# µ-LIBS imaging of archaeological ceramics: Quantification of clay fraction in provenance study

Nicolas Herreyre, Valérie Thirion-Merle, Loan Lemaître, Anne Schmitt, Christine Oberlin, Clothilde Comby-Zerbino, Vincent Motto-Ros

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Nicolas Herreyre, Valérie Thirion-Merle, Loan Lemaître, Anne Schmitt, Christine Oberlin, et al.. µ-LIBS imaging of archaeological ceramics: Quantification of clay fraction in provenance study. Talanta, 2026, 303, pp.129452. 10.1016/j.talanta.2026.129452. hal-05493845

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# µ-LIBS imaging of archaeological ceramics: Quantification of clay fraction in provenance study

Nicolas Herreyre<sup>a,b,©</sup>, Valérie Thirion-Merle<sup>a</sup>, Loan Lemaître<sup>a,b</sup>, Anne Schmitt<sup>a,©</sup>, Christine Oberlin<sup>a,©</sup>, Clothilde Comby-Zerbino<sup>b</sup>, Vincent Motto-Ros<sup>b,* ©</sup>

## ARTICLE INFO

Keywords:

Archaeometry

Ceramic geochemistry

Coarse ware

LIBS imaging

Quantitative elemental imaging

## ABSTRACT

The provenance and circulation of archaeological ceramics are key to understanding ancient societies' trade networks and cultural exchanges. However, comparing coarse and fine wares using bulk compositional analysis remains challenging due to the variable chemical contribution of temper (e.g., sand), which masks the signature of the raw clay. This study introduces a novel quantitative µ-LIBS (micro-Laser-Induced Breakdown Spectroscopy) imaging methodology to isolate and analyse the clay fraction composition of archaeological ceramics, enabling direct geochemical comparisons between tempered coarse wares and fine wares for provenance studies.

By combining multi-elemental mapping (Ca, Fe, Ti, K, Si, Al, Mg, Mn, Na, P, Zr, Rb, Sr, Ba) with calibration based on bulk X-ray fluorescence spectrometry, the method provides accurate microscale quantification. Elemental maps are segmented to extract the clay fraction composition, overcoming the limitations of traditional bulk analysis. The protocol was validated using fired briquettes with controlled sand contents and firing temperatures, confirming its accuracy and robustness.

Applied to four coarse ware specimens (mainly amphorae) from *Lugdunum* (Roman Lyon (France) during the Augustan-period, the reconstructed clay compositions were compared to a reference database of 235 contemporaneous ceramics, including coarse wares and three *Lugdunum* Terra sigillata production groups. Results reveal a shared raw clay source between calcareous amphorae and La Muette B sigillata, supporting earlier hypotheses, while other sigillata wares remain compositionally distinct. This approach significantly advances ceramic provenance studies, particularly for complex assemblages, by enabling direct comparisons between ware types previously hindered by temper variability, together with the common total bulk elemental composition measurements.

## 1. Introduction

Archaeological ceramics are among the most frequently recovered artifacts from excavation sites. Besides dating and technological analyses, a key focus of their study is determining the provenance, circulation, and diffusion of objects within ancient societies, typically achieved through geochemical analysis. For decades, archaeometrists have demonstrated that the elemental composition of ceramics provides reliable evidence for tracing a common origin among fired clays, pottery, and architectural materials [1–6]. With sufficiently large databases, ceramics can be classified by their composition–even when the precise workshop location or clay deposit is unknown.

Such analyses are commonly carried out using wavelength-

dispersive X-ray fluorescence (WD-XRF) [7,8] or other atomic spectrometry techniques such as Neutron Activation Analysis (NAA) [9] or Inductively Coupled Plasma-Atomic Emission Spectrometry or Mass Spectrometry (ICP-AES, ICP-MS) [10]. These require the preparation of samples through fusion into a homogeneous glass disc (or into solution for ICP methods) to minimize matrix effects and ensure representative measurements for reliable comparisons. Nevertheless, a major limitation of this method lies in grouping fine and coarse wares that, while potentially originating from the same clayey raw material, have undergone different processes. Coarse wares (e.g. amphorae or architectural materials) are typically tempered with sandy additives, whereas fine wares often result from purified clays, processed by sieving or decantation [4,11]. The contribution of granular fractions, either

<footnote><sup>a</sup> Archéologie et Archéométrie, UMR5138, Univ. Lyon 2-CNRS-Univ. Lyon 1, Maison de l'Orient et de la Méditerranée, 7 rue Raulin, 69007, Lyon, France</footnote>

<footnote><sup>b</sup> Institut Lumière Matière, UMR5306, Univ. Lyon 1-CNRS, Université de Lyon, 69622, Villeurbanne, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: vincent.motto-ros@univ-lyon1.fr (V. Motto-Ros).</footnote>
natural or added, can significantly affect the global elemental composition of ceramics, making it difficult to identify a common origin with confidence. Such situation has been studied in the case of *Lugdunum* (Lyon, France) ceramic production for instance, for which sigillata are a fine ware while amphorae and common ware are coarse [12,13].

Since firing makes these grains inseparable from the clay matrix, previous studies have addressed this issue using petrographic analysis [13,14]. By determining the nature and proportion of the granular fraction, a theoretical chemical composition of the temper can be estimated and subtracted from the global ceramic composition to isolate the clay signature. However, this approach remains an approximation, limited in precision (especially for minor and trace elements), and requires time-consuming microscopic observations.

To overcome these limitations, total analysis approaches must give way to targeted and spatially resolved measurements, recognizing the heterogeneous nature of ceramics, which cannot be accurately characterized by a single point analysis. Non-invasive techniques such as Particle-Induced X-ray Emission (PIXE) [15,16] and Electronic Probe Micro-Analysis (EPMA) [17] have been used for targeted elemental analysis of ceramics. For instance, studies using EPMA [18,19] have analysed less tempered zones by avoiding mineral grains, but this approach does not guarantee accurate clay composition isolation, especially because of the ceramics' heterogeneity. Promising results have also been obtained using laser ablation (LA) ICP-MS [20], which enables precise and localized analysis, but it is not yet applicable for routine use. The main limitations appear with the lack of standards useable for such heterogeneous samples, and the low number of point analyses as much as their size of 30 µm that may be discussed for reliable analyses.

