First-principles calculations to study the effect of pressure on the structural and physical properties of M ₃ PbC ₂ (M =  <b>Zr, Hf)</b>

MAX-phase materials are important in various fields as pressure modifies their microstructure and consequently influences their properties. This study employs DFT simulations to investigate the structural, electrical, mechanical, and optical properties of Pb-based MAX-phase M 3 PbC 2 ([Formula: see text] Zr, Hf) under varying pressures. The simulations reveal greater stiffness along the c-axis compared to the a-axis. Thermodynamic stability is indicated by the negative enthalpy of formation across the applied pressure range. Although the band structure changes under pressure, the compounds retain their metallic nature. The elastic constants satisfy the criteria for mechanical stability. Regarding anisotropy, Hf 3 PbC 2 exhibits greater resistance to deformation than Zr 3 PbC 2 . Hf 3 PbC 2 transitions from a brittle to a ductile state at a pressure of 25 GPa. The optical properties of M 3 PbC 2 suggest its potential use as an alternative material in reflective coatings.