A8.7 X-Ray Diffraction

## Author's tip 📌

This is a very involved topic but you only need to know the basics. You will not be examined on the operating principles of X-ray diffraction).
In order to work out the arrangement of atoms or ions in a crystal lattice (to be able to construct models or diagrams of unit cells) it is necessary to know the distances between them.
X-ray diffraction enables these measurements to be made.
A beam of X-rays is passed into a crystal and the radiation is reflected by the layers of atoms in the crystal. By measuring the angles involved, the distance between two layers of atoms can be measured. By taking many measurements a three dimensional lattice can be deduced. Constructive interference only occurs at certain angles, dependent on the distance of separation of the layers of atoms. The first order reflection is used (see diagram) to work out the structure.
$\theta$
= angle of X-ray beam that gives a diffraction measurement d = distance between layers in the crystal
Figure 8.4 X ray diffraction (simplified)

## Key information 🗝

### The Bragg Equation

$\textsf{nλ = 2d sinθ}$
is used to work out the value of d, the distance between the two layers causing the diffraction. n = a whole number*
λ = wavelength of X rays used
* the crystal will reflect and give constructive interference at a number of angles, the smallest angle is called the first reflection, when the value of n=1