In this context, Laser-Induced Breakdown Spectroscopy (LIBS) imaging offers a compelling alternative. Over the past 20 years, it has been first applied on ceramics through macro-LIBS configuration for spotted composition for characterization or provenance purposes [21–24]. More recently, with the development of imaging in a µ-LIBS configuration, such analyses provide more information for characterization [25–28]. Its high spatial resolution configuration (approximately 15/20 µm for ceramics in our instrumentation) coupled with a frequency rate of 100 Hz allows a large number of measurements to be performed quickly over large surfaces [28]. In addition, current developments, through improvements and reductions in lateral resolution, as well as increase of the acquisition rate, make the technique even more robust and suitable for various applications in imaging [29,30]. For our purposes, what makes µ-LIBS imaging particularly suitable is the ability to segment different sample components and thus the exclusion of granular fractions from compositional analyses, allowing targeted elemental characterization of the clay matrix alone.

The main challenge remains the quantification capability of LIBS on bulk material with several matrices. Like main of spectroscopic methods, quantitative results require calibration with reference standards, actually unavailable for ceramics under bulk format due to their intrinsic heterogeneity. Vannoorenberghe et al. [20] highlighted the lack of matrix-matched standards, which limits traditional calibration approaches. While we considered using archaeological ceramics analysed by WD-XRF in the ArAr laboratory, their high matrix variability made them unsuitable as references.

To address the determination of clayey composition of ceramics without temper/sandy fraction contribution, we propose an alternative approach based on elemental LIBS imaging combined with internal calibration using a support-independent technique. In our method, intensity elemental maps of a single sample made through µ-LIBS are calibrated against its global concentrations measured by WD-XRF. This allow to get a semi-quantitative map that can be segmented to isolate the clayey fraction, leading to clay matrix-specific analysis. This paper aims to validate the proposed methodology on experimental ceramics made from clays of known composition, with its uncertainties, exploring the influence of firing temperature and temper proportion. We also

demonstrate its application on a small archaeological specimen set (4 ceramics) from ancient *Lugdunum*, comparing one calcareous coarse ware (amphorae and mortar) with three different calcareous fine wares (Lyon Terra sigillata), dating from August Period, to confirm the protocol efficiency in attributing a common clayey material origin.

## 2. Preamble: general overview of the proposed methodology

The method developed in this work was designed to be readily integrated into the conventional analytical workflows used by archaeologists for the study of ceramics. Typically, only a small fragment (around 2 g) of the ceramic sherds collected from an archaeological site is subjected to bulk compositional analysis (e.g., by XRF or ICP). The composition obtained from this small portion is assumed to represent the bulk composition of the entire artifact. Over the past decades, several laboratories have progressively built extensive reference databases linking chemical compositions of ceramic materials to their archaeological contexts. The approach developed in this work builds upon these existing datasets. By performing µ-LIBS imaging on a polished cross-section of a sample with known bulk composition, it enables the use of bulk compositional data to (i) produce semi-quantitative elemental maps, and (ii) evaluate the average composition of clay fraction, with associated uncertainties, specifically associated with the clay matrix.

The different steps of the methodology are illustrated in Fig. 1. The LIBS elemental images obtained are used to calculate an average intensity within the regions exclusively corresponding to the sample — for instance, voids or holes were naturally excluded. Each element's intensity was then calibrated using its bulk concentration, previously measured by WD-XRF on a small fraction of the same sample. Since the primary objective was to quantify the clay matrix, the instrumental parameters were optimized for measurements within this phase. Observation of results however revealed noticeable matrix effects mainly due to matrix difference between the clayey and sandy fractions, the latter being denser than the clay, which leads to apparent total concentrations exceeding 100 % in these regions whereas clay exhibits sums of concentrations much lower than 100 %. To correct for this effect, an additional normalization step was applied, as described later, allowing the generation of semi-quantitative maps for all analysed elements. Finally, a mask was applied to these maps to remove sand grains, retaining only the clay matrix. The average clay composition was then determined by computing the mean value over this masked region.

It should be noted that this approach relies on two main assumptions. First, both the bulk XRF composition and the LIBS images are considered representative of the sample. According to Delesse's principle [31,32], there is a strict equivalence between the volume fraction of a given phase and its surface fraction observed on a random section of an isotropic material, such as rock or ceramic. Based on this principle, a direct relationship can be established between bulk geochemical analysis and surface-based elemental mapping. To ensure the best correspondence, a sufficiently large area (>2 cm²) of the sample is analysed—close to the region characterized by XRF—with a lateral resolution of about 15–20 µm, which is required to account for the contribution of fine sand and silt particles. Second, it is assumed that the proportion of the granular fraction remains low compared to the clay matrix, rarely exceeding the third of the natural clayey mixture or the clayey material processed by the ceramist. This assumption is critical, as the matrix effects observed on dense aggregates naturally affect the accuracy of the quantitative estimation.

## 3. Materials and methods

### 3.1. *Samples*

#### 3.1.1. *Experimental ceramic*

Several laboratory briquettes were produced using the same ingredients, with different grain proportions and firing temperatures. A
<figure><img src="image_3.png" /><figcaption>Fig. 1. Global overview of the quantification strategy.</figcaption></figure>

fine fraction of commercial clay (from Cultura, Mérignac, France; density of 1.9) was used with a crushed siliceous and slightly calcareous sand (density of 1.6) from the Vicat gravel pit at Saint-Germain-au-Mont-d'Or, France. Further features of specification for each material have been determined in the laboratory through measurements as mineralogy by X-Ray Diffraction (D2 Phaser Bruker) and grain size analysis by sieving. The clay is reddish, composed almost entirely of illite, chlorite and smectite, including calcite, quartz and feldspars as very light siltic fraction. The sand is composed mainly of quartz, feldspars, a few ferromagnesian minerals and calcium carbonate grains. Its particle size distribution was originally between 0 and 4 mm according to the seller's documents, but a 1600 µm sieving was applied to obtain inclusions corresponding to a moderately sorted coarse sand (200–1600 µm) with a low proportion of finer particles.

Series of briquettes were prepared, dried and placed in the electric oven (Thermolyne from Thermo Scientific). After reaching the peak temperature, they remain inside the oven for 1.5 h before it is turned off, followed by gradual cooling, fully in oxidising atmosphere. One set of samples is made using raw clay fired at high temperatures, reaching 1000 °C, with an increasing content of sand, for mass ratios at 5 %, 10 %, and 20 %, corresponding to approximate volume ratios of 5.9 %, 11.7 %, and 22.9 %, respectively (next sand % will refer to that volume ratio). Furthermore, a lower temperature of firing, i.e. 850 °C, is applied on a 11.7 %-tempered briquette for comparison. Two other briquettes with no added temper and fired at 850° and 1000 °C were made. Chemical composition of raw materials and raw fired clay are shown in Table 1, measured by WDS-XRF, as detailed hereafter. Briquette's compositions are detailed in Supplementary materials (STable 1).

