In 1913, the physicist William Bragg discovered that atoms in a crystalline matrix will reflect x-rays along specific planes. His discovery demonstrated that the angle of reflection within the atom could determine the crystal’s shape. Due to the Law of Constant Angles, already knew that every crystal structure for a given material would have the same angles between corresponding faces of the crystal.
Let’s look at the math first.
The Bragg Equation: n\lambda=2d sin \theta
n is an integer representing the multiple angles that a given reflection may occur at.
\lambda is the wavelength of the x-rays being sent through the crystal sample during a given test.
\theta is the angle of reflection that the x-rays will undergo which will create bands and groupings that let us define our crystal structure
d is the distance between the atomic planes
Here’s how it was originally done: A crystal that is a fraction of a millimeter thick is placed on a spindle. X-rays are shot through it at a photographic plate. The x-ray scatter will be recorded on the photographic plate. Scientists then analyze the plate to determine the structure of the crystal. Think of it like reconstructing a stained-glass window by looking at the colors of light scattered inside of a church by a sunbeam. Thankfully, modern systems use rotating spindles and sensors, sensitive x-ray detectors, and high speed computer algorithms to quickly determine the crystalline structure for the material being tested.