What is X-ray diffraction (XRD)

On This Page:

• Bragg's Law
• Features of Electron, X-ray, or Neutron Diffraction
• The ``Ultimate'' (Technically Challenging) Experiment
• Powder vs. Single Crystal X-ray Diffraction

Bragg's Law

or

A real 3-dimensional crystal contains many sets of planes. For diffraction, crystal must have the correct orientation with respect to the incoming beam.

Perfect, infinite crystal and perfectly collimated beam: diffraction condition must be satisfied ``exactly.''

Strains, defects, finite size effects, instrumental resolution: diffraction peaks are broadened.

More formally, the scattered intensity is proportional to the square of the Fourier transform of the charge density:

where is the charge density.

For perfect crystals, I(q) consists of delta functions (perfectly sharp scattering). For imperfect crystals, the peaks are broadened. For liquids and glasses, it is a continuous, slowly varying function.

Features of Electron, X-ray, or Neutron Diffraction

• For a known structure, pattern can be calculated exactly.
• Symmetry of the diffraction pattern given by symmetry of the lattice.
• Intensities of spots determined by basis of atoms at each lattice point.
• Sharpness and shape of spots determined by perfection of crystal.
• Liquids, glasses, and other disordered materials produce broad fuzzy rings instead of sharp spots.
• Defects and disorder in crystals also result in diffuse scattering.

The ``Ultimate'' (Technically Challenging) Experiment

• Sample is tiny (micron-sized).
• The effect is weak (light elements, small modulations, subtle modifications of the long-range order).
• Instrumental resolution (angle and energy) is ``perfect'' allowing detailed measure- ments of structural disorder.
• Measurement is time-resolved (nanosecond time scale).

To achieve all of the above, will need lots of intensity in the primary beam together with sensitive detection systems.

Powder vs. Single Crystal X-ray Diffraction

SINGLE CRYSTAL

Put a crystal in the beam, observe what reflections come out at what angles for what orientations of the crystal with what intensities.

Advantages

In principle you can learn everything there is to know about the structure.

Disadvantages

You may not have a single crystal. It is time-consuming and difficult to orient the crystal. If more than one phase is present, you will not necessarily realize that there is more than one set of reflections.

POWDER

Samples consists of a collection of many small crystallites with random orientations. Average over crystal orientations and measure the scattered intensity as a function of outgoing angle.

Disadvantage

Inversion of the measured intensities to find the structure is more difficult and less reliable.

Advantages

It is usually much easier to prepare a powder sample. You are guaranteed to see all reflections. The best way to follow phase changes as a function of temperature, pressure, or some other variable.

Copyright 1995, 1996, Paul A. Heiney. Individuals should feel free to make links to this document or any images contained in it, or to make a copy for their own personal use. However, you may not further disseminate copies in electronic, printed, or any other form without the express permission of the author, and this copyright notice must appear on any copy.

Last updated December 30, 1996