Relation between Self-Diffusion and Viscosity in Dense Liquids: New Experimental Results from Electrostatic Levitation

By using the technique of electrostatic levitation, the Ni self-diffusion, density, and viscosity of liquid ${\mathrm{Zr}}_{64}{\mathrm{Ni}}_{36}$ have been measured in situ with high precision and accuracy. The inverse of the viscosity, $\eta$, measured via the oscillating drop technique, and the self-diffusion coefficient $D$, obtained from quasielastic neutron scattering experiments, exhibit the same temperature dependence over 1.5 orders of magnitude and in a broad temperature range spanning more than 800 K. It was found that $D\eta =\mathrm{const}$ for the entire temperature range, contradicting the Stokes-Einstein relation.

Figure 1

Vertical radius $R_z$ versus time $t$ measured at 1182 K during the decay of the oscillation (symbols). The solid line is a fit of a damped sine law.

Figure 2

Viscosity of ${\mathrm{Zr}}_{64}{\mathrm{Ni}}_{36}$ as a function of temperature. The solid symbols correspond to data obtained from samples with different masses and the solid line a corresponding fit of the Vogel-Fulcher-Tammann law, Eq. (3). Shown for comparison are data from Ohsaka, Chung, and Rhim [18] (open symbols) with a corresponding fit of an Arrhenius law (dashed line).

Figure 3

Diffusion constants versus inverse temperature. The circles represent $D_{\eta }$ obtained from $\eta$ via the Stokes-Einstein relation, Eq. (1). The squares correspond to the Ni self-diffusion constant $D_{\mathrm{Ni}}$, directly measured by quasielastic neutron scattering. Corresponding fits of the VFT law are shown by solid lines.

Figure 4

$D_{\mathrm{Ni}}·\eta$ versus temperature (symbols). In order to guide the eye, a linear fit to the data is also shown (solid line). The dashed and dotted lines correspond to the Stokes-Einstein relation, Eq. (1), with different choices of the hydrodynamic radius $r_{\mathrm{H}}=c{r}_{\mathrm{Ni}}$.