point_defect_diffusion calculation style

Lucas M. Hale, lucas.hale@nist.gov, Materials Science and Engineering Division, NIST.

Description updated: 2019-07-26

Introduction

The point_defect_diffusion calculation style estimates the diffusion rate of a point defect at a specified temperature. A system is created with a single point defect, and subjected to a long time molecular dynamics simulation. The mean square displacement for the defect is computed, and used to estimate the diffusion constant.

Version notes

  • 2022-03-11: Notebook updated to reflect version 0.11.

Additional dependencies

Disclaimers

  • NIST disclaimers

  • The calculation estimates the defect’s diffusion by computing the mean square displacement of all atoms in the system. This is useful for estimating rates associated with vacancies and self-interstitials as the process is not confined to a single atom’s motion. However, this makes the calculation ill-suited to measuring diffusion of substitutional impurities as it does not individually track each atom’s position throughout.

Method and Theory

First, a defect system is constructed by adding a single point defect (or defect cluster) to an initially bulk system using the atomman.defect.point() function.

A LAMMPS simulation is then performed on the defect system. The simulation consists of two separate runs

  1. NVT equilibrium run: The system is allowed to equilibrate at the given temperature using nvt integration.

  2. NVE measurement run: The system is then evolved using nve integration, and the total mean square displacement of all atoms is measured as a function of time.

Between the two runs, the atomic velocities are scaled such that the average temperature of the nve run is closer to the target temperature.

The mean square displacement of the defect, \(\left< \Delta r_{ptd}^2 \right>\) is then estimated using the mean square displacement of the atoms \(\left< \Delta r_{i}^2 \right>\). Under the assumption that all diffusion is associated with the single point defect, the defect’s mean square displacement can be taken as the summed square displacement of the atoms

\[\left< \Delta r_{ptd}^2 \right> \approx \sum_i^N \Delta r_{i}^2 = N \left< \Delta r_{i}^2 \right>,\]

where \(N\) is the number of atoms in the system. The diffusion constant is then estimated by linearly fitting the change in mean square displacement with time

\[\left< \Delta r_{ptd}^2 \right> = 2 d D_{ptd} \Delta t,\]

where d is the number of dimensions included.