First-principles analysis of structural stability, mechanical anisotropy, and thermophysical and electronic properties of Cu–Pd intermetallic compounds: a comparative study of CuPd, CuPd3, Cu3Pd, and Cu4Pd

Abstract

This study employs density functional theory to examine the intermetallic compounds CuPd, CuPd₃, Cu₃Pd, and Cu₄Pd for use in advanced microelectronic packaging. Static elastic-constant calculations verify mechanical stability, and phonon dispersions along high-symmetry directions display no imaginary frequencies, confirming dynamical stability. All four phases are metallic according to band structures and density-of-states analyses. Among the series, Cu₃Pd delivers the greatest shear modulus at 55 GPa and the highest average Vickers hardness at 5.22 GPa, a consequence of its balanced tetragonal bonding network. Cu₄Pd is the most compliant, exhibiting the largest ductility index with K over G equal to 3.35 but the lowest hardness at 3.81 GPa. Fracture-toughness predictions indicate that CuPd₃ reaches the maximum K_IC at 1.47 MPa m^1/2, whereas Cu₄Pd records the minimum at 1.23 MPa m^1/2, reflecting differences in bonding character and symmetry. Universal, equivalent Zener and log Euclidean anisotropy indices identify CuPd as strongly anisotropic and Cu₃Pd as nearly isotropic with A^U equal to 0.86. Thermophysical analysis shows Cu₃Pd possessing the highest Debye temperature at 338 K, the greatest lattice thermal conductivity under ambient conditions at 6.86 W m⁻¹ K⁻¹ and the lowest thermal-expansion coefficient at 29.1 × 10⁻⁶ K⁻¹, all consistent with stiff bonds and limited phonon scattering. Cu₄Pd displays pronounced anharmonicity, with the largest expansion at 36.4 × 10⁻⁶ K⁻¹ and the weakest conductivity at 1.38 W m⁻¹ K⁻¹. Calculated melting temperatures span 1178 to 1285 K and track with bulk-modulus trends. The brittleness index highlights CuPd as the most damage tolerant, whereas Cu₃Pd is the most brittle. External hydrostatic pressure up to 15 GPa markedly enhances bulk and shear moduli, raises Debye temperatures and boosts lattice thermal conductivity. For example, the conductivity of Cu₃Pd increases to 9.78 W m⁻¹ K⁻¹, and elastic anisotropy in CuPd is slightly reduced. These findings indicate that Cu₃Pd is well suited for high-temperature high-power assemblies that demand mechanical rigidity and thermal stability, whereas Cu₄Pd offers superior compliance for joints that must accommodate large thermal strains. The results provide a comprehensive foundation for tailoring Cu–Pd intermetallics for next generation electronic packaging.