### 3.1.2. Archaeological sample: Lugdunum calcareous ware

Four sherds of different specimens from the same coarse ware from Lugdunum (Lyon, France) have been selected (Table 2), identified as very calcareous production of La Muette workshop (noted B' in Schmitt, 1996). The selection is made randomly but the small set have been then validated in accordance with some criteria: samples with both low and

<caption>Table 2</caption>

- Archaeological sample identity.

<table><thead><tr><th>Sample number</th><th>Site</th><th>Typology</th><th>Sherd location</th></tr></thead><tbody><tr><td>AMT371</td><td>Ilot 24, Lyon</td><td>Amphora, Dressel 1</td><td>Neck or body</td></tr><tr><td>AMT376</td><td>Ilot 24, Lyon</td><td>Amphora, Dressel 2/4</td><td>Lip</td></tr><tr><td>AMT673</td><td>Bas de Loyasse, Lyon</td><td>Amphora, Dressel 9</td><td>Lip</td></tr><tr><td>AMT896</td><td>Ilot 24, Lyon</td><td>Common ware, mortar</td><td>Lip</td></tr></tbody></table>

huge amount of non-plastic fraction (about 11–24 %); different typologies of ware, with amphorae of different types and a common ware mortar; material previously studied, analysed, and classified in Lugdunum ceramic production; enough material for section preparation. They are from two sites of Augustan period in Lyon: ilot 24 and Bas-de-Loyasse.

These specimens are compared with the group of calcareous coarse ware from La Muette B' (76 specimens excluding them), most of which are assumed to originate from there since they were found mainly on consumption sites in Lyon [33] (group references have been updated since the 1996 publication but stay unpublished before this work). They are also compared with three different fine wares of Lyon, well documented: three calcareous sigillata productions dating from the beginning of the Early Roman Empire as well. Two sigillata groups are also from La Muette workshop [33], A-calcareous (57 specimens) and B-very calcareous (67 specimens), while the third group (27 specimens) is sigillata imitation from Loyasse workshop [34]. The details and chemical analysis (WD-XRF) for each specimen are provided as supplementary material (STable 3), while group means are exposed in results (Table 5).

### 3.2. WD-XRF of total sherd: preparation and technique

The chemical composition of the samples was determined using WD-XRF with a Bruker 4 kW-S8 Tiger spectrometer equipped with a Rh

<caption>Table 1</caption>

Elemental composition of commercial sand and clay measured by WDS-XRF (14 elements selected as explained in section 3.4). Clay values are the arithmetic mean of the concentrations from raw clay and 5 fired briquettes (as no significant difference was observed), with the standard deviation (s).

<table><thead><tr><th></th><th>CaO</th><th>Fe<sub>2</sub>O<sub>3</sub></th><th>TiO<sub>2</sub></th><th>K<sub>2</sub>O</th><th>SiO<sub>2</sub></th><th>Al<sub>2</sub>O<sub>3</sub></th><th>MgO</th><th>MnO</th><th>Na<sub>2</sub>O</th><th>P<sub>2</sub>O<sub>5</sub></th><th>Zr</th><th>Rb</th><th>Sr</th><th>Ba</th></tr><tr><th></th><th colspan="2">wt.%</th><th colspan="2"></th><th colspan="2"></th><th colspan="2"></th><th colspan="2"></th><th colspan="3">ppm</th></tr></thead><tbody><tr><td>SAND (1 measure)</td><td>4.19</td><td>1.19</td><td>0.147</td><td>1.68</td><td>86.6</td><td>4.94</td><td>0.42</td><td>0.0255</td><td>0.71</td><td>0.07</td><td>81</td><td>73</td><td>90</td><td>300</td></tr><tr><td>CLAY μ (6 measures)</td><td>6.13</td><td>6.94</td><td>0.871</td><td>3.99</td><td>58.9</td><td>19.4</td><td>3.11</td><td>0.1146</td><td>0.23</td><td>0.17</td><td>181</td><td>176</td><td>147</td><td>866</td></tr><tr><td>s</td><td>0.04</td><td>0.01</td><td>0.010</td><td>0.04</td><td>0.1</td><td>0.2</td><td>0.03</td><td>0.0003</td><td>0.01</td><td>&lt;0.01</td><td>3</td><td>4</td><td>1</td><td>7</td></tr></tbody></table>
<table><caption>**Table 3**
Selected elemental emission lines for µ-LIBS imaging, covering 15 elements on 3 spectrometers. Wavelengths from Kurucz database.</caption><thead><tr><th>Spectrometer</th><th>Element</th><th>Specie</th><th>Wavelength (nm)</th></tr></thead><tbody><tr><td rowspan="6">Shamrock 500</td><td>Al</td><td>I</td><td>308.2</td></tr><tr><td>Mg</td><td>I</td><td>285.2</td></tr><tr><td>Mn</td><td>II</td><td>259.4</td></tr><tr><td>P</td><td>I</td><td>255.3</td></tr><tr><td>Si</td><td>I</td><td>288.2</td></tr><tr><td>Ti</td><td>II</td><td>323.5</td></tr><tr><td rowspan="6">Shamrock 300</td><td>Zr</td><td>II</td><td>267.9</td></tr><tr><td>Ba</td><td>II</td><td>455.4</td></tr><tr><td>Ca</td><td>I</td><td>431.9</td></tr><tr><td>Fe</td><td>I</td><td>438.4</td></tr><tr><td>Sr</td><td>I</td><td>460.7</td></tr><tr><td>K</td><td>I</td><td>769.9</td></tr><tr><td rowspan="4">AVANTES</td><td>Na</td><td>I</td><td>819.5</td></tr><tr><td>O</td><td>I</td><td>777.2</td></tr><tr><td>Rb</td><td>I</td><td>780.0</td></tr></tbody></table>

excitation source (Karlsruhe, Germany). Prior preparation of the samples must be carried out: fragments of about 2 g (minimum 1 g) are cut

out with a diamond-coated saw (the minimum quantity of 1 g per sample was fixed in accordance with several other laboratories as a compromise between the representativity of the analysed portion with respect to the ceramic and the destruction of the sherd). To avoid alterations linked to burial, external surfaces of archaeological sherds are removed as well as any traces of slips. The samples are then calcined at 950 °C in an electric oven, cooled and ground in a tungsten-carbide ball mill. From this powder, 800 mg are mixed with 3200 mg of flux (33.5 % lithium metaborate and 66.5 % lithium tetraborate) and fused to form a homogeneous glass bead (or glass disc) using an automatic fusion fluxer (Breitländer autofluxer®, Dortmund, Germany).

