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

Abstract

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, S(Q), becomes less clear in the change of the overall shape of the S(Q), the structure related to this shoulder seems to be present even at 1873 K. The first-principle molecular-dynamics ͑FPMD͒ simulation was performed for the first time for liquid Sn by using the cell size of 64 particles. The calculated results well reproduced S(Q) obtained by the neutron experiments. The angle distribution, g (3) (,r c ), was evaluated for the angle between vectors from centered atom to other two atoms in spheres of cutoff radii r c 's. The g (3) (,r c ) shows that, with the decrease of r c 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 r c ϭ0.3 nm 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, D's, obtained from this FPMD for liquid Sn do not agree with those obtained by the microgravity experiments though the structure factors, S(Q)'s, 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 D's are in good agreement with the microgravity data.

Structural, dynamic, and electronic properties of liquid tin: An ab initio molecular dynamics study

“…2 shows the calculated static structure factor, S͑q͒, at 573 K, whose main characteristics are an asymmetrical main peak located at q p Ϸ 2.26 Å −1 along with a small hump at the high-q side of the 19 at the same temperature and with the XR data of Waseda 16 at 523 K shows a very good agreement theory/experiment for the whole q range. Similar comments can be made on the results at the higher temperature, 1273 K, shown in Fig.…”

“…In this paper we extend the AIMD study to the temperature of 573 K, which, despite being closer to the triple point, was not studied by Itami et al 19 Additionally we also consider a higher temperature, 1273 K, for which experimental data for the dynamic properties are available.…”

“…Also Itami et al 19 have performed AIMD calculations for the static structure of l-Sn for some thermodynamic states within the range 773-1873 K. They used 64 particles, the norm-conserving Troullier-Martins pseudopotential and the local density approximation for the electronic exchange and correlation energies. The calculated S͑q͒ showed good agreement with experiment although the corresponding diffusion coefficients, partly because of the small number of particles used, were somewhat smaller than experiment.…”

“…On the experimental side, the S͑q͒ of l-Sn has been determined, at several temperatures within the range of 505-1873 K, by means of x-ray 16 ͑XR͒ and neutron [17][18][19] ͑NS͒ scattering experiments. Within that temperature range, the measured S͑q͒'s showed an asymmetrical main peak at q p Ϸ 2.2 Å −1 along with a hump at q Ϸ 2.8 Å −1 .…”

“…11 Liquid Sn has attracted an important amount of experimental and theoretical work. Measurements have been performed for several thermodynamic magnitudes, [12][13][14][15] as well as for the static [16][17][18][19][20] and dynamic structure factors. 21,22 On the theoretical side a number of studies, using either semiempirical 23 or more fundamental 6,24 approaches have addressed a variety of structural and thermodynamical magnitudes.…”