## 3 Results  
### Particle Size Distribution of Samples  
There are also parameters that influence the separation of particles by sieving such as amplitude, frequency, angle of vibration direction, opening and size of the sieving holes, average particle size, and the properties of the material taken for analysis [53; 54]. The ground powder with different particle sizes is shown in Figure 1.  
The initial step was to confirm that the established grinding/sieving process would produce granulometric fractions with distinct particle sizes. Table 1 shows the results of the particle size distribution by illustrating the masses of the sieves used and the masses of material left on each sieve following the sieving process. Using data from the particle size distribution table (Table 1), a number of characteristics were determined corresponding to the sieving mesh size (l\({}_{i}\)), such as the average particle size of fraction (d\({}_{i}\)), the cumulative percentage of material with a size between dimensions l\({}_{i}\) and l\({}_{i+1}\) of the adjacent sieves (a\({}_{i}\)), the percentage of material smaller than the size of the sieve mesh (T\({}_{i}\)), and the cumulative percentage of material larger than the size of the sieve mesh (R\({}_{i}\)). All these resulting characteristics can be observed in Table 2.  
For a more suggestive illustration of the data in Table 2, the data were represented graphically; T and R(%) were represented on the ordinate on a conveniently chosen scale, and on the abscissa, the size \(\mathrm{l_{i}}\) of the mesh sizes. The data obtained above were also used to calculate the average particle size of the initial material. Granulometric distribution curves, along with the Rosin-Rammler equation, can be seen in Figure 2. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Mesh Size of the** & **Sieve Mass** & **The Sample Mass** & **The Mass of the Sample** \\
**Sieve (mm)** & **(g)** & **Found on the Sieve (g)** & **Taken for Analysis (g)** \\ \hline
1.000 & 392.2 & 1.4 & \\
0.800 & 474.8 & 21.0 & \\
0.630 & 458.6 & 14.7 & \\
0.450 & 305.9 & 13.6 & \\
0.315 & 413.9 & 12.5 & \\
0.200 & 335.3 & 10.1 & \\
0.125 & 391.9 & 14.3 & \\
0 & 342.5 & 12.4 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The masses of the sieves used and the masses of material left on each sieve following the particle size distribution. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & & **The Percentage** & **The Percentage** & **The Percentage** \\
**Mesh Size of** & **The Average** & **a Size between** & **of Material** \\
**the Sieve** & **Particle Size of** & **Dimensions \(\mathrm{l_{i}}\)** & **Smaller Than** & **of Material** \\
**\(\mathrm{l_{i}}\) (mm)** & **Fraction \(\mathrm{d_{i}}\) (mm)** & **and \(\mathrm{l_{i+1}}\) of the** & **the Size of the** & **Larger Than the** \\  & & **Adjacent Sieves** & **Sieve Mesh** & **Mesh \(\mathrm{R_{i}}\) (\%)** \\  & & **a\({}_{1}\) (mm)** & **T\({}_{1}\) (\%)** & **Mesh \(\mathrm{R_{i}}\) (\%)** \\ \hline
0 & 0.063 & 12.40 & 0.00 & 100.00 \\
0.125 & 0.163 & 14.30 & 12.40 & 87.60 \\
0.200 & 0.258 & 10.10 & 26.70 & 73.30 \\
0.315 & 0.383 & 12.50 & 36.80 & 63.20 \\
0.450 & 0.540 & 13.60 & 49.30 & 50.70 \\
0.630 & 0.715 & 14.70 & 62.90 & 37.10 \\
0.800 & 0.900 & 21.00 & 77.60 & 22.40 \\
1.000 & 1.207 \({}^{*}\) & 1.40 & 86.20 & 13.80 \\ \hline \hline \end{tabular} \({}^{*}\) It was supposed that the mesh sizes of the sieves followed a ratio \(l_{i}=l_{i-1}\times\sqrt{2}\).  
\end{table} 
Table 2: Variation in ground material characteristics according to mesh size (\(\mathrm{l_{i}}\)).