## 2 Materials and Methods
A Au foil (3 mm \(\times\) 6 mm) was located in good electrical contact with the sample, and it was used as a reference to calibrate the binding energy position. Electrons were detected at a 20\({}^{\circ}\) angle relative to the surface normal using a Phoibos electron energy analyzer (SPECS GmbH, Berlin, Germany), equipped with a custom delay-line detector. The measurements were taken with the X-ray beam impinging at a 50\({}^{\circ}\) angle relative to the normal of the sample surface. The size of the X-ray beam on the sample was approximately 100 \(\upmu\)m \(\times\) 10 \(\upmu\)m.  
Survey spectra were acquired at photon energies of 650 eV to confirm alignment and examine potential interference from inorganic substances and contaminants. The selected photon energy allowed for the inclusion of both O\({}_{\text{1s}}\) and C\({}_{\text{1s}}\) peaks in the survey spectrum. Core-level spectra for C\({}_{\text{1s}}\) and O\({}_{\text{1s}}\) were measured at photon energies of 400 eV and 650 eV, respectively, with overall energy resolutions of 80 meV and 150 meV. After the removal of a Shirley background [8], C\({}_{\text{1s}}\) and O\({}_{\text{1s}}\) spectra were fitted with Doniach-Sunjic functions convoluted with Gaussians [16]. The XPS curve fitting was performed in agreement with the procedure developed by [PERSON] et al. [7; 15] and compared with the results of [9; 13]. The following Table 4 reports the binding energies used by [PERSON] et al. [15]. Microstructural investigations of raw materials were carried out by means of X-ray powder diffraction (XRD) analysis in the 2\(\Theta\) range of 3-90\({}^{\circ}\) using a Rigaku Miniflex 600 automated diffractometer (Rigaku, Tokyo, Japan) equipped with a CuK\(\alpha\) radiation source. Phases were identified by using the PDF-5 + 2024 database (ICDD--International Centre for Diffraction Data(r), Newtown Square, PA, USA) and the Rigaku Smart Lab II software v4.5.162.0. The determination of Reference Intensity Ratios (RIRs) was performed without considering the amorphous phase. The mass fraction of each crystalline phase can be determined using the ratio of diffraction peak intensities between crystalline phases, allowing quantitative analysis. The equation of the RIR method is shown as follows:  
\[w_{i}=\propto\frac{I_{i}^{max}}{R_{i}} \tag{1}\]  
where \(w_{i}\) is the mass fraction of an analytical phase \(i\), \(I_{i}^{max}\) is the highest peak intensity, and \(R_{i}\) is the RIR value [55]. Microstructural investigation of raw samples, SA milled, fly ash, and Carboxen, have been performed by XRD and the results are reported in Figure 1. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**C\({}_{\text{1s}}\)**} & \multirow{2}{*}{**C \(Sp^{\text{2}}\)**} & \multicolumn{2}{c}{**C \(Sp^{\text{3}}\)**} & \multirow{2}{*}{**C Vacancy b**} & **Ether,** & **Epoxy,** & **Carboxyl,** \\  & & & **C-C(O) a** & & **Carbonyl** & **Hydroxyl** & **Lacton** \\ \hline  & 284.3–284.5 & 284.9–285.0 & 283.8–284.7 & 285.7–285.6 & 286.3–286.0 & 287.7–288.2 \\ \hline O\({}_{\text{1s}}\) & epoxy & ether, hydroxyl & \multicolumn{2}{c}{carbonyl, carboxyl, lacton} \\ \hline  & 532.6–532.0 & 533.5–533.2 & \multicolumn{2}{c}{531.1–530.7} \\ \hline \end{tabular}  
* nearest and next-nearest neighbours to O-bonded C atoms. b C atoms surrounding a single C surface vacancy.  
\end{table} 
Table 4: C\({}_{\text{1s}}\) and O\({}_{\text{1s}}\) binding energies (BEs) of various carbon–oxygen groups in electron volts (eV) [15]. The XRD pattern of fly ash shows diffraction peaks (labelled as 1) corresponding to crystalline phases of Al\({}_{2}\)(Al\({}_{2}\)-Si)O\({}_{10}\), with an RIR of 82.2 wt%, and a minor diffraction peak attributable to \(\alpha\)SiO\({}_{2}\) (labelled as 2), with an RIR of 17.8 wt% Figure 1a. Conversely, the XRD pattern of SA milled shows the presence of an amorphous phase and the coexistence of two different phases of silicon dioxide, which were \(\alpha\)SiO\({}_{2}\), with an RIR of 90 wt%, and SiO\({}_{2}\), with an RIR of 10 wt%, (labelled as 3).