Reducing Particle Size and Crystallite Size Tim Fawcett ICDD, emeritus

Powder X-ray diffraction operates under the assumption that the sample is randomly arranged. Therefore, a statistically significant number of each plane of the crystal structure will be in the proper orientation to diffract the X-rays. Therefore, each plane will be represented in the signal.

State of the material ZnS Single Crystal Oriented Film Random Al Powder Complete Debye rings Friedrich, W., Knipping, P., and Laue, M., (1912), “Interferenz-Erscheinungen bei Röntgenstrahlen” Bayerische Akad. d. Wissenshaften zu Munchen, Sitzungsberichte, math.-phys. Kl, p. 303-322. Partially crystalline, oriented polymer Hull, (1917), “A new method of X-ray Crystal Analysis”

Powder X-ray diffraction operates under the assumption that the sample is randomly arranged. Therefore, a statistically significant number of each plane of the crystal structure will be in the proper orientation to diffract the X-rays. Therefore, each plane will be represented in the signal. The random powder allows us to scan in the two theta direction to produce a powder pattern

Particle statistics In a famous series of calculations published in Klug and Alexander it was calculated that IF a powder was crushed to 1 micron in size, the amount of powder in a large cavity mount, would be barely sufficient to achieve 1% reproducibility in intensity. This calculation assumed a single point detector having a small detection volume which in this example, at 1 micron, would detect 38,000 out of 38 billion particles in the sampling volume. Notice the dramatic increase in available particles as the size is decreased.

Particle statistics The theoretical calculation was backed by this experiment showing that small particle sizes were required to achieve any reproducibility in intensity.

Particle reduction Crush Grind Mill Sieve There are dozens of ways to reduce particle size but the common means are by mechanical force. This usually involves crushing, grinding and milling. This can be done in ton volumes with large industrial ball mill or small volumes in an agate mortar and pestle

Fine Dust M 200 mesh is a fine dust and equivalent to 74 microns

Particle reduction to 50 microns is usually very difficult especially with hard materials such as metals, cements and many minerals. Even if we reduced all the particles to 1 micron there would still be safety concerns due to dust hazards and increased chemical reactivity caused by high surface areas. At 50 microns you might have 2-10% relative error in intensity measurement – that could directly translate to a quantitative analysis. This is a very practical and real limitation to quantitative analysis by X-ray diffraction methods. The error in a single experimental determination can be very small since it is a function of the experimental signal to noise. Particle statistics errors are typically much larger since it relates to the ability to reproduce the experiment repeatedly and have each phase randomly distributed in each experiment for a given sampling volume.

But wait there is more …………

What to do ? The prior and historic calculations use several assumptions which were common for Bragg-Brentano diffractometers, using point detectors and cavity mounts. The particles are packed in a stationary position in a cavity mount The detector is a point detector and samples a small area of the total volume of the diffraction sphere surrounding the specimen The calculation uses particle sizes Improve your statistics by Move the particles so a single particle can contribute to many peaks Use an area detector (2D, detector array, photographic film) to increase the detection volume 3) Diffraction physics require crystallite size and crystallites to be in proper orientation – there can be many crystallites in a particle. For example there can be 100,000 nanocubes of 100 Å crystallites in a 1 micron cubic particle.

ChemMin on Mars rover Piezoelectric coupler Integration with CCD (low resolution) 3) Long data collection First dataset from Mars ! Constant particle rotation and data integration over 8 hours

Example: ChemMin and the Mars rover Improve your statistics by: Move the particles so a single particle can contribute to many diffraction peaks The Mars team developed an innovative piezoelectric coupling device that vibrates the particles within the specimen volume improving the particle statistics by rotating different particles into the proper diffracting position. To do quantitative analysis they integrated their data over long periods of time – improving signal to noise as the time allowed the individual particles to rotate into position. Use an area detector (2D, detector array, photographic film) to increase the detection volume The Mars team used a CCD camera allowing for 2D area detection. While this configuration resulted in a lower resolution, intensity statistics were dramatically improved.

For this specific case with a single isolated particle. The particle, grain and crystallite size might be very similar. More typically particles are composed of many grains. The relationship between grain and crystallites is determined by the microstructural defects and surface chemistry which can disrupt the crystallite size but might not change the grain size. The particle size is almost always the largest size since it includes multiple grains and crystallites. Different methods measure different sizes particles versus crystallites. 10-12 nm scattering 7 nm (XRD) Crystallite Size (XRD) “The perfect crystalline domain” Particle Size - Light scattering Grain Size (TEM) (Note: size measured using multiple TEM images)

Diffraction measures crystallite size and distribution not particle size and sometimes you get lucky ! These are photomicrographs of corrosion on iron and copper. In each picture the particles are 10-40 microns in size, but each particle is actually a cluster of crystals. The crystals themselves have many orientations and are composed of thousands of crystallites. Many corrosion processes will produce a random powder pattern even if the particles are larger, due to the random orientation of smaller crystallites within a crystal cluster. This is also the reason why one can often analyze a piece of corroded metal with very little specimen preparation and still produce a random pattern of the corrosion products good enough for phase identification.

Move the particles so a single particle can contribute to many peaks In the early diffraction experiments by nobel prize winners W.H. Bragg and W.L. Bragg they rotated single crystals to bring multiple planes into the diffraction condition to produce a pattern. In subsequent years small specimens could be mounted on a capillary and were precessed to produce a powder pattern. The schematic shows the rotation of a specimen through different axes using a Gondolfi camera. This concept is used in several different devices today.

Move the particles so a single particle can contribute to many peak In general any device that translates, rotates, vibrates or precesses the specimen will improve your particle statistics. Vibration and precession are the most effective since they will move the particles in three dimensions. Translation devices work a little differently since they tend to bring more specimen into the sampling volume (area irradiated by the X-ray beam). Many diffractometers use a line focus and have a circular specimen holder, rotation tends to bring all the specimen into the irradiated sampling volume. Rotation Sampling volume with a line focus tube

Conclusions The majority of diffraction experiments are limited in getting reproducible intensities by particle statistics. This limits our abilities in quantitative analysis and structure solution The most effective way to improve particle statistics is to reduce particle size to ~1 um. This greatly increases the number of particles in a given sampling volume usually by several orders of magnitude. Statistics can also be improved by moving the specimen and using multidimensional detectors that sample more of the diffraction volume