Measurements performed on these discs reflect the average chemical composition of the initial material, including both the ceramic matrix and inclusions, thus characterizing the raw material used in manufacture. For each sample, 24 elements (CaO, Fe₂O₃, TiO₂, K₂O, SiO₂, Al₂O₃, MgO, MnO, Na₂O, P₂O₅, MgO, MnO, Na₂O, P₂O₅, Zr, Rb, Zn, Cr, Ni, La, Ba, V, Ce, Y, Th, Pb and Cu) were quantified, based on calibration curves established with 40 international geostandards. The statistical uncertainties *u*<sub>XRF</sub> (defined at the 1σ level) associated with each calibration model is reported in **S**Table 2 in the supplementary materials (for all the 14 elements of interest in our study, as explained in section 3.4).

<table><caption>**Table 4**
Chemical composition of commercial clay and reference briquettes measured by WDS-XRF, together with the composition of clay fraction from same briquettes obtained by the LIBS quantitative method and their uncertainties *u*<sub>clay</sub>.</caption><thead><tr><th></th><th>CaO</th><th>Fe₂O₃</th><th>TiO₂</th><th>K₂O</th><th>SiO₂</th><th>Al₂O₃</th><th>MgO</th><th>MnO</th><th>Na₂O</th><th>P₂O₅</th><th>Zr</th><th>Rb</th><th>Sr</th><th>Ba</th></tr><tr><th></th><th colspan="12">wt.%</th><th colspan="5">ppm</th></tr></thead><tbody><tr><td>CLAY</td><td>6.13</td><td>6.94</td><td>0.871</td><td>3.99</td><td>58.9</td><td>19.4</td><td>3.11</td><td>0.1146</td><td>0.23</td><td>0.17</td><td>181</td><td>176</td><td>147</td><td>866</td></tr><tr><td>Total briquette 5.9 %-temp.</td><td>5.95</td><td>6.55</td><td>0.813</td><td>3.76</td><td>60.5</td><td>18.8</td><td>2.98</td><td>0.1078</td><td>0.25</td><td>0.16</td><td>176</td><td>144</td><td>170</td><td>827</td></tr><tr><td>Total briquette 11.7 %-temp.</td><td>5.88</td><td>6.20</td><td>0.769</td><td>3.63</td><td>62.2</td><td>17.8</td><td>2.82</td><td>0.1022</td><td>0.27</td><td>0.16</td><td>170</td><td>140</td><td>165</td><td>810</td></tr><tr><td>Total briquette 22.9 %-temp.</td><td>5.50</td><td>5.65</td><td>0.682</td><td>3.34</td><td>65.6</td><td>16.0</td><td>2.49</td><td>0.0910</td><td>0.33</td><td>0.14</td><td>158</td><td>132</td><td>152</td><td>720</td></tr><tr><td>Clay – 5.9 %-temp. & fired at 1000 °C</td><td>6.11</td><td>6.81</td><td>0.852</td><td>3.89</td><td>59.0</td><td>19.6</td><td>3.08</td><td>0.1084</td><td>0.26</td><td>0.17</td><td>182</td><td>150</td><td>172</td><td>859</td></tr><tr><td>u<sub>clay</sub></td><td>0.39</td><td>0.45</td><td>0.033</td><td>0.27</td><td>1.6</td><td>0.4</td><td>0.11</td><td>0.0088</td><td>0.06</td><td>0.02</td><td>10</td><td>15</td><td>16</td><td>24</td></tr><tr><td>Clay – 11.7 %-temp. & fired at 1000 °C</td><td>6.13</td><td>6.82</td><td>0.871</td><td>3.79</td><td>59.3</td><td>19.4</td><td>3.02</td><td>0.1073</td><td>0.28</td><td>0.17</td><td>189</td><td>150</td><td>168</td><td>872</td></tr><tr><td>u<sub>clay</sub></td><td>0.16</td><td>0.25</td><td>0.028</td><td>0.16</td><td>1.2</td><td>0.4</td><td>0.11</td><td>0.0048</td><td>0.06</td><td>0.03</td><td>10</td><td>12</td><td>11</td><td>27</td></tr><tr><td>Clay – 22.9 %-temp. & fired at 1000 °C</td><td>6.16</td><td>6.82</td><td>0.845</td><td>3.75</td><td>60.1</td><td>18.7</td><td>2.81</td><td>0.0990</td><td>0.35</td><td>0.15</td><td>191</td><td>152</td><td>162</td><td>830</td></tr><tr><td>u<sub>clay</sub></td><td>0.23</td><td>0.21</td><td>0.030</td><td>0.17</td><td>1.1</td><td>0.3</td><td>0.10</td><td>0.0058</td><td>0.05</td><td>0.02</td><td>10</td><td>12</td><td>11</td><td>28</td></tr><tr><td>Clay – 11.7 %-temp. & fired at 850 °C</td><td>6.09</td><td>6.81</td><td>0.871</td><td>3.81</td><td>59.5</td><td>19.3</td><td>3.00</td><td>0.1061</td><td>0.23</td><td>0.17</td><td>187</td><td>145</td><td>168</td><td>868</td></tr><tr><td>u<sub>clay</sub></td><td>0.22</td><td>0.15</td><td>0.028</td><td>0.09</td><td>0.1</td><td>0.4</td><td>0.10</td><td>0.0044</td><td>0.05</td><td>0.03</td><td>9</td><td>8</td><td>9</td><td>26</td></tr></tbody></table>

