Crystal lattices are highly ordered, repeating 3D patterns consisting of symmetrical arrangements of atoms or groups of atoms. Each group of atoms is assigned to a representative point and these points collectively form a periodic framework that defines the entire crystal lattice’s spatial structure. This periodicity gives rise to sets of equally spaced, parallel planes of atoms throughout the lattice. These planes are a direct consequence of the repeating structure and play a central role in X-ray diffraction, as they provide the surfaces from which incident X-rays are scattered and can constructively interfere. 

X-rays are high-energy electromagnetic waves with wavelengths on the order of Angstroms, comparable to the spacing between atoms in a crystal lattice. This length-scale match allows X-rays to probe atomic structure, since resolving features requires the wavelength of the probing radiation to be on the same order as the feature size. In contrast, visible light, with much longer wavelengths, cannot give atomic-scale resolution. 

When a monochromatic X-ray beam interacts with a crystal, it scatters primarily from the electron clouds surrounding each atom. This scattering is elastic, meaning the energy of the X-rays is conserved and the scattered waves retain the same wavelength as the incident beam. Each atom acts as a source of scattered radiation, emitting waves in different directions. 

Due to the periodic structure of the crystal lattice, atoms can be modeled as lying on a series of equally spaced, parallel planes, as previously mentioned. As X-rays interact with atoms on successive planes, the scattered waves travel different path lengths depending on the depth at which they are scattered. The interference between these waves determines whether the resulting signal is enhanced or suppressed. 

Constructive interference occurs when the path length difference between waves scattered from adjacent planes is an integer multiple of the wavelength, as described by Bragg’s Law,