A general expression for the statistical error in a diffusion coefficient obtained from a solid-state...

Area of Science:

• Materials Science
• Computational Chemistry
• Solid-State Physics

Background:

• Molecular dynamics (MD) simulations are crucial for determining tracer diffusion coefficients.
• The statistical error in diffusion coefficients is often underestimated in MD simulations.
• Accurate error estimation is vital for reliable simulation results.

Purpose of the Study:

• To investigate the statistical error in diffusion coefficients derived from MD simulations.
• To develop a more accurate method for calculating statistical errors in tracer diffusion coefficients.
• To provide guidelines for efficient computational resource utilization in MD simulations.

Main Methods:

• Utilized kinetic Monte Carlo (KMC) sampling to analyze mean squared displacement (MSD) curves.
• Examined the influence of simulation time, cell size, and point defect concentration on statistical error.
• Derived a closed-form expression for the relative uncertainty in the diffusion coefficient.

Main Results:

• Statistical error in diffusion coefficients is intricately linked to simulation parameters.
• The number of particles that have jumped at least once is a key factor determining uncertainty.
• A novel closed-form expression for relative uncertainty was derived and validated.

Conclusions:

• The derived expression accurately quantifies statistical errors in diffusion coefficients.
• The findings offer practical rules for optimizing MD simulation efficiency.
• Improved error estimation enhances the reliability of diffusion coefficient calculations from simulations.