# What is "phase" information ?

Paul D. Boyle boyle at laue.chem.ncsu.edu
Wed Jan 20 09:36:49 EST 1999

```Web Master (web at pcjfn.msc.com) wrote:
: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.

[some stuff deleted]

: 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.

To add to Bev explanation a little:  The "phase" of a diffracted beam is
always relative to something.  The way I think of it is that the phase
a diffracted beam for a structure is relative to an imaginary reference
electron at the origin of the unit cell.  Mathematically, the phase can
be expressed in fractional coordinates of the scattering atom as below:

phi = 2 * PI * (hx + ky +lz )

where phi is the phase angle, h, k, l are the Miller indicies for the
reflection and x, y, z are the fractional coordinates of the atom.

The original poster may want to look at Appendix 5 in "Crystal Structure
Analysis A Primer" by Jenny Glusker and Ken Trueblood for a proof of the
equation above.  The book's ISBN is 0-19-503543-7, published by Oxford
University Press.

Paul

--
Paul D. Boyle			    |	boyle at laue.chem.ncsu.edu
Director, X-ray Structural Facility |	phone: (919) 515-7362
Department of Chemistry - Box 8204  |	FAX:   (919) 515-5079
North Carolina State University     |
Raleigh, NC, 27695-8204
http://laue.chem.ncsu.edu/web/xray.welcome.html

```