peak broadening

Real diffraction peaks are not infinitely thin lines; each has a width. That width is a message. Big, well-ordered crystals give tall, needle-sharp peaks, while very small crystallites or heavily strained, defect-riddled material give short, fat, blurry peaks. So the third reading from a diffractogram — how broad each peak is — is a fingerprint of the material's microstructure.

Two physical effects broaden peaks. Small crystallite size: with only a limited number of parallel planes to interfere, the cancellation just off the exact Bragg angle is incomplete, so the peak spreads (this is what the Scherrer equation quantifies). Microstrain: a spread of slightly different d-spacings, from dislocations, composition gradients, or defects, smears the peak because different regions diffract at slightly different angles. The instrument itself also adds a fixed width, which you measure with a well-crystallised standard and subtract. Helpfully, the two physical causes scale differently with angle — size broadening goes as 1/cos(theta) while strain broadening goes as tan(theta) — so a Williamson-Hall plot can separate them.

This makes peak width a genuinely useful, nondestructive probe of crystallite size and internal strain in nanomaterials, thin coatings, and ball-milled or deformed metals. Two honest cautions matter. Crystallite size is not the same as particle size or grain size — a single particle can be built of many crystallites, and diffraction sees the coherently ordered domains. And size broadening fades out above roughly 100 to 200 nanometres, where peaks become instrument-limited and Scherrer can no longer see a difference.