The first-principles molecular-dynamics simulation was performed for liquid Ge at $1253\mathrm{K}$ 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., $66\mathrm{ps}$ for the cubic cell and $75\mathrm{ps}$ 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 $100°$ 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 $30{\mathrm{ps}}^{-1}$ 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.

A new kind of suspension liquid was developed by dispersing Ti nanoparticles (10 nm) in liquid Na, which was then determined by TEM (transmission electron microscopy) analysis. The volume fraction was estimated to be 0.0088 from the analyzed Ti concentration (2 at. %) and the densities of Ti and Na. This suspension liquid, Liquid Sodium containing nanoparticles of titanium (LSnanop), shows, despite only a small addition of Ti nanoparticles, many striking features, namely a negative deviation of 3.9% from the ideal solution for the atomic volume, an increase of 17% in surface tension, a decrease of 11% for the reaction heat to water, and the suppression of chemical reactivity to water and oxygen. The decrease in reaction heat to water seems to be derived from the existence of excess cohesive energy of LSnanop. The excess cohesive energy was discussed based on simple theoretical analyses, with particular emphasis on the screening effect. The suppression of reactivity is discussed with the relation to the decrease of heat of reaction to water or the excess cohesive energy, surface tension, the action as a plug of Ti oxide, negative adsorption on the surface of LSnanop, and percolation.