peak intensity

Peak intensity is how bright — how tall or how much area — each diffraction peak has. If peak positions told you the size and shape of the box, intensities tell you what is inside it: which atoms sit at which spots (the motif). Two crystals with identical unit cells but different atoms in them share the same peak positions yet have completely different peak heights.

The core of the intensity is the structure factor F(hkl), a sum over all the atoms in the cell, each contributing its atomic scattering factor f (roughly proportional to its number of electrons, so heavy atoms shout loudest) with a phase e^(2 pi i (hx + ky + lz)) set by where it sits. The measured intensity is proportional to |F|^2, further multiplied by several bookkeeping factors: the multiplicity (how many symmetry-equivalent planes contribute), the Lorentz-polarization factor, absorption, and the temperature (Debye-Waller) factor that damps peaks as atoms vibrate. Some reflections come out exactly zero — the systematic absences — and their pattern reveals lattice centering, screw axes, and glide planes.

Because intensities encode the motif, they are what let you locate atoms, refine occupancies, and do quantitative phase analysis (relative peak areas tell you how much of each phase is present). Two honest cautions live here. First, you measure |F|^2, which loses the sign or phase of F — the phase problem, and the reason structures are solved rather than simply read. Second, in a powder, preferred orientation of platy or needle-like grains can badly inflate some intensities and starve others, so trust intensities only from a properly randomised sample.