## Materials and Methods
### Methods
#### 2.2.3 Compact Characterization (Analysis)  
Crushing Strength  
Samples of Avicel PH-101, Avicel PH-101 subjected to 1 st, 2 nd, and 3 rd compaction cycles were compressed (500 mg each) into tablets using a single punch tablet press (Manesty F3 single stroke tablet press; West Pharma services Ltd., Dorset, UK) at an applied pressure of 35 units on the scale of the machine. The fitted die was flat, round and 12 mm in diameter. The crushing force of the tablets produced was tested using a hardness tester (Pharma Test PTB 311E, Hainburg, Germany).  
Compression Analysis Using Heckel and Kawakita Models  
Samples of non-compacted Avicel PH-101 and Avicel PH-101 subjected to 1 st, 2 nd, and 3 rd compaction cycles were compressed into tablets using an instrumental tablet press (GTP-1, Gamlen Tablet Press Ltd., Nottingham, UK). The compression speed was fixed at 60 mm/min for five applied loads; 100, 200, 300, 400, and 500 kg. The samples, 100 \(\pm\) 1 mg, were poured into 6 mm dies. Kawakita and Heckel models were utilized in order to describe the compression behavior of the powders [31; 32; 33].  
Figure 1: Illustrative demonstration of the peak heights of microcrystalline cellulose (MCC) used for the calculation of the CrI and full-width at half-maximum (FWHM) values.  
1. Heckel Analysis  
The most universally accepted method used to describe the porosity of a powder bed during compaction and the applied pressure is the Heckel model (Equation (1)) [37]:  
\[ln\left(\frac{1}{1-D}\right)=KP+A \tag{1}\]  
where \(P\) is the pressure applied, \(D\) is the relative density (compact density at pressure \(P\)/powder true density), \(A\) is a constant, and \(K\) is the slope of the linear portion of the Heckel plot [37]. True density was measured using a gas pycrometer (Ultrapycrometer 1000, Quantachrome, Boynton Beach, FL, USA). The average of 5 readings for each sample was used.  
Heckel curves were then constructed by plotting \(ln(1/1-D)\), the variation of powder porosity, and P (compression pressure in MPa). The reciprocal of the slope of the linear portion of the Heckel curve is referred to as the yield pressure (Py) that indicates the mechanism occurring during compression and measured deformability.  
When D\({}_{0}\) is considered as the relative loose powder density at zero pressure describing the initial rearrangement of the powder during die filling, it is equal to the point of intersection of the Heckel plot with the \(y\)-axis representing the left-hand side of Equation (1) [37; 38]. From the intercept of the linear portion of the Heckel plot, the relative density parameter, Da, can be obtained as follows [38]:  
\[\mathrm{D_{a}}=1-\mathrm{e^{-A}} \tag{2}\]  
The relative density of a powder at low pressure (D\({}_{\mathrm{b}}\)) can then be obtained:  
\[\mathrm{D_{b}}=\mathrm{D_{a}}-\mathrm{D_{0}} \tag{3}\]  
D\({}_{\mathrm{b}}\) is the difference in the actual relative densities between the powder at zero pressure (measured as the intercept of the Heckel curve at P = 0.0 MPa) and extrapolated from the linear portion of the Heckel plot. The relative density, D\({}_{\mathrm{b}}\), describes the rearrangement phase of particles during the initial stages of compression [38; 39]. The \(P_{Y}\) value is a measure of the extent of plastic deformation. This extent increases when the \(P_{Y}\) value decreases. In contrast, materials undergo fragmentation by brittle-fracture if the value increases.  
1. Kawakita Analysis  
The Kawakita equation describes the relationship between the volume reduction and applied pressure as follows (Equation (4)) [40]:  
\[\frac{P}{C}=\frac{P}{a}+\frac{1}{ab} \tag{4}\]  
where \(P\) is the applied pressure; \(a\) and \(b\) are constants characteristic of the powder being compressed. \(C\) is the degree of volume reduction, as defined in (Equation (5)).  
\[C=\frac{V_{0}-V}{V_{0}} \tag{5}\]  
where \(V_{0}\) is the initial bulk volume and \(V\) is the volume at pressure of \(P\)[40; 41].  
From the graphical presentation of \(