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21.3: Join the Crystals to Form the Dislocation

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  • We have determined that the displacements of the atoms are:

    \[u_{A}(x)=-\frac{b}{2 \pi} \tan ^{-1}\left(\frac{x_{A}}{w}\right)\]

    \[u_{B}(x)=-\frac{b}{2 \pi} \tan ^{-1}\left(\frac{x_{B}}{w}\right)\]

    From below, the displacements of the atoms on the A-plane are symmetrical on either side of the dislocation line, and are zero at the centre. It is clear that the misfit around the dislocation is of two types: a strain in the planes above and below the dislocation and a misalignment of the atoms across the slip plane.

    The process of determining the energies is shown in the following animation:

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