Powder X-ray diffraction

Powder X-ray diffraction measures X-ray diffraction from many crystal grains with different orientations. For each allowed set of lattice spacings, suitable grains satisfy Bragg's law and produce a cone of diffracted directions, seen as a ring on an area detector or a peak in an angular scan. Several peak positions and systematic absences can identify a crystal structure even when a sample no longer retains one single-crystal orientation. Preferred orientation, strain and phase coexistence can complicate interpretation.

At fixed radiation wavelength, differentiating Bragg's law for an isotropically expanding cubic specimen gives the displayed angular sensitivity, with angles in radians. Accurate temperature inference requires a calibrated lattice-parameter versus temperature curve, stable wavelength and angular zero, and separation of thermal expansion from stress or composition shifts. Counting statistics can permit centroid precision finer than the observed diffraction-line width.

For cubic diffraction, $4{\sin }^2\theta /{\lambda }^2=(h^2+k^2+l^2)/a^2$. Ratios identify the allowed integer sequence after applying both FCC centring and diamond-basis selection rules. A common sequence starts $3,8,11,16,19$ for111,220,311,400,331. The absolute parameter remains proportional to the explicitly selected radiation wavelength.