Determining the chronological sequence of inks deposited with different writing and printing tools using ion beam analysis

Determining the sequence of inks in a questioned document is important in forensic science. Conventional and micro beam‐based ion beam analysis using Rutherford backscattering spectrometry (RBS) and particle‐induced X‐ray emission were employed to study the depth distribution of chemical elements in plain paper and inks/toner deposited by different pens as well as inkjet and laser printers. Composition depth profiling with high lateral resolution was performed with focus on areas where two different coloring agents overlapped. We identify under which conditions the sequence of inks deposited can be reconstructed, analyzing the continuity of characteristic contributions to the obtained signals, with a focus on the depth‐resolved RBS data. The order of deposition was correctly determined for combinations of two different laser printers and in certain cases for pens. Results indicate a potential for analysis, depending on the composition of staining agent, that is, in particular if heavy species are present in sufficiently high concentration. In such cases, also characters obscured or modified by an agent of different composition can be revealed. Changing the probing depth by modifying the beam energy could yield additional information.


| INTRODUC TI ON
Determining the deposition sequence of inks, that is, if a questioned document is a document with overlapping lines from, for example, signatures and print, or possibly multiple printing instances, finding the first printed ink can be useful to identify forged documents. Many methods have been employed to find the order of deposition of inks in documents due to its importance in forensic investigations [1]. In particular, optical methods using light microscopes have been used for identifying the sequence of inks in a document. In these methods, authors used various interpretations and methodologies, that is, ink investigations using reflected light, grazing light, and transmitted light [1,2]; thus optical methods need a trained expert for analysis, and results may be of qualitative character. Raman spectroscopy and Raman imaging techniques have been used for discriminating inks and finding the sequence of inks in a questioned document [3][4][5].
Near-infrared hyperspectral imaging has been applied for predicting forgery in a document prepared by different pens and this method correctly predicted 17 out of 20 samples [6]. Mass spectrometry imaging using easy ambient sonic-spray ionization has been used to find the sequence of inks at intersection of stamp and pen ink [7]. Atomic force microscopy has been used to measure height profiles of inks deposited on paper, and the sequence of inks has been predicted by the height profiles at the intersection [8]. Many other methods have been reported to be capable to determine the chronological deposition order inks on paper, such as using adhesive taps [9], FTIR spectroscopy [10], laser desorption ionization mass spectrometry (LDI-MS) [11], and scanning electron microscope [12].
Recently, ion beam analytical techniques, in particular MeV secondary ion mass spectrometry (MeV-SIMS) and particle-induced X-ray emission (PIXE), have been used for forensic analysis of inks/ laser toners deposited on the documents. The order of ink deposition was identified by the presence of a gap at the ink distribution map, for example, the ink deposited first showed a gap or discontinuity at the crossing and the ink deposited on top showing continuity [13][14][15][16].
As a complement to these earlier studies highlighting the potential of some ion beam-based tools for forensic analysis of documents, in this study, we assess the potential of Rutherford backscattering spectrometry (RBS) to identify the deposition sequence of different inks from pens and printers as well as printer toners. Different from PIXE, which is superior in sensitivity for heavy elements, Rutherford backscattering spectrometry enables straightforward and quantitative depth profiling of materials [17]. As such the method provides a powerful tool for thickness and composition analysis of bulk and thin film samples down to a few µm depth from the sample surface, primarily used for materials science [18], but has also shown its potential for analysis of organic systems containing traces of heavy elements [19]. Specifically, in our present study, combined micro-RBS and micro-PIXE mapping is performed at the intersection of two different inks (laser toner, inkjet ink, ballpoint pen, and gel pen). The results are correlated with the deposition sequence of the inks present on the document.

| MATERIAL S AND ME THODS
Conventional RBS and micro-RBS were performed on the inks deposited by printing and writing tools. All ion beam experiments were performed at the tandem laboratory, Uppsala University, employing a 5 MV pelletron accelerator. For obtaining reference spectra using RBS and PIXE, the inks (described in Table 1) were homogeneously deposited on paper. Conventional RBS was performed employing a beam of 2 MeV He + primary ions and using a silicon-solid state detector (SSD) kept at 170° scattering angle. Simultaneously, PIXE data 135° detection angle. The conventional RBS spectra were analyzed using simulations with the SIMNRA software package [20].
To determine deposition sequences, combinations of two different inks were deposited in a document such that the inks intersect at some points using laser printers/inkjet printer/gel pen/ballpoint pen. Subsequently to deposition, the samples were mounted on a sample holder to perform micro-RBS and micro-PIXE at the intersection of the inks. In the experiment, 2 MeV He ions were directed to the sample at normal incidence and the backscattered He were detected using an SSD detector with scattering angle of 168.5°. The ions with typical beam currents of 100 pA were focused to a beam spot size of a few micrometers using a triple magnetic quadrupole lenses. The typical size of the ion beam spot was 6 × 4 µm which was confirmed by scanning the ions over a Cu-TEM grid. Since the ion beam resolution is sufficient for the analysis of the inks, the He ions were scanned on samples and the RBS and PIXE spectra were recorded. RBS and PIXE 2D maps were obtained from energy-resolved backscattering yields and X-ray yields.

