## 3 Materials and Methods
### Analysis of Samples and Sub-Samples  
The materials, obtained through the sampling and the previously described work procedure, were quartered to extract a representative aliquot for the analytical phase. Each of them was then ground to a fine powder using an electronic mortar Laarmann LMMG 100 equipped with an agate jar and pestle (Laarmann Group B.V., Roermond, The Netherlands). The resulting powders were then dried in an oven at 105 \({}^{\circ}\)C to remove any trace of moisture. The samples and sub-samples were then subjected to loss on ignition (L.O.I.) analysis to determine the quantity of volatile phases: about 0.5 g of each powdered sample was weighed in ceramic crucibles. These were then placed in a muffle furnace and heated at a rate of 3 \({}^{\circ}\)C/min to 1000 \({}^{\circ}\)C, and this temperature was maintained for 6 h. The crucibles were allowed to cool in the muffle furnace and placed in a desiccator to complete the cooling process. Finally, the crucibles were weighed, and the percentage L.O.I. was calculated. Following that, analyses were conducted to determine the major oxides composition using the WD-XRF analytical technique: each powdered sample and  
Figure 2: Schematic illustration of the working process. sub-sample was pressed by means of a hydraulic press onto a boric acid support to obtain pressed powder tablets. These latter were then analyzed using a Thermo ARL AdvantXP+ Wavelength Dispersive X-ray Fluorescence Spectrometer (Thermo Scientific, Waltham, MA, USA). This technique allowed the determination of the major elements, expressed as a percentage by oxide weight (SiO\({}_{2}\), TiO\({}_{2}\), Al\({}_{2}\)O\({}_{3}\), Fe\({}_{2}\)O\({}_{3}\), MnO, MgO, CaO, Na\({}_{2}\)O, K\({}_{2}\)O, and P\({}_{2}\)O\({}_{5}\)) [38]. The accuracy of the instrument, estimated based on the results obtained for international standards of geological samples, and the precision, expressed as the standard deviation of replicated analyses, were between 2% and 5% with a detection limit of 0.01%. The processing of the acquired intensities and the correction of the matrix effect were performed according to the model proposed by [PERSON] and [PERSON] [39]. The obtained results were subsequently processed on the R platform (Version 4.3.1; URL: [[https://cran.r-project.org/bin/windows/base/old/](https://cran.r-project.org/bin/windows/base/old/)]([https://cran.r-project.org/bin/windows/base/old/](https://cran.r-project.org/bin/windows/base/old/))) using the GCDKit package [40], through which the following graphs were plotted for the classification and geochemical characterization of the granite waste samples: the R1-R2 diagram, by [PERSON] et al. [41], for the classification of plutonic rocks; the ASI/SiO\({}_{2}\) and MALI/SiO\({}_{2}\) diagrams, by [PERSON] [42], for the tectonic discrimination of granites. Additionally, the GCDKit package was utilized for calculating the CIPW norm on all samples and sub-samples examined in this study, aiming to obtain an indicative mineralogical composition, with a specific focus on quartz and feldspars. The results obtained from the CIPW calculation were then used to classify granite waste according to the QAP classification diagram for plutonic rocks proposed by [PERSON] [43]. Based on the results of the WD-XRF analyses, specific samples and sub-samples were chosen for analyses to determine the concentration of REEs, uranium, and thorium. Specifically, the following were selected: 12 initial granite waste samples, 3 crushing powder samples, and 9 diamagnetic phase sub-samples (3 for the light fraction, 3 for the intermediate fraction, and 3 for the heavy fraction). The analyses were conducted by OMAC Laboratories Ltd. (IDA Business Park, Dublin Road, Loughrea, Ireland), accredited by the Irish National Accreditation Board in accordance with ISO/IEC 17025:2017 [44]. The samples underwent the ME-MS81\({}^{\text{TM}}\) procedure, which involved analysis via ICP-MS following lithium metaborate fusion.