Published in the August-September issue of the American Mineralogist is a study I performed with Dr. Roberta Flemming and Dr. Phil McCausland at The University of Western Ontario where we investigated the applicability of a method for measuring the grain size of geological materials using two-dimensional X-ray diffraction. In this post I aim to explain this study in shared language for everyone.

X-ray diffraction

X-ray diffraction was invented at the start of the 20th century, and is a method to measure the spacing of atoms in a solid when they form a regular and repeating pattern. Crystals (rocks, minerals, metals, solid elements, and molecules) all have repeating patterns of atoms that build up to create the larger form. The best example of this is normal table salt, the mineral halite. The sodium and chlorine atoms bound together in a squarish pattern, and if you look closely you can see that salt is made up of tiny cubes, a macroscopic expression of the order on the atomic scale. The sodium and chlorine atoms make thin sheets of atoms that form cubes when stacked together, and when X-rays interact with these sheets they ‘reflect’ off (diffract) at equal incident and reflected angles and using Bragg’s Law  the distances between these sheets can be measured.

braggs_law

The geometry of diffracting X-rays in accordance with the Bragg “reflection” analogy (from Klug & Alexander, 1974).

When these reflected/diffracted X-rays are viewed in three-dimensions, they form Debye-Scherrer cones that originate from the reflection point and expand to infinity. When a two-dimensional detector intersects these cones, rings are observed on the two-dimensional detector image (see below). Using trigonometry, the spacing between these rings can tell you the spacing of planes of atoms in the atomic structure when the instrumental setup is known.

diffraction_cones

A depiction of the three-dimensional nature of diffracted X-rays. The method of production of Debye rings is portrayed and hypothetical d-spacings and 2-theta angles are shown (from Klug & Alexander, 1974).

mg__0p24

Smooth Debye  diffraction rings of a fine grain (0.24 µm) magnetite sample.

Grain Size and X-ray Diffraction

Important for our study is the fact that the characteristics of these rings (smooth lines, spotty, discontinuous) alter as a function of the sample’s grain size (as well as other factors). Very fine grain sizes (~5 µm and less) display uniform smooth rings. As the grain sizes of samples increase there is a progression of the fine lines becoming spotty, the spots then begin to separate, and finally at large grain sizes (~100 µm and larger) the crystals produce large and spaced out spots on the detector image.

px_10_15

Spotty Debye diffraction rings of a coarser grain (10–15 µm) pyroxene sample.

The method we investigated was proposed in 2009 and, to the best of my knowledge, our investigation appears to be the first to apply this method the laboratory. This method uses physical theory to calculate the volume of material that is irradiated by the X-ray beam using constraints such as the diameter of the X-ray beam and the X-ray absorption characteristics of the material, and then this method divides this volume by the number of irradiated crystals within this volume. The number of crystals irradiated is calculated by counting the number of spots in a ring (using a computer algorithm) and then, when factors such as atomic planes that multiply reflect are taken into consideration, the number of irradiated crystals are enumerated. Essentially, a volume irradiated is calculated, and when this volume is divided by the number of crystals in this volume, the size of these crystals is measured (assuming that the crystals are spherical).

We applied this method to pyroxene, magnetite, and basalt sample suites of known grain size (as measured by sieve or scanning electron microscopy). The original proposer of the method suggested that the method should work on samples 0.1 to 100 µm in size. We found that for our samples and our instrument (a Bruker D8 Discover micro-X-ray diffractometer) correlating grain sizes were only measured in the range of ~15–63 μm. That is the main finding of this study. One cannot blindly assume that this method will generate an accurate grain size measurement in the range of 0.1–100 µm. The method needs to be calibrated for each instrument and experimental setup. The difficulty measuring correlating grain sizes in the upper size range was likely the result of fewer diffraction spots reaching the detector for a given Debye ring because of the instrumental setup. The lower limit disagreements in calculated grain sizes are likely due to the ‘spottiness’ of the Debye rings approaching the pixel density of the detector, and therefore the grain sizes calculated reached an asymptotic lower limit. With the current setup of the micro-X-Ray diffraction laboratory, the grain size measurement technique appeared most effective in the grain size range of ~15–63 µm.

This study is available through American Mineralogist, but is it behind a paywall. I have a link to the author’s copy that I am free to distribute to anyone. So please ask if you wish to know more and hit the paywall.

CheMin on MSL

I also applied this method to the two-dimensional X-ray diffraction data returned by the Chemistry and Mineralogy (CheMin) instrument on the Mars Science Laboratory Curiosity. CheMin vibrates its samples in front of the X-ray beam to provide a random distribution of crystal orientations for diffraction, and this method quickly blurs out any grain size contribution to the Debye rings. One experiment was attempted without sample vibration, but the low signal-to-noise ratio resulting form the short integration times similarly blurs any grain size contribution to the image into the background noise. The NASA Planetary Data System label files for the images also question whether the halting of the vibration was successful. Portions of these analyses were presented at the 2014 Lunar and Planetary Science conference, and the abstract and poster are available.

Klug, H. P., & Alexander, L. E. (1974). X-ray diffraction procedures for polycrystalline and amorphous materials (2d ed.). New York: Wiley.