## 1 Introduction
The differential charging effect depends on many factors, such as the size and specific resistivity of the sample, the lateral and vertical inhomogeneity of the structure, the chemical constitution of the surface phases within the sample, the total photoionization cross-section of the materials being analyzed, and the features of the incoming X-ray beam (size, shape, intensity, homogeneity, etc.) [42; 43; 44]. For such inhomogeneous samples, the use of a low-energy electron flood gun to compensate for the positive charge on the sample surface [42; 43; 44; 45]--a common procedure with fully insulating samples--may not be resolute. The interpretation of carbon XPS analysis has been debated in the literature [46; 47]. The XPS analysis of the core-level spectra of carbon materials has been discussed in [46], underlining the ill-informed approach to analyzing the spectroscopic data. Indeed, the carbon species and banding energies for several carbon materials (graphite, carbon black, graphene, carbon nanotubes, carbides, and polymers) are summarized in [46], underlining that carbon materials with different preparation and analytical methods or storage time differ in carbon species and banding energies. The effect on the surface properties of carbon samples exposed to solar radiation was also investigated in [47]. Surface charging during XPS analysis has been accurately scrutinized in recent literature [48; 49; 50; 51; 52]. [PERSON] et al. [48] summarize methods to control surface charging during the XPS analysis of insulating samples and different possible approaches for extracting useful information on binding energy. Because of the variety of approaches followed to extract binding energies for insulating materials, each with its own limitations, it is critical for researchers to identify the best procedure. [PERSON] et al. [49] presented a method which employs XPS imaging to chemically detect spatially segregated multiwalled carbon nanotubes (MWCNT)-rich regions on an composite surface by exploiting differential charging methods. The results demonstrated that the XPS imaging of differentially charging MWCNT composite samples was an effective means for assessing dispersion quality. [PERSON] and [PERSON] [50; 51; 52] revised essential concepts and key experiments related to BE referencing. They discussed appropriate energy reference levels for conducting and insulating samples with and without electrical contact with the spectrometer, and defined criteria for the ultimate charge-reference method, based on adventitious carbon (AdC), which turned out to be the least reliable. They suggested easy-to-perform control experiments that refute the notion that the C\({}_{\text{1S}}\) peak has a constant BE. In this study, we investigate non-homogeneous carbons in which a conductive matrix (near-graphitic carbonaceous domains) coexists with dispersed dielectric domains (the mineral fraction of the coal, mainly aluminosilicates). The spectral features from the dielectric areas are expected to show significant shifts towards higher binding energy because of the net positive charge, whereas the spectral features of the conducting domains are expected to show no (or limited) binding energy shift by means of XPS. The bias deriving from the influence of ash material is assessed by a comparative analysis of spectroscopy data obtained with different samples:  
* Carboxen has been selected as an essentially ash-free reference carbon. It is an ideal model carbon to ensure the reliable peak assignment of XPS carbon-oxygen functionalities, ruling out interference due to the presence of inorganics. * Char from a sub-bituminous coal, characterized by a large content of both inertinite and vitrinite macerals, has been investigated as a sample of an ash-bearing carbon. * Fly ash from entrained flow combustion of the same sub-bituminous coal has been selected as an ideal sample of ash-enriched carbon. The sample contains 68.0% carbon and 15.7% ash.