Pair potential in liquid lead

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Abstract
An effective pair interionic potential for liquid lead has been found using the molecular-dynamics (MD) simulation method. The assumed form of the potential includes long-range soft repulsion as well as steep repulsive and oscillating ‘‘Friedel’’ components. An extensive simulation using 16 384 particles has been carried out in order to fit the assumed parametrized form of the pair potential to the static structure factor of liquid lead measured by neutron scattering close to the melting point. The fit covers the first three peaks in S(Q), as well as the small-Q region, including the long-wavelength limit. The use of a relatively large number of particles avoids the systematic errors typical of smaller-scale simulations and allows us to obtain a quantitatively reliable relationship between the pair potential and S(Q). The calculated diffusion coefficient is in good agreement with the experimental value. Simulation of liquid lead at 1170 K and at the corresponding density using the same pair potential also gave good agreement with the experimental data on S(Q) and the self-diffusion at that temperature. This fact indicates that the interionic interaction in lead may be independent of temperature and density within the liquid domain. The potential for liquid lead derived earlier from the fourth moment of S(Q,ω) was also tested in an MD simulation and proved to be inadequate. A revised version of this potential obtained after removing constraints has a shape similar to that reported in this paper. The self-diffusion coefficient was found to be highly sensitive to the potential’s shape.