Ab initio investigation of the elastic properties of bismuth-based alloys

Density functional theory has been used to investigate the elastic properties of various Bi-based alloy materials as potential replacements of lead-based solders. We compare calculated quantities which can be used to determine the effectiveness of our proposed replacements, such as the bulk (K), shear (G), and Young's (E) moduli. We also computed the Pugh ratio (=K/G), a quantity that is used to estimate the ductility of a solid, for each of the alloys. The effect of spin-orbit coupling on these materials has also been investigated. By analyzing the changes in charge density as Bi is substituted, we link the predicted changes in ductility in these materials to atomistic descriptors; specifically, delocalization of the charge density is known to be a signature of increased ductility, whereas more localized charge density is typically associated with brittleness. Through Bader charge analysis we provide quantitative insight into the uniformity of charge distribution and how this alters the ductility of these alloys. By using density functional theory to calculate the elastic properties of different Bi₁-ₗZₗ alloys (Z = Sb, Te, In, Sn; 04pt{0ex}x4pt{0ex}1), we correlate changes in ductility and corresponding changes in the electronic structure of a material. We have found that low concentrations of Sn and Te, substituted into the hexagonal crystal structure of Bi, induce significant increases in ductility.