# Applications of accelerator mass spectrometry in forensics

### Gianluca Quarta, Lucio Calcagnile

1 Introduction

Carbon occurs in nature in three different isotopes: 12C, 13C and 14C. The first two are stable while 14C (radiocarbon) is radioactive decaying to 14N through $\beta^{-}$ decay. Radiocarbon is a cosmogenic nuclide naturally and continuously produced in the terrestrial atmosphere through the interaction of cosmic radiation with atmospheric gases. Cosmic rays (mainly protons) produce secondary neutrons which are slowed down through scattering events with atmospheric gases before being captured by 14N producing 14C through the nuclear reaction 14N ( n, p ) 14C. Radiocarbon is produced at a rate of the order of ≈2 14C at/s cm2. This rate is not constant and is influenced by different, complex phenomena such as the fluctuations of the solar activity and of the Earth magnetic field. Once produced 14C undergoes chemical reactions in the atmosphere being oxidised to CO2 and entering the different terrestrial reservoirs such as the hydrosphere, the biosphere and the cryosphere. As the results of these processes 14C is uptaken by living organisms (for instance through photosynthesis or the alimentary chain) such that the concentration in their tissues mirrors the atmospheric value. When an organism dies, the 14C uptake ceases and its concentration in the tissue of the dead organism decreases by following the known exponential radioactive decay law with a half-life of 5700 years. Radiocarbon dating is then based on the measurement of the residual 14C concentration measured in a sample such that the time elapsed since the death of the organism can be calculated. Radiocarbon dating was developed by W. Libby who was awarded with the Nobel prize in 1962 for its discovery. Since its first developments 14C dating represented a major breakthrough in different fields spanning from archaeology to Earth Sciences where it has allowed the set-up of absolute chronological timescales with unprecedented levels of precision and accuracy.

2 The measurement of 14C

From the experimental point of view the main difficulty associated with 14C dating is related to its very low natural abundance: in a modern sample the 14C/12C ratio is of the order of 10–12. The first experimental approaches used to determine the 14C in a sample were based on $\beta$-counting techniques: 14C concentration is obtained by measuring the electrons released by14C during its $\beta^{-}$ decay. The low radioactivity of 14C (0.226 Bq per gram of modern carbon) results in the main drawbacks of these techniques: long measurement times and large sample size are needed to achieve acceptable level of precision. A major step forward was done in 1977 when the possibility to detect 14C by using spectrometric technique was demonstrated.

In AMS (Accelerator Mass Spectrometry), carbon ions are extracted (typically using a sputtering ion source) from the sample properly processed and reduced to graphite while electrostatic and magnetic dispersive elements are used to separate unwanted species from carbon ions and the three C isotopes. 14C particles are then detected by using particle detectors such as gas ionisation chambers. State-of-the-art systems are nowadays capable of measuring samples with mass in the microgram range with uncertainty levels of the order of 0.2–0.3% in routine measurements, corresponding to ±20/30 years in the radiocarbon age determination. Figure 1 shows the schematics of the AMS system installed at the Centre for Applied Physics, Dating and Diagnostics (CEDAD) at the University of Salento where one of the six experimental beamlines is dedicated to AMS 14C detection. The system is based on a 3 MV Tandetron-type accelerator (Mod. 4130HC manufactured by High Voltage Engineering Europa) which is equipped with two low-energy injectors and six experimental beamlines. The multipurpose injector is formed by two ion sources and a 90° magnet. The two sources – a HVEE 860A sputtering source and a 358 duoplasmatron source (both from HVEE) – are used to produce ion beams from solid targets and gases (hydrogen and helium). The AMS injector hosts two ion sources (a multicathode and a hybrid solid-gas sputtering ion sources) both equipped with automatic systems for sample loading and unloading allowing unattended operations. A 90° magnet is used to sequentially inject the beams into the accelerator. Along the high-energy side there are two AMS spectrometers dedicated to 14C analysis and to the detection of rare nuclides other than 14C (10Be, 26Al, 129I and actinides). A switching magnet is used to deflect the ion beams in the other four beamlines: RBS/Channelling in vacuum, IBA (PIXE-PIGE) in external beam mode, ion implantation and nuclear microprobe.

