a close-packed direction

Picture a single straight row of oranges pushed together until each one touches its neighbours. A close-packed direction in a crystal is exactly that: the direction along which atoms sit shoulder to shoulder, actually touching, with no gaps between their centres. It is the direction of highest linear density, and there is at least one in almost every crystal structure.

You can spot it from the geometry of touching. In face-centred cubic the atoms touch along the face diagonal, so the close-packed direction is <110> and the diagonal length obeys a times sqrt(2) = 4r (four atomic radii). In body-centred cubic the atoms touch along the body diagonal, so the close-packed direction is <111> with a times sqrt(3) = 4r. In hexagonal close packing the touching rows lie in the basal plane, along the a-axis directions written <11-20>.

This matters because the close-packed direction is the slip direction — the direction along which a dislocation carries slip through the crystal, so the Burgers vector of the dominant dislocation points along it. Notice a subtlety worth being honest about: body-centred cubic has a genuine close-packed direction <111>, yet it has no truly close-packed plane. That mismatch is why BCC metals have a sharply defined slip direction but slip on several competing plane types rather than one clear favourite.