How does X-ray diffraction reveal the structure of a crystal?

X-ray diffraction reveals the internal structure of a crystal by utilizing the uniform spacing of its atoms, which act as a diffraction grating for an incident beam of X-rays.1

When X-rays strike the atomic planes of a crystal, they reflect off these planes. For a strong signal to occur, the waves must interfere constructively. This requires the difference in path length between beams reflecting off different planes to be a whole number of wavelengths, a relationship defined by the Bragg law: $n\lambda =2d\sin \theta$.12

The resulting interference pattern—consisting of spots with specific directions and intensities—provides raw data about the atomic arrangement. Because there is no direct algorithm to convert this data into a structure, crystallographers propose theoretical models and compute how they would scatter X-rays. The model that best matches the measured interference pattern is then chosen as the determined structure. This process is essential for mapping complex arrangements, such as those found in protein molecules.13