the dislocation line
A dislocation is a one-dimensional defect, so it is helpful to ask: what shape does it take, and where can it go? The answer is that a dislocation is a continuous LINE threading through the crystal — the running boundary between the part of a slip plane that has already slipped and the part that has not yet. Like the frontier of a spreading spill on a floor, it is a curve, and it separates done from not-done. We give it a direction, a little unit arrow along its length usually called the line direction (xi), which lets us say which way is forward along the line.
The single most important rule about this line is severe and exact: a dislocation line cannot simply STOP inside a perfect crystal. Think about why — the line is the edge of a region that has slipped by one Burgers vector; if the line just ended in mid-crystal, then on one side of that end the crystal would be slipped and on the other side not, with nothing marking the transition, which is impossible. So a dislocation line must do one of only a few things: run out to a free surface, run into a grain boundary or other interface, close on itself as a loop, or meet other dislocations at a junction called a node (where the Burgers vectors balance, just as currents balance at a wire junction).
This closure rule has real teeth. It means dislocations come as loops or as networks that reach the crystal's boundaries; they are never little floating line-segments. When several dislocations meet at a node, their Burgers vectors must sum to zero if you count them all as pointing into (or all out of) the node — the exact analogue of Kirchhoff's current law. That conservation is what lets dislocations combine and split in controlled reactions, and it underlies everything from tangles to multiplication sources.
At a three-dislocation node the Burgers vectors obey b1 = b2 + b3 (with a consistent sense convention). In FCC this is exactly how a perfect dislocation a/2[10-1] can split at a node into two Shockley partials a/6[2-1-1] + a/6[11-2]; check: a/6([2-1-1]+[11-2]) = a/6[3 0 -3] = a/2[10-1], so the Burgers vectors balance at the node.
A dislocation line must close on itself, reach a boundary, or meet other lines at a node where Burgers vectors sum to zero.
The line direction xi is a choice of sense you make, and reversing it flips the sign convention for b — but the physical dislocation is unchanged. Only the combination of line sense plus Burgers vector is physically meaningful.