11.21: X-ray Crystallography
The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring atoms in crystals (on the order of a few angstroms). When a beam of monochromatic X-rays strikes a crystal, its rays are scattered in all directions by the atoms within the crystal. When scattered waves traveling in the same direction encounter one another, they undergo interference, a process by which the waves combine to yield either an increase or a decrease in amplitude (intensity) depending upon the extent to which the combining waves’ maxima are separated.
Bragg’s Law and Bragg’s Equation
When X-rays of a certain wavelength, λ, are scattered by atoms in adjacent crystal planes separated by a distance, d, they may undergo constructive interference when the difference between the distances traveled by the two waves prior to their combination is an integer factor, n, of the wavelength. This is Bragg's law. This condition is satisfied when the angle of the diffracted beam, θ, is related to the wavelength and interatomic distance by the equation: nλ = 2d sin θ. This relation is known as the Bragg equation in honor of W. H. Bragg and W. L. Bragg, the English physicists who explained this phenomenon. They were awarded the Nobel Prize in Physics in 1915 for their contributions.
This text has been adapted from Openstax, Chemistry 2e, Section 10.6: Lattice Structures in Crystalline Solids.