Viscous flow and self-diffusion in densely and loosely packed metallic melts

The Ni self-diffusion, density, and viscosity of the densely packed liquid ${\mathrm{Ni}}_{66.7}{\mathrm{B}}_{33.3}$ and the more loosely packed liquid ${\mathrm{Ge}}_{66.7}{\mathrm{Ni}}_{33.3}$ were measured with high accuracy using different experimental methods. The viscosity $\eta$ was obtained using the oscillating-drop method combined with electrostatic levitation and the oscillating-cup technique in a rheometer. The Ni self-diffusion coefficient $D_{Ni}$ was obtained from quasielastic neutron scattering experiments. For ${\mathrm{Ni}}_{66.7}{\mathrm{B}}_{33.3}$, it was found that the activation energies for self-diffusion and viscous flow, $E_D$ and $E_{\eta }$, respectively, are almost equal. Hence, the product of the viscosity $\eta$ and self-diffusion coefficient $D$ is fairly constant over the entire temperature range measured, spanning almost 800 K. In contrast, for ${\mathrm{Ge}}_{66.7}{\mathrm{Ni}}_{33.3}, D\eta$ increases with increasing temperature, indicating that the dynamics in liquid ${\mathrm{Ge}}_{66.7}{\mathrm{Ni}}_{33.3}$ shows better agreement with an activated process. This temperature dependence is in line with the Stokes-Einstein relation.

Figure 1

Change in the vertical radius $r_z\left(t\right)$ normalized to the radius of the damped, spherical sample ${\mathrm{r}}_0$ versus time $t$ at 1458 K (black symbols). The red solid line is a fit of the data according to a damped sinus oscillation [12].

Figure 2

Dynamic structure factor $S(q,\omega )$ of liquid ${\mathrm{Ni}}_{66.7}{\mathrm{B}}_{33.3}$ at 1593 K and $q$ values of 0.5 and 1.1 ${\AA }^{-1}$. Solid lines are fits with a Lorentzian function convoluted with the energy resolution function. Inset: Inverse relaxation time $1/\tau$ versus $q^2$. The diffusion coefficient is then derived according to the slope $D=1/\tau q^2$.

Figure 3

Top: Density of ${\mathrm{Ni}}_{66.7}{\mathrm{B}}_{33.3}$ (red squares), ${\mathrm{Ge}}_{66.7}{\mathrm{Ni}}_{33.3}$ (purple triangles), and ${\mathrm{Zr}}_{64}{\mathrm{Ni}}_{36}$ [12] (blue diamonds) in dependency of temperature measured by using ESL. Bottom: Packing fraction of ${\mathrm{Ni}}_{66.7}{\mathrm{B}}_{33.3}$ (red squares), ${\mathrm{Ge}}_{66.7}{\mathrm{Ni}}_{33.3}$ (purple triangles), and ${\mathrm{Zr}}_{64}{\mathrm{Ni}}_{36}$ [12] (blue diamonds). The solid lines are linear fits.

Figure 4

Top: Viscosity of ${\mathrm{Ni}}_{66.7}{\mathrm{B}}_{33.3}$ versus temperature. Blue diamonds represent $\eta$ measured with the OCM in the rheometer. The red squares correspond to data measured for different sample masses using the ODM in combination with ESL. Solid red squares show data obtained using a sample mass of 30 mg; open red squares represent data for a 50-mg sample. Bottom: Ni self-diffusion coefficient of ${\mathrm{Ni}}_{66.7}{\mathrm{B}}_{33.3}$ versus temperature. Red squares show data obtained using ESL; blue diamonds show data using the Nb electrical resistance furnace.

Figure 5

Top: Ni self-diffusion coefficients of ${\mathrm{Ni}}_{66.7}{\mathrm{B}}_{33.3}$ (red squares) and ${\mathrm{Ge}}_{66.7}{\mathrm{Ni}}_{33.3}$ (purple triangles) as a function of temperature in comparison with the Ni self-diffusion coefficient of ${\mathrm{Zr}}_{64}{\mathrm{Ni}}_{36}$ (blue diamonds) [12]. Bottom: Viscosity of ${\mathrm{Ni}}_{66.7}{\mathrm{B}}_{33.3}$ (red squares), ${\mathrm{Ge}}_{66.7}{\mathrm{Ni}}_{33.3}$ (purple triangles), and ${\mathrm{Zr}}_{64}{\mathrm{Ni}}_{36}$ [12] (blue diamonds). The blue and red solid lines are corresponding fits of the power law; the purple solid line and the red dashed line are fits of Arrhenius's law.

Figure 6

$D_{Ni}\eta$ as a function of temperature. Red squares show the data for ${\mathrm{Ni}}_{66.7}{\mathrm{B}}_{33.3}$, and purple triangles show data for ${\mathrm{Ge}}_{66.7}{\mathrm{Ni}}_{33.3}$. In comparison $D_{Ni}\eta$ of ${\mathrm{Zr}}_{64}{\mathrm{Ni}}_{36}$ is shown by blue diamonds [12]. The SER is shown as a dashed line with different values of $c$ [see Eq. (1)], where the covalent radius of Ni is chosen as the hydrodynamic radius $r_{Ni}=r_H=1.15$ Å [43]. Solid lines are guides to the eye.