Materials Science 101
02 Defects & Transport
Chapter 04

Imperfections in Solids

Dislocations · Edge & Screw · Burgers Vector

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Edge Dislocation — ⟂

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.

Dislocation line
along y
Burgers vector b
along x
Relationship
b ⟂ line
Slip plane
xy plane (z = 0)

Burgers Circuit (Circuit Method)

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.

| b | = a · ⟨uvw⟩ (one lattice spacing along the slip direction)

Use the Trace Burgers Circuit button above to walk the circuit step-by-step on the formed crystal.

Key feature: the Burgers vector is perpendicular to the dislocation line. Slip propagates the extra half-plane sideways one atomic spacing at a time.

Legend

Dislocation line
Burgers vector b
Burgers circuit path
Extra half-plane   Above slip (compression)   Below slip (tension)

Screw Dislocation — ⟳

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.

Dislocation line
along z
Burgers vector b
along z
Relationship
b ∥ line

Helical Displacement

Each lattice cell is displaced along the dislocation line by an amount proportional to its angular position around the core:

uz(x,y) = b2π · θ,   θ ∈ [0, 2π)

Burgers Circuit (Circuit Method)

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.

Key feature: the Burgers vector is parallel to the dislocation line. No extra half-plane exists — the cells remain on their original lattice sites but are sheared into a spiral.

Legend

Dislocation line (screw axis)
Burgers vector b (closure of circuit)
Helical Burgers circuit
Lattice cells (uniform)