## 1 Introduction
### By-Product Types in SFS and Their Relevance  
Due to the SFS working principle besides the target oxide nanoparticles, solely CO\({}_{2}\) and water are released in case the organic metal precursor, as well as organic solvent components, oxidize entirely. Nitrogen-containing precursors, such as INN, do additionally yield NO\({}_{\rm x}\) and/or N\({}_{2}\). Since these corresponding gaseous by-products can be easily separated from the particle product, SFS gives access to materials with high purity. Nevertheless, even in SFS, side products can emerge, at least in SFS in three ways:  
1. Precursor and solvent residues can be by-products in case these species do not react/disintegrate entirely [13]. 2. CO\({}_{2}\) can lead to the formation of carbonates, and incompletely burned hydrocarbons can physi- and chemisorb on the particle surface [14; 15; 16; 17; 18]. 3. Elemental carbon can evolve as a side product, typically forming core-shell structures together with Fe\({}_{\rm x}\)O\({}_{y}\)[13; 19; 20; 21]. It is noteworthy to mention that it depends on the perspective whether such by-products are a disadvantage or not. For instance, the formation of carbon shells can even be beneficial if the fabrication of reduced phases is intended (e.g., Fe, FeC, and FeO) due to limited mass transfers hindering the oxidation of Fe, FeO, or Fe\({}_{3}\)O\({}_{4}\)[13; 20; 21; 22]. However, in case the fabrication of \(\gamma\)-Fe\({}_{2}\)O\({}_{3}\) for biomedical applications is intended, the above-mentioned co-products are undesired and can mitigate particle functionalities in several ways. For instance, most practical applications are weight-related. Hence, the presence of some wt.% co-product does mitigate the materials' functionality accordingly. Moreover, elemental carbon and carbonates/carboxylates can be located on the particle surface, determining the particles' surface chemistry. Unfortunately, little is known about how the formation of the above-mentioned by-products can be influenced/mitigated by adapting the operation conditions in SFS. Admittedly, the literature already indicated that sufficient atomisation conditions, a high specific flame enthalpy, and low oxygen stoichiometries (\(\phi\)) are advantageous for achieving complete decomposition of the burner feeds [13; 19; 20]. However, it is still not possible to foretell the evolution of these side products for individual SFS experiments, and some findings in the literature show slight contradictions. For instance, [PERSON] and [PERSON] systematically manipulated \(\phi\) by adjusting burner operation conditions, and carbon depositions were avoided by adapting global oxygen excess, \(\phi\)\(<\) 1 [19]. However, in other SFS setups, simply applying a global oxygen excess does not necessarily yield carbon-free particle outcomes. [PERSON] et al. operated SFS their burner setup at even lower \(\phi\), and particles exhibited considerable core-shell structures anyway [13]. Although these studies seem to be in contradiction in a first glance, they solely demonstrate the necessity of considering local/temporal flame conditions to investigate the formation of by-products rather than relying on global values only. In addition to the fact that the utilisation of identical parameter sets with different burners may give rise to divergent gas phase properties, the SFS community demonstrated that gas phase properties can also vary considerably over time in individual flames. This was evidenced, for instance, in studies using the SpraySyn1 burner [23; 24; 25]. This burner type was introduced in 2019 by [PERSON] et al. to unify SFS experiments [26] and served as groundwork for numerous experimental and numerical SFS studies [27; 28; 29; 30; 31; 32; 33; 34; 35; 36]. In this context, [PERSON] at al. determined the flame luminescence (representing the flames' activity) by high-speed monitoring during the synthesis of \(\gamma\)-Fe\({}_{2}\)O\({}_{3}\) using 0.1 M INN in EtOH + EHA, which demonstrated considerable transient combustion conditions for SpraySyn1 [24].