1. Reducing Particle Size and Crystallite Size
Tim Fawcett
ICDD, emeritus

2. 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.

3. 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
Partially crystalline,
oriented polymer
Hull, (1917), “A new method of X-ray
Crystal Analysis”

4. 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

5. 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.

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

7. 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

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

9. 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.

10. But wait there is more …………

11. 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.

12. 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

13. 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.

14. 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)

15. 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.

16. 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.

17. 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

18. 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