Origin of the Stokes–Einstein deviation in liquid Al–Si

ABSTRACT

One goal in materials simulation is finding relationships between atomic scale and continuum properties. The Stokes–Einstein–Sutherland (SES) equation relates diffusion and viscosity in liquids through the effective diameter d, which is frequently observed to be constant with the ratio $T/\left(D\eta \right)$ where T is the temperature, D is the diffusion coefficient, and η is the viscosity. The SES has a practical use in estimating diffusion from viscosity or vice versa as they can be difficult to measure experimentally. The constant effective diameter observed in the SES holds for many liquids within a temperature range, but at low temperatures, deviations where d is not constant have been observed. This work investigates SES in liquid Al–Si using molecular dynamics. We analyze the local order using Voronoi polyhedrons and agglomerative clustering. Clustering methods from machine learning allowed us to analyze the large amount of data generated from molecular dynamics trajectories in an efficient manner. We found that clusters have minimal effect on diffusion while increasing viscosity, which is a likely origin of the SES deviation for liquid Al–Si at low temperatures near the melting temperature.

KEYWORDS:

• Stokes–Einstein deviation
• molecular dynamics
• liquid alloy

Acknowledgments

The computations were performed on the Bridges machine [33] at the Pittsburgh Supercomputing Centre.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work used the Extreme Science and Engineering Discovery Environment [34] (XSEDE), which is supported by National Science Foundation [Grant Number ACI-1548562].