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Powder X-ray Diffraction Basic Course - Sixth Installment: Evaluation of crystallite size

Masaaki Konishi

Summer 2023 Volume 39, No. 2 , 18-22

Powder X-ray diffraction (PXRD) can obtain a variety of information, not just a single piece of information. In the fifth installment of the powder X-ray diffraction basic course, quantitative analysis was described. This sixth installment describes the evaluation of crystallite sizes.

The Scherrer method is one analysis technique commonly used to evaluate crystallite sizes. This method assumes there is no crystallite size distribution or lattice strain, and simply calculates the crystallite size from the width of a single diffraction peak using the Scherrer equation. This method requires the measurement of a width standard material to correct the width to obtain an accurate crystallite size.

On the other hand, evaluation of crystallite sizes using a FP (Fundamental Parameter) method can be corrected by calculating the width attributed to the equipment. This method can analyze crystallite sizes less than 300 nm with an accuracy of a few nm regardless of the optical system conditions and measurement instruments. Even for large crystallite sizes of 100–300 nm, it is possible to calculate highly accurate crystallite sizes and their distributions and, furthermore, to evaluate them accounting for crystallite anisotropy.

Highlights

  • Crystallite size is not the same as particle size; it is the size of a single diffracting domain, and smaller crystallites produce broader diffraction peaks.
  • Peak broadening can come from both small crystallite size and lattice strain, so strain can make a simple size estimate look smaller than it really is.
  • The Scherrer method is quick and useful, but it depends on good instrument-broadening correction and becomes much less reliable once crystallite size gets above about 100 nm.
  • The FP method separates instrument effects more rigorously and can measure roughly 100–300 nm crystallites with accuracy of only a few nanometers, largely independent of slit settings or instrument used.
  • The FP method can also estimate size distributions and detect anisotropy, such as zinc oxide crystallites being larger along the c-axis than along the a-axis.

Summary

In XRD, crystallite size means the size of a region that behaves like a single crystal during diffraction. That is different from particle size, because one particle can contain multiple crystallites. A basic rule is that smaller crystallites give broader diffraction peaks.

The catch is that peak broadening is not caused only by crystallite size. Lattice strain also broadens peaks, and the instrument itself adds broadening too. Because of that, a simple calculation can be misleading unless those effects are corrected. The Scherrer method is the easiest approach and works reasonably well for smaller crystallites, especially below about 100 nm, but it becomes less dependable for larger sizes.

A more advanced approach is the FP method. Instead of using just one peak width in a simple equation, it models the instrument and fits the diffraction profile more completely. That makes it much more accurate for larger crystallites, lets you estimate size distributions, and can even show whether crystallites grow differently in different crystal directions. Results were also consistent with SEM, laser diffraction, and USAXS measurements in the comparison shown.

Frequently asked questions

Crystallite size is the size of the smallest coherent domain that contributes to diffraction as if it were a single crystal. It is not automatically the same as particle size. A nanoparticle may be one crystallite, but a larger particle can contain several crystallites.

When crystallites get smaller, the diffraction peak width increases. In practice, this means broad peaks often suggest fine crystallites. But broad peaks are not proof of small size by themselves, because other effects can broaden peaks too.

Lattice strain is a major second cause. If the lattice spacing varies slightly across the sample, diffraction from slightly different spacings overlaps and broadens the peak. Instrumental broadening also contributes, so the measured peak width is a combination of sample effects and instrument effects.

It is a good choice when you want a simple, fast estimate and the crystallites are relatively small. It works best when strain is negligible and instrument broadening has been corrected with a width standard. The results are generally reliable below about 100 nm, but accuracy drops for larger crystallites.

Because lattice-strain broadening becomes more pronounced at higher angles. Using lower-angle peaks reduces the strain contribution and gives a size estimate that is less distorted by strain. If the goal is to study the strain itself, measuring out to high angles is more useful.

A width standard is used to measure how much broadening comes from the instrument rather than the sample. A standard such as NIST LaB6 is measured under the same slit conditions, and that instrumental contribution is then removed or refined during analysis. Without that correction, the calculated crystallite size can be wrong.

The FP method models the instrument profile and fits the observed diffraction pattern more rigorously. That makes it much less sensitive to hardware differences and optical settings. In the comparisons shown, sizes around 200 nm stayed consistent to within only a few nanometers across different slit settings and instruments.

Yes. With FP-based whole-pattern fitting, XRD can estimate a crystallite size distribution and can also account for anisotropy. In the zinc oxide example, the crystallites were larger along the c-axis than along the a-axis, showing direction-dependent growth rather than a purely spherical size model.

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