| RE SULTS AND D ISCUSS I ON S
Experimental and simulated RBS and experimental PIXE spectra of plain paper and inks are shown in Figure 1.  Table 1. However, the composition of the top surface (900-1800 × 10 15 atoms/cm 2 ) is found different from this value for all the samples. We also find, that (except thin layer at surface), the concentration of carbon is higher than that of plain paper in all investigated inks. The concentration of oxygen is found lower than in plain paper in all the inks/toner. Ca, used as a bleaching agent, is the heaviest element expected in the plain paper detectable by conventional RBS. The measured Ca concentration is reduced drastically in laser print 1 and laser print 2 compared with plain paper. A significant decrease in Ca concentration is observed in all the inks compared with plain paper. Analyzing plain samples of the different coloring agents, in laser print 1, the heaviest element observed by RBS is Fe (Fe edge can be seen clearly in Figure 1A). From the RBS simulations, the depth distribution of Fe was analyzed, and from simulation (shown in Figure 1), ~7% of Fe is found throughout the sample depth analyzed by RBS. Thus, the thickness of deposited toner is expected to be up to a few microns. Altogether, these results show that the different inks and toners have significantly different properties when casted on paper. While laser printers may deposit toners on the surface of the material, inkjet ink and gel pen are water-based writing tools and therefore are completely soaked into the paper which can induce gradients in composition over several µm until bulk composition is reached.
As discussed earlier, the composition is uniform in the probed depth range except for a thin surface layer in all samples. Particularly, concentrations of heavy elements are found slightly lower in a thin surface layer compared with larger depth. For example, in laser print 1, the Fe concentration is lower (on average ~5 at.%) at the thin surface layer (1400 × 10 15 atoms/cm 2 ) compared with higher depth (~7 at.%).
In the RBS spectrum obtained for laser print 2, a signal due to Ti can be observed in both RBS and PIXE. Different from the laser print 1, Ti is clearly present in a very thin layer on the surface only (thickness is 300 × 10 15 atoms/cm 2 and composition is ~1%). From RBS simulations, significant portion of Si is found on the top of the paper/ink and the other light elements may be penetrated bit deeper into paper in laser print 2. In the ballpoint pen, gel pen, and inkjet, the Ca concentration is decreased by ~0.5 at.% at the surface (thickness of 1200, 1800, 900 × 10 15 atoms/cm 2 , respectively) compared with larger depths.
Thus, these inks are expected to at least partially penetrate the paper.
This result shows that RBS can yield additional complementary information on inks deposited from the acquired depth profile for both ink and paper constituents.
In the following, different combinations of coloring agents are analyzed using micro-RBS and micro-PIXE imaging as shown in Figure 2A. For the combination of the two laser printers, in agreement with the data from conventional RBS obtained for plain samples as discussed before, the Fe signal is dominant in laser print 1 while the total number of counts in laser print 2 is lower than that of plain paper. Thus, the signal from laser print 1 appears very pronounced while laser print 2 appears to be less intense in the total RBS image (shown in Figure 2A). Note, that, this discrimination is not apparent in the total PIXE image, as the majority of the signal originates from Ca, as apparent from Figure     Note, however, that the condition of an RBS spectrum being distinct from plain paper does not necessary suffice for resolving deposition sequence. As an example, we present an analysis for both the gel pen and toner 2, which feature both RBS spectra quite distinct from plain paper, but qualitatively similar to each other. Optical image and total RBS, Ti-RBS, Si-PIXE, and Ca-PIXE maps of gel pen on top of laser print 2 is shown in Figure 4. Small Ti peak was observed from total RBS spectrum. Since the Ti is from laser print 2 (known from conventional RBS and PIXE), the Ti-RBS map can be used to find the order of deposition. The laser print 2 is seen from total RBS and Si-PIXE and Ti-RBS maps. But the expected gap is not observed in all the maps. The gel pen ink may be penetrated into the laser print ink 2 and finding the sequence of deposition is difficult with the present statistics.
Finding the deposition sequence of the inkjet, and ball-point pen inks is expected to be most challenging due to the similarity in RBS spectra. They are thus expected to be not visible in total RBS as the expected yield per incident charge is similar to that of the plain paper (compare Figure 1). So, the analysis for finding the order of deposition is difficult with present methods for combinations of these inks. However, these inks in combination with laser print inks may be studied as laser print inks showed distinct RBS spectra and feature a different yield/charge in the total RBS maps.
As an example, the combination of laser print 1 and inkjet ink was studied and the total RBS, Fe-RBS, total PIXE, and Fe-PIXE maps are shown in Figure 5.