**1. Introduction**

The use of delayed luminescence in dating ceramic objects dates back to the Sixties of the past century. It is based on dosimetric principles; in practice, the first type of delayed luminescence, thermoluminescence (TL), uses the light emitted obtained by heating a sample as a measurement of the previously absorbed radiation dose by the sample under study, since its last heating to high temperature. In the next section, a few details are given to better describe the phenomenon.

The linear relationship between emitted light and accumulated dose is fundamental in making TL a very good dosimetric technique. It is currently used to measure the exposure to radiation of professionals working in radiation fields, such as radiologists. Of course, in these cases the materials used are tailored to present an intense emission as a consequence to radiation exposure, well suited to be detected, as it is detailed in the following.

On the contrary, in the application of TL to dating, the material to be used cannot be chosen. In many ceramics and bricks, quartz is contained in relatively large amounts and acts as a good natural dosimeter [1]. Other minerals, such as feldspars, could be good dosimeters, even if some problems are often present, such as the lack of stability of the source of TL signal in time, the so-called "anomalous fading" [2].

In order to date a ceramic by TL, the total absorbed dose since the last heating that generally corresponds to its making in a kiln can be determined by comparing the light

**Citation:** Martini, M.; Galli, A. Thermoluminescence Analysis of the Clay Core of Bronze Statues: A Re-Appraisal of the Case Studies of Lupa Capitolina and Other Masterpieces in Rome. *Appl. Sci.* **2021**, *11*, 7820. https://doi.org/10.3390/ app11177820

Academic Editor: Dimitris Mossialos

Received: 31 July 2021 Accepted: 24 August 2021 Published: 25 August 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

emitted due to the exposure to the natural radiation environment in the centuries to artificial irradiations in laboratory. It must be noted that different radiation doses can be accumulated in different samples of the same age, depending on the dose rate, that is, the higher the dose rate, the more intense the natural irradiation. Therefore, the intensity of the mentioned natural radiation environment must be measured. This can generally be achieved by determining the amount of radioactivity of the sample itself and of the surrounding environment. These measurements and the connected experimental troubles are briefly described in the next sections.

In the last decades, many applications of TL dating have demonstrated their feasibility in determining with acceptable precision the sequence in an archaeological stratigraphy or in determining the various phases of construction, modification and restoration in a historical building.

The basic idea of dating by TL can be applied, in principle, to the material remaining in the interior of a bronze statue after its casting, the so-called clay core. In favourable cases, this material behaves like a ceramic and the procedures used for dating ceramics can be also applied to clay cores. This is extremely important, considering that, with very few exceptions that are not treated here, metal objects cannot be dated by absolute techniques.

In this work, the application of TL dating to clay cores is introduced and the specific difficulties deriving from the characteristics of this material, together with the complex determination of the radiation environment, are commented on. Very few cases of application of TL to the dating of clay cores are present in the literature [3,4], mainly due to the many sources of uncertainty mentioned above and to the difficulties in correctly managing the experimental data. The first application of TL techniques to clay cores dates back to 1974, when D.W. Zimmermann [3] succeeded in testing the authenticity of core materials from a Bronze Horse of the New York Metropolitan Museum of Art. Other examples of TL applied to clay core are reported, still in the field of authenticity test [5].

In the last decades a few interesting studies of TL dating were carried out in our laboratory (*Lupa Capitolina*, the horse bronze statue from Musei Capitolini and the Saint Peter statue); they are re-considered in this work aiming at obtaining more accurate results by applying new statistical approaches.

The cases of clay-core dating by TL presented here regard important bronze statues in Rome, including the *Lupa Capitolina*. Sometimes, a rather precise age determination was reached; in some others, it was possible to solve the doubt between two different proposed ages. In this paper, a few results already preliminarily presented are discussed, together with new data and some statistical new calculations aimed at better understanding the dates by TL, when compared with dating results obtained by other techniques.

### **2. Luminescence Dosimetry**

As already mentioned, it is possible to record the exposure to a radiation field by the use of delayed luminescence. Two main types of this kind of feature are currently exploited, thermally- and optically-stimulated luminescence, TSL and OSL, respectively.

Thermoluminescence, or thermally-stimulated luminescence (TL or TSL) is a particular way in which a material emits light, i.e., a luminescence phenomenon [6]. It is a long-lived phosphorescence, in that the light emission is retarded due to the presence of metastable levels, which act as charge "traps", where generally these charges are electrons, of the material. In simple terms, the absorption of energy, mainly from ionising radiation, causes the excitation of electrons in the material, some of which are trapped at the previously mentioned metastable levels, the traps. A subsequent heating of the material, de-trapping the electrons, allows the recombination at luminescence centres, with a consequent light emission, the TL. Similarly, OSL is based on the light emission under optical stimulation; of course, the stimulating light must be different, i.e., with a different wavelength, from the detected emitted light.

