Atomic order and interionic pair potentials in Cu–Sn liquid alloys

Abstract

A statistical mechanical theory based on compound formation (CF) model has been used to investigate the energetics of the formation of intermetallic compounds, Cu 3Sn in the melt of Cu–Sn liquid alloys through the study of concentration dependence of various thermodynamic as well as microscopic functions such as excess free energy of mixing ( G M xs ) , heat of mixing ( H M), entropy of mixing ( S M), concentration fluctuations in the long wavelength limit ( S cc(0)) and chemical short range order parameter ( α 1). Besides, the interionic interactions between component atoms (Cu and Sn) of the alloy have been understood through the study of interionic pair potentials ( ϕ i− j ( r)), calculated from pseudopotential theory in the light of CF model. Our theoretical investigation not only reproduces the concentration dependence of G M xs , H M and S M but also suggests the existence of compounds, Cu 3Sn in Cu–Sn liquid alloys at C Cu = 0.75. The maximum deviation of S cc(0) from ideal values [ S cc(0) − S cc(0, id)] and minimum negative value of α 1 around C Cu = 0.75 substantiates above findings. Our study of ϕ i− j ( r) suggests that the effective interaction between Cu–Cu atoms decreases on alloying with Sn atoms. ϕ Cu–Cu( r) for CF Cu 0.75Sn 0.25 alloy lies in between the pure state (Cu) and Cu 0.5Sn 0.5 alloy whereas the effective interaction between Sn–Sn atoms increases in the order, pure < Cu 0.5Sn 0.5 < Cu 0.75Sn 0.25; being maximum in CF alloys. The computed values of S M from pseudopotential theory are positive at all concentrations but the agreement between theory and the experiment is not satisfactory. This might be happening due to parameterization of σ 3 and ψ comp.