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Breakdown of the Stokes-Einstein relation in Stillinger-Weber silicon

Himani Rautela¹, Shiladitya Sengupta¹, Vishwas V Vasisht²

¹Department of Physics, Indian Institute of Technology Roorkee, Roorkee 247667, Uttarakhand, India.

The Journal of Chemical Physics

|April 8, 2025

Summary

The Stokes-Einstein relation for liquid silicon shows a weak breakdown in the high-temperature liquid phase. A distinct breakdown occurs in the supercooled liquid, revealing complex dynamics and length-scale dependent behavior.

Area of Science:

Condensed Matter Physics
Materials Science
Computational Chemistry

Background:

The Stokes-Einstein relation connects macroscopic transport coefficients to microscopic dynamics.
Understanding its validity in liquid and supercooled states is crucial for materials science.
Silicon's phase diagram offers a complex system to test these relations.

Purpose of the Study:

To investigate the validity of the Stokes-Einstein relation in liquid and supercooled silicon.
To examine the relationship between transport coefficients, relaxation times, and length-scale dependent dynamics.
To identify the phase diagram regions where the Stokes-Einstein relation breaks down.

Main Methods:

Molecular dynamics simulations using the Stillinger-Weber potential.
Analysis of self-diffusion coefficient (D), viscosity (η), and relaxation times (τα).
Computation of length-scale dependent relaxation times (τα(q)) across various temperatures, pressures, and densities.

Main Results:

A weak breakdown of the Stokes-Einstein relation was observed between D and η in the high-temperature liquid phase.
Using relaxation time (τα) as a proxy for viscosity revealed a distinct breakdown in the supercooled liquid phase.
Loci of onset of slow dynamics were found below Stokes-Einstein breakdown loci in certain regions, indicating Arrhenius but non-Fickian behavior.

Conclusions:

The Stokes-Einstein relation exhibits breakdown in both equilibrium and metastable liquid silicon states.
Length-scale dependent dynamics play a critical role in the breakdown of the Stokes-Einstein relation.
The study highlights distinct dynamical regimes and their relation to phase behavior in silicon.

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