Calculation of structural parameters using XRD patterns:

Step 1: Procedure for finding peak positions and full width at Half-maxima (FWHM).

Select the data for one of the peaks as shown in Figure 4.09 and execute the Gaussian single peak fit using any software (say, Origin).

Figure 4.09: Fitting of XRD pattern using Gaussian fit and the resulting parameters.

The peak position and FWHM can be directly obtained from xc and FWHM

The obtained values are
(1) Peak 1 (110); 2θ = 44.68°; FWHM = 0.80901°.
(2) Peak 2 (200); 2θ = 65.045°; FWHM = 1.50079°.
(3) Peak 3 (211); 2θ = 82.39°; FWHM = 1.5103°.

While the values of d decreases with increasing the diffraction angle, the lattice constant remains almost constant, irrespective of the peak we use for analysis.

Furthermore, the crystallite size varies significantly with the peaks. Considering the majority of the planes [as (110)] based on the intensity in the XRD pattern, the average crystallite size can be quantified as simply as 10.6 nm.