Statistical-mechanical model in the evaluation of partial and total structure factors, atomic distribution functions, and diffusion coefficients of silver-tin liquids at various concentrations.

Abstract

Lebowitz's solution of ${\mathit{C}}_{\mathit{i}\mathit{j}}^{0}$(r) for hard-sphere mixtures with a square-well attractive tail has been applied to compute three partial structure factors ${\mathit{S}}_{11}$(k), ${\mathit{S}}_{22}$(k), and ${\mathit{S}}_{12}$(k) of molten silver-tin alloy consisting of the peculiar metal tin, which shows a conspicuous right-hand shoulder in the structure factor in the pure state. The total structure factors obtained from these partial structure factors agree excellently with experimental results. The Bhatia-Thornton structure factors ${\mathit{S}}_{\mathit{N}\mathit{N}}$(k), ${\mathit{S}}_{\mathit{C}\mathit{C}}$(k), and ${\mathit{S}}_{\mathit{N}\mathit{C}}$(k) are computed for this melt at various concentrations of Ag. In this molten Ag-Sn system it is found that the potential parameters are independent of the concentrations of Ag or Sn, in spite of the presence of the peculiar metal Sn. The compressibilities at various concentrations of Ag have been computed from the Kirkwood-Buff formula, while the diffusion coefficients have been computed from Helfand's linear-trajectory principle for mixtures. The radial distribution function g(r) is obtained by Fourier transform of S(k). The nearest-neighbor distances vary from ${\mathit{r}}^{\mathrm{max}}$=2.85 \AA{} for Ag to ${\mathit{r}}^{\mathrm{max}}$=3.15 \AA{} for Sn, while the coordination number increases rapidly from \ensuremath{\Psi}=8.8 for Sn to \ensuremath{\Psi}=12.2 for Ag. The diffusion-coefficient ratio, namely ${\mathit{D}}_{\mathrm{Ag}}$/${\mathit{D}}_{\mathrm{Sn}}$, is found to be a good constant at various concentrations of Ag, which indicates that the alloy forms a regular solution.