**4. Discussion**

Within the literature studying SSA for P-recovery, it has been mentioned that the phosphate content is present as whitlockite [3–7]. The data presented here cannot confirm this. Whitlockite is easily acid-accessible, but none of the recovered material (as represented by the spectra that are present in the original material, but missing from the residue) show good agreemen<sup>t</sup> with the material studied here. By generic labelling, whitlockite would appear as PCaMgFeO, and at 20% P-content, fall into the >15 % P group of our target grouping. Neither an appropriate spectrum nor the majority of the P-content of this material in the >15 P group are found here. This is in agreemen<sup>t</sup> with other SSA studies [20].

This work suggests grouping EDX-spectra found in SEM-AM investigations of SSA for P-recovery by P-content. As shown, grouping them by their main component is less helpful when assessing the elemental deportment of phosphates and recovery success. Both options, however, show important characteristics for P-recovery. With regards to incineration, the reorganization of P-phases from those generated during P-precipitation in wastewater treatment to those present in ashes does currently not favor a clean recovery of calcium-phosphates. Thus, studies such as these can help assess different combustion regimes and their suitability towards P-recovery. With regards to P-recovery processes, an SEM-AM investigation reveals why recent works of P-recovery always had to deal with Al, Fe, and other macro elements in their process [8,21].

Particle sizes of the groups identified in this work are subject to the error of density settling of material during sample preparation and should be taken as "relative to each other"—this effect should affect all samples alike. Sawing up prepared epoxy blocks of the sample and turning the bands 90◦, then analyzing them could show the extent of this error. A comparative study could potentially quantify this effect.

The generic labelling used in [9] allowed for the sorting of spectra by their main component, however, oftentimes material phases found in SSA are very complex and the "main" component is only "major" over other components by a few percent. Thus, the focus on P—as the target constituent which should be extracted—expresses itself in the target grouping. This data evaluation shows the extent to which remnant P-phases are still present in residues and the quality of SSA; a larger proportion of material containing relatively high levels of P is better suited than high levels of overall P-content. This P-recovery quality assessment cannot be done by XRF analyses, which determine the overall P-content of the material or XRD studies, where signals are overlain by a large scatter of random directions due to the large amorphous part of SSA. EDX data as obtained from a polished surface from a multitude of mapped grains, are a suitable method. To accentuate, three spectra were found which are exclusively present in the untreated material. These three spectra, named "key", were completely digested by HCl, regardless of thermochemical pre-treatment of the digestion. In addition, this is the reason why thermochemical treatment resulted in an improved P-recovery: thermochemically treated SSA contained more key material, i.e., was able to generate key material. While other P-containing material phases varied in their response to treatment and thermochemical pre-treatment, these three phases always vanished completely, highlighting the P-recovery success of acid digestion.

It has been shown that generic labelling data evaluation [9] is limited when analyzing the P-contents of residues. A reduction in P-content in the residue is shown—the proportion of spectra containing less P rises, while the fraction of spectra containing more P decreases. Only half of this is illustrated by the conventional grouping: here, high P-phases are seen to vanish, but the rise of reduced P-species is not documented. The shift from 5–10 wt% P to 1–5 wt% P by simple digestion and to <1 wt% P in digestion after pre-treatment is obvious. This may be interpreted as the result of one of two processes: the material is removed, and thus, the relative proportion of remaining components

rises—so, there is no actual enrichment; or the extraction mechanism by acid digestion only recovers a part of the P-content and not the full amount. In the latter case, it would be likely for new, mildly P-bearing spectra to appear in the residue but not in SSA. Since the same list of spectra was applied to all samples, this would either show certain spectra only present in residues or a significant increase in "unknown" material in residues. Neither is the case. Thus, there are shifts, triggered by the processes, but no generation of distinct phases. While the benefit of thermochemical pre-treatment is also visible using conventional grouping, it looks only marginal: digestion residues contain <5 area-% of the spectra with high P-content, and pre-treated show none. Using the target grouping, it is obvious that thermochemical pre-treatment a ffects more parts of the sample than specifically the heavy metal content only. The aforementioned shift in P-phase contents becomes visible. Fe-oxides are extracted by thermochemical pre-treatment.

As has been outlined in mathematical approaches (e.g., [22,23]), it is di fficult to give estimates on uncertainty and error based on automated SEM mineral liberation analyses. The primary signal of MLA measurements is a backscattered electron image and energy dispersive spectra composed of data from numerous detector channels. The latter signal is based on ~12,000 counts gained within 10 ms. There is no specific time or channel resolution which could allow uncertainty and error estimates based on peak-to-background ratios and standard deviations for counting rates for distinct peaks. In consequence, for further estimates, the mineral mode appears as the most prominent parameter in comparison to the particle and grain sizes and their shape geometries.

During the preparation of the grain mount block, particle separation may be induced by the stirring of the particles into the liquid epoxy and subsequent gravitational subsidence of high-density particles during epoxy hardening. These e ffects can lead to heterogeneous particle distributions in the surface of a polished block, an e ffect that is particularly prominent for sample materials (mineral mixtures) with large di fferences in particle sizes and/or densities. As all samples thus prepared are affected by this bias towards particle distribution, it is suggested to study more than one sample—SSA and digestion residue, for example, or two types of SSA.

There are also uncertainties related to spectra classification. The EDX spectra classification algorithm for the MLA software packages follows the principle of best match along a scale of reliability between 1 × 10−<sup>10</sup> (absolute conformance) to 1 × 10−<sup>100</sup> (no conformance), as outlined by [10]. The phosphorus-bearing particles display a comparably complex pattern of X-ray emission lines, with many peaks and sub-peaks that are marked by considerable interference. Due to the complex X-ray spectra characteristics, there is considerable risk that EDX spectra are not at all classified, if classification is carried out at a high reliability value. The classification algorithm allows no alternative assignment to another EDX reference spectrum or to another mineral in the list. Due to this principle, the spectra which cannot be classified by the higher reliability scale value will remain as unknown and increase the mode of unknown grains [11]. For the study presented here, the sample EDX spectra were thus classified by the reliability values of 1 × 10−<sup>10</sup> (high degree of conformance) and 1 × 10−<sup>25</sup> (fair degree of conformance). The latter reliability value is applied to process samples, in an e ffort to reduce the amount of unknowns below 0.1 area-% mode. Applying a reliability value of 1 × 10−<sup>25</sup> to the samples of the third case study, the modes of unknowns remained low, ranging between 0.53 and 0.16 area-%.
