the Burgers circuit

How do you actually MEASURE a dislocation's Burgers vector — where would you put your ruler? The trick, invented for exactly this, is the Burgers circuit: you take a walk. Starting at some atom near the dislocation, you step from atom to atom in a closed loop — say ten steps right, ten up, ten left, ten down — always following bonds to nearest neighbours, and you come back to where you started. In a perfect crystal such an atom-by-atom loop always closes. Around a dislocation, it does not. The gap by which it fails to close is the Burgers vector.

Here is the method precisely. First draw your closed atom-to-atom loop in the real, dislocated crystal, going all the way around the dislocation line, and note the exact sequence of steps (so many right, so many up, and so on). Now make the identical sequence of steps in a PERFECT reference crystal of the same material. Because there is no defect there, that same recipe of steps leaves you short of your start point. The vector you must add to get back to the start — the closure failure — is the Burgers vector b. (Conventions differ on the sign; a common one is FS/RH: Finish-to-Start in the perfect crystal, with a Right-Hand rule fixing the line sense. As long as you are consistent, the physics is the same.)

This construction is not just a definition; it is a proof of two deep facts. It shows that b does not depend on the size or shape of the circuit or how far it is from the core — enlarge the loop and the closure failure stays exactly b, because any deformation you enclose that ISN'T a dislocation adds nothing. And it shows why the Burgers vector is conserved along a line and balances at nodes: a single big circuit around two dislocations picks up the SUM of their Burgers vectors. The Burgers circuit is the operational meaning of the Burgers vector — what it would take to measure it.