Dislocations · Edge & Screw · Burgers Vector · Small-Angle Grain Boundaries
An extra half-plane is wedged into the crystal from above. The dislocation line is the bottom edge of that half-plane, where it terminates inside the lattice. Cells above the slip plane are in compression; cells below are in tension. Press Play to watch the half-plane descend and the surrounding lattice squeeze to accommodate it.
Walk an equal number of lattice steps right, up, left, down around the dislocation core. In a perfect crystal the loop closes; around a dislocation it does not. The closure failure — the vector from end-point back to start — is the Burgers vector b.
Use the Trace Burgers Circuit button above to walk the circuit step-by-step on the formed crystal.
Cut the crystal along a half-plane and slide one face parallel to the cut by one lattice spacing. Atomic planes that were originally flat now spiral around the dislocation line like a spiral staircase — each full circuit around the line steps up by one Burgers vector. Press Play to watch the shear develop.
Each lattice cell is displaced along the dislocation line by an amount proportional to its angular position around the core:
For screw, walk a closed loop around the dislocation line. The path lifts smoothly along z as it goes — when it returns to the starting x,y, it sits one b higher (or lower) than it started. That offset along the line direction is the Burgers vector.
Use the Trace Burgers Circuit button above to watch the helical path close on itself with a vertical offset.
A small-angle tilt boundary is built from a row of edge dislocations sitting in the boundary plane. Two crystal grains meet at this plane, rotated about an axis that lies in the boundary by a small misorientation θ. Press Play to rotate the right grain and watch the dislocation array appear along the boundary as the lattice mismatch is accommodated dislocation-by-dislocation.
In the animation, as the right grain rotates, one wedge of its lattice swings into grain A (overlap) while the opposite wedge swings away (gap). This is the raw lattice misfit — the geometric mismatch you would get if the two lattices were rigid and forced to share a boundary.
In real materials atoms cannot overlap or leave empty space. The misfit is absorbed by a regular array of edge dislocations spaced D ≈ b/θ apart along the boundary — each dislocation accommodates exactly one atomic plane of mismatch. That is exactly what a small-angle tilt boundary is.
For a small misorientation θ (radians), the spacing between adjacent edge dislocations in the wall is set by a simple geometric relation:
As θ grows the array densifies (smaller D). Beyond ≈ 10–15° the dislocation cores overlap and the small-angle picture breaks down — the boundary becomes a true high-angle grain boundary instead.
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