<table><caption>**Table 5**
Chemical composition of archaeological samples through LIBS Q-Method compared to reference groups. Each group is described by its mean (µ) and its standard deviation (s). 8 specimens from references have a Na₂O concentration unmeasured, replaced by the arithmetic mean of their group.</caption><thead><tr><th></th><th></th><th>CaO</th><th>Fe₂O₃</th><th>TiO₂</th><th>K₂O</th><th>SiO₂</th><th>Al₂O₃</th><th>MgO</th><th>MnO</th><th>Na₂O</th><th>P₂O₅</th><th>Zr</th><th>Rb</th><th>Sr</th><th>Ba</th></tr><tr><th></th><th></th><th colspan="12">wt.%</th><th colspan="5">ppm</th></tr></thead><tbody><tr><td rowspan="6">XRF global analysis</td><td>AMT371</td><td>20.8</td><td>4.65</td><td>0.430</td><td>2.39</td><td>57.6</td><td>11.4</td><td>1.66</td><td>0.1104</td><td>0.63</td><td>0.30</td><td>113</td><td>307</td><td>126</td><td>454</td></tr><tr><td>AMT376</td><td>18.7</td><td>4.63</td><td>0.420</td><td>2.63</td><td>59.2</td><td>11.7</td><td>1.54</td><td>0.1018</td><td>0.64</td><td>0.34</td><td>108</td><td>270</td><td>136</td><td>556</td></tr><tr><td>AMT673</td><td>19.8</td><td>5.58</td><td>0.511</td><td>2.39</td><td>54.5</td><td>14.3</td><td>1.78</td><td>0.1134</td><td>0.57</td><td>0.31</td><td>101</td><td>339</td><td>131</td><td>543</td></tr><tr><td>AMT896</td><td>17.2</td><td>4.62</td><td>0.456</td><td>2.39</td><td>60.2</td><td>11.8</td><td>1.55</td><td>0.1002</td><td>0.78</td><td>0.71</td><td>127</td><td>315</td><td>118</td><td>583</td></tr><tr><td>AMT371</td><td>24.9</td><td>5.42</td><td>0.444</td><td>2.12</td><td>52.2</td><td>12.1</td><td>1.82</td><td>0.1146</td><td>0.49</td><td>0.34</td><td>126</td><td>341</td><td>116</td><td>473</td></tr><tr><td>AMT376</td><td>24.4</td><td>5.58</td><td>0.441</td><td>2.23</td><td>52.3</td><td>12.6</td><td>1.80</td><td>0.1153</td><td>0.19</td><td>0.37</td><td>127</td><td>289</td><td>122</td><td>509</td></tr><tr><td rowspan="6">Q-LIBS-clay</td><td>AMT673</td><td>23.8</td><td>5.47</td><td>0.486</td><td>1.64</td><td>51.0</td><td>14.7</td><td>1.97</td><td>0.1188</td><td>0.52</td><td>0.26</td><td>102</td><td>323</td><td>113</td><td>468</td></tr><tr><td>AMT896</td><td>23.7</td><td>5.66</td><td>0.471</td><td>2.20</td><td>51.9</td><td>12.9</td><td>1.78</td><td>0.1025</td><td>0.28</td><td>0.82</td><td>147</td><td>379</td><td>112</td><td>605</td></tr><tr><td>Coarse ware</td><td>19.2</td><td>4.86</td><td>0.456</td><td>2.57</td><td>57.4</td><td>12.6</td><td>1.62</td><td>0.10</td><td>0.62</td><td>0.44</td><td>113</td><td>306</td><td>126</td><td>583</td></tr><tr><td>La Muette B'</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>μ (80 spe)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>s</td><td>2.2</td><td>0.37</td><td>0.037</td><td>0.23</td><td>1.8</td><td>1.1</td><td>0.18</td><td>0.01</td><td>0.19</td><td>0.27</td><td>19</td><td>32</td><td>14</td><td>130</td></tr><tr><td>Sigillata</td><td>20.4</td><td>4.72</td><td>0.504</td><td>2.06</td><td>57.3</td><td>11.9</td><td>1.60</td><td>0.1087</td><td>0.75</td><td>0.42</td><td>167</td><td>307</td><td>101</td><td>802</td></tr><tr><td>Loyasse</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>μ (27 spe)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>s</td><td>1.6</td><td>0.23</td><td>0.014</td><td>0.08</td><td>1.4</td><td>0.3</td><td>0.19</td><td>0.0159</td><td>0.07</td><td>0.13</td><td>16</td><td>15</td><td>19</td><td>181</td></tr><tr><td>Sigillata</td><td>14.6</td><td>5.54</td><td>0.597</td><td>2.14</td><td>60.1</td><td>14.9</td><td>1.26</td><td>0.1062</td><td>0.47</td><td>0.24</td><td>163</td><td>244</td><td>98</td><td>411</td></tr><tr><td>La Muette A</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>μ (57 spe)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>s</td><td>1.7</td><td>0.21</td><td>0.017</td><td>0.12</td><td>1.3</td><td>0.5</td><td>0.13</td><td>0.0072</td><td>0.24</td><td>0.05</td><td>26</td><td>16</td><td>8</td><td>46</td></tr><tr><td>Sigillata</td><td>26.2</td><td>5.28</td><td>0.455</td><td>1.79</td><td>50.46</td><td>12.43</td><td>2.14</td><td>0.1142</td><td>0.65</td><td>0.37</td><td>103</td><td>385</td><td>78</td><td>445</td></tr><tr><td>La Muette B</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>μ (67 spe)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>s</td><td>1.8</td><td>0.17</td><td>0.014</td><td>0.32</td><td>1.37</td><td>0.37</td><td>0.23</td><td>0.0049</td><td>0.31</td><td>0.10</td><td>12</td><td>19</td><td>19</td><td>95</td></tr></tbody></table>
### 3.3. µ-LIBS imaging of sherd section: preparation and technique

Prior to analysis, preparation as sections was necessary. Briquettes were polished on the main upper face for getting a flat surface, with a manually rotating polisher, decreasing granulometry of polishing paper until P 1200. The same preparation was done for archaeological specimens; sections have been cut on the piece of sherd, close to the part sampled for WDS-XRF measurements.

The µ-LIBS imaging system used is the one from the Institut of Light and Matter (iLM) in Lyon [35–37]. It consists of a 100 Hz Nd:YAG pulsed laser emitting at 1064 nm (Centurion GRM, Quantel, Les Ulis, France), with a 15× magnification objective used to focus the laser pulse on the surface of the sample. The pulse energy was set at 1000 µJ, and the plasma emission is measured using three spectrometers in order to record the lines of all the elements of interest from different wavelengths. The first two spectrometers, Shamrock 500 and 303 (Andor Technology, Belfast, UK), are equipped with an ICCD camera (iStar, Andor Technology, Belfast, UK), which recorded the spectral ranges between 245 and 334 nm and between 419 and 486 nm, respectively. The third spectrometer is a compact Avantes spectrometer (Evo Sensline XL, Apeldoorn, Netherlands) configured for the detection in the range 636–960 nm. Acquisitions were made for a plasma observation window with a delay of 1 µs (time between the laser shot and the recording of the optical emissions) and a gate of 5 µs (recording time). All the experiments were carried out under ambient temperature and pressure conditions. An argon flow of 0.9 L/min directed onto the plasma was used both to enhance emission and to prevent surface contamination due to the deposition of material ablated by previous laser shots.

