Sunday, April 20, 2014

Using X-rays to locate atoms in a crystal




Most of us are familiar with famous Young's Double Slit experiment which confirmed the wave nature of light by demonstrating interference between light from two distinct but coherent sources. The idea behind the interference is quite simple. 

Waves from spatially different sources meeting at the same location on a screen travel different distances (path length). Expressing these path lengths in terms of wavelength followed multiplication with 2pi, we obtain the phases of light originating from different sources but meeting at the same location on the screen. The resultant amplitude at that particular location on screen is then obtained by adding amplitudes of all the waves (the waves with positive amplitude reinforce each other but are cancelled by waves of negative amplitudes). The resultant intensity is then given by square of the resultant amplitude. This phenomenon where light from different sources interact is known as interference.

Thus, the result of an interference depends on differences in distances that waves had to travel to reach that point on the screen simultaneously. It is not very hard to imagine that these difference are directly related to relative positions of sources. Hence, interference pattern from a set of sources is determined by relative positions of sources. Hence, given an interference pattern we should be able to infer relative position of sources.

We use this idea to find position of atoms in a crystal. Here atoms act as sources of light. Since distances between atoms in a crystal are typically of the order of few angstroms, we use x-rays (their wavelengths are of order of few angstroms). The following article explains the mathematical formulation of this technique.


 XRD structure factor.pdf

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