In this paper, we focus on TL, but most of the presented procedures are very similar in TL and OSL studies. It must be noted, however, that, in case of TL, the measured radiation amount refers to the period since the last high temperature heating, while in OSL the measured radiation refers to the period since the last light exposure. It can then be applied to materials that have remained in the dark since then, such as sediments. More details on OSL fundamentals and applications can be found elsewhere [6].

When it was discovered that the amount of TL was somehow proportional to the previously absorbed radiation dose, the possibility of using TL as a dosimetric technique was manifested. It was only in 1960 that the practical procedure for quantitative TL measurement was exploited and many TL materials have since then been studied and developed to be used in radiation dosimetry. The result of a TL measurement is the socalled "glow curve" (see Figure 1), which reports the intensity of the emitted light as a function of the temperature; the presence of a peak is related to a previous charge trapping at a certain site. It is strongly dependent on the heating rate, as the position of a peak moves toward higher temperature with increased heating rate.

**Figure 1.** TL glow-curves, example of a clay core extracted from the *Lupa Capitolina*.

The main characteristics needed by a TL material are: (i) the linearity between emitted TL and absorbed dose, or at least a good knowledge of the relationship between TL and absorbed dose, (ii) the presence of peaks in the glow curve at suitable temperature and (iii) the emission wavelength in the visible or near UV region.

## **3. Thermoluminescence Dating**

A particular kind of TL dosimetry is TL dating that was developed in the 1960s. It rapidly became one of the most diffused dating techniques, somehow complementary to radiocarbon dating; TL is used to date inorganic materials, mainly ceramics, while radiocarbon can be applied to organic materials. Luminescence dating has also turned out to be useful in different fields apart from archaeology and historical architecture, in particular in accident dosimetry, while OSL is widely exploited in sediment dating.

In both TL and OSL dating, the materials whose luminescence can be measured are, of course, the minerals naturally present in the objects to be dated; quartz and feldspars are the most diffused minerals contained in ceramics. Looking at TL, their properties are generally good enough, even if the emitted TL is not always proportional to the absorbed dose, due to possible variations in the TL efficiency that must be checked. Besides, in feldspars, the already mentioned phenomenon of "anomalous fading" is often present; it consists in the de-trapping of electrons not due to thermal stimulation and it results in the

erasure of part of the TL signal before its measurements. The ways of dealing with such complex behaviours, in order to correctly determine the absorbed dose, have been deeply treated [2].

Looking at the natural radiation field, it comes from both outside, the cosmic rays, and from inside the Earth, the natural radionuclides. These latter are mainly Potassium 40, Uranium 238 and Thorium 232, the last two together with their decay products that are also radioactive, so that they constitute two radioactive families, originating a number of alpha, beta and gamma emissions.

Due to its decay, the intensity of a radioactive substance, its "activity", measured in decays per second, varies with time. In the case of natural radionuclides, being their decay time in the order of 109 years, the activity can be considered constant for relatively "short" times, as they are when treating historic periods (less than 104 years). The interaction of ionising radiation with matter results in a transfer of energy that depends on the type of emitted particles and on the absorbing medium.

The possibility of dating pottery and other materials using TL is based on the same principles on which dosimetry is ground. In fact, the quartz and feldspars crystals usually present in clays act as TL dosimeters; when the clay is heated, to make a pottery or a brick, all the traps are emptied. From that moment, a new filling of the traps starts due to the irradiation by the natural radioactive elements contained in the pottery and in the surrounding environment.

To summarize these mechanisms, there is a fundamental TL dating equation:

$$\text{Age} = \frac{\text{Palaeodose}}{\text{Dose} - \text{rate}} \tag{1}$$

The palaeodose is the total absorbed dose since the last heating at high temperature that generally coincides with the making of the pottery (it can sometimes be due to accidental heating, such as in the case of a fire). It is calculated from a comparison between the "natural" TL produced by the irradiation by the natural radioactivity and the "artificial" TL due to laboratory irradiation with artificial sources, whose intensity is known (see Figure 1).

