Please tell me how to calculate Crystal Size using XRD Data?
No. Pos. [°2Th.] FWHM [°2Th.] d-spacing [Å]
1. 6.0974, 0.3149, 14.49535,
2. 40.9764, 0.576, 2.20077,
out of different diffracted peaks, which peak we have to select for particle size calculation using Sherrer formula.
The calculation using Scherrer formula assumes a certain shape factor and generally isotropic. In real life crystals neither of those assumptions are true but far from it.
"usually an average of all peaks" will only smudge the data and give you an average "isotropic" reciprocal space parameter and hence a "smudged" interpretation. The use of "(h00), (0k0) and (00l) peaks" will give a better estimate of the an-isotropic character of the real life sample.
The broadening of X-ray diffractions reflections can be investigated using different methods: (1) the Scherrer method, (2) the Warren-Averbach approach, (3) the Langford method, (4) several whole pattern analysis approaches (Kojdecki method, Leoni method,...), (5) and others.
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Another point is that Scherrer not always gives you a real crystallite size value, this because the FWHM is affected not only by the particle size as by the structural strain. It must be pointed out also that the shape constant (k = 0.89 ~0.9) is used for spherical particles, so that you need to be sure that your crystallits are spherical.
1) lambda is the wavelength of the radiation used to collect the data. For example 1.54Å for Cu K-alpha or 1.79Å for Co K-alpha. So it is independent of the sample chemistry.
2a) the answer might be: "both" - the so-called Scherrer constant is a function of the crystallite geometry so 0.94 and 0.89 are both potentially "correct" values of this constant. You can look this up in a variety of references.
2b) the useful answer might also be: "it probably doesn't matter" - because except in unusual circumstances the error in the derived crystallite size is likely much larger than the ~4% difference between the two constants.