X-Ray Diffraction

Introduction: The interference between waves underlies the diffraction methods for structure determination. There are three main methods in this category. The first is based on the wave nature of electromagnetic radiation in the x-ray region (x-ray diffraction) while the other two utilize the wave aspect of electrons and neutrons (electron diffractions and neutron diffraction).All these techniques provide the values of bond distances and bond angles. X-rays moving with a definite velocity and wavelength are therefore used for molecular and crystal structure determination.

X-ray diffraction: Diffraction of x-rays by crystals is the most powerful method available at present for determination of crystal structure. The method also provides accurate structural parameters of molecules present in molecular crystals.

To understand the mathematical requirement for interference, consider two parallel X-ray waves of wavelength λ, strike parallel lattice planes of a crystal. The dots in these planes denote either atoms or ions or molecules. One of the waves is reflected by the surface plane of the crystal in such a way that the angle is reflected by the surface plane of the crystal in such a way that the angle of reflection is equal to the angle of incidence. The second wave penetrates the crystal and reflected by the lattice plane immediately below the surface plane. It is obvious that if the two waves are in phase before reflection they will continue to be in phase after reflection provided the extra distance (2d sin θ) that the second wave has to traverse is an integral multiple of the wavelength.

In other words, the condition for constructive interference is

n λ = 2d sin θ, where n is an integer and d the spacing between successive lattice planes.

The above equation is referred to as the Bragg condition for diffraction in honour of W.L. and W.H. Bragg pioneered the X-ray diffraction.

Some limitations:

One important limitation of the X-ray method is that it cannot locate hydrogen atoms precisely. This is because the hydrogen atom has only one electron and consequently it scatters x-rays very weakly. Another limitation is the time factor. Complete analysis of the diffraction pattern is a laborious process spanning several months, but the advent of high-speed computers is making this limitation less severe.