Dissemination of IT for the Promotion of Materials Science (DoITPoMS)

DoITPoMS Teaching & Learning Packages Dislocation Energetics Change in the misfit energy of a dislocation as it moves
Dislocation Energetics AimsBefore you startIntroductionMaking a dislocationJoin the crystals to form the dislocationDislocation widthForm of the displacementChange in the misfit energy of a dislocation as it movesPeierls energyWhat is the Peierls stress? Determining the Peierls stressLattice resistanceUses and limitations of the atomistic modelSummaryQuestionsGoing further
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Change in the misfit energy of a dislocation as it moves

The dislocation remains fixed (at the origin) and the lattice moves around it, therefore the initial positions of atoms xA and xB are given by

\[{x_A}{\rm{ }} = {\rm{ }}nb{\rm{ }}-\alpha b\]

\[{x_B}{\rm{ }} = {\rm{ }}nb{\rm{ }}-b/2{\rm{ }}-\alpha b\]

We use the same method as for the α = 0 case to determine the in-plane displacement and misalignment. As a result, the potentials for different α values can be determined. The following animation (which is a magnified version of the strain energy graph on the previous page) demonstrates how changing the parameter alpha affects the position of the energy minimum and the dislocation width.

By calculating the misfit energy for each value of alpha, we can determine the change in misfit energy \(\Delta {U_T}(\alpha )\) as the dislocation moves.

  • ΔUT(x) is the difference in total energy from α = x and α = 0. 
  • At first, as the dislocation moves across the unit cell 0<|α|<0.25, ΔUT increases to a maximum. 
  • At the maximum (α = 0.25), the value of ΔUT is the Peierls energy, ΔUP
  • Then for 0.25<|α|<0.5, ΔUT decreases. At α = 0.5, ΔUT = 0.
  • w also changes as the dislocation moves across the cell as seen. This is because the configuration of the dislocation changes as the dislocation moves across the unit cell. For the energy maxima, the dislocation width is also a maximum. 
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