Hope this helps!

I think the main issue is the data collection- very low intensity and low S/N ratio. Try setting your diffractometer on one of the lower diffraction peaks (say ~81) and work with your sample mounting to maximize intensity. You can also vary the slits and collection time on that peak only to maximize s/n.

Once you've done that, try another wide angle collection, slow as you can, with the conditions you've optimized. For the analysis, I believe data points are selected based on the phase, but your effective resolution of the data has room to improve. Better data = better derived calculations.

Best of luck with experiments!

Dear Robert Haaring,

as straight answer, yes it is wrong.

The ideal is to fit your diffraction using Rietveld and calculate your particle size and strength. In this way, the result would be represented by all peaks from your diffraction.

One perfect crystal would extend itself in all directions up to infinity.

However, no crystal is perfect due to their finite size, geo-formation or synthetic route.

Their intrinsic natural deviation from perfect crystallinity is responsible for the broadening of the diffraction peaks, imposing or not some directional strength. The two main properties that we may extract from peak width are crystallite size and lattice strain.

Crystallite size may be treated as a direct measure of the size of a coherently diffracting domain, in a two-dimensional point of view.

The significance in the broadening of peaks evidences grain unconformity with the considerable strain associated with the whole powder.

The Williansom-Hall equations assume that the crystal is uniform in all crystallographic directions, so it considers the isotropic nature of the crystal.

In some sense, the material properties are independent of the direction along which they are measured.

It is somewhat a mistake to consider the isotropic nature of the crystal as pure independent of the direction along which they are measured, based on some points not important in this answer.

Aim to correct the assumption that only isotropic solid is reasonable to be directly measured, the anisotropic nature of Young's modulus of the crystal is more realistic and may be applied.

Thus, it is clear and somehow expected that a Williamson-Hall plot for a given sample may result in different values for lattice strain and crystallite size if compared with some other mathematical approaches where the anisotropic nature of a crystal is considered. The same limitation would be valid for Scherrer equation, which considers all your particles as spherical ones with about the same diameter. That condition is never achieved in real samples. Nevertheless, it is a widely used evaluation, sometimes ignoring the limitations, giving you a particle size range idea of your sample.

Best regards,

WNM

Dear Robert Haaring, if you want to obtain an accurate result by Williamson-Hall analysis in XRD, I think you have to select all reflections.

But, there are some reflections at high angles (where the precision is usually lower) on your XRD pattern and Williamson-Hall analysis is not a precise method in these cases. Therefore, I suggest you to use "size estrain plot” (SSP) method which has the advantage that less weight is given to data from reflections at high

angles.

You can read more about SSP method in this article:

Article Low temperature facile synthesis of Pseudowollastonite nanop...