3 The “bomb peak”

As already mentioned, the 14C production rate is not constant over the time and significant variations are observed as the result of complex, natural phenomena such as variation of the Earth magnetic field and of the solar activity. The determination of the 14C concentration in proxy records of the atmospheric concentration such as tree ring sequences dated by dendrochronology or other biological (i.e. corals) or geological archives (i.e. lake sediments) has allowed us to reconstruct these fluctuations with a high resolution which, for some time periods, can be at the annual or even sub-annual level. Indeed, starting from the mid 1950’s the 14C concentration in the atmosphere has been extensively influenced by the anthropogenic release of this nuclide as the results of aboveground nuclear detonation tests. After the first detonation of a nuclear weapon in US on July 16th 1945 in the frame of the Manhattan project, 543 detonations were carried out in the following years by different countries: USA, USSR, UK, France, China with a total yield of 440 Megatons (equivalent to more than 29000 Hiroshima bombs). Figure 2 shows the atmospheric detonation tests carried out in different years in terms of number of explosions and yield (data from UNSCEAR).

These tests produced large amounts of radionuclides, including 14C, which was produced mainly through the reaction 14N ( n, p ) 14C, and released by nuclear mushrooms in the stratosphere and troposphere. To have an idea of the magnitude of this event a comparison between natural and man-induced variation of the atmospheric 14C concentration is given in fig. 3. In the figure the atmospheric 14 C concentration is expressed as ∆ 14C which is defined as the relative difference between the value in the considered year and in 1950 which is assumed as reference. Positive and negative values of ∆ 14C correspond to an enrichment or a depletion of the 14C concentration when compared to 1950, respectively. The tremendous effect due to the nuclear weapon testing is evident: the 14C concentration almost doubled in 1963–1964 when compared with the pre-bomb era. The curve representing the 14C concentration in the atmosphere as a function of year after 1950 is often referred to as the “bomb peak curve” and has been reconstructed in several locations in the world both in the Northern and in the Southern hemisphere by analysing different archives such as tree rings or through the direct analysis of atmospheric CO2 (fig. 4). In the figure the radiocarbon concentration is expressed as Fraction Modern ( $f_M$ ) that is the measured radiocarbon concentration, corrected for mass fractionation and relative to the reference value assumed to be 95% of the 14C concentration in the Oxalic Acid 1 (OX1) standard in 1950. The curve shows a steep increase of the 14C concentration starting from 1950–1955 reaching a maximum in 1963–1964. After this date the input of anthropogenic 14C into the atmosphere was enormously reduced as the result of the Limited Test Ban Treaty which allowed a dramatic reduction of atmospheric tests. Since then the 14C concentration has constantly dropped as a result of the dissolution of the excess of 14C into the hydrosphere and its uptake by the biosphere and because of dilution effects associated with the release of 14C-depleted carbon dioxide from fossil sources. Currently the 14C value is approaching the pre-bomb value meaning that the “bomb peak” has almost completely vanished.

4 Bomb peak dating

Forensics dating applications typically demand for the analysis of samples younger than ∼70 years and for high chronological resolutions of the order of a few years or less. These requirements are typically beyond the possibility of conventional 14C dating where uncertainty levels of the order of decades are typical. The possibility to use 14C for dating purposes in forensics is then associated to the detection of “bomb” 14C from nuclear fallout and in the comparison between the measured levels in a sample with the “bomb peak curve” which is used as reference. The method is shown in its principle in fig. 4. Let us assume that a concentration of 1.5 (expressed in Fraction Modern where a value >1 indicates ages younger than 1955) is measured in a sample. A first piece of information is immediately obtained: the sample is from an organism which has been labelled by bomb 14C and which lived, then, after 1950 AD. If we now compare this value with the proper reference curve we can determine when this value was present in the terrestrial atmosphere. We found in this way two possibilities: 1963 and 1971 AD (note that here we are not considering at the moment uncertainties for easiness). This approach allows then to obtain an age for “recent” samples (at least in the radiocarbon timescale) and with the high chronological resolution which, as said, is mandatory in forensics applications. The advantages of this approach are significant and have triggered its application in different areas relevant in forensics as will be better discussed in the following. Among these advantages those which appear to be more relevant are the possibility to analyse organic samples which often retain the highest information content such as bones, textiles, organic residues, paper and its scarce sensitivity to environmental factors such as light exposure, temperature and humidity.

