Vibrational and cohesive properties in 4d and 5d transition metals: systematics and interrelations.

Motivated by the striking regularities between experimental quantities related to the vibrational properties of the 4d and 5d series early noted by Fernández Guillermet and Grimvall [Phys. Rev. B, 1989, 40(3), 1521], a systematic theoretical study has been made of the vibrational density of states (VDOS) of Ag, Au, Pd, Pt, Rh, Ir, Ru, Os, Tc, Re, Mo, W, Nb, Ta, Zr and Hf. The frequency moments ωD(j), expressed as Debye temperatures θD(j) for 0 ≤ j ≤ 100 were evaluated. Various remarkable correlations between these quantities are reported, which have their roots in the relations of homology between the VDOS. From the θD(j), several k(j) quantities with dimensions of force constants are calculated. For the elements 4d and 5d transition series, these quantities are shown to be strongly correlated, with independence of the value of j. It is suggested that the various interrelations between the θD(j) and k(j) parameters arrived at in the current work have their roots in the homologous variations of the cohesion forces across the 4d and 5d transition series, as revealed by thermophysical properties such as the bulk modulus and the cohesive energy.

Systematics of vibrational properties of Au nanoparticles: a molecular dynamics approach.

This paper reports the results of a Molecular Dynamics (MD) study of the vibrational properties of spherical Au nanoparticles with a number of atoms (N) varying in the range 1985 ≤ N ≤ 53 117. The LAMMPS code is adopted to calculate the vibrational density of states (VDOS), represented by D(ω) versus ω function. Two interatomic potentials, an EAM and a MEAM are used. The first part of the work is devoted to the D(ω) versus ω relation of macroscopic Au, which is obtained by MD simulations as well as by a density-functional-theory calculation using the Vienna Ab Initio Simulation Package and the PHONOPY code. Additional experimental and theoretical results on the VDOS of Au are used to compare with the present results. Next, the effect of changing N and the interatomic potential upon the VDOS of the nanoparticles is established. In particular, the effect of the surface vibrational modes upon the results is discussed. Various moment frequency parameters ωD(j) expressing averages of the D(ω) versus ω function are evaluated, and expressed as Debye temperatures θD(j), using standard relations. Attending to the relevance of these quantities in the description of the thermodynamic properties of macroscopic solids, values of θD(j) corresponding to j = -3, 0, 1, 2 and 4 are reported. On this basis, a picture of the systematic effects of changing N upon the θD(j) values is established both for the EAM and the MEAM potential. In addition, various interrelations between the θD(j) values for nanoparticles are presented. In particular, remarkably simple correlations are reported between the average quantities θD(0), θD(1), θD(2) and θD(4) and θD(-3) i.e., the Debye temperature which accounts for the low-frequency part of the spectrum. Finally, a discussion is reported of the relation between θD(-3) and other properties that are usually adopted as a measure of cohesion in macroscopic solids. To this aim, new correlations involving the nanoscopic counterpart of the temperature of fusion of macroscopic elements as well as the cohesive energy for Au nanoparticles are presented.

Phenomenology of the heating, melting and diffusion processes in Au nanoparticles.

The paper reports the results of a molecular dynamics study of the heating and melting process of nanoparticles with 1985 to 84 703 atoms. Building on a previous study by the present authors [Bertoldi, et al., J. Phys. Chem. Solids, 2017, 111, 286-293] involving the energy versus temperature, the Lindemann index and the radial distribution function, the current work relies on the mean-square displacement, the Lindemann ratio and the simulated snapshots to characterize four regions in the process of heating-to-melting. A general pattern of the atomic configuration evolution upon heating and a systematics of the transition temperatures between the various identified steps, is proposed. In addition, the most significant, so-called "melting step" in this process is analyzed in terms of the quasi-chemical approach proposed by Bertoldi et al., which treats this step by invoking a dynamic equilibrium of the type Au (LEA-SPL) ⇌ Au (HEA-LPL) involving low-energy atoms (LEA) and high-energy atoms (HEA) forming the solid phase-like (SPL) and the liquid phase-like (LPL) states of the system, respectively. The "melting step" is characterized by evaluating the equal-Gibbs energy temperature, i.e., the "T0 temperature", previously introduced by the current authors, which is the thermodynamic counterpart of the temperature of fusion of macroscopic elemental solids. The diffusion coefficients at T0 are determined, and their spatial and temperature dependence is discussed. In particular, the activation energy for the atom movements in the HEA-LPL/LEA-SPL mixture at T0 is reported. The consistency between the current phenomenological picture and microscopic interpretation of the thermodynamic, kinetic and atomic configuration information obtained is highlighted.