My sample was ZnO doped PVA film. There is negative slope obtained from plotting the graph to find micro-strain. Could you explain the results so obtained ?
Your fit doesn't match your data very well so I would say something else is going on. Probably you have some anisotropy which makes peaks in some directions much wider than in others, and this effect is much more prominent than a W-H fit which only works for isotropic material.
Your fit doesn't match your data very well so I would say something else is going on. Probably you have some anisotropy which makes peaks in some directions much wider than in others, and this effect is much more prominent than a W-H fit which only works for isotropic material.
I believe, there is some problem in lower angle part. Please check. Otherwise, the slope is positive towards higher angle side. Again, your fit does not match the data points.
I would suggest to repeat your XRD measurements once again, a slow scan with much higher resolution, and then try replot and study your W-H plots once again.
K. Sreenivas
In comparison, if positive slope decreases with doping, then can we say that lattice is shrinking?
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).
Possible reasons:
1. Strain may not be the main cause [videJ. I. Langford, J. Appl. Cryst., 24 (1991) 913].
2. Gaussian stain distribution does not hold good for your sample [vide K.R. Beyerlein, R.L. Snyder, M. Li and P. Scardi, Philosophical Magazine, 90 (2010) 3891].
3. Due to stacking faults in the sample [vide K.R. Beyerlein, R.L. Snyder, M. Li and P. Scardi, Philosophical Magazine, 90 (2010) 3891 and B.E. Warren, Progr. Met. Phys., 8 (1959)147].
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