the Burgers vector
/ BUR-gers /
Every dislocation carries a kind of ID card that says exactly how much slip it produces and in which direction. That ID is the Burgers vector, written b. It is an arrow: its length tells you how far the crystal shifts when the dislocation sweeps through, and its direction tells you which way that shift goes. When a dislocation glides all the way across a slip plane, the two halves of the crystal end up offset by exactly one Burgers vector — no more, no less.
You find it with a simple accounting trick called the Burgers circuit. In a perfect region of crystal, trace a closed loop atom-to-atom — say ten steps right, ten up, ten left, ten down — and you return to your starting atom; the loop closes. Now trace the very same step-count loop around a dislocation line, and it fails to close: there is a leftover gap. The vector needed to jump from the finish back to the start, closing the loop, is the Burgers vector. For an edge dislocation b comes out perpendicular to the line; for a screw dislocation it comes out parallel to the line — that perpendicular-versus-parallel relationship is the cleanest way to tell the two apart.
Two facts make b powerful. First, it is invariant: the same Burgers vector runs the entire length of a single dislocation, even where the line curves from edge-like to screw-like character, and it is conserved where dislocations meet. Second, in real crystals b is always a short lattice translation — the shortest one available, because the energy stored in a dislocation scales with b squared, so nature picks the cheapest. In an FCC metal, for instance, b = (a/2) times [110], meaning half a face diagonal of the cubic cell. The magnitude of b sets the size of the slip step and feeds directly into how strong the dislocation's strain field is, and therefore into strength calculations.
In FCC aluminum the lattice parameter a is 0.405 nm, so the Burgers vector b = (a/2)[110] has magnitude a divided by sqrt(2) = 0.405/1.414 = 0.286 nm — one atomic spacing along the close-packed direction. Slip always runs along these shortest vectors on the close-packed planes, which is why FCC metals have so many slip systems and deform so easily.
b measures the slip: shortest lattice vector, perpendicular to an edge line, parallel to a screw line.
Named after Dutch physicist Jan Burgers. Because dislocation energy goes as b squared, dislocations with large b are unstable and often split into two lower-energy 'partial' dislocations with smaller Burgers vectors, leaving a stacking fault between them.