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Real Materials

The creation of an Edge dislocation via slip is illustrated below.
The ideal crystal is cut over the plane ADEF, and the material above this plane is displaced by b with respect to the material below the plane.

From: Hull,
"Introduction to Dislocations,"
Pergamon (1965)

The boundary between the slipped and un-slipped regions of the plane ABCD is the dislocation line, EF with the line vector, t.
The Burgers vector, b, is the slip vector of the displacement.
Even if EF is not straight, the same slip vector characterizes the process and has the same magnitude and direction for all points on the dislocation line.