Damping of the collective modes in liquid Fe

Abstract

The dynamic structure factor $S(Q,\ensuremath{\omega})$ of liquid Fe was measured at $1570\phantom{\rule{0.2em}{0ex}}\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ near the melting point of $1535\phantom{\rule{0.2em}{0ex}}\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ by using a high-resolution inelastic x-ray scattering (IXS). The IXS spectra obtained show well-defined collective excitations, which is in contrast to predictions based on macroscopic thermodynamics. From the detailed analysis using both a damped harmonic oscillator model and a generalized Langevin formalism, it was found that the value of the specific heat ratio $\ensuremath{\gamma}$ and the longitudinal kinematic viscosity $\ensuremath{\nu}$ rapidly decrease with $Q$. However, even when these $Q$ dependent values are used in the generalized hydrodynamic theory, the width of the inelastic excitations is overestimated by about 1 order of magnitude. A description of the damping of the collective excitation in liquid Fe that agrees with the data is instead obtained by using a modified version of the generalized hydrodynamic theory, in which fast viscoelastic relaxation dominates and thermal dissipation is nearly negligible. Compared to liquid alkali metals, the slow (structural) contribution to the longitudinal viscosity is much larger than the fast viscoelastic contribution for small $Q$. This might reflect the formation of a stable icosahedral intermediate-range order in liquid Fe.