# External Beam IBA Measurements for Cultural Heritage
## 3 Pixe
### Differential PIXE  
Whereas PIXE does not provide elemental depth profiles, it is indeed possible to perform PIXE measurements in such a way that semi-quantitative information on stratigraphy in cultural heritage objects can be still obtained. The so-called \"Differential PIXE\" consists of performing point measurements on the same area with proton beams of different energies. At different beam energies, proton ranges, probed depths, and cross sections of X-ray production are different. Since the X-ray yields change as a function of the beam energy in a layered or heterogeneous in depth material depending mainly on the elemental distribution and the X-ray absorption in the material itself, by comparing PIXE spectra collected at different proton energies, stratigraphic information can be obtained, and, in layered objects, typical in cultural heritage, for example, paint layers [27], the sequence of layers can be inferred, although at a semi-quantitative level.  
Operatively, for each measurement, first the apparent composition assuming a homogeneous matrix is obtained by analysing the PIXE spectra. If the material was legitimately homogeneous in depth, the ratios for the composition of the detected elements would be expected to be the same at different energies [28]. If not, the sample reveals a layered structure and if a composition ratio, for instance, element A-to-element B, increases (decreases) with increasing beam energy, this means that element A is present in a deeper (shallower) layer than element B. Moreover, when comparing two composition ratios, element A-to-element B and element C-to-element B and one ratio, for instance, element A-to-element B, increases more steeply than the other ratio, element C-to-element B, with increasing beam energy, then it means that element A is present in a deeper layer than element C.  
As an example, we report here a differential PIXE analysis to reveal the stratigraphy of a tintype photograph. A selected homogeneous light-grey area of the tintype was investigated at three different proton energy: 2, 3, and 4 MeV in vacuum, corresponding to 1.91, 2.93, and 3.95 MeV on the sample surface, respectively (Figure 3, left panel). Several metallic elements were identified: Ti, Mn, Fe, Cr, Cu, Zn, and Ag. In case of a not-layered tintype, the same ratios of the concentrations of the main metallic elements would be  
Figure 2: Comparison of PIXE spectra of a NIST 1412 glass obtained with 3 MeV protons, collected with a 150 mm\({}^{2}\), 450 μm thick SDD and with a traditional 80 mm\({}^{2}\), 5 mm thick Si(Li) detector. The spectra are normalised by the proton beam charge accumulated during the measurements.  
expected at different energies. With reference to the right panel of Figure 3, where only the elements Cr, Fe, Cu, Zn, and Ag are considered, practically the Cu-to-Ag and Cr-to-Ag composition ratios remain relatively constant at the different energies, showing that these elements could be either in the same layer or in contiguous thin layers, whereas both Zn-to-Ag and Fe-to-Ag composition ratios decrease with increasing beam energy, evidencing that Fe and Zn are present in a deeper layer than Ag. However, since the diminution of the Fe-to-Ag composition ratio has a steeper slope than the Zn-to-Ag one, it can be deduced that Fe is in a deeper layer than Zn. The semi-quantitative layered structure of the tintype revealed by differential PIXE measurements is Ag/(Ti, Mn, Cr, Cu)/Zn/Fe. The semi-quantitative approach proposed here is very easy to apply since it is based only on processing the PIXE spectra collected at different proton beam energies with the widespread GUPIXWin program and considering the departure of the calculated concentrations from those of a homogeneous sample as indication of a layered structure. Of course, compared to RBS/EBS, discussed in Section 5, it cannot provide quantitative results on the layer thickness and composition. Moreover, this simple differential PIXE approach typically fails when the same element appears in more than one layer.