Structure of liquid Sn over a wide temperature range from neutron scattering experiments and first-principles molecular dynamics simulation: A comparison to liquid Pb

The structure of liquid Sn was studied by neutron scattering experiments in the widest temperature range that was ever performed. Though, on increasing temperature, the existence of the shoulder in the structure factor, (formula presented) becomes less clear in the change of the overall shape of the (formula presented) the structure related to this shoulder seems to be present even at 1873 K. The first-principle molecular-dynamics (FPMD) simulation was performed for the first time for liquid Sn by using the cell size of 64 particles. The calculated results well reproduced (formula presented) obtained by the neutron experiments. The angle distribution, (formula presented) was evaluated for the angle between vectors from centered atom to other two atoms in spheres of cutoff radii (formula presented) The (formula presented) shows that, with the decrease of (formula presented) from 0.4 to 0.3 nm, a rather sharp peak around 60 ° disappears and only a broad peak around 100 ° remains; the former peak may be derived from the feature of the closely packed structures and the latter one is close to the tetrahedral angle of 109 °. In addition, the coordination number, n, of liquid Sn counted within the sphere of (formula presented) is found to be 2–3 and does not change with the increase of temperature even up to 1873 K. These facts indicate that at least the fragment of the tetrahedral unit may be essentially kept even at 1873 K for liquid Sn. For comparison, the FPMD simulation was performed for the first time also for liquid Pb. No sign of the existence of the tetrahedral structure was observed for liquid Pb. Unfortunately, the self-diffusion coefficients, (formula presented) obtained from this FPMD for liquid Sn do not agree with those obtained by the microgravity experiments though the structure factors, (formula presented) are well reproduced. To remove the limitation of the small cell size of the FPMD, the classical molecular-dynamics simulations with a cell size of 2197 particles were performed by incorporating the present experimental structural information of liquid Sn. Obtained (formula presented) are in good agreement with the microgravity data.