By compiling the plasma emissions produced by the sequence of laser shots (single shot without accumulation), we can obtain raw spectral data for the entire surface of the sample analysed. This is realised on a surface large enough to be representative of the volume, with a high number of shots (>500 000 at least, 1 000 000 being a better sampling). The lateral resolution between each laser shot was set to 20 µm.

### 3.4. Spectral processing and images treatments

Treatments of LIBS spectra are done with a homemade software (LasMap) leading to high-resolution elemental images. To do so, for each spectrum, a same process is replicated. The emission lines of all the elements of interest are selected, and intensity extracted according to Motto-Ros et al. results [38]. By associating a line intensity with each shot position, images of variations in elemental intensities are reconstructed, with each pixel being a shot position. These images are elemental maps of relative abundance [37,39]. This procedure was applied to all the 10 major and minor elements from the XRF list assay (Al, Ca, Fe, K, Mg, Mn, Na, P, Si, Ti), and oxygen. For the 14 trace elements usually measured, as a part was not detected or even not assayed in the old measurements, we choose to apply our methodology only on the ones which were the most concentrated and vary in our samples. They are Ba, Rb, Sr and Zr, for a total of 14 elements. Based on LIBS-quantification recommendations [40], the elemental lines have been chosen based on several flexible criteria: atomic line preferred, no systematic interference, avoiding line auto-absorption. Such criteria must be met for elemental lines emitting in close range for a minimal number of spectrometers. The selected lines are detailed in Table 3.

Once the elemental maps done, they are registered in a text format, allowing for next treatments of our methodology. They come with noise maps for each spectrometer (variation of background over all spectra in a range with no line, as much as possible). Semi-quantitative images, as explained here after, are then made using Python (version 3.9, Python Software Foundation, USA) coding directly on text images, through matrixes manipulation. Mask production is led under ImageJ software (version 1.52a, National Institutes of Health, USA), with the options merging channels and brightness/contrast and colour thresholding in image menu.

## 4. Results

### 4.1. µ-LIBS imaging

Results are raw LIBS elemental intensity distributions, meaning relative abundance maps. The elemental images of the 14 elements of interest are provided in the supplementary materials for the four reference briquettes (SFigs. 1–4). They make it possible to distinguish the different phases of the specimen, especially through major and minor elements. Indeed, the macroscopic homogeneity of the clay observed in the optical image is clearly reflected in the elemental maps: Al, Si, Fe, K, and other major constituents are uniformly distributed throughout the matrix, and the same holds true for trace elements such as Ba and Rb. This strongly indicates that the chemical composition of the clay fraction corresponds to aluminosilicates derived mainly from the alteration of felsic minerals rich in potassium and sodium, while also incorporating elements commonly associated with mafic minerals, such as iron, magnesium, and manganese. The presence of various trace elements further illustrates the ability of natural clays to retain such species in a homogeneous manner that µ-LIBS can image.

Same information and further can be obtained for the temper on elemental images. The sand fraction, qualified as a silico-calcareous sand on the gravel pit supplier's documentation, appears clearly heterogeneous with various kind of minerals: Si map shows intense silicate grains, above all quartz (uncorrelated with other elements), with some of the silicate being correlated with Al map, and K and/or Na images; these latter are feldspars grains, slightly represented over the sample surface. Then, Ca map underlines calcium carbonates presence with a proportion higher than feldspars, anticorrelated with Si maps; by the way, dark rims around carbonate grains on this latter show the reactivity of calcined carbonates over 900 °C firing with silicate. Finally, we note the presence of some rare mafic minerals, on Fe, Mg or Mn maps, and some fine grains of metallic oxides with Fe and Ti images. Besides, such distribution images exhibit the correlations between elements into a same phase or between different phases: we notice for example that granular fraction bears less trace elements than clay, but that some are linked to major elements in grains, for instance Rb to K or Sr to Ca.

Although these elemental maps provide a wealth of information, they also present inherent limitations. The first relates to matrix effects: in the Si and Al maps, feldspar grains are difficult to distinguish from the clay matrix, even though their actual concentrations differ significantly. Differences in ablation behaviour between the two materials generate plasma with similar emission intensities despite distinct compositions. As a result, some grains cannot be reliably identified on the raw maps. The second limitation concerns the comparison between elemental maps, which are based on relative abundances rather than quantitative values. Consequently, there is no direct correlation between the intensity levels of different maps, as each one is displayed using its own independent scale. For example, when comparing the K and Fe maps, K may appear more abundant based on the colour scale, even though the actual concentration of Fe is higher. The methodology proposed here specifically addresses these limitations.

### 4.2. Quantitative methodology

In this section, the method is detailed using the dataset presented in Section 4.1, of the briquettes prepared with a clay of known composition; the focus is made on the reference briquette 22.9 %-tempered and fired at 1000 °C. The results on the three other briquettes are displayed with corresponding figures in supplementary materials. Once the LIBS dataset has been processed to generate the 14 elemental maps together with the oxygen map, all subsequent treatments are applied on a pixel-by-pixel basis. It should be noted that the optical image of the sample is acquired prior to any LIBS measurement and then geometrically transformed to match exactly the analysed area at the spatial resolution of the LIBS images.
### 4.2.1. 'Bulk-equivalent' elemental intensity images

The first step consists in removing the spectra acquired in air or within macroporosity regions from all elemental maps. To achieve this, and since the mineral phases present contain oxygen in their structure, the oxygen map is used as a reference [37]. Pixels with oxygen intensity values below a defined threshold (corresponding to a very low oxygen signal) are thus identified as voids and converted to NaN (Not a Number) values, meaning they are ignored in subsequent calculations. Additional masking is applied along the image borders to exclude measurement sites affected by stage acceleration, ensuring that only stable and representative areas of the sample are considered.

