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First-principles phonon calculations along with Kohn-Sham density functionaltheory (DFT) is an essential tool to study the lattice dynamics,thermodynamical properties and phase-transitions of materials. The twofull-Heusler compounds Fe$_{2}$VAl and Fe$_{2}$TiSn are studied for latticevibration dependent properties using finite displacement method and supercellapproach. For the investigation, four density functionals viz., LDA, PBE,PBEsol and meta-GGA SCAN are employed. Using these functionals, phonondispersion, phonon density of states (DOS), partial density of states (PDOS)thermal propertis and zero-point energy are calculated at equilibrum latticeparameters under harmonic approximation. For the two compounds the Debyetemperatures are calculated from the obtained phonon DOS which are $\sim$660 Kand $\sim$540 K, respectively. The obtained results from different functionalsare compared among each other. The overall phonon energy in the dispersion isfound to be $\sim$15 meV higher in Fe$_{2}$VAl than the Fe$_{2}$TiSn compounds.For the two compounds PBE is yielding the lowest phonon frequencies while LDAor SCAN functional is giving the highest. The same pattern is observed inphonon DOS plots of two compounds. The zero-point energy calculated is thehighest from SCAN (21.04 and 16.95 J) and the lowest from PBE functionals(20.09 and 16.02 J) obeying the same trend as frequency for both compounds. Ageneral prediction of nature of lattice thermal conductivity is made based onthe velocities of acoustic phonons which is in agreement with the qualitativebehavior of reported experimental thermal conductivity of two compounds. Phononspectra obtained from PBE and SCAN have similar general features while thosefrom LDA and PBEsol have resembling features for Fe$_{2}$VAl, while this trendis not observed for the compound Fe$_{2}$TiSn.

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