There are many ways to calculate crystallite size and lattice strain of a sample, based on XRD peaks: "Scherrer" calculation, "Williamson-Hall" or "Rietveld".
Each method or calculation is used for what kind of combination, and grain size? and what are the limitations and drawbacks of each method?
Laroussi Chaabane
Accuracy is always defined by comparison against a known, certified reference material. One of the few available is the SRM 1979 material from NIST which contains both 15 and 60 nm crystallite sizes. See attached certificate for the way the values were certified. The Scardi & Leoni model was used for crystallite size.
In broad terms there are 3 contributions to broadening:
- Size (I've always used 100 nm as an upper limit based on determining the width for broadening. Other people claim bigger top limits. Practical constraints limit the lower limit to 1 nm or so )
- Strain
- Instrument
The Warren correction should be used for the instrumental broadening (LaB6 can be used to determine this). Scherrer does not distinguish between these 3 forms of broadening; Williamson-Hall will deal with stress/strain and Rietveld is basically a peak-fitting solution.
Youssef Larbah
On what basis? The Rietveld analysis is named after a person and should always be upper-case...
The results of these methods are better defined peak parameters and, for the Rietveld refinements, optimized atomic positions. These methods are often used to deconvolute strongly overlapping peaks, to describe minor differences between a reference material and the unknown sample, for unit cell refinements or for quantitative analysis
Youssef Larbah
OK, then please display a Rietveld analysis for the NIST SRM 1979 material.
Scherrer method is the best method to calculate the average crystallite size from XRD pattern.
K. Manjunatha
Scherrer does not separate out the broadening due to the 3 factors: crystallite size, strain, and instrumental...
The instrumental broadening is assessed with a known crystalline substance (often LaB6 from NIST but there are many other materials) followed by the Warren correction. Strain and size can be separated by the Williamson-Hall approach. The degree of broadening is difficult to assess at crystallite sizes > 100 nm.
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