In addition, for each of the 14 elemental images, an intensity limit of detection (ILD) is applied, with any value below this threshold replaced by zero. This ILD is evaluated in a manner similar to the conventional limit of detection (LOD) used for concentrations and corresponds to three times the baseline noise of the spectra, estimated within a region free of spectral lines. The calculation of this ILD thus allows the removal of intensities too low to be considered as genuine signal. SFig. 5 (in supplementary materials) illustrates the sample mask (b) of the reference briquette obtained from the oxygen image (a) following this procedure, as well as an example of the zeroed pixels elemental map

through ILD application. Finally, this sample mask is applied to all 14 elemental intensity maps, so do the zeroing of pixels under ILD (as exposed on the example of Mn image on SFig. 5 c).

### 4.2.2. Calibration into concentrations and generation of semi-quantitative images

The next step consists in the calibration of the LIBS intensities into concentrations. This process is based on the principle that the average LIBS intensity of an elemental image $\bar{I}(X)_{LIBS}$, X being the element, should be proportional to the bulk XRF concentration measured on the sherd $C(X)_{XRF}$, such that:

$$ \bar{I}(X)_{LIBS} = k_X \cdot C(X)_{XRF} \quad (1) $$

It should be noted that the 14 analysed elements are assumed to account for the entire composition of the sample, and their total is normalized to 100 %. A calibrated concentration value is then assigned to each pixel i, calculated as the ratio between the LIBS intensity and the proportionality factor $k_X$ obtained from the total map equation (1), as:

$$ C(X)_{LIBS}^{i} = \frac{I(X)_{LIBS}^{i}}{k_{X}} \quad (2) $$

<figure><img src="image_4.png" /><figcaption>Fig. 2. Image of the sum of all the concentrations of the 14 measured elements (a), with details (b) for briquette 22.9 %-tempered & 1000°C-fired. Silicates and carbonates grains are edged by thresholding Si and Ca map. The frequency distribution of total concentration is given with colormap (c).</figcaption></figure>
The process is done directly by going from elemental intensity to calibrated data in oxide expression, as the geochemistry of ceramics is historically expressed in this form.

However, resulting calibrated maps cannot be used as is, because of uncorrected LIBS matrix effects. As visible in Fig. 2, the sum of such maps shows concentrations that are distributed on a large pseudo-gaussian curve (c), with a mean slightly >100 wt%. It is above all the distribution of concentrations across the different matrices that are remarkable (a and b): clay stays almost around 100 wt% or slightly

above (gray-reddish colour) with the zones with very thin cracks and microporosity being lower due to a smaller plasma (blue spread over the surface), whereas quartz and feldspars exhibit higher concentrations (silicate-surrounded grains, appearing in red) and calcium carbonates much lower concentrations (blue surrounded grains). These latter minerals are underlined by silicate and carbonate edges made through classical masking approach by thresholding intensity map of Si and Ca.

Such overall discrepancies can be readily corrected under the reasonable assumption that matrix effects influence all elements in a

<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Semi-quantitative µ-LIBS images obtained through our methodology, for 14 elements in log scale (ordered by decreasing mean image concentration). Example of briquette 22.9 %-tempered & fired at 1000 °C.</figcaption></figure>
similar manner. In other words, they result in a global enhancement or attenuation of all emission lines. A normalization to 100 % is therefore applied by dividing, on a pixel-by-pixel basis, the concentration of each element by the total concentration of all elements at that pixel:

$$C^N(X)_{LIBS}^i = \frac{C(X)_{LIBS}^i}{\sum_{X=1}^{m} C(X)_{LIBS}^i} \times 100, \quad (3)$$

where $C^N(X)_{LIBS}^i$ is the normalized concentration at the pixel $i$ expressed in wt.%, and $m$ is the number of elements, 14 here. This approach preserves the proportionality between all elements and ensures that each pixel is directly comparable to the others, thereby enabling the production of semi-quantitative maps of the sample.

The results obtained are illustrated in Fig. 3 (see also SFigs. 6–8), which presents the 14 semi-quantitative μ-LIBS images of the reference briquette. These images use a log-scale colormap to highlight the dynamic range of the technique when calibrated, covering five orders of magnitude in concentration across all elements. This approach not only reveals the relative differences between elements but, more importantly, the absolute differences among them. For instance, the clay fraction appears more concentrated in iron and calcium than in potassium and magnesium, a distinction that was not possible with the raw LIBS intensity maps. At the intra-element scale, each map further reveals both the spatial distribution and the absolute concentration differences between phases. For example, Na₂O reaches up to ~8 wt% in sodo-alkali feldspars, while the clay matrix exhibits sodium concentrations over an order of magnitude lower. While raw intensity maps already allowed identification of the dominant phase contributing to each elemental concentration, this calibration now enables quantification of their respective contributions.

However, the most important outcome of this calibration methodology may be its ability to mitigate matrix effects. Phases that were previously indistinguishable, such as some grains from clay, are now clearly contrasted based on their actual concentrations. This is particularly evident in the aluminium map, where the feldspars (previously invisible in intensity maps) are now distinctly resolved. Similarly, the SiO₂ map clearly differentiates clay, quartz, and other silicates, while raw intensity image rather separate only clay from all silicate grains (a distinction further emphasized in linear-scaled images, provided in the supplementary materials).

### 4.2.3. Clay composition

To accurately determine the clay fraction composition, segmentation is a prerequisite before applying the resulting mask to semi-quantitative images. This segmentation step is crucial, as it defines what constitutes clay material and what is excluded as non-clay grains. Such distinctions cannot be made without considering the sample's nature, grain size characteristics and, at the archaeological scale, the potter's techniques and processes.

For our reference briquettes, we aim to exclude all grains equal to or larger than our resolution limit (approximately 20 µm). To achieve this, we explored several segmentation approaches. The most intuitive method relies on optical image edging, leveraging colorimetric features. This is possible because of the spatial correspondence between the optical and elemental images. However, this approach falls short: nearly transparent grains are misclassified as clay, particularly finer particles, while reddish grains are erroneously included in the clay mask. A classical alternative involves thresholding each mineral family separately on elemental maps, as done in SEM-EDS imaging [41–43] or LIBS monoelemental maps [28,37]. By subtracting these thresholds from the sample mask, the clay matrix is isolated. Yet, this method is time-consuming and overlooks the most challenging grains, those difficult to distinguish from the clay matrix, such as the finest quartz fractions. Fig. 4 (a and d) illustrates this limitation: the mask (white edges) fails to capture the smallest quartz grains (green particles) and

micas (e.g., the reddish grain near the central green quartz in the (d) zoom). This approach is thus inadequate for isolating the clay fraction in our purpose, especially if comparing an archaeological sample to pottery made with clay subjected to decantation.

