Visible light requires very narrow slits for
diffraction to occur. The wavelength
of x-rays was far shorter than visible light. In 1912 Max von Laue
recognised that the wavelength of x-rays was apparently similar to the
distances between planes of atoms in crystals
and perhaps therefore crystals could act as a diffraction grating for
x-rays. Suitable experiments were performed in the next year.
The atoms
in a crystal are arranged in a regular lattice as shown. The
spacing between planes of atoms is comparable to the wavelength
of x-rays.
In 1913 W.L. Bragg successfully interpreted a diffraction pattern
obtained when x-rays were directed at a crystal.
The atoms in a crystal may be thought of as defining families of
parallel planes (now called Bragg planes). Bragg devised conditions for
constructive interference to arise in radiation scattered by crystals.
·
The first condition resembles the law of reflection for visible light by
a mirror.
· The second condition may be stated as
2d sin
=
n
where d is the spacing between adjacent Bragg planes in
the crystal
and
is the wavelength of the x-rays.
The angle between the x-ray beam and the plane of atoms is
and n is the order of the image.
(Students will recognise a resemblance to the condition for the
diffraction of visible light).
Demonstration of Diffraction (Bragg)
By using crystals with simple structures where d was known, then the
wavelength ? of x-rays was accurately determined. Then by directing
x-rays of known wavelength at more complex crystals, diffraction
patterns were obtained and examined enabling the spacing of the Bragg
planes to be determined and so the crystal structure established. Hence
x-rays helped the development of crystallography.
The structure of some crystals is so complex that x-ray diffraction patterns take years to analyse. Computers have offered great advantages.
eight="169" src="../protein%20crystal.gif" width="200"X-rays played a significant part in the discovery of the helical structure of DNA.