Vibrations of Au₁₃and FeAu₁₂nanoparticles and the limits of the Debye temperature concept

Abstract

We present first-principles calculations of the vibrational density of states (VDOS), the specific heat and the mean-squared displacement of the five lowest-energy isomers of Au(13) and of two low-energy FeAu(12) nanoparticles. We find that the vibrational contributions to the Helmholtz energy do not affect the energy ordering of the isomers. As expected, for nanoparticles the vibrational density of states differs dramatically from the function proposed by the Debye model. We demonstrate that, for the nanoclusters we studied, the alternative calculations of the 'Debye temperature' yield significantly inconsistent results. We conclude that T(D) obtained from a particular thermodynamic property is neither applicable for deriving conclusions about other thermodynamic properties nor correlated with atomic bond strengths. Instead, in order to describe the temperature dependence of a nanoparticle's mean-squared displacement and its specific-heat capacity, what is necessary is its discrete phonon spectrum.

Neutron diffraction measurements and first-principles study of thermal motion of atoms in selectMn+1AXnand binaryM

“…The DFT calculations were performed using the projector-augmented wave (PAW) 23 method, as implemented in the VASP code. [21][22] The exchange-correlation function used was the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA). 24 The plane-wave cutoff was set to 500 eV, and the total energy was converged to 10 -8 eV with a Γ-centered k-point grid of 6x6x4.…”

“…Previously, first principles phonon calculations have been used to predict the thermal atomic displacements in other systems including SiO 2 , [14][15] MgB 2 , 16 skutterdites, [17][18] CoO, 19 NaAlH 4, 20 and gold nanoparticles. 21 To our knowledge, the mean-squared atomic displacements have not been calculated from first principles phonon calculations for any carbides or nitrides.…”

Vibrational properties and stability of FePt nanoalloys

“…Dynamical properties of nanoobjects are significantly modified comparing to bulk systems due to reduced dimensionality and surface effects [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. The theoretical studies on vibrational properties of isolated NPs, performed with the empirical potentials [10][11][12][13] and density functional theory (DFT) [18,19], demonstrated the pronounced changes in the vibrational density of states (VDOS) comparing to bulk systems.…”

“…Dynamical properties of nanoobjects are significantly modified comparing to bulk systems due to reduced dimensionality and surface effects [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. The theoretical studies on vibrational properties of isolated NPs, performed with the empirical potentials [10][11][12][13] and density functional theory (DFT) [18,19], demonstrated the pronounced changes in the vibrational density of states (VDOS) comparing to bulk systems. The increase of the VDOS at low energies is caused mainly by the surface atoms with the reduced coordination number, while the shift of the energies to higher values above the bulk cutoff is induced by the inner atoms with shorter interatomic distances [10,11].…”

“…The increase of the VDOS at low energies is caused mainly by the surface atoms with the reduced coordination number, while the shift of the energies to higher values above the bulk cutoff is induced by the inner atoms with shorter interatomic distances [10,11]. Vibrational properties of a NP depend substantially on its size and geometry [19], as well as on the presence of adsorbate atoms [18]. In nanoalloys, dynamics of atoms depends additionally on local environment and atomic coordination [23].…”