## 3 Results
### Calculation of Synthesis Toxicity Index (STI)  
With the data from Section 3.1 the (dimensionless) STI can be calculated according to Equation (1) [28; 29; 30]. The needed parameters T\({}_{i}\), C\({}_{\text{N}}\) and E\({}_{\text{j}}\) are listed in Table 1.  
\[STI_{M}=\sum_{i=1}^{n}\left(T_{i}(\sum_{j=1}^{n}E_{j}Q_{i}^{j})/C_{N}^{i}\right) \tag{1}\]  
T\({}_{i}\) is the toxicity coefficient of the element i; the bioavailability coefficient E\({}_{\text{j}}\) with j is the step of the sequential extraction; Q is the extracted amount of element i in step j; and C\({}_{\text{N}}\) is the risk screening value of element i.  
The bioavailability coefficient E is highest for F1 because this fraction is readily mobilizable under natural conditions. On the contrary, E is zero for F4 because this content cannot be mobilized in the environment. The toxicity coefficient is highest for Cd and as low as 1 for Zn. The risk screening value C\({}_{\text{N}}\) acts as a threshold value and can be associated with background values of the elements in the natural environment. The numerical values and the listed elements have been adopted unchanged from the work of [PERSON] et al. [28]. Although arbitrarily set, the values consider the environmental properties of the different elements and the intended purpose of the test conditions in the sequential extraction. A comprehensive discussion of the values for the model parameters can be found elsewhere [30].  
The calculation results are listed in Table 2. The numerical values of parameter E\({}_{\text{j}}\), i.e., the extracted amount of the respective element in counted fractions F1-F3 are listed in Table S2 in the Supporting Information (SI). It is clearly visible that the MSWI fly ash has the largest value for the STI. Actually, fly ash from MSWI is commonly classified as hazardous waste. That with the most impact in the calculation has the element Cd with the highest risk screening value C\({}_{\text{N}}\) and toxicity coefficient T\({}_{\text{i}}\). This also led to the higher value for STI of IBA3 in comparison to the other IBA samples. On the contrary, CS has the lowest STI. There is almost no contamination with heavy metals. The utilization as secondary building material is only affected by the presence of polyaromatic hydrocarbons and sulfate [34]. The STI of SSA is lower than that of IBA due to lower heavy metal contents, at least when municipal sewage sludge is incinerated [35].  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Heavy Metals** & **Cu** & **Zn** & **Pb** & **Ni** & **Cr** & **Cd** \\ \hline T\({}_{i}\) & 5 & 1 & 5 & 5 & 2 & 40 \\ \hline C\({}_{\text{N}}\) (mg/kg) & 200 & 300 & 240 & 190 & 350 & 0.8 \\ \hline
**Bioavaliability coefficient** & **F1** & **F2** & **F3** & **F4** & \\ \hline E\({}_{\text{j}}\) & 7 & 5 & 2 & 0 & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Model parameters for the calculation of the synthesis toxicity index (STI).  
\begin{table}
\begin{tabular}{l c} \hline \hline
**Sample** & **STI** \\ \hline IBA1 & 494 \\ \hline IBA2 & 882 \\ \hline IBA3 & 1218 \\ \hline IBA4 & 576 \\ \hline FA & 15,366 \\ \hline SSA & 219 \\ \hline CS & 38 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Results of the STI calculation for the seven tested materials.