Atomic structure of small Si clusters and thermodynamic properties of metals

Abstract

We investigate the atomic structure of Si$_n$ (n = 9 - 14) clusters using the first-principles pseudopotential method within the local-density functional approximation (LDA). The equilibrium geometries of small clusters with n ≤ 12 are found to have a tendency to form capped prismatic structures. For n = 13, we find a surface-like metallic compact structure which is derived from a capped icosahedron and competes with a stable trigonal prism, while this structure is most stable for n = 14. These results are compatible with the observed stability of Si$_{13}$ and Si$_{14}$ against chemical reactions with simple molecules, as compared to nearby Sin clusters. The effect of electron-electron correlations on the energetics of isomers at n = 13 is examined through variational quantum Monte Carlo calculations, and the LDA energy ordering remains unchanged, consistent with previous diffusion quantum Monte Carlo calculations. We investigate the Hugoniot melting point of Al using a molecular-dynamics approach based on an embedded-atom method. We calculate the Gibbs free energies of the crystalline and liquid phases as a function of pressure and temperature using the coupling-constant integration method and obtain the melting curve up to 1.6 Mbar, in good agreement with experiments. We also examine the melting properties near zero pressure. The Hugoniot equation of states (EOS) up to 1.8 Mbar is obtained from the Rankine-Hugoniot relation and the isotherms determined for different temperatures. Comparing the melting curve with the Hugoniot EOS``s for the solid and liquid phases, the Hugoniot melting is found to begin at 1.2 Mbar and to end at 1.4 Mbar, consistent with shock-wave data. We investigate the shock melting of transition metals using a molecular-dynamics approach based on an embedded-atom method. Cu, Pd, and Pt are chosen as prototypes for transition metals in face-centered cubic lattice. We calculate the Gibbs free energies of the crystalline and liquid phases...