Phase Stability, Phase Transformations, and Elastic Properties of Cu₆Sn₅: Ab initio Calculations and Experimental Results

Among many Sn-based intermetallics, Cu₆Sn₅(η and η′) is ubiquitous in modern solder interconnects. Using the published structural models of η and η′ and also related structures, the total energies and equilibrium cohesive properties are calculated from first-principles employing electronic density-functional theory, ultrasoft pseudopotentials, and both the local density approximation (LDA) and the generalized gradient approximation (GGA) for the exchange-correlation energy. The accuracy of our calculations is assessed through comparisons between theoretical results and experimental measurements for lattice parameters, elastic properties, and formation and transformation energies. The ambient-temperature experimental lattice constants of η and η′ are found to lie between the LDA and GGA level calculated zero-temperature lattice constants. The Wyckoff positions in the structural models of η and η′ agree very well with the ab initio results. The calculated formation energy of η′ lies between −3.2 and −4.0 kJ/mol, which is more positive by about 3 to 4 kJ/mol compared to reported experimental data obtained by solution calorimetry. Our systematic differential scanning calorimetry (DSC) experiments show that the η′ → η transformation enthalpy is 438 ± 18 J/mol, which is about 66% higher than the literature value. In view of our DSC results on heating and cooling, the nature of η′ → η and η → η′ is discussed. Our experimental bulk modulus of η and η′, and the heat of η′ → η transformation agree very well with the ab initio total energy calculations at the GGA level. Based on these results, we conclude that other isotropic elastic moduli (Young’s modulus, shear, and Poissons ratio) of η and η′ phases measured by pulse-echo technique are representative of their actual properties. The scatter in experimental elastic constants in the literature may be attributed to various factors, such as the measurement technique (pulse-echo versus nanoindentation), type of specimen (bulk, Cu₆Sn₅-layer in diffusion couple, thin-film), and anisotropy effects (particularly in Cu₆Sn₅-layer in diffusion couples).