optic) phononic band-analog vibrational modes in fullerenes

“…[21] For example, exploiting the symmetry breaking in supported metal nanoparticles (NPs), Carles' group developed a technique to directly measure the vibrational density of states (VDOS). [22,23] Such a breakthrough [24] lead to the understanding of intricate experimental results using well established theoretical results, [21,[25][26][27][28][29] which link the VDOS as a NP vibrational fingerprint that correlates to the morphology of the system. [18,21] Contrasting these results, organic macro-molecules' spectroscopy relies only on Raman and IR spectroscopy to experimentally study them.…”