On the other hand, there are also drawbacks and critical aspects which have to be properly addressed and discussed for an effective application of the methodology.

We first observe that any measured post-bomb 14C level corresponds to two possible intercepts with the bomb peak curve: one along the rising (before 1964) and the other one along the falling part (after 1964) of the curve. This means that any measured 14C concentration results always in two possible ages: one before the peak and the other one after it. This is an intrinsic limitation of the method which can be overcome only when other information is available and can be properly combined with the dating results. This is, for instance, the case of a priori known information (a terminus post or ante quem, for instance) or when relative dating information is available for multiple samples.

The second aspect is common with the interpretation of any 14C date but it is more relevant in bomb peak dating because of the achievable high resolution: what does the measured date represent? The answer is easy when we consider a sample living just one year (short living samples) but it becomes significantly more complex when considering samples living for longer periods. When we date a human bone what does the measured age represent? Is it the birth or the death age or something else? The answer is not easy and complex considerations about carbon fixation time and carbon turnover rates in living organisms are needed. For instance, carbon (and then radiocarbon) in bones is fixed along the entire life but with rates which are significantly higher during childhood and youth than during the adult life. These considerations make interpretation of data not straightforward but at the same time supply a tool to improve resolution when different samples with different remodelling or carbon fixation times can be analysed from the same individual, as will be discussed later. Other aspects to be considered are related to intra and inter hemisphere differences (which are anyway particularly evident only along the rising part of the curve), possible effects on the 14C determination as due to dietary offsets (input from reservoirs having different 14C levels when compared with the atmosphere such as the oceans) or local deviations of the 14C concentration from the global average as related, for instance, to higher levels associated with nuclear activities or to depletion effects due to fossil sources of 14C-depleted 14CO2. For instance, a plant fixing CO2 partially coming from the combustion of coal or oil in a power plant will appear “older” in terms of its 14C age.

The last aspect to be discussed is related to current 14C values, which have reached pre-bomb levels making “bomb peak dating” not applicable in the future. Different models predict different scenarios for our future atmosphere depending on the levels of fossil carbon dioxide emissions for the next decades but in any of them the bomb peak has vanished.

We also underline that, in order to address these issues, highlight the potential of the method and promote its use in forensics, the IAEA (International Atomic Energy Agency) is supporting a research program: CRP F11021 “Enhancing Nuclear Analytical Techniques to Meet the Needs of Forensic Sciences: objectives and status” which has a work package dedicated to forensics applications of 14C.

Bomb peak data can be analysed and interpreted by using different software freely available such as CALIbomb (http://calib.org/CALIBomb) developed by the Centre for Climate, Environment and Chronology at the University of Belfast and OxCal (https://c14.arch.ox.ac.uk/oxcal.html) developed by the Oxford Radiocarbon Accelerator Unit at the University of Oxford, UK. In the following we will review some applications of the method in different fields presenting also some case studies where it is revealed to be an extremely powerful tools in forensics investigations.

5 Application in forensics anthropology

The analysis of human remains plays often a relevant role in forensics investigations. Bones, teeth, hair and other tissues are routinely submitted to radiocarbon dating to obtain information which is often preliminary to other analyses. Among the questions which 14C is requested to answer there are:

• Do the remains have a forensics interest?
• Are the remains compatible with a certain missing person or a certain crime?
• Can 14 C supply information about the birth age, the death age, the age at death?
• What is the relative timing between different rests?

To which extent 14C can answer these questions largely depends on the type of available samples and their preservation status and on the definition of a proper sampling and analysis strategy which often requires the selection of different materials and the use of complementary techniques. For instance, stable isotopes analysis by IRMS (Isotope Ratio Mass Spectrometry) to obtain information about the dietary inputs, the provenance of the analysed rests or infrared, elemental or molecular analyses to assess the preservation status of the samples.

