Bragg's Law
An X-ray which reflects from the surface of a substance has travelled less distance than an X-ray which reflects from a plane of atoms inside the crystal. The penetrating X-ray travels down to the internal layer, reflects, and travels back over the same distance before being back at the surface. The distance travelled depends on the separation of the layers and the angle at which the X-ray entered the material. For this wave to be in phase with the wave which reflected from the surface it needs to have travelled a whole number of wavelengths while inside the material. Bragg expressed this in an equation now known as Bragg's Law:
When n is an integer (1, 2, 3 etc.) the reflected waves from different layers are perfectly in phase with each other and produce a bright point on a piece of photographic film. Otherwise the waves are not in phase, and will either be missing or feint.
Bragg compared his new equation with the results that von Laue's group had published. His explanation seemed far more satisfying than von Laue's, as it didn't require that only certain wavelengths be present.
In one experiment, the group in Germany had rotated the crystal by 3 degrees. The resulting X-ray diffraction pattern had moved by 6 degrees. This is the expected angle if the rays were reflecting off the crystal, so confirming Bragg's theory that the diffraction could be considered as reflection from planes in the crystal.
The most satisfying result was on von Laue's photograph of diffraction from zincblende crystals. Von Laue had assumed that atoms in zincblende are arranged in a simple cubic lattice, but if this was true Bragg's Law wouldn't explain the diffraction pattern. But if the arrangement of atoms was slightly different, arranged in a face centred cubic lattice, the diffraction pattern was explained perfectly.
Not only did Bragg's Law work, but it could be used to work out how atoms are arranged inside a solid crystal!
To examine the reflection of X-rays from crystals at various angles, Bragg's father developed the X-ray spectrometer in Leeds. X-rays were passed through slits to produce a narrow beam, which fell on a crystal at the centre of the spectrometer. The reflected beam was then measured in an ionisation chamber, finding the strength as well as direction of reflected beams.
By changing the angle of the incident X-rays, W.H. Bragg measured the reflections at different angles from the faces of the crystal. He found that very strong reflections occured at certain angles. These strong reflections depended on the spacing of the planes of atoms inside the crystal, according to his son Bragg's Law. By measuring all the angles at which strong reflections occurred, the Braggs worked out the arrangement of individual atoms inside the crystals.
W.H. Bragg continued to study X-rays and improve the X-ray spectrometer, while his son Lawrence analysed the arrangements of atoms inside different crystals. Together they created the science of X-ray crystallography.
![+:: $i[Q]u3 ::+](/data/avatars/m/2/2831.jpg?1559318848){kind=avatar}
