Ab initio Calculations of Phonon Dispersion Relations in Aluminium

Abstract

A direct method and ab initio force constants were used to calculate phonon dispersion curves and phonon density in Al. The force constants were determined from the Hellmann-Feynman forces induced by the displacement of an atom in the 2 x 2 x 2 fcc crystallographic supercell. This size of the supercell gives exact phonon frequencies at Γ, X, L, W points of the Brillouin zone. The calculated phonon dispersion curves are in good agreement with the experimental data.PACS numbers: 63.20.-e, 71.15.Nc .The vibrational properties determine a wide range of macroscopic behaviour of solids, e.g. specific heat and the sound velocity. In addition, very low-frequency modes can be associated with phase transformations, while imaginary frequencies provide an indication that the calculated structure is not the most stable. Finally, the phonon spectrum enables a good approximation to free energies to be made via the quasiharmonic approximation. In view of these, derivation of phonons from αb initio calculations has become a very important topic [1]. Generally the αb initio calculations of phonon frequencies fall into two methods: the linear response and the direct approach. Works still appear in the literature, in which various combinations of materials/methods/approximations and codes are tested. Aluminium is often considered to be a representative free-electron like metal and in recent years several calculations of phonons spectra for this material have been published. For example, the different approaches based on the phenomenological and the pseudopotential force constants have been compared in Ref. [2]. The αb initio cohesive energies were used to evaluate the phonon dispersion relations with and without three-body interaction [3]. Calculations based on the linear response theory which

Reconstruction of the phonon relaxation times using solutions of the Boltzmann transport equation

“…Our goal is to obtain an accurate and reliable approximation to the function τ ω from the experimental measurements, with the latter typically in the form of a temperature (relaxation) profile. Reconstruction of the free path distribution follows from relationship (5); in other words, the group velocities v ω are assumed known, since they can be reliably calculated either experimentally [19][20][21][22] by means of Raman spectroscopy, x-ray scattering, etc, or theoretically [23][24][25][26] using methods such as density functional theory (DFT). We propose the use of an optimization framework in which the experimental measurements provide targets that need to be reproduced by the BTE solution; in other words, τ ω is determined as the function that optimizes (minimizes) the discrepancy between the experimental result and the BTE prediction for the same quantity.…”

“…Our goal is to obtain an accurate and reliable approximation to the function τ ω from the experimental measurements, with the latter typically in the form of a temperature (relaxation) profile. Reconstruction of the free path distribution follows from relationship (5); in other words, the group velocities v ω are assumed known, since they can be reliably calculated either experimentally [19][20][21][22] by means of Raman spectroscopy, x-ray scattering, etc, or theoretically [23][24][25][26] using methods such as density functional theory (DFT).…”

Role of the electron–phonon coupling in tuning the thermal boundary conductance at metal-dielectric interfaces by inserting ultrathin metal interlayers

“…Interlayer Substrate Al Ni α-Al 2 O 3 θ D = 428 K [51] θ D = 450 K [51] θ D = 1035 K [53] ν L = 9.6 THz [52] ν L = 9.1 THz [29] ν L = 10 THz [31] ν T = 5.7 THz [52] ν T = 4.5 THz [29] ν T = 6.9 THz [31] g = 0.24 × 10 18 W (m −3 •K −1 ) [51] g = 0.36 × 10 18 W (m −3 •K −1 ) [51] ν optical = 26 THz [31] Au Ta Si θ D = 165 K [51] θ D = 225 K [55] θ D = 645 K [57] ν L = 4.6 THz [54] ν L = 5.5 THz [28] ν L = 12 THz [30] ν T = 2.8 THz [54] ν T = 2.6 THz, 3.7 THz [28] ν T = 4 THz [30] g = 0.023 × 10 18 W (m −3 •K −1 ) [51] g = 3.1 × 10 18 W (m −3 •K −1 ) [56] ν optical = 15.5 THz [30] Cr θ D = 630 K [38] ν L = 10 THz [28] ν T = 6 THz, 7.7 THz [28] g = 0.42 × 10 18 W (m −3 •K −1 ) [58]…”

Thermodynamics of Fcc Al Crystal from First Principles - Performance of Local Density and Generalized Gradient Approximations

“…One may also note the general tendency: the bigger is the phonon energy the bigger is the decrease rate. [16] for the XC functional, calculated with the use of the ABINIT code [13]; dashed line -direct method result [22].…”