What is "phase" information ?

Web Master web at pcjfn.msc.com
Tue Jan 19 09:18:41 EST 1999

R.N. Leach <BMBRNL at leeds.ac.uk> wrote:
: I apologise in advance for asking such a basic question but I've been trying 
: to understand some basic principles of X-ray crystallography.
: One such principle that still baffles me is what phase information is.
: In ordinary light microscopy I have read that this information is not lost, 
: and I presume that this is how you then get a visible image, although I'm 
: still not exactly sure how.
: Following on from my original question is how does heavy atom replacement 
: give you the necessary information for solving a crystal structure? Why 
: doesn't the original diffraction data work?
: I've tried reading around the subject but I just seem to have a mental 
: block.Any information / simple analogies / useful references will be 
: gratefully received.

When X-rays interact with a crystal, they are diffracted by the periodic
arrangement of atoms within the lattice. Each replicate of a unique
atom in the structure acts as a diffraction grating to the X-ray beam,
and all of these different diffracted beam-lets interfere with each other
to yield the net diffracted beam.

In centrosymmetric structures, because of the arrangement of the atoms,
the diffracted beam is either completely in phase with the original,
or completely out of phase with it. In noncentrosymmetric structures
(as in natural products, proteins, etc) the situation is much more complex
and each diffracted beam can in theory have any phase shift relative
to the original. 

The detectors that we use can measure the intensity of the diffracted
beam, but have no ability to discriminate the different relative phases
of the waves. If we knew that information, it would be just manual labor
to reconstruct the electron density pattern.

When there is a heavy atom present in the structure, we can use
alternate methods of determining its location -- a technique known as
the Patterson method, the details of which are not important to this
discussion, other than to say that a Patterson is an "electron density"
style map computed assuming all phases are zero. Since X-ray scattering
is proportional to atomic number, if the heavy atom has a sufficiently
large number of electrons relative to the structure in general, then
its beam-let contribution to the total diffracted beam will be major.
Calculating what the phases would be assuming that the heavy atom was
the ONLY atom in the structure gives us approximate phases which, in
many cases, are sufficiently close to reality to reveal the structure.

Of course, I'm talking from the perspective of a small molecule
crystallographer, where a single S or P atom is often enough to
elucidate the structure of a moderately complex organic molecule.
In proteins, a single heavy atom is seldom sufficient because the
atomic number of any element relative to the total number of
electrons in the protein is going to be quite small and the phase
approximation will be poor at best. But it gives you a start in
the right direction.

Hope this helps.

Bev Vincent
Molecular Structure Corporation
The Woodlands, TX 77381

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