= Solution
Randomly oriented crystallites supply planes with their normals in each required scattering-vector direction. Of the five families considered, \b[$(111)$, $(200)$ and $(220)$ can therefore give accessible <copper> $K_\alpha$ powder peaks; $(300)$ remains absent and $(640)$ remains beyond a roughly $130^\circ$ detector limit.] Other allowed families also appear if their <Bragg angles> lie inside the instrument range; orientation averaging does not restrict the pattern to these five examples.
Only a small fraction of randomly oriented <crystal grains> satisfy the Bragg condition for a given detector setting, and each family scatters around a cone rather than concentrating all its intensity into one single-crystal spot. A narrow detector aperture therefore receives a relatively weak signal from a small powder specimen compared with a well-oriented large <single crystal>. Adequate <crystal grain> statistics, longer counting, suitable powder packing and detector acceptance matter. The odd-parity peaks additionally involve the difference of ionic scattering factors. No absolute single-crystal/powder intensity ratio follows without illuminated <volumes>, absorption and instrumental geometry.
Back to article page
