In literature, for plotting the Williamson-Hall plot the x-axis is given as both Sin (theta) or 4 Sin (theta). Which are the proper parameters to plot Williamson-Hall plot? Please explain the corect procedure.
both are correct
you can plot graph using either sin theta or 4 sin theta. according to your plot calculation of strain will be changed.
For more accurate calculation, you may use size-strain plot. refer following link
http://file.scirp.org/pdf/WJNSE_2014031314102564.pdf
Dear Swamini,
The following paper will be helpful for you
Solid State Sciences 13 (2011) 251-256
Best regards, A. Ahad
Dear Swamini,
Please go through these links,
1). http://www.sciencedirect.com/science/article/pii/S1293255810004607
2). http://link.springer.com/article/10.1186/2251-7235-6-6
3). http://file.scirp.org/pdf/WJNSE_2014031314102564.pdf
Best regards
Sandeep
For Scherrer equation, crystallite size was calculated based on the measurement of a(hkl) peak using the following equation:
L =Kλ / Bsize cos θ
where L is crystallite size, K is a dimensionless shape factor (0.9), Bsize is line broadening at half of the maximum intensity (FWHM) in radian, λ is the X-ray wavelength for example for Cu Kα radiation (1.5406 Å) and θ is Bragg angle in degree.
Meanwhile, Williamson–Hall plot was used to estimate the crystallite size and lattice strain of the samples using the following formalism:
Btot = Bstrain + Bsize = 4Cε tanθ + Kλ/ L cosθ
where Cɛ is the lattice strain, Βsize is the particle size broadening, Βstrain is the strain broadening, L is the crystallite size, K is a dimensionless shape factor (0.9), λ is the X-ray wavelength for Cu Kα radiation (1.5406 Å) and θ is Bragg angle in degree.
Then Eq. 2 is multiplied by cosθ to yield:
Btot cosθ = 4Cε sinθ + Kλ/L
Hence, by plotting the graph of Βtot cosθ against 4 sinθ, the lattice strain, Cɛ of the sample can be obtained from the slope (gradient) while the crystallite size can be estimated from the intercept (Kλ/L).
Swamini Chopra The Williamson-Hall Plot. W-H plot is used to calculate the crystallite size and microstrain from complex XRD data. That's when both the crystallite size and microstrain vary as a function of the Bragg's angle, we can only calculate these parameters from XRD data using W-H plot. I have provided the practice file (Origin file) as well as the calculation file (Excel file) in the video description. Thanks
https://youtu.be/ipX3iUJ5VcU
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