X-Ray Powder Diffraction

Core Idea

X-ray powder diffraction (XRPD) is the primary technique for identifying crystalline phases and determining crystal structures from polycrystalline samples. When monochromatic X-rays strike a powdered crystalline sample, they diffract from lattice planes according to Bragg's law: n-lambda = 2d sin(theta). Because a powder contains crystallites in all orientations, every set of lattice planes simultaneously satisfies the Bragg condition at its characteristic angle, producing a unique pattern of peak positions and intensities. Peak positions reveal the unit cell dimensions; peak intensities encode the atomic arrangement; peak shapes carry information about crystallite size and strain.

Explainer

X-ray diffraction is the most important technique in materials chemistry for answering the question: what crystalline phases are present, and what are their structures? The physical basis is straightforward — X-rays have wavelengths comparable to interatomic distances (about 1.5 Angstroms for Cu K-alpha radiation), so they diffract from the regularly spaced planes of atoms in a crystal. Bragg's law gives the condition for constructive interference: the path difference between X-rays reflecting from adjacent planes must equal a whole number of wavelengths.

In a powder diffraction experiment, the sample is a finely ground polycrystalline material. The random orientation of crystallites ensures that for every set of lattice planes, some fraction of crystallites will satisfy the Bragg condition. The detector sweeps through angles, recording intensity as a function of 2-theta. The resulting pattern — a series of peaks at specific angles with specific intensities — is a fingerprint of the crystal structure. Phase identification works by matching the observed pattern against a database (the ICDD Powder Diffraction File contains over 400,000 reference patterns). If your pattern matches entry number 04-0787, your sample contains aluminum.

Beyond identification, XRPD provides quantitative structural information. The peak positions are determined by the unit cell dimensions through Bragg's law and the Miller index relation for d-spacings. By fitting peak positions, you extract the lattice parameters a, b, c, alpha, beta, gamma with high precision. The peak intensities depend on which atoms are at which positions within the unit cell — heavy atoms scatter X-rays more strongly, and the relative intensity of different reflections encodes the atomic arrangement. Rietveld refinement fits a complete structural model (atom types, positions, thermal parameters) to the entire diffraction pattern simultaneously, refining all parameters to minimize the difference between observed and calculated patterns. This method has become the standard approach for structure determination and refinement from powder data.

Peak shapes carry additional information. Broadening beyond the instrumental resolution arises from two main sources: small crystallite size (Scherrer broadening) and microstrain (non-uniform lattice distortions). These can be separated by their different angular dependences. For nanomaterials, where crystallite sizes are below 100 nm, peak broadening analysis is often the quickest way to estimate particle size. For engineering materials, strain broadening reveals residual stresses from processing. The combination of phase identification, structure refinement, and microstructural analysis makes XRPD an indispensable tool across all of materials chemistry.