## 3 Results and Discussion
### XRD Analysis  
The crystalline structures of the samples were investigated using X-ray diffraction. The XRD spectrum plots of the CNCs sample and the commercially sourced MCC are shown in Figure 6. The two samples' general X-ray diffraction patterns were similar, with four distinct \(2\theta\) diffraction peaks (15\({}^{\circ}\), 16.4\({}^{\circ}\), 22.7\({}^{\circ}\), and 34.5\({}^{\circ}\)) that correspond to the (1'10), (110), (002), and (004) crystallographic planes of the monoclinic cellulose \(l\beta\) lattice [33], in agreement with published reports by [PERSON], [PERSON], and [PERSON] [34]. The crystalline structure of the cellulose is represented by the third prominent diffraction peak (22.7\({}^{\circ}\)) for the cellulose \(l\beta\) structure. The similarity of these patterns indicates that the crystalline structure of the cellulose \(l\beta\) within the MCC sample was preserved after sulfuric acid hydrolysis [35]. Crystallinity indices for samples are tabulated in (Table 11); these values were calculated using Equation (3) [36], where \(I_{002}\) is the intensity of the 002 peaks (\(2\theta=22.7^{\circ}\)) and \(I_{am}\) is the intensity of the local minima between the 002 and 110 peaks (\(2\theta\) between 18\({}^{\circ}\) and 19\({}^{\circ}\)). Although the ultrasonic method and enzymatic hydrolysis were claimed to enhance crystallinity by 22.29%, the crystallinity indices of the MCC and CNCs samples were found to be 74.90% and 83.84%, respectively, representing an appreciable increase of 8.9% in the samples' crystallinity indices [10; 13]. The addition of a strong acid like sulfuric acid (H\({}_{2}\)SO\({}_{4}\)) not only serves to break the amorphous area of the cellulose, but also to  
Figure 5: FTIR spectra of cellulose nanocrystals (CNCs) with reference of standard (MCC). destroy parts of the crystalline structure; this is why this observation of comparably lesser rise agrees with [PERSON], [PERSON], and [PERSON] [9]. \[X(crystallinity)=\frac{I_{002}-I_{am}}{I_{022}}\times 100\% \tag{3}\]  
According to Equation (4), where \(d\) is interplanar distance; \(h,k,\) and \(l\) are crystal indices; \(a\), \(b\), and \(c\) are lattice parameters; and \(\beta\) is the angle between the incident X-ray beam and the crystal plane. The interplanar distance (from Bragg's = 2\(d\) sin\(\theta\)), crystal indices and lattice parameters were utilized to determine the lattice geometry and unit cell volumes [37]. Samples of MCC and CNCs had interplanar distances of 5.20, 4.13, and 1.97, based on their (020), (200), and (004) crystal orientations, respectively. The estimated values for the three constants of the lattice structure are as follows: \(a\) = 8.26, \(b\) = 10.40, and \(c\) = 7.88. The refined unit cell has a volume of 677 A\({}^{3}\). The data is given in Table 1, and it is consistent with previous research that found the unit cell volume to be 685.3 A\({}^{3}\)[35]. \[\frac{1}{d^{2}}=\frac{1}{sin\beta^{2}}\left(\frac{h^{2}}{a^{2}}+\frac{k^{2}sin \beta^{2}}{b^{2}}+\frac{l^{2}}{c^{2}}-\frac{2 hlcos\beta}{ac}\right) \tag{4}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Samples**} & **Peak** & **Crystal** & **Interplanar** & **Lattice** & **Volume of** \\  & **Position, 20** & **Indices,** & **Distance,** & **Parameter, \(a\
eq\pm b\
eq c\)** & **the Unit Cell, (Å\({}^{3}\))** & **Cell, (Å\({}^{3}\))** \\  & **(\({}^{\circ}\))** & **(\({}^{\circ}\))** & **(\({}^{\circ}\))** & **(Å)** & \(V\) = (\(abscin\beta\))** \\ \cline{3-6}  & & & & & \\ \cline{3-6}  & & & & & \\ \hline MCC\& 17.09 & 020 & 5.20 & & & \\ CNCs & 22.98 & 200 & 4.3 & & & \\ \cline{3-6} CNCs & 34.54 & 004 & 1.97 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Calculated values of lattice parameter (\(a\), \(b\) and \(c\)) of (MCC) and (CNCs). Figure 6: XRD spectrum of synthesized (CNCs) with reference to the spectrum of standard (MCC) (JCPDS No. 00-060-1502). Dislocation strain on the crystal lattice and crystallite size can be evaluated by analyzing the peak broadening in an XRD pattern [38].