In order to show how the application of a proper sampling strategy can enormously enhance the information which can be obtained from the radiocarbon analysis of human rests, we present a case studied at CEDAD in collaboration with the group of Prof. Cristina Cattaneo at the University of Milan. Different samples were obtained from a corpse found in 2010 in a lake in Northern Italy: teeth (mandibular right canine and second molar), different bones (pubic symphysis and base of the skull) and hair. Aim of the analysis was to determine the death age, the birth age and the age at death. The results of the analysis are summarized in fig. 5. We immediately note that all the samples gave different 14C levels although they were all taken from the same individual. This is, of course, due to the fact that each of them reflects different time of formation or carbon fixation and different carbon turnover rates. Of course each measured radiocarbon concentration corresponds to two possible ages when referred to the bomb curve but a significant enhancement of the chronological resolution can be achieved when relative dating information is considered. For instance, if we take into account that the canine is always formed before the molar, we can exclude the rising part of the bomb peak curve and date them to 1976.0±0.7 and 1978.6 ±0.7, respectively. The 14C concentration measured for hair is the value reflecting, within a few months, the age at death which can then be determined to be 2009.0 ±2.0, having excluded the first intercept in the mid 1950’s on the basis of the results obtained for the teeth. Concerning the results on bones, two different fractions were dated: the cortical and the trabecular ones. In this case the different 14C values correspond to different carbon remodelling rates: the trabecular part has a faster carbon turnover and its “age” is closer to the death age. This is an alternative way to establish that the obtained ages refer to the falling part of the curve (after 1964). By using all these data, the birth date can be obtained by subtracting the corresponding time of formation from the age determined for the teeth. In this way a birth age of 1971.5±2.2 and 1973.1±3.2 can be estimated from the two teeth which are statistically consistent between them and can be combined in order to determine a weighted age of birth corresponding to 1972.0±1.8. The age at death of 37.0±3.8 can then be calculated as the difference between the birth and the death dates.

This example shows how the proper selection of the samples and the analysis of the obtained 14C data on the basis of known information about 14C uptake mechanism allows to significantly enhance the obtainable information. Another point, often critical in forensics applications, is related to the proper and robust estimation of the uncertainty associated with the measurements. In the presented example uncertainties are obtained by combining measurement errors, calibration uncertainties and by propagating them during calculations.

6 Analysis of ivory

The illegal trade of elephant ivory is responsible for the decline of animal populations in different countries due to poaching. Asian and African elephants are both included in the list of endangered species with the highest level of protection of the Convention on International Trade in Endangered Species of Wild Fauna and Flora (CITES) signed in Washington (USA) in 1973. This convention has now 183 parties and has been implemented at the European level in the Regulation n. 338/97 of the European Council and in Italy is regulated by the law n. 150/1992. Following this convention, the commercial trade of freshly obtained elephant ivory is prohibited and persecuted in all the adhering countries. It is then often extremely important, in the legal enforcement of the ban, in the forensics and legal practice, to establish whether an ivory sample, object or artefact can be dated before or after the trade ban. This is the crucial point in legal disputes where the contribution of bomb peak 14C dating is often to supply a conclusive answer about the age of samples, certifying them as “pre-CITES”.

