A comprehensive first-principles analysis of the dynamical, structural, mechanical, electronic and thermodynamic properties of full-Heusler alloys X (2)MgSi X = Ru, Rh, Pd.

CONTEXT: Full-Heusler alloys X₂MgSi X = Ru, Rh, Pd crystallizing in the cubic L2₁ structure have been investigated via first-principles density functional theory to fill the knowledge gap regarding their mechanical stability, electronic structure, lattice dynamics, and thermodynamic behavior. The optimized lattice constants are 5.986 Å (Ru₂MgSi), 5.997 Å (Rh₂MgSi), and 6.167 Å (Pd₂MgSi), in good agreement with available theoretical data. The negative formation enthalpies (-0.432, -0.682, and -0.527 eV/atom, respectively) confirm thermodynamic stability and experimental synthesizability. The electronic band structures and density of states reveal metallic characteristics for all three compounds, with the highest density of states at the Fermi level (3.389 states/eV·cell) obtained for Ru₂MgSi. The calculated elastic constants satisfy the Born-Huang stability criteria, and the derived polycrystalline moduli decrease from 198.4 GPa (Ru₂MgSi) to 135.4 GPa (Pd₂MgSi). Pugh's ratio (B/G > 1.75), positive Cauchy pressure, and Poisson's ratio (0.31-0.42) consistently indicate ductile behavior, with Pd₂MgSi exhibiting the highest ductility. The phonon dispersion curves display no imaginary frequencies, confirming the dynamic stability; distinct phonon bandgaps arise from the large mass differences between the constituent atoms. The thermodynamic properties obtained via the quasiharmonic Debye model yield Debye temperatures of 457.6 K (Ru₂MgSi), 392.7 K (Rh₂MgSi), and 223.2 K (Pd₂MgSi), correlating with the trend in elastic stiffness. METHODS: This research employs ab initio density functional theory methods implemented within the Quantum ESPRESSO package to explore the structural, elastic, electronic, thermodynamic, and phonon characteristics of XMgSi X = Ru, Rh, and Pd full-Heusler compounds with the generalized gradient approximation (GGA-PBE) and projector augmented wave (PAW) pseudopotentials. Elastic constants were obtained from the energy-strain method, phonon dispersions from density functional perturbation theory (DFPT), and thermodynamic properties from the quasi-harmonic Debye model. A variety of material properties were accurately identified via first-principles computational methods. Through the quasiharmonic approximation, the thermodynamic behavior of the compounds was examined, revealing for the first time the temperature-dependent variations in internal energy, free energy, specific heat, and entropy.