the slip plane
When a metal deforms permanently, one block of crystal slides over another like a deck of cards fanned by a push. The flat surface along which that sliding happens is the slip plane. A dislocation does its everyday work — gliding — by travelling within one such plane, and where it has passed, the crystal above has slipped by one Burgers vector relative to the crystal below. So the slip plane is simply the plane the dislocation lives and moves in.
There is a precise geometric constraint on which plane it is. The slip plane of a dislocation must contain BOTH the dislocation line and its Burgers vector b — the plane is defined by those two directions. For an edge dislocation, where line and b are perpendicular, those two directions pin down a unique plane, so an edge dislocation has just one glide plane. For a screw dislocation, line and b are parallel, so they do NOT define a single plane — any plane containing the line will do — which is exactly why a screw can cross-slip from one plane to another. Nature does not pick these planes at random: real slip planes are the CLOSE-PACKED planes, the ones where atoms are packed most tightly and the layers slide most smoothly over each other, like well-oiled sheets.
Why close-packed? Because the spacing between close-packed planes is the widest of any plane family, and widely separated, smooth planes offer the least resistance to sliding — the lattice friction (Peierls stress) is lowest there. In face-centred-cubic metals the slip planes are the four {111} planes; in hexagonal close-packed metals it is usually the basal (0001) plane; in body-centred-cubic, which has no truly close-packed plane, slip is messier and spreads over several plane families. Identifying a metal's slip planes is the first half of identifying its slip systems, which govern how — and how easily — it can be shaped.
In FCC copper, glide happens on {111} planes. The (111) plane has the largest interplanar spacing of any family, d_111 = a/sqrt(3) = 3.6/1.732 = 2.08 angstrom, wider than d_200 = 1.8 angstrom or d_220 = 1.27 angstrom. Widest spacing, smoothest slide, lowest friction — so {111} wins as the slip plane.
A dislocation glides in the plane holding both its line and its b; nature favours the widely spaced close-packed planes.
Only glide is confined to the slip plane. A dislocation can also leave its slip plane by climb (edge, using vacancies) or cross-slip (screw, onto another plane containing the line) — but ordinary low-temperature deformation is glide, and it stays in-plane.