XRay Diffraction: Quantification of Phase Concentration

Understanding why a particular failure took place commonly depends on an understanding of the details of the chemistry of the failure process. That is, if a part failed because of corrosion, for example, knowing the chemical circumstances of the corrosion may be extremely valuable, even key to understanding the failure. And very commonly a failure analysis begins with little or no knowledge of the chemistry of the materials involved.

MATCO has a wide range of tools to use to determine chemistry. One of the most useful newer ones is the Niton x-ray fluorescence alloy analyzer which gives a near instantaneous answer to both chemistry of a metal plus the common alloy designation. And of course MATCO has excellent energy-dispersive x-ray spectroscopy facilities for semi-quantitative elemental analysis of inorganic solids and Fourier-transform infra-red spectroscopy for analysis and identification of organic materials.

But all too commonly what is needed is a phase identification, rather than an elemental analysis. That is, it’s all very well to know a sample contains iron and oxygen, but how are those elements combined, that is, what is their chemical state of combination, what phase do they constitute? Are they hematite, magnetite, goethite, lepidocrocite? What are they, not what is the sample made of? The most common way today of answering that question is by x-ray diffraction (almost the only alternative is light microscopy, an almost forgotten tool).

Consider how x-ray diffraction works. An ideal x-ray sample has the following characteristics:

A) It is 100% crystalline, that is, it has long-range order at the atomic level,

B) When the sample is in the diffractometer, its particles

1. are less than 400 mesh, ideally in the 1 um range,
2. are distributed so that they have all possible orientations, that is they have no preferred orientation,
3. are infinite in number.

The operator has to run the sample so that the result has a reasonable signal-to-noise ratio, that means, run the instrument slowly enough to accumulate a strong, clear diffraction pattern. But many things can prevent this from happening, some of those out of the operator’s control. For example, there may be so little sample small that it doesn’t approximate “infinite particles,” making the pattern unavoidably noisy. It may be comprised of flat crystals, so that preferred orientation is difficult to avoid. It may be partly amorphous, giving the pattern a large “amorphous hump”. In fact, all of these problems are quite common. But worst of all is that the sample may contain non-stoichiometric, non-equilibrium, poorly crystallized material. Much of the material out there in the world is what is known in the trade as “garbage minerals” something that is effectively undefinable.

If, however, you are so fortunate as to have a sample with only a few well-crystallized, well-defined phases, your x-ray pattern will be clear and contain identifiable peaks. What do those peaks represent?

The first answer is that they tell you nothing about the sample chemistry – necessarily. They actually tell you very precisely what the sample crystal structure is, that is, the angles, symmetry and dimensions of the atomic structure of the material. The atoms in your material, distributed in such a way as to have this symmetry, diffract x-rays in certain characteristic patterns of orientation and intensity. These patterns are documented for thousands of materials. Most materials have on the order of ten to fifteen intensity peaks in the range usually scanned in a diffraction study. If you have three phases in your sample, you can imagine then that there may be 30 to 45 peaks in the pattern, some of them overlapping more or less severely. Sorting out that complexity is quite a challenge.

One thing that may be a great help in sorting it out is a knowledge of the sample chemistry, allowing you to choose between likely present phases and ones with identical structure and symmetry but totally different chemistries.

The power of modern computers has simplified what used to be a laborious manual process, but it’s still no silver bullet. It is possible now to synthesize a computed diffraction pattern iteratively trying various concentrations of the likely phases until you get a match between the experimental pattern and the computed one. This is what it known as “whole pattern refinement (WPR).” There are two major hitches. For accurate quantitative analysis, it is imperative that  A) you have identified ALL the phases in the sample, and B) that you know all their crystal structures.

It is possible to work around this last point, but it involves a tedious standardization process.

To summarize:

• X-Ray Diffraction (XRD) is a powerful tool with which it is commonly possilbe to identify solid crystalline phases in unknown mixtures.  It can work effectively with samples down to vry small amounts.
• XRD can also help to detect the presence of amorphous meaterial is solid samples.
• XRD is especially effective in monitoring changes in samples as reaction takes place, for example, watching amorphous material disappear and crystalline material appear in a cooling glass as it crystallizes.
• Under correct circumstances, quantitative phase identification can be done on mixtures.
• XRD works best in conjunction with energy-dispersive x-ray spectroscopy (EDS) which provides information on phase composition.