X-ray diffraction, or XRD, is a powerful analytical technique used to investigate the crystal structure of materials. When X-rays interact with a crystalline sample, they are scattered by the atoms in the crystal lattice. If the scattered waves satisfy Bragg's Law, they interfere constructively, creating a diffraction pattern. This pattern provides valuable information about the crystal structure, atomic arrangement, phase identification, and lattice parameters of the material. XRD is widely used in materials science, chemistry, and pharmaceutical research.
Bragg's Law is the fundamental principle behind X-ray diffraction. It states that when X-rays hit a crystal, they are scattered by atoms arranged in parallel planes. For constructive interference to occur, the path difference between rays reflected from adjacent planes must equal an integer multiple of the wavelength. This is expressed by the equation n lambda equals 2d sine theta, where n is an integer, lambda is the wavelength of the X-rays, d is the spacing between crystal planes, and theta is the angle of incidence. When this condition is met, diffraction peaks appear in the XRD pattern, allowing us to determine the crystal structure.
A typical X-ray diffraction system consists of three main components. First, the X-ray source, usually an X-ray tube that generates monochromatic X-rays, commonly copper K-alpha radiation with a wavelength of 1.5418 angstroms. Second, the sample stage or goniometer, which holds the crystalline sample and can be precisely rotated to change the incident angle theta. Third, the detector, which measures the intensity of the diffracted X-rays and moves along a circular path to collect data at different 2-theta angles. During the experiment, both the sample and detector are rotated to maintain the Bragg condition, with the detector always positioned at an angle of 2-theta relative to the incident beam.
An XRD pattern is a plot of diffracted X-ray intensity versus the diffraction angle 2-theta. This pattern contains valuable information about the crystal structure of the material. The peak positions, determined by the 2-theta values, are used to identify the crystal structure and phases present in the sample. Each crystalline material has a unique diffraction pattern that serves as its fingerprint. Peak intensities are related to the positions and types of atoms in the unit cell, as well as their quantities. Peak widths provide information about crystallite size and strain - sharper peaks indicate larger crystallites and less strain. The background of the pattern can reveal the presence of amorphous content in the sample. In this example, we see the characteristic pattern of a face-centered cubic crystal structure, with peaks labeled according to their Miller indices.
X-ray diffraction has numerous applications across various scientific and industrial fields. In materials science, it's used for phase identification, crystal structure determination, and texture analysis of materials. The pharmaceutical industry relies on XRD for polymorph screening, drug formulation studies, and quality control of medications. Geologists use XRD for mineral identification and characterization of geological samples. In metallurgy, XRD helps analyze metal alloys, measure residual stress, and investigate material failures. The field of nanotechnology benefits from XRD for characterizing nanomaterials and thin films. The non-destructive nature of XRD, combined with its ability to provide detailed structural information, makes it an invaluable tool in research and industry. As technology advances, XRD continues to evolve with improvements in detectors, data analysis software, and integration with other analytical techniques.