When a monochromatic X-ray comes into contact with a crystal lattice, interference patterns are produced by each atom hit by the beam. Many of these patterns will interfere with each other and cancel each other out. However, at the right distance and angle these patterns can be in-phase with one another and cause constructive interference. This is known as diffraction.
This type of waveform interaction can be seen in all wave systems. The image to the right shows a simulated wave pattern where the lattice is placed on its side and two slits are present. The interfering wave propagation can be seen amplifying three waves. A crystal lattice can be thought of as a source of multiple tiny slits, where the X-ray beam is acting like the waveform in the image.
In 1912 W. L. Bragg noticed there was a relationship between the wavelength of radiation, the angle of the X-rays and the internal spacing in the crystal, which is expressed in the form:
nλ = 2dsinθ
where n is an integer, λ is the wavelength of the x-rays (in our case 1.54Å for a copper tube source), d is the spacing between planes in the atomic lattice of the sample, and θ is the diffraction angle in degrees. This is known as Bragg’s law. Although Bragg's law was used to explain the interference pattern of X-rays scattered by crystals, diffraction has been developed to study the structure of all states of matter with any beam, e.g., ions, electrons, neutrons, and protons, with a wavelength similar to the distance between the atomic or molecular structures of interest.
There are two important things to note about Bragg’s Law:
- The smaller the distance d, the larger the diffraction angle θ.
- The bigger the wavelength λ, the larger the diffraction angle θ.
(i.e. sinθ = nλ / 2d)
Bragg conditions of diffraction: To maintain the same path length and remain in-phase, the x-rays must be deviated at an angle equal to the angle of incidence (θ). The deviated rays combine to form a diffracted beam if they differ in phase by a whole number of the ray wavelength (λ).
Although it doesn’t play a major role in the technique of x-ray powder diffraction we must at least mention the phenomenon of absorption of x-rays. When x-rays encounter any form of matter, they are partly transmitted and partly absorbed. The mass absorption coefficient μ/ρ is a constant of the material and is independent of its physical state. The absorption of x-rays is utilized in experiments on X-ray synchrotron sources where the high intensity of the X-ray beam is adjusted at low angles by the use of absorbers, typically Ni foils.