Static and dynamic structure and the atomic dynamics of liquid Ge from first-principles molecular-dynamics simulations

Abstract

The first-principles molecular-dynamics simulation was performed for liquid Ge at $1253\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ by using two kinds of simulation cells: The cubic cell of 64 atoms and the rectangular parallelepiped one of 128 atoms. The rectangular parallelepiped cell of 128 atoms was adopted to obtain the dynamic structure factor of liquid Ge in the small wave number region. The long simulation time was adopted, i.e., $66\phantom{\rule{0.3em}{0ex}}\mathrm{ps}$ for the cubic cell and $75\phantom{\rule{0.3em}{0ex}}\mathrm{ps}$ for the rectangular parallelepiped one. The present first-principles molecular-dynamics simulation reproduces well the experimental static structure factor and radial distribution function. A broad peak around $100\ifmmode^\circ\else\textdegree\fi{}$ in the obtained bond angle distribution function implies the existence of the tetrahedral atomic unit in liquid Ge. The self-diffusion coefficient for the rectangular parallelepiped cell is 20% larger than that of the cubic one. The obtained dynamic structure factor agrees well with the experimental one obtained by the inelastic x-ray scattering experiment [Hosokawa et al., Phys. Rev. B 63, 134205 (2001)], which shows the ``de Gennes narrowing'' of the main peak and the existence of the side peaks. These side peaks represent a longitudinal vibrational motion, which was also supported by the subsidiary peak around $30\phantom{\rule{0.3em}{0ex}}{\mathrm{ps}}^{\ensuremath{-}1}$ in the spectral density of the velocity autocorrelation function. The gradient of the dispersion relation in the present simulation agrees well with the experimental sound velocity. This ``no positive dispersion'' accords well with the inelastic x-ray scattering experiment of Hosokawa et al. The reason for this ``no positive dispersion'' for liquid Ge is discussed in particular concern with its low kinematic viscosity. Though the velocity autocorrelation function itself does not show a cage effect, a microscopic cage effect can be found by the detailed analysis for the trace and environment of the single atomic motion. The atomic movement as a group of 3--5 atoms seems to be present in liquid Ge in addition to individual atomic motions. The covalent bond seems to be also present at least instantaneously in liquid Ge.