The dose rate is due to internal radioactive impurities in the object to be dated and external impurities in the surrounding environment, e.g., the burial soil in an archaeological excavation, or the building itself when dating bricks. The internal dose is given by alpha and beta radiation, while the external dose comes from the environmental gamma radiation and, to a lesser extent, to cosmic rays; more details can be found in the specialized literature on the topic [2]. In most cases, the internal radioactivity gives 70–80% of the total dose rate. This constitutes a sizable advantage, because uncertainties in the past environment give limited errors in the calculation of the age. As we explain here, this is not always true when dating clay cores, where it can be a relevant source of uncertainty.

With potteries of Roman–Greek periods, we are dealing with a palaeodose ranging from a few grays to a few tens of grays, where the gray (Gy) is the unit for absorbed dose, i.e., energy per unit mass, and corresponds to 1 Joule per kilogram of absorbing material. The dose rate is usually within the range from 1 milligray per year (mGy/a) to 10 milligrays per year (mGy/a).

As regards the evaluation of the dose rate, due to the very low levels of natural radioactivity, very sensitive techniques have been developed. It must also be taken into account that the effective dose rate is dependent on the water contents of the sample and the soil; this is because one can calculate the exposure to radiation when the radioactive contents of the sample and the environment are known. However, the water present in the pores of the sample absorbs part of the energy emitted by the radionuclides; this means that the dose effectively absorbed by the sample is reduced due to the presence of water. As a result, it is necessary to know, with the highest possible accuracy, the amount of water present in the sample in the centuries, which cannot always be achieved. Typically, there may have been changes in the position of the sample to be dated and in the water

content in the past. This source of uncertainty can be a limiting factor when dealing with clay-core dating.

#### **4. TL Dating of Clay Cores: Materials and Method**

In the preceding section, the main steps of TL dating and the sources of uncertainty are shortly summarized. It is important to consider how these factors can limit the application of TL dating to clay cores. The precise evaluation of both palaeodose and dose rate requires considering the various factors affecting the calculations.

As regards the measurement of the palaeodose, it must be remembered that the composition of the various clay cores can widely vary from case to case. In fact, the materials that remain in a bronze statue after its casting by the lost-wax technique can be composed not only by clay, but also by many materials of various origin; they were added to allow the attenuation of the huge variations in volume, as an effect of high temperature changes during the casting and after it. Not only inorganic materials, such as clay, but also organic materials, for example, straw, were put inside the object to be cast, in order to attenuate expansion and contraction deriving from the temperature variations. The effects on the TL properties of the materials that can possibly be extracted from the inside of a bronze statue can be important; the presence of organic material is generally a source of the so-called "spurious TL", that is, a light emission independent of the absorbed dose. This phenomenon can also be present in potteries. It is generally attenuated by carrying out the measurements in an inert atmosphere, typically in nitrogen. This is also conducted with clay cores, but the low intensity of the "good" TL signal, as compared with the spurious TL, can constitute a limiting factor in dating clay cores by TL.

A further important point in dating clay cores by TL, especially meaningful with statues found in archaeological excavations, is the presence of materials that were not submitted to the original casting, typically some soil remains that obviously were not submitted to high temperature heating.

In the cases presented in this work, the material extracted from the clay core was submitted to grain selection in order to apply the "fine grain" technique [2]. This implies that the contribution of the natural alpha dose had to be taken into account; alpha irradiation by an 241Am source was carried out in laboratory in order to determine the efficiency of alpha irradiation with respect to the gamma and beta ones [2].

As concerns the measurement of the dose rate, as we explore in some of the following case studies, it would be very important to know, with a good accuracy, the history of the statue to be dated, in order to estimate the external contribution to the dose rate, that is known not to depend on the clay core, but rather on the environmental radiation field.

A second factor affecting the dose rate is the knowledge of the water content of the clay core in the past, whose effect is the attenuation of the dose rate, hence the increase in the date obtained for the measured clay core, as calculated from the radioactivity content of the clay core itself and its environment.

In the cases presented in this work, the radioactivity content of the clay cores was calculated by alpha counting using ZnS (Ag) detectors [2] and through the measurement of the total Potassium content by flame photometry; the contribution due to the radioactive 40K content is easily calculated on the base of its well-known isotopic concentration [2]. The environmental dose rate, as it is detailed in the following, could not be measured due to the lack of information on the external irradiation in the centuries and only speculations could be proposed.

We summarise the specific application of TL dating to clay cores and its difference when compared with the application to potteries and to bricks as follows:



Similar speculations are valid for the role of the absorbed water, whose effect is the increase in the calculated date, when known. As discussed above, it is generally possible to estimate, sometimes with good accuracy, the water content for an object coming from an archaeological excavation and, even better, from a building. Very difficult is the estimation of the water content inside a bronze statue in the centuries.
