X-RAY DIFFRACTION

Introduction

When electromagnetic radiation is incident upon a periodic array of scattering centers, there are certain discrete directions for the incident ray that result in strong reflections. This is because of constructive interference of the radiation scattered from each of the centers. The directions for which these strong reflections occur are related through the Bragg law to the geometry of the arrangement. Therefore, measurements of the angles and intensities of the Bragg reflections can be used to deduce the arrangement and spacings of the scatterers.

Equipment

•  X-ray diffraction system (Tel-X-Ometer) and its instruction manual
•  Geiger-Mller tube and stepping motor
•  Computer and interface
•  Alkali halide large single crystals
Measurements

Read and understand the first two chapters of C. Kittel, Introduction to Solid State Physics, or an equivalent text, about crystal structures, Bravais lattices, Miller indices, reciprocal space vectors, diffraction and the Bragg law. Before beginning these experiments you should understand how x-rays are produced in the x-ray tube, know what the x-ray spectrum looks like, know how the Geiger-Mller tube works, and have a basic understanding about how x-ray film works. A modern physics textbook such as Fundamentals of Modern Physics by Eisberg is a good place to start to learn about x-rays.

You should then familiarize yourself with the Tel-X-Ometer apparatus with the help of the manual. To open or close the scatter shield (the main cover), the whole shield must be displaced to the right or the left of center, depending on the position of the detector. To turn on the power to the unit, depress the POWER ON switch on the control panel; the unit will only function when the TIME SWITCH is rotated away from zero. The filament of the x-ray tube should be illuminated. Wait 5 minutes, then depress the X- RAYS ON switch. Use the radiation test kit (at the gamma ray experiment) to measure radiation levels outside the unit.

To measure Single Crystal Diffraction, set up and carry out basic diffraction experiments on at least two of the large single crystal alkali halide samples. The goal here is to first observe how the crystal spacing d changes with atomic number. First verify that the spectrum is symmetric about the center by measuring on both sides. If the spectrum is not symmetric, adjustments may be required. Measure the x-ray spectra on both sides, plot the spectra, and then determine in detail for one crystal how the observed reflections relate to the real space structure of the crystal. A detailed procedure for this is described in the Tel-X-Ometer manual, sections D.22-D.26. For purposes of plotting and analyzing your data you may wish to use one of the graphics packages available on the lab computers.

What does the d spacing mean in terms of the crystal's lattice constant?

Draw the crystal structure and label the d-spacing.

Compare the experimental value of the lattice constant to the published value.

If you rotated the crystal by 9  , would you get the same result? If you have time, try this experiment quickly.

What are the possible sources of error in this experiment?

References

C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1985).

R. Eisberg, Fundamentals of Modern Physics (Wiley, New York, 1961).

R. Eisberg and R. Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles (Wiley, New York, 1985).