Effect of density functionals on the vibrational and thermodynamic properties of Fe$_{2}$VAl and Fe$_{2}$TiSn compounds

Abstract: First-principles phonon calculations along with Kohn-Sham density functional theory (DFT) is an essential tool to study the lattice dynamics, thermodynamical properties and phase-transitions of materials. The two full-Heusler compounds Fe${2}$VAl and Fe${2}$TiSn are studied for lattice vibration dependent properties using finite displacement method and supercell approach. For the investigation, four density functionals viz., LDA, PBE, PBEsol and meta-GGA SCAN are employed. Using these functionals, phonon dispersion, phonon density of states (DOS), partial density of states (PDOS) thermal propertis and zero-point energy are calculated at equilibrum lattice parameters under harmonic approximation. For the two compounds the Debye temperatures are calculated from the obtained phonon DOS which are $\sim$660 K and $\sim$540 K, respectively. The obtained results from different functionals are compared among each other. The overall phonon energy in the dispersion is found to be $\sim$15 meV higher in Fe${2}$VAl than the Fe${2}$TiSn compounds. For the two compounds PBE is yielding the lowest phonon frequencies while LDA or SCAN functional is giving the highest. The same pattern is observed in phonon DOS plots of two compounds. The zero-point energy calculated is the highest from SCAN (21.04 and 16.95 J) and the lowest from PBE functionals (20.09 and 16.02 J) obeying the same trend as frequency for both compounds. A general prediction of nature of lattice thermal conductivity is made based on the velocities of acoustic phonons which is in agreement with the qualitative behavior of reported experimental thermal conductivity of two compounds. Phonon spectra obtained from PBE and SCAN have similar general features while those from LDA and PBEsol have resembling features for Fe${2}$VAl, while this trend is not observed for the compound Fe${2}$TiSn.