## 2 Materials and Methods
### Characterization  
Particle characterization was performed for all the fractions by considering a variety of specifications and methods: density and size of particle, the weight percentage distribution, LOI (according to ASTM C311-04), mineralogical analysis (XRD), chemical composition (XRF), morphological analysis using FTIR spectroscopic and SEM-EDX analysis. Laser particle analyzer (i.e., the same equipment used in other studies such as Malvern Mastersizer 2000 and Malvern Instruments, Malvern, UK) was used in conjunction with a dispersal device for analyzing particle size distributions of the magnetic particle samples. To measure the magnetic and nonmagnetic fractions, samples underwent X-ray diffraction (XRD) with a D8-Advance Bruker with radiation of Cu-K\(\alpha\) (\(\lambda\) = 1.5406 nm) generated at 40 kV and 40 mA. The data were recorded in the Bragg angle (20) with a range of 3-70\({}^{\circ}\) and a scanning speed of 2\({}^{\circ}\) min\({}^{-1}\). To define minerals, Evaluation software 10.0 was employed with a database (PDF-2 2004) provided by International Centre for Diffraction Data.  
Davies tube apparatus was used for magnetic separation. To obtain carbon-depleted and carbon-rich fractions from the samples of fly ash fraction, column floatation was used. In this regard and to perform the tests two chemicals of methyl isobutyl carbinol (MIBC) and distilled water were consumed. The carbonaceous matter was floated over the MIBC layer and was subsequently separated after the carbon-depleted fraction subsided at the bottom. To analyze the morphology of the magnetic particles and elements present in samples, scanning electron microscope (SEM) was used in conjunction with energy dispersive X-ray spectroscopy (EDS) (Quanta 450). In this study, coal chemical composition was specified indirectly. The low-temperature ash (LTA) was determined for coal samples which were subsequently analyzed for their mineral matter elements through the use of XRF. Also, feed coal underwent a sieve analysis.  
The chemical composition analysis of the feed coal shows in Table 1. Such results are the sum content of SiO\({}_{2}\), Al\({}_{2}\)O\({}_{3}\), and Fe\({}_{2}\)O\({}_{3}\) is significant (\(\sim\)90%). It also shows that the ash includes fewer amounts of CaO, K\({}_{2}\)O, MgO and other elements. The loss on ignition (LOI) for the samples is approximately 3 and 5.6%, respectively. However, SEM analysis indicates the presence of a considerable amount of extrinsic mineral matter.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Element (\%)**} & **UB** & **PL** \\ \hline SiO\({}_{2}\) & 43.64 & 42.85 \\ TiO\({}_{2}\) & 0.83 & 0.76 \\ Al\({}_{2}\)O\({}_{3}\) & 21.97 & 21.05 \\ T-Fe\({}_{2}\)O\({}_{3}\) & 23.54 & 22.79 \\ MnO & 0.26 & 0.22 \\ MgO & 1.89 & 1.96 \\ CaO & 1.85 & 1.53 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The elements concentrations (%) of magnetic fractions of UB and PL fly ashes as determined by XRF analysis.  
According to XRF analysis of the size-fractionated fly ash samples, the total content of Fe\({}_{2}\)O\({}_{3}\), Al\({}_{2}\)O\({}_{3}\), and SiO\({}_{2}\) increases as the particle size decreases. Both samples display an appreciable amount of the oxides. In general, LOI decreases as the size of the particles decreases.