International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C. ch. 2.3, p. 62

Section 2.3.3.1.2. Crystallite-size effects

W. Parrisha and J. I. Langfordb

a IBM Almaden Research Center, San Jose, CA, USA, and bSchool of Physics & Astronomy, University of Birmingham, Birmingham B15 2TT, England

2.3.3.1.2. Crystallite-size effects

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In addition to profile broadening, which begins to appear when the crystallite sizes are [\lt] 1–2 μm, the sizes have a strong effect on the absolute and relative intensities (de Wolff, Taylor & Parrish, 1959[link]; Parrish & Huang, 1983[link]). The particle sizes have to be less than about 5 μm to achieve 1% reproducible relative intensities from a stationary specimen in conventional diffractometer geometry (Klug & Alexander, 1974[link]). The statistical errors arising from the number of particles irradiated can be greatly reduced by using smaller particles and rotating the specimen around the diffraction vector. This brings many more particles into reflecting orientations.

The particle-size effect is illustrated in Fig. 2.3.3.2[link] for specimens of NIST silicon standard powder 640 sifted to different size fractions. The powders were packed in a 1 mm deep cavity in a 25.4 mm diameter Al holder using 5% collodion/amyl acetate binder. They were rotated by a synchronous motor (a stepper motor can also be used) around the axis normal to the centre of the specimen surface with the detector arm fixed at the peak position and the intensity recorded with a strip-chart. Rapid rotation, ∼60 r min−1, gives the average peak intensity for all azimuths of the specimen and the small variations result only from the counting statistics. Scaling the intensities to (111) = 100% for the 5–10 μm fraction, the 10–20 μm fraction is 94%, 20–30 μm 88% and [\gt\, 30] μm 59%. The decrease is probably due to lower particle-packing density and increasing interparticle microabsorption. The [\gt \, 5] μm fraction = 95% may be due to the larger ratio of oxide coating around the particles to the mass of the particles.

[Figure 2.3.3.2]

Figure 2.3.3.2| top | pdf |

Effect of specimen rotation and particle size on Si powder intensity using a conventional diffractometer (Fig. 2.3.1.3[link]) and Cu Kα. Numbers below fast rotation are the average intensities.

Slow rotation, ∼1/7 r min−1, shows the variation of the peak intensity with azimuth angle [\varphi]. The pattern repeats after 360° rotation and the magnitude of the fluctuations increases with increasing particle sizes and resolution. There is no correlation between the fluctuations of different reflections, as can be seen by comparing the 111, 220 and 311 reflections of the 10–20 μm specimen (lower left side) for which the incident-beam intensity was adjusted to give the same average amplitude. The horizontal lines are ±10% of the average. This shows the magnitude of errors that could occur using stationary specimens. Similar particle-size effects were found using the integrated intensities derived from profile fitting. The above discussion and Fig. 2.3.3.2[link] refer to a continuous scan. If the step-scan mode is used to collect data, it is clearly not necessary to rotate the specimen through more than one revolution at each step.

The rotating specimen also averages the in-plane preferred orientation but has virtually no effect on the planes oriented parallel to the specimen surface. The slow rotation method is useful in testing the grinding and sifting stages in specimen preparation. When calibrated with known size fractions, it can be used as a rough qualitative measure of the particle sizes.

References

First citation Klug, H. P. & Alexander, L. E. (1974). X-ray diffraction procedures for polycrystalline and amorphous materials, 2nd ed. New York: John Wiley.Google Scholar
First citation Parrish, W. & Huang, T. C. (1983). Accuracy and precision in X-ray polycrystalline diffraction. Adv. X-ray Anal. 26, 35–44.Google Scholar
First citation Wolff, P. M. de, Taylor, J. & Parrish, W. (1959). Experimental study of effect of crystallite size statistics on X-ray diffractometer intensities. J. Appl. Phys. 30, 63–69.Google Scholar








































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