First-principles study of the mechanical, dynamical and thermodynamic properties of MgAl ₂ X ₂ (X=Si and Ge)

First-principles calculations based on density functional theory (DFT) with stringent convergence parameters were employed to investigate the mechanical, dynamical and thermodynamic properties of MgAl₂X₂ (X = Si and Ge) compounds with a CaAl₂Si₂-type structure. The calculated structural parameters agree well with existing experimental and theoretical results. The important mechanical parameters such as elastic moduli, Poisson’s ratio, sound velocities, Vickers hardness, elastic anisotropy, Debye temperature, and melting temperature were derived from our calculated elastic constants, providing a comprehensive picture of the material’s mechanical behaviour. The results indicate that both MgAl₂Si₂ and MgAl₂Ge₂ are mechanically stable, possess ductility, exhibit relatively low hardness, and display elastic anisotropy. Phonon dispersion curves and phonon density of states were calculated to assess dynamical stability. The absence of imaginary frequencies in the phonon spectra confirms the dynamic stability of these compounds. In addition, the thermodynamical properties such as volume thermal expansion coefficient, heat capacity, entropy, and Gibbs free energy were evaluated within a temperature range of 0–1000 K.