Last Update 24/ 11/ 2003
in English/ in Esperanto/ in Portuguese
The aim of this application is to handle the method of measurement of crystallographic distances, also known by the very popular term data collection up from x-ray diffraction by a crystal represented in one dimension. The data can be collected with a Buerger precession camera or with a detector from an automatic diffractometer. This model uses Ewald sphere and allows to obtain the reciprocal parameter a* from the reciprocal unit cell. Table-1 displays all the labels used in this application.
Table-1 Meanings of labels used in the figure
| Label | Meaning |
| I | x-ray source |
| C | crystal centered on the Ewald sphere |
| a* | reciprocal crystal axis |
| (1 0 0) | reciprocal lattice point with Miller indices h = 1, k = 0 and l = 0 |
| O | origin of the reciprocal lattice |
| B | origin on the film, spot of the direct x-ray beam |
| X'' | spot of the diffracted x-ray by crystal at C on film F |
| grau | degrees of rotation after dragging the mouse on the green square |
| l2 | wavelength of x-ray and CO = 1/l2 |
A mouse drag action on the green square will rotate the crystal by an angle given as "grau".
We observe exactly the same degrees of rotation on the reciprocal axis a* that supports the reciprocal points (h 0 0) as on the photographic film (or the electronic detector), so that a parallelism among axis and film is preserved.
After a click on button L a reciprocal lattice scheme will be visible. A second click on the same button will remove the scheme.
The x-ray leaves the source I and reaches the crystal at C. When point (1 0 0) is tangent on the Ewald sphere part of the incident x-ray is diffracted along the direction given by C and (1 0 0). This diffracted x-ray hits the photographic film (or an electronic detector) on the point X''.
A selection of distances on the figure and their respective meanings is presented at table-2.
Table-2 Meanings of selected distances
| Distance | Meaning |
| C O | radius of the Ewald sphere = 1/l2 |
| O (1 0 0) | reciprocal parameter of the reciprocal unit cell |
| C B | crystal to film distance |
| X'' B | distance measured on the photographic film |
The triangle C (1 0 0) and O is similar to triangle C B and X”. We conclude the value of the reciprocal parameter can be calculated as a* = (X'' B /l2 )/(C B).
Exercises
1) After a click on button l2 the x-ray wavelength is decreased to l1. What is the effect caused by shortening the wavelength on the amplification factor of the diffraction method for distances measurement?
2) What would be the most convenient wavelength to measure the cell parameter of the unit cell of a macromolecule, l1 or l2?
3) What wavelength will be able to print higher number of diffracted rays on the photographic film F, l1 or l2?
Please send your comments.
Table of subjects.