Researchers often calculate the dislocation density from XRD by using the Warren-Averbach method or by using the outputs of Williamson-Hall method . I want to know which is better and why? and what are the limitations of both? Does the type of peak fitting profile function used also affect the outputs (and how much)?
Dear Akeshwar Singh Yadav,
1. Williamson-Hall method :
The Williamson-Hall method confirms its merit for a rapid overview of the line broadening effects and possible understanding of the main causes. The anisotropic character of line broadening for deformed hematite as a function of grinding variables was revealed. From the Williamson-Hall plots, it is understood that strain and size contributions exist simultaneously in the milled samples.
The Williamson – Hall approach, can be used to deconvolute the contributions from both stress and particle size contributions on XRD peak broadening. As mentioned previously, this approach assumes strain broadening is strictly caused by dislocations and relates FWHM and IB to crystallite size, dislocation density and the Burgers vector.
2. Warren-Averbach method :
The Warren–Averbach derived another definition of domain size: the surface weighted average. The Warren-Averbach method originally was developed for plastically deformed material, but since its introduction it found successful applications to many other materials. The method is described extensively by Warren (1969). Each domain is represented by columns of cells along the direction normal to the diffracting planes (001). According to Warren, the distribution of diffracted power can be expressed as a Fourier series. The convolution of the size and strain contributions on the profile in reciprocal space corresponds to the product of the Fourier transforms in real space.
As seen by the Warren-Averbach method, the planetary mill products yield the smallest crystallites and the maximum root mean square strain (RMSS) (with the exception of the ground sample within one hour and low media surface). Similar to the W-H approach, the Warren – Averbach (W-A) approach considers size broadening to be angle independent and strain broadening to be diffraction angle dependent. The W-A approach that is often used to deconvolute size-strain broadening is perhaps the least constrained method for analyzing XRD peak broadening.
I hope I have answered your question.
With Best Wishes,
Samir G. Pandya
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