Correlation of Successive Atomic Steps in Crystals by Relaxation Mode Analysis

Area of Science:

• Solid-state physics
• Materials science
• Computational chemistry

Background:

• Understanding ion diffusion mechanisms is crucial for materials properties.
• Vacancy-mediated diffusion is a key transport process in solids.
• Existing methods may lack computational efficiency or broad applicability.

Purpose of the Study:

• To introduce and validate the relaxation mode analysis for computing diffusion parameters.
• To provide a computationally efficient method for analyzing ion diffusion.
• To assess the applicability of the technique for both self-diffusion and impurity diffusion.

Main Methods:

• Utilizing relaxation mode analysis to compute the average cosine of the angle between successive diffusion steps.
• Applying the technique to lattices with finite size and specific boundary conditions (reflecting or transparent).
• Solving the secular equation using eigenvalues and eigenvectors for machine computation.

Main Results:

• The relaxation mode analysis successfully computes diffusion parameters for tracers and impurities on various lattices.
• Sample computations for self-diffusion on an fcc lattice demonstrate the method's efficacy.
• Convergence rates differ significantly between self-diffusion (rapid) and impurity diffusion (slower) based on boundary centering.

Conclusions:

• Relaxation mode analysis offers a robust and computationally feasible approach to study ion diffusion.
• The method's efficiency and applicability are confirmed for different diffusion scenarios.
• Boundary condition choices critically influence convergence, particularly for impurity diffusion studies.