X-Ray Diffraction (XRD)

The Malvern PANalytical X-ray Facility at Georgia Tech is located on the ground floor of the Marcus Nanotechnology Building and houses three state-of-the-art Malvern PANalytical X-Pert Pro X-Ray Diffractometers (XRD’s).  XRD is a rapid analytical technique primarily used for phase identification of a crystalline material and can provide information on unit cell dimensions. The three diffractometers are:

  • The Alpha-1 which has an incident beam Johannsson monochromator and an X’Celerator solid-state detector,
  • The Materials Research Diffractometer (MRD) The all-purpose MRD cradle is an Eulerian cradle designed to accommodate large samples and provide five motorized movements (FY, X, Y, and Z). The mounting disk is parallel to the X-Y plane, Z direction is perpendicular to the mounting disk. The sample can be rotated (F movement) and tilted (Y movement).
  • The Empyrean which has a high temperature furnace capable of reaching 1200 degrees Celsius for in-situ experiments, a 15-slot automatic sample changer, and Small Angle X-Ray Scattering (SAXS) capability.

The MCF has recently taken over the Materials Processing Diffractometer (MPD) which has a non-ambient stage capable of operating between (-196C – 450C), a reflectivity stage, as well as a flat sample stage (default) for powder and small solid sample analysis. This is located in the Ford Building in room 2385.

Functionality

The functionality of these instruments is greatly multiplied by Malvern PANalytical’s revolutionary “PREFIX” optics system whereby instrument optics may be reconfigured with little more than the turn of a set screw, and an instrument may be changed from diverging beam optics to parallel beam optics in less than 5 minutes while still being completely aligned. The extensive range of measurements that can be performed using these instruments includes:

  • Phase identification, Crystal structure refinement, Diffraction peak profile analysis, Quantitative analysis
  • Thermal expansion analysis, Unit cell refinement, High temperature diffraction,
  • Texture and pole figure analysis, Residual stress analysis, Rocking curve and Reciprocal space mapping.

Some Useful Links:

Crystallography Frontiers: How Chemistry Reveals the Wonder of Everyday Materials
Symmetry and Space Group Tutorial
 (Jerry P. Jasinski & Bruce M. Foxman)
International Union of Crystallography (IUCr) teaching pamphlets

X-Ray Basics

This is intended as a (very) brief introduction to some of the common x-ray diffraction techniques used in materials characterization. It is designed for people who are novices in this field but are interested in using the techniques in their research. Extensive and authoritative discussions can be found in the numerous books and journal articles on this subject. Some references are listed below.

  1. Elements of Modern X-ray Physics, by Jens Als-Nielsen and Des McMorrow, John Wiley & Sons, Ltd., 2001 (Modern x-ray physics & new developments)
  2. X-ray Diffraction, by B.E. Warren, General Publishing Company, 1969, 1990 (Classic x-ray physics book)
  3. Elements of X-ray Diffraction,2nd Ed., by B.D. Cullity, Addison-Wesley, 1978 (Covers most techniques used in traditional material characterization)
  4. High Resolution X-ray Diffractometry and Topography, by D. Keith Bowen and Brian K. Tanner, Taylor & Francis, Ltd., 1998 (Semiconductors and thin film analysis)
  5. Modern Aspects of Small-Angle Scattering, by H. Brumberger, Editor, Kluwer Academic Publishers, 1993 (SAXS techniques)
  6. Principles of Protein X-ray Crystallography, by Jan Drenth, Springer, 1994 (Crystallography)

 

Bragg's Law and Lattice Planes

X-rays primarily interact with electrons in atoms. When x-ray photons collide with electrons, some photons from the incident beam will be deflected away from the direction where they originally travel, much like billiard balls bouncing off one anther. If the wavelength of these scattered x-rays did not change (meaning that x-ray photons did not lose any energy), the process is called elastic scattering (Thompson Scattering) in that only momentum has been transferred in the scattering process. These are the x-rays that we measure in diffraction experiments, as the scattered x-rays carry information about the electron distribution in materials. On the other hand, in the inelastic scattering process (Compton Scattering), x-rays transfer some of their energy to the electrons and the scattered x-rays will have different wavelength than the incident x-rays.

Diffracted waves from different atoms can interfere with each other and the resultant intensity distribution is strongly modulated by this interaction. If the atoms are arranged in a periodic fashion, as in crystals, the diffracted waves will consist of sharp interference maxima (peaks) with the same symmetry as in the distribution of atoms. Measuring the diffraction pattern therefore allows us to deduce the distribution of atoms in a material.

The peaks in a x-ray diffraction pattern are directly related to the atomic distances. Let us consider an incident x-ray beam interacting with the atoms arranged in a periodic manner as shown in 2 dimensions in the following illustrations. The atoms, represented as green spheres in the graph, can be viewed as forming different sets of planes in the crystal (colored lines in graph on left). For a given set of lattice planes with an inter-plane distance of d, the condition for a diffraction (peak) to occur can be simply written as

2dsinq = n l

which is known as the Bragg’s law, after W.L. Bragg, who first proposed it. In the equation,l is the wavelength of the x-ray, q the scattering angle, and n an integer representing the order of the diffraction peak. The Bragg’s Law is one of most important laws used for interpreting x-ray diffraction data.

It is important to point out that although we have used atoms as scattering points in this example, Bragg’s Law applies to scattering centers consisting of any periodic distribution of electron density. In other words, the law holds true if the atoms are replaced by molecules or collections of molecules, such as colloids, polymers, proteins and virus particles.

 

Representative Publications

 

Training

If you would like training on any of these instruments and have a GTLogin; please log into SUMS, find the tool you would like to get trained on, and click on the request training button. That will start a forum conversation where we can discuss your sample and what kind of data you would like to generate, and we can determine the best instrument for your needs.

 

If you have any questions, please contact: David Tavakoli (david.tavakoli@mse.gatech.edu)