9 Jun 2009

Fourier Transforms and the Phase Problem

Web Resources and Apps

Submitted by Adam R. Johnson, Harvey Mudd College

At the end of my inorganic course, I teach several "cool" spectroscopic techniques that inorganic chemists use.  These techniques are discussed within the context of bioinorganic chemistry, and I typically cover EXAFS/XANES, X-ray crystallography, EPR and Mössbauer.  

This website introduces (or reviews) Fourier Transforms in a neat graphical way, but most importantly, illustrates the phase problem.  Given the intensities from your crystal and the phases from your model, the phases are more important!  Which is too bad, as we don't have ready access to that information.

Learning Goals: 

After using these web resources, a student should have an appreciation for the "phase problem" in X-ray crystallography and a better understanding of the importance of good modeling.

Implementation Notes: 

 I really like the graphical approach to the phase problem illustrated by Cowtan.  I run through some of the introductory FT pages and then the "duck" and "cat" illustration of the phase problem, followed by the "manx cat" illustration.  The students gain quite an appreciation for model building without having to actually build models or work with diffraction data.

Time Required: 
various; I use one lecture period
Evaluation Methods: 

The only thing I really expect my students to get out of my X-ray unit is an appreciation for limitations (resolution), the iterative process between model and fit, and that your result is only as good as your data and your model.  I hope that the students gain an appreciation for the technique, and can understand a bit better what the X-ray data mean in the next research paper that they read.

Creative Commons License: 
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