## 3 Results and Discussion
### X-Ray Diffraction
The Scherrer equation (Equation (1)) can be used to obtain the average particle size using the adjusted physical broadening [43,51]:  
\[D_{Sh}=\frac{k\times\lambda}{\beta\times cos\theta} \tag{1}\]  
where \(D_{Sh}\) is the crystallite size, \(\beta\) is the full width at half maximum of the peak, \(2\theta\) is the peak position, k is the shape factor (typically around 0.89), and \(\lambda\) is the incident X-ray wavelength (0.15418 nm). The dislocation density is calculated by the inverse of the square of crystallite size:  
\[\delta=1/D_{Sh}^{2} \tag{2}\]  
The calculated parameters are regrouped in Table 1.  
However, [PERSON]'s method takes only into account the crystallite size effect on XRD peak broadening, but it says nothing about the lattice microstructures such as intrinsic stress, which occurs in nanocrystals due to point defects, grain boundaries, triple junctions, and stacking faults [40,52]. These effects induce XRD peak broadening and are taken into account in the Williamson-Hall (W-H) method. This approach can be used for the calculation of intrinsic stress and crystallite size (\(D_{W-H}\)). The Williamson-Hall method \begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{**Samples**} & **Miller** & & & **Average** & **Dislocation** & **Average** & **Dislocation** \\  & **Indices** & **20 (\({}^{\circ}\))** & \(\beta\) (\({}^{\circ}\))** & **Crystallite** & **Density (\(\delta\))** & **Crystallite** & **Density (\(\delta\))** \\  & **(hkl)** & & & **Size (nm)** & **(nm\({}^{-2}\))** & **Size (nm)** & **(nm\({}^{-2}\))** \\ \cline{5-8}  & & & & **By Scherrer Method** & & **By WSH Method** \\ \hline \multirow{8}{*}{Powder} & (111) & 10.97 & 0.184 & & & & \\ \cline{2-8}  & (220) & 17.83 & 0.227 & & & & \\ \cline{2-8}  & (311) & 20.90 & 0.224 & & & & \\ \cline{2-8}  & (222) & 21.88 & 0.208 & & & & \\ \cline{2-8}  & (331) & 27.56 & 0.293 & & & & \\ \cline{2-8}  & (420) & 28.27 & 0.201 & & & & \\ \cline{2-8}  & (422) & 31.03 & 0.264 & & & & \\ \cline{2-8}  & (511) & 32.975 & 0.243 & & & & \\ \hline \multirow{8}{*}{C60-3h} & (111) & 10.84 & 0.1976 & & & & \\ \cline{2-8}  & (220) & 17.72 & 0.258 & & & & \\ \cline{2-8}  & (311) & 20.80 & 0.213 & & & & \\ \cline{2-8}  & (222) & 21.45 & 0.168 & & & & \\ \hline \multirow{8}{*}{C60-5h} & (111) & 11.02 & 0.236 & & & & \\ \cline{2-8}  & (220) & 17.92 & 0.355 & & & & \\ \cline{2-8}  & (311) & 21.00 & 0.266 & & & & \\ \cline{2-8}  & (222) & 21.67 & 0.181 & & & & \\ \hline \multirow{8}{*}{C60-8h} & (111) & 10.85 & 0.230 & & & & \\ \cline{2-8}  & (220) & 17.77 & 0.246 & & & & \\ \cline{1-1} \cline{2-8}  & (311) & 20.82 & 0.188 & & & & \\ \cline{1-1} \cline{2-8}  & (222) & 21.45 & 0.166 & & & & \\ \hline \end{tabular}
\end{table} 
Table 1: Microstructural values for powder C\({}_{60}\)-3h, C\({}_{60}\)-5h, and C\({}_{60}\)-8h using the Scherrer and W-H approaches. is comparably easy and simple [53; 54]; the uniform deformation model is given by the following equation:  
\[\beta\times cos\theta=\varepsilon\;(4 sin\theta)+\frac{k\times\lambda}{D_{W-H}} \tag{3}\]  
Equation (3) plots as a line; \(\varepsilon\) is the slope of the line, which specifies the intrinsic strain value, while the intercept gives the average crystalline size of C\({}_{60}\) nanocrystals. The origin of the lattice strain is attributed mainly to the lattice expansion or contraction in nanocrystals due to size confinement, as the atomic arrangement can be altered due to size confinement. The extracted W-H values are presented in Table 1 and shown in Figure 5.  
From Table 1, the Scherrer method presents acceptable results as the crystallite sizes of the deposed films are adjacent to that of the powder, while by the WSH method there is a large rise in the value of this parameter from that of the powder to those of the deposed layers. As Figure 5 shows, the strain (\(\varepsilon\)) can be negative, indicating the lattice contraction (compression), or positive, meaning dilatation.