widths themselves (roughly λL/d where λ/d is approximately twice the Bragg angle for the corresponding plane) are well under 1°, because the wavelength λ of electrons (about 1.97 picometres in this case) is much less than the lattice plane d-spacing itself. For comparison, the d-spacing for silicon (022) is about 192 picometres while the d-spacing for silicon (004) is about 136 picometres. The image was taken from a region of the crystal which is thicker than the inelastic mean free path (about 200 nanometres), so that diffuse scattering features (the Kikuchi lines) would be strong in comparison to coherent scattering features (diffraction spots). The fact that surviving diffraction spots appear as disks intersected by bright Kikuchi lines means that the diffraction pattern was taken with a convergent electron beam. In practice, Kikuchi lines are easily seen in thick regions of either selected area or convergent beam electron diffraction patterns, but difficult to see in diffraction from crystals much less than 100 nm in size (where lattice-fringe visibility effects become important instead). This image was recorded in convergent beam, because that too reduces the range of contrasts that have to be recorded on film. Compiling Kikuchi maps which cover more than a steradian requires that one take many images at tilts changed only incrementally (e.g. by 2° in each direction). This can be tedious work, but may be useful when investigating a crystal with unknown structure as it can clearly unveil the lattice symmetry in three dimensions. Kikuchi line maps and their stereographic projection The figure at left plots Kikuchi lines for a larger section of silicon's orientation space. The angle subtended between the large [011] and [001] zones at the bottom is 45° for silicon. Note that four-fold zone in the lower right (here labeled [001]) has the same symmetry and orientation as the zone labeled [100] in the experimental pattern above, although that experimental pattern only subtends about 10°. Note also that the figure at left is excerpted from a stereographic projection centered on that [001] zone. Such conformal projections allow one to map pieces of spherical surface onto a plane while preserving the local angles of intersection, and hence zone symmetries. Plotting such maps requires that one be able to draw arcs of circles with a very large radius of curvature. The figure at left, for example, was drawn before the advent of computers and hence required the