the Burgers vector
/ BUR-gers /
If a dislocation is a flaw in a crystal, the Burgers vector is the one number-with-direction that says exactly WHAT the flaw is and HOW BIG it is. It answers a simple question: when this dislocation glides all the way across a crystal, by how much, and in which direction, does the top half slip over the bottom half? That amount and direction, packed into a single arrow, is the Burgers vector b. It is the fundamental fingerprint of a dislocation — two dislocations with the same b are, in the ways that matter for deformation, the same defect.
Its magnitude is not arbitrary. A dislocation that leaves a perfect crystal behind after it passes must slip by a vector that is itself a lattice translation — one full step of the crystal's own repeat — otherwise it would leave a smear of mismatch in its wake. So b is (for a perfect dislocation) a lattice vector, and to keep the energy low the crystal picks the SHORTEST one, which points along the most densely packed direction. In face-centred-cubic metals that shortest vector is a/2<110>, of length a/sqrt(2); for aluminium (a = 4.05 angstrom) that is about 2.86 angstrom — roughly one atomic diameter. The relation to character is clean: b perpendicular to the line means edge, b parallel means screw.
The Burgers vector carries more weight than any other single quantity in dislocation theory. The stored energy of a dislocation goes as b squared, which is why crystals prefer short Burgers vectors and why a big one may split into smaller ones. The force a stress exerts on a dislocation depends on b. And b is conserved: it is constant along a line and balances at every node like current in a circuit. Learn to read a dislocation's Burgers vector and you can predict how it moves, how much energy it costs, and what reactions it will undergo.
Because line energy scales as b^2, a perfect FCC dislocation with b = a/2[10-1] (so b^2 proportional to a^2/2 = 0.5 a^2) can lower its energy by splitting into two Shockley partials of type a/6<112>, each with b^2 proportional to a^2/6 = 0.167 a^2; the pair total 0.333 a^2, which is less than 0.5 a^2. Frank's rule (compare sums of b^2) predicts the split, and it happens.
b sets a dislocation's identity, energy (proportional to b^2), and the force it feels; the crystal picks the shortest lattice vector.
The Burgers vector is named after Jan Burgers (Dutch), so it is a proper noun — always capitalised. A perfect dislocation has a lattice-vector b; a partial dislocation has a b that is NOT a lattice vector and so must drag a stacking fault behind it.