Microscopic damage in eutectic SnPb alloy: First-principles calculations and experiments

Abstract

This study aims to comprehensively elucidate the microscopic origins of damage in eutectic SnPb alloy through atomic-scale investigations, a crucial endeavor for enhancing the alloy’s properties and furthering the development of Pb-free solders. First-principles calculations based on density functional theory (DFT) were employed to examine the mechanical constants and defect formation energies of the Pb phase, the β-Sn phase, and potential Sn/Pb eutectic phases in the SnPb alloy. The Voigt-Reuss-Hill approximation was utilized to derive the mechanical parameters of the elastically stable structure in SnPb alloy, facilitating the prediction of its mechanical properties. The defect formation energy calculations revealed a higher difficulty in forming vacancy defects in the β-Sn phase compared to the Pb phase. This discrepancy can be attributed to the stronger interactions between Sn atoms, resulting in the formation of more stable Sn-Sn bonds, thereby impeding vacancy generation in the β-Sn phase. Furthermore, the Pb phase exhibited a tendency for Sn atoms to occupy octahedral interstitial sites, whereas in the β-Sn phase, Pb atoms tended to displace neighboring Sn atoms along the [110] orientation into adjacent interstitial sites and occupy their lattice positions. Experimental observations complemented these calculation findings, demonstrating significant Sn element presence, up to 27.22 at%, in the Pb-rich phase, with notable microvoid damage primarily concentrated within this region. This observation aligns with the conclusions drawn from first-principles calculations and unveils the microscopic origins of damage in eutectic SnPb alloys.