## 3 Results and Discussion
### Mass Yields of PM\({}_{10}\)
#### 3.4.1 PM\({}_{0.5}\)
\[\text{Na}_{2}\text{O}+\text{SO}_{2}+0.5\text{O}_{2}\rightarrow\text{Na}_{2} \text{SO}_{4} \tag{6}\]  
\[2\text{NaCl}+\text{SO}_{2}+\text{CO}_{2}+\text{H}_{2}\text{O}\rightarrow \text{Na}_{2}\text{SO}_{4}+2\text{HCl}+\text{CO} \tag{7}\]  
Therefore, it is mainly the homogeneous nucleation and heterogeneous condensation of Na\({}_{2}\)SO\({}_{4}\) that forms ultrafine particles, as shown in Figure 7a. Figure 1 shows that most Na is water-soluble and organically bound; the vaporization of Na and S can obviously be enhanced by higher combustion temperatures. [PERSON] et al. [46] have indicated that when the concentration of nascent ultrafine particles is below a critical concentration, the vaporized Na\({}_{2}\)SO\({}_{4}\) tends to nucleate, but if the concentration number of nascent particles is higher than the critical number, condensation begins to dominate nucleation. The nucleation of Na\({}_{2}\)SO\({}_{4}\) is indeed found to be dominant for OXY21 (Figure 6c,d), forming a higher concentration of particles of less than 0.07 \(\upmu\)m and a smaller peak size of the ultrafine mode, as mentioned above (Figure 3). By contrast, with a higher vaporization of Na and S, the condensation of Na\({}_{2}\)SO\({}_{4}\) should obviously form larger particles for AIR and OXY32, causing lower concentrations of Na\({}_{2}\)SO\({}_{4}\) in PM\({}_{0.5}\) (Figure 7a). It has already been noted that the yields of Na and S from AIR are obviously less than those for OXY27 and OXY32. This cannot be explained by the higher vaporization, condensation and growth of Na\({}_{2}\)SO\({}_{4}\) considering their comparable particle combustion temperatures. Most of the studies listed in the review by [PERSON] et al. [19] reported a decreased emission of gaseous SOx from oxy-fuel combustion compared to air, because of the higher retention of ash particles for oxy-fuel combustion. This is in line with the higher S contents found in both PM\({}_{0.5}\) and PM\({}_{0.5-10}\) from oxy-fuel combustion (Figure 7). More S is thus emitted in gaseous form for AIR, causing the lowest yields in PM\({}_{0.5}\) observed in Figure 7a. In addition, very high contents of Mg and Ca are reported in PM\({}_{0.5}\) from AIR, which should serve as a core of submicron particles. This was detected by [PERSON] and [PERSON], who confirmed the core of MgO and Fe in submicron particles of Montana lignite [47]. The most abundant existing core of Mg and Ca for AIR is beneficial for the heterogeneous condensation of Na vapor, therefore a lot of Na grows to PM\({}_{0.5-10}\) and causes the lowest Na retained in PM\({}_{0.5}\). The combination form of major elements in PM\({}_{0.5}\), i.e., Ca, Na, S and Mg, was also tested. The mole numbers of these elements are depicted in Figure 8. It is noteworthy that the MgO was reported to be inert to the sulfation reaction, and MgSO\({}_{4}\) is thermodynamically unfavorable at a temperature of \(>\)800 \({}^{\circ}\)C [48], therefore Mg should serve as a core of ultrafine particles and shows little reaction with S. It can also be observed in Figure 8 that the mole number of S is almost equal to the sum of Ca and Na during oxy-fuel combustion. This shows that during oxy-fuel combustion, the occurrence forms of sulfur in PM\({}_{0.5}\) are mostly Na\({}_{2}\)SO\({}_{4}\) and CaSO\({}_{4}\), and more Ca is found in OXY32 which should serve as a CaO core. For the AIR condition, the highest Ca as well as the lowest Na and S in PM\({}_{0.5}\) shown in Figure 7a imply that more Ca exists as the inner core of ultrafine particles correspondingly.