For radiocarbon analyses it is straightforward to distinguish, on the basis of the age, between elephant and mammoth ivory. This is very important since elephant ivory is declared as mammoth, whose trade is not restricted, in order to by-pass trade regulations. When higher chronological resolution is required, bomb peak dating can be used by detecting the 14C signal from nuclear fallout. In order to show the level of resolution which can be achieved and, at the same time, the complexity of the approach which is often required, we report the discussion of a case study. The owner of a single ivory tusk, seized by police, was asked to demonstrate that it was imported in Italy before 1992. Two samples were taken from the tusk, one (sample A) at the base of the tusk (and thus the part closer to the death age of the animal) and the other one (sample B) at a distance of five centimetres from the previous sample. The radiocarbon concentrations measured by AMS were 1.2422 ±0.0056 and 1.2059 ±0.005 (Fraction Modern) for sample A and B, respectively. When calibrating these results against the bomb peak curve, two possible ages are obtained for each of the samples: 1961–1962 or 1982–1983 for sample A and 1959–1961 or 1983–1987 for sample B. If we now consider the relative dating information resulting from the sampling points, and knowing that the growth rate for the elephant tusk is of the order of 4–5 cm per year, the only possibility is that sample B is dated to 1959–1961 and sample A to 1961–1962. This approach, based on the combination of 14C dates and a priori known information, can be implemented in a more statistically robust frame by using the Bayesian tools available in the OxCal package used for calibration. A statistical model is then built in which a priori known information (in our case the chronological order and the time difference between the two samples) is used to constrain the radiocarbon ages. A model is set through the Defined sequence function in OxCal in which the samples are considered in a fixed order with a known time gap between them. In the presented case the results of this Bayesian analysis are given in fig. 6. The light grey intervals represent the calibrated time ranges before the application of the statistical constraints while the dark grey areas represent the probability distribution function for the age of the sample after the application of the model. The age of sample #A can then be given in the range 1961–1962 AD with a confidence level of 95.4%. The tusk can be dated definitely before the CITES convention.

7 Analysis of bio-derived products

Other application fields where 14C AMS analyses can have a forensics value are related to the determination of the biogenic fraction in different types of carbon-based compounds or products such as foodstuff, beverages, plastics and atmospheric emission from industrial sources.

In this case 14C is used as tracer of the biogenic component by using the large isotopic difference, in terms of 14C isotopic signature, between fossil and biogenic-derived materials. In particular fresh bio-based samples, directly or indirectly obtained from living organisms, have a 14C concentration reflecting current atmospheric values while fully fossil materials (such as petroleum-based products) are completely depleted in 14C which is completely decayed. In terms of 14C concentration expressed as Fraction Modern we go then from zero for purely fossil materials to one for fully biogenic samples. The radiocarbon analyses can then be used to analyse different kinds of materials such as plastics and fuels to control the level of bio-derived carbon declared by manufacturers or to solve legal issues related, for instance, to commercial disputes. Important applications are also those related to food quality control. In this case it is possible to check, for instance, the presence of undeclared synthetic, petroleum-derived components or additives in food and assess their fully biogenic origin.

The method is also largely used and nowadays included in different national and international protocols for the determination of the biomass-derived fraction of carbon dioxide released into the atmosphere by different industrial sources such as waste-to-energy plants or biomass-burning power plants. It is then possible to check the compliance of environmental regulations and assess the level of financial support related to the reduction of greenhouse gases emissions.

8 Cultural heritage

In cultural heritage there are several applications of 14C dating which are often relevant in forensics. These are related to the authentication of works of art through the comparison between the determined and the expected age of the sample. A typical example is when the age of a sample extracted from a painting is compared with the death age of the supposed painter or the known timing of the use of a certain painting technique or support. It is worth mentioning here that these investigations are always complex and a conclusive answer requires an approach which integrates history of art considerations and different investigations, such as dating and the compositional analysis of pigments. We want also to stress how the analysis by scientific methods, and in particular by 14C dating, of cultural heritage objects rises ethical and legal issues which are a topic of discussion in the scientific community. These issues are related to the consideration that scientific analyses can be used to secure the age and then authenticate a certain work of art then assessing its commercial value. To avoid contributing to the authentication of artefacts which could have been illegally obtained, for instance by looting in countries at war, should be a widely accepted commitment of the scientific community involved in this kind of analysis.

9 Conclusions

The applications of 14C dating by Accelerator Mass Spectrometry in forensics are mainly (though not only) related to the use of “bomb peak dating”. This approach is based on the detection of 14C released in the atmosphere by nuclear detonation tests and labelling all the organisms living on Earth after the second world war. Proper sampling strategies and data analyses allow to achieve chronological resolution of a few years in the analysis of different kinds of samples such as bones, teeth and ivory. 14C bomb peak dating is then a mature technique which can be largely used in different forensics applications including forensics anthropology, the fight against the illegal trade of endangered species, the quality control of food stuff and cultural heritage.