a low-angle grain boundary

Imagine two crystal patches that are turned relative to each other by only a tiny angle, a degree or two. Their atomic rows are almost parallel, so most atoms across the seam still line up fine. The mismatch is small and, remarkably, it can be accommodated by inserting a neat row of dislocations, extra half-planes, spaced out along the boundary. A boundary like this, with a small misorientation built from a tidy array of dislocations, is a low-angle grain boundary.

The classic picture is a tilt boundary: a vertical wall of edge dislocations stacked one above another, each one taking up a little of the misfit. Simple geometry (the Read-Shockley model) gives the spacing D between dislocations as D = b / (2 sin(theta/2)), which is roughly b/theta for small angles, where b is the Burgers vector length and theta the misorientation. So a 1-degree boundary in a metal with b = 0.25 nm has dislocations about 0.25/0.017 = 14 nm apart. As theta grows the dislocations crowd closer together, and their energy per unit area rises with angle (steeply at first, then levelling off).

Low-angle boundaries (below roughly 10 to 15 degrees) have LOWER energy than random high-angle boundaries and behave differently: they are less effective at blocking slip and often form inside a deformed grain as subgrains. They are direct visual proof that a grain boundary really is made of dislocations, because you can image the individual dislocations in a low-angle boundary under a microscope. Honest note: the dislocation-wall description works only while the angle is small; once the dislocations are so close that their cores overlap (around 15 degrees), the picture breaks down and the boundary is called high-angle.