# Calculating Dislocation Mobility

## Abstract

This example shows the procedure for calculating dislocation mobility. The molecular dynamics simulations were performed using LAMMPS. Ovito is used for visualization and Excel is used for data analysis and plot generation. This example uses data generated from LAMMPS simulation for pure Vanadium.

## Step by step instruction

• Generate the atomic dislocation, click for instructions. Perform LAMMPS simulation to study dislocation motion under different shear stress values. See video for instructions.
• Extract the position vs. time data from OVITO. See video for instructions.
• Plot the position vs. time for different shear stress as shown in the figure below. The velocity of the dislocation is the slope of the position vs. time plot.
Position vs. time plot for various applies shear stresses for an edge dislocation in Vanadium.
• Plot the velocity vs. shear stress as shown in the figure below. From Equation (9.2) in [1], the slope of the linear region ($m$) is $b/B$, where $b$ is the magnitude of burgers vector and $B$ is dislocation drag coefficient. Calculate $B = b/m$. Dislocation mobility $M = 1/B$.
Dislocation velocity vs. applied shear stress for edge dislocation in Vanadium. Where $m$ is the slope of the linear region, $b$ is the magnitude of burgers vector, $B$ is dislocation drag coefficient, and $M$ is dislocation mobility

### References

1. Horstemeyer, Mark F. Integrated Computational Materials Engineering (ICME) for metals: using multiscale modeling to invigorate engineering design with science. John Wiley & Sons, 2012.