Atomic distribution and electronic transport properties in liquid alloys studied by X-ray diffraction

Abstract

Abstract The distribution of atoms in liquid alloys is obtained by Fourier transform of the measured interference function I(K). The density function ρ(r), thus obtained, is the weighted sum of the atomic densities ρ ij (r) which specify the number of j-type atoms per unit volume at the distance r from the i-type atom. The weighting factors depend not only on the atomic concentration ci but also on the atomic scattering factors fi of the atoms. In binary alloys three radial density functions are needed to determine the atomic distribution. In general, three interference functions I a(K), I b(K) and I ab(K) must be determined to obtain these densities. The electronic transport properties depend on these three interference functions and on the Fourier transform U a(K) and U b(K) of the pseudopotentials of the atoms. The coherently scattered intensity I e.u. coh(K) per atom in electron units can be written as: If f a≃f b, the Laue monotonic scattering c a c b(f a-f b)2 will be small and This relation can be applied to determine ρ(r)≃c aρa(r)+c bρb (r) in Ag-Sn, Hg-Tl and Al-Mg alloys. In these systems the interatomic distances r 1 and the coordination numbers were obtained as a function of concentration from the radial distribution function (RDF) 4πr 2 ρ(r). Negative deviation from a linear law (Vegard's law) was observed in Ag-Sn, and positive deviation in Hg-Tl. In Hg-In, f Hg > f In, and the density function ρ(r) is dominated by the more strongly scattering Hg atoms. The interatomic distances as obtained from the weighted RDF show a slight negative deviation from Vegard's law. The atomic distribution in Au-Sn, Al-Mg and Ag-Mg are also briefly discussed. The predicted electrical resistivity in Hg-Tl and Hg-In follow the decreasing trend at higher Tl or In concentration as observed for the measured resistivities. There is however discrepancy between the observed and calculated values of the resistivity for Hg and the dilute Hg alloys. The calculated resistivities of the Ag-Sn alloys agree with the experimental values. The thermoelectric powers were also calculated for these three alloy systems.