Atomic radius dependence of impurity diffusion coefficients in liquid Pb

This study aims to verify a prediction formula for impurity diffusion coefficients described by a proportional relationship with the atomic radius ratio and a thermodynamic factor, scaled by the self-diffusion coefficient in the solvent. The validity of this formula was investigated using effective atomic radii calculated from the partial pair distribution functions in liquid metals obtained via molecular dynamics (MD) simulations. Precise shear cell experiments employing stable density layering provided reliable reference data for Pb-Cu and Pb-Sn systems at 773 K. Molecular dynamics simulations were performed for Pb-Ag, -Cu, -Ga, and -Sn using a neural network potential at 773 K, with the number density calibrated to reproduce experimental impurity diffusion coefficients. The solute atomic radius was calculated by subtracting the solvent radius from the first peak position of the solute-solvent partial pair distribution function. The derived radii deviated from Goldschmidt radii, reflecting thermodynamic interactions in the liquid state. Specifically, the radii decreased for solutes with high affinity (Cu, Ag, and Sn) to Pb, while the radius increased for the solute exhibiting repulsive interaction (Ga). Incorporating these radii into the prediction formula yielded results in agreement with the linearity of the equation. The maximum relative error was reduced to within 2.4 %, demonstrating the effective atomic radius calculated from the partial pair distribution functions via MD simulations.