Elasticity and stability of GdAl₂ under pressure and temperature investigated using DFT+AI

The cubic ferromagnetic Laves phase intermetallic compound [Formula: see text] is a promising candidate for aerospace, defense, and advanced engineering applications due to its thermal stability and reliable elastic properties under pressure. However, two key gaps persist: discrepancies between theoretical and experimental elastic constants, and a lack of systematic pressure-dependent investigations. This study addresses these gaps, highlighting [Formula: see text]'s exceptional thermal stability, with melting temperatures rising linearly under pressure, its near-isotropic compressive behavior, and mild anisotropy in shear and Young's moduli. Using density functional theory, elasticity theory, and AI-driven neural networks, we systematically analyzed the elasticity and stability of the system under pressure and temperature. A rigorous energy-based methodology resolves the first gap, setting a benchmark for cubic systems. To address the second gap, we analyzed mechanical stability up to 20 GPa via the Born stability criteria, finding consistent increases in elastic constants, bulk modulus, and Young's modulus under compression. Phonon dispersion and density of states analyses confirm dynamic stability and reveal that low-frequency acoustic modes dominated by Gd atoms drive elastic behavior, reflecting spin-dominated mechanics. Poisson's ratio shows mild anisotropy, while ductility assessments reaffirm the material's brittle nature, consistent with Laves phase intermetallics. By integrating advanced computational methods and AI predictions, this work resolves theoretical-experimental discrepancies, establishes a framework for spin-dominated systems, and positions [Formula: see text] as a benchmark for spin-lattice interactions and anisotropy in next-generation engineering under pressure.