## 2 Application of Portable XRF for Ceramic Investigations: The State of the Art  
Highly sensitive benchtop analytical techniques for a chemical investigation of heterogenous samples, such as inductively coupled plasma mass spectrometry (ICP-MS), X-ray fluorescence (XRF), neutron activation analysis (NAA) and scanning electron microscopy and energy dispersive X-ray spectrometry (SEM-EDX), have been extensively used for the geochemical characterization of both ceramic materials and clay sources [10; 11; 12; 13]. Despite their high accuracy and precision, these methods suffer from high costs and long acquisition times, together with the partial or total destruction of the sample [4]. In the last decades, the use of non-destructive methods in conservation science has gained general acceptance [14; 15; 16; 17; 18], however due to the reduced sensitivity to trace elements, the use of XRF in the investigation of archaeological materials remained poor compared to more accurate analytical techniques [19]. The successful application of pXRF to the investigation of highly heterogeneous materials, such as ceramics and soils, is, however, still strongly discussed [20; 21; 22; 23; 24; 25; 26; 27; 28]. Central to the debate is the complex nature of the matrix itself and the quest for both high analytical precision and reproducibility [29; 30]. A number of dedicated analytical strategies have been proposed so far to overcome the main disadvantages that affect the application of pXRF to the investigation of ceramics. The analysis of homogenized powdered samples and the acquisition of multiple spots are methods used to average and assess the variations caused by the heterogeneity of the fabric (typically consisting either of a clay matrix and a mineral skeleton and/or a temper of variable particle size) and the possible presence of surface alterations (caused by firing or post-depositional conditions) or coatings [20; 21; 31]. A semi-quantitative estimation of the chemical concentration of each element could be achieved by the application of several calibration methods. Portable XRF spectrometers offer built-in calibration packages for a number of different substrates. Internal calibrations methods can also be adjusted by the user thanks to the measurement of certified reference materials (CRMs), or standards, which improves the accuracy of the reported concentrations within a specific dynamic range [23]. The application of built-in calibrations is, however, strongly matrix dependent, and the reduced versatility of internal software represents one of the main disadvantages to  
Figure 1: (**a**) Map of central Italy where the locations of the ceramic assemblages that have been explored in the text are reported. (**b**,**c**) The site of Vetricella. the use of pXRF in ceramic studies [19; 20; 23; 32]. While pre-installed calibrations that are based on commercial algorithms are considered satisfactory for more homogenous substrates, the development of a material-specific calibration is strongly recommended to help users manage the complex nature of more heterogeneous materials. Previous studies, in particular, reported relative errors of around 50% for most factory calibrations, while custom standardizations typically induced a relative error of less than 10% [32; 33; 34]. The development of an empirical calibration for ceramic studies has thus been considered mandatory for obtaining valid and solid results for an inter-instrument comparison with data extracted by the tests, or for a future evaluation of a database outside the original experiment [21; 32; 35; 36]. Nevertheless, despite the high reliability of the correction coefficients that is provided by empirical matrix-matched calibrations, the accuracy of an intra-instrument comparison is not without issues, since different instruments have been demonstrated to report varying values even following the same calibration method [37].