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The adjacent planes are on either side of the half plane. So the spacing between them is 2d where d is the interplanar spacing. Below the slip plane since the half plane is absent these two plane try to attain equilibrium separation d. This causes distortion near the bottom edge of the half plane.
If I cut the whole crystal and slide it by one step, I just get a slip by one step, but I do not get any dislocation inside the crystal. When I cut only half and slide, I create an edge dislocation at the boundary between slip and no-slip regions.
Dear sir, the boundary of ‘slip’ and ‘no slip’ region looks like a plane, extra half plane, in your slide. I cannot understand why is a dislocation line. sincerely!