Structure Determination By X-ray Diffraction

It is well known that, for visible electromagnetic radiation to be diffracted, the spacing between lines in a two-dimensional grating should be regarding the similar to order as the wavelength section for light 3900-7800 A. The similar to principle holds good for diffraction by the three-dimensional grating regarding the periodic array of atoms in crystals. The typical interatomic spacing in crystals is 2-3 A. So, the wavelength regarding the radiation used for crystal diffraction should be within the similar to range. X-rays have wavelengths in this section and are, therefore, diffracted by crystals.

This property is widely used for the read of crystal structures. The Bragg Law of X-ray Diffraction, when electrons moving at high speeds are directed to a metal target, a tiny percentage of their kinetic life is converted into x-rays. The x-rays emitted by the target consist of a continuous section of wavelengths, called clean radiation, by analogy with clean light consisting of a section of wavelengths. The minimum wavelength within the continuous spectrum is inversely proportional to applied voltage which accelerates the electrons towards the target. If the applied voltage is sufficiently high, in addition to clean radiation, a characteristic radiation of a critical wavelength and high intensity shall also be emitted by the target.

The radiation emitted by a molybdenum target at 35 kV includes most categories of radiation. In spectroscopic notation, the characteristic A beam of x-rays directed at a crystal interacts together with the electrons regarding the atoms within the crystal. The electrons oscillate below the impact and grow to an unique source of electromagnetic radiation. The waves emitted by the electrons have the similar to frequency as the incident x-rays. The emission is in all directions.

As there exists millions of atoms in a crystal, the emission in a critical direction is the combined effect regarding the oscillations of electrons of all the atoms. The emissions should be in phase and reinforce one another only in sure critical directions, which depend on the direction regarding the incident x-rays, their wavelength as well as the spacing between atoms within the crystal. In other directions, there is destructive interference regarding the emissions from different sources. The easiest method to visualize the diffraction effects produced by the three-dimensional grating provided by the crystal is to think about the Bragg law In Bragg law, the interaction described above between x-rays and the electrons regarding the atoms is visualized like a process of reflection of x-rays by the atomic planes. This is an equivalent description regarding the diffraction effects produced by a three-dimensional grating.

The atomic planes are regarded to be semi-transparent, that is, they let a component regarding the x-rays to pass through and reflect the other part, the incident angle 9 called the Bragg angle being equal to reflected angle. There is a path difference between rays reflected from plane two and the adjacent plane 3 within the crystal.