A third method, which is the approach we selected, employs a multielemental image derived from a combination of semi-quantitative maps (Fig. 4). The most effective combinations include elements concentrated in grains, such as Na–K–Si–Ca–Fe–Mn for a silico-calcareous sand, identified through elemental map observations. Each element is assigned to a colour channel (red, green, blue, yellow, cyan, or magenta), ensuring mineral phases appear distinct from clay (see Fig. 4 legend). Brightness and contrast for each channel are manually adjusted in ImageJ to maximize phase distinguishability: minimum values are raised to avoid clay-related brightness (which has lower elemental levels except for aluminium, we deliberately ignored in multielemental combination), while maximum values are lowered to highlight high-content minerals. Pixels exceeding the clay-related brightness threshold are excluded, producing a mask that removes all grains (Fig. 4b), even fine quartz near the resolution limit (compare Fig. 4d and e). This precautionary method ensures a homogeneous clay representation, though it may exclude more pixels than strictly necessary (Fig. 4c and f). Once clay fraction mask produced (SFig. 9 for other briquettes), arithmetic mean is applied to all pixels corresponding for all 14 quantitative images. We get that way the result of clay fraction mean composition.

### 4.2.4. Uncertainties determination

When considering first the semi-quantitative images, according to Eqs. (1) and (2), the uncertainty associated with the concentration at each pixel is primarily governed by both the shot-to-shot repeatability of the LIBS signal $u_{LIBS}$ and the uncertainty of the XRF concentration measurements, $u_{XRF}$. The LIBS repeatability itself remains difficult to quantify accurately, as it would require a perfectly homogeneous reference material of identical nature, which does not exist. Nevertheless, it can reasonably be assumed to be on the order of ~10 % on a shot-to-shot basis. However, when focusing on the average clay composition, the statistical contribution of the LIBS measurement is strongly reduced owing to the large number of averaged pixels (scaling as $1/\sqrt{N}$), with N exceeding 10 000 for all samples investigated here. As a result, the uncertainty associated with the XRF measurements becomes the dominant contribution to the final uncertainty.

Additional independent uncertainty terms must nevertheless be considered. First, we evaluated the potential concentration bias induced by the mask generation process. Several users independently applied the same segmentation protocol, which involves manual thresholding, allowing us to estimate a statistical uncertainty term, $u_{mask}$, associated with this step. This contribution remains low, on the order of a few percent for each element, which is averaging to a cautious deviation of 1.5 % for all. A further uncertainty term, $u_{rep}$ related to representativeness must also be included, in order to assess how well the analysed surface reflects the bulk XRF measurement. This assessment is not straightforward; to address it, the clay images were divided into 16 sub-images (grid of 4x4 rows and columns), each corresponding to a distinct zone of the sample. The standard deviation of the mean concentrations obtained from these sub-images was then calculated. This standard deviation provides a relevant indicator of the elemental homogeneity within the clay matrix.

Consequently, assuming that the statistical uncertainty of the LIBS measurement is negligible owing to the large number of averages, the uncertainty on the clay concentration can be estimated for each element as the quadratic sum of three independent contributions.

$$u_{clay} = \sqrt{u_{XRF}^2 + u_{mask}^2 + u_{rep}^2} \quad (4)$$

Here, $u_{XRF}$ denotes the uncertainty associated with the bulk XRF con-
<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Clay fraction mask determination based on multielemental map (Na–K–Si–Ca–Fe–Mn) from briquette 22.9 %-tempered & 1000°C-fired. 4a and 4d are multi-elemental maps; 4b and 4e are similar but with applied mask of clay by thresholding on multi-elemental image; 4c and 4f are the optical image with the same mask applied. 4d, e, f are zooms from 4a, b, c respectively.</figcaption></figure>

centration used for calibration, $u_{mask}$ accounts for the variability introduced by the mask generation procedure, and $u_{rep}$ represents the contribution related to the spatial representativeness of the analysed area. In this section, uncertainties are reported at a 70 % confidence level (1σ). However, a 95 % confidence level (2σ) is adopted for the results presented below.

### 4.2.5. Evaluation of the method

The evaluation of the proposed quantitative method relies on the known composition of the raw clay used to produce the briquettes. This allows us to directly compare the concentrations derived from the protocol for the four reference samples with the actual clay composition measured by WD-XRF. Fig. 5 illustrates this comparison for the 22.9 %-tempered briquette fired at 1000 °C, plotting protocol-derived concentrations against XRF-measured values on a linear log-scale (other briquettes on SFigs. 10–12). The results show excellent agreement across four orders of magnitude: all elements, from trace to major, align closely with the y = x line, within the stated measurement uncertainties. Notably, no element deviates by more than 15 % from its expected value (red curve envelope), except for Na, a minor element whose behaviour is discussed in Section 2.2.

Detailed results for all four reference briquettes, including their total compositions, are provided in Table 4. Previously to the protocol, these data highlight the impact of sand tempering on the briquettes' bulk chemistry: silicon content increases significantly, while iron, aluminium, and other elements are diluted, as do trace elements due to the sand's lower contribution (but not for Sr, likely due to carbonate contributions). Crucially, the proposed method effectively mitigates these tempering effects, restoring the clay fraction's true composition:

<figure><img src="image_7.png" /><figcaption>**Fig. 5.** Linear correlation between actual clay composition and clay composition determined using the proposed method (log-scale) on briquette 22.9 %-tempered and fired at 1000 °C. XRF uncertainties are the quadratic sum of the clay mean standard deviations (Table 1) and $u_{XRF}$ (STable 2). The 1:1 red line (y = x) is shown, together with confidence bounds corresponding to ±15 % deviation from the unity line. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>
silicon is reduced, and other elements (including traces) are propor-
tionally increased. A minor exception is Sr, whose concentration rises
with sand tempering but is not corrected by the protocol. Except with
calcination of carbonates that may participate to reaction of lime with
silicates and the diffusion of trace elements, no explanation is clearly
identified.

Furthermore, some trends can be seen over the references, which will
be discussed in the next section. Therefore, this validation confirms that
we succeed to accurately isolate and quantify the clay matrix, even for
low-concentration elements. By using reference samples with precisely
known compositions, we ensure that the observed agreement is not
coincidental but reflective of the protocol's reliability.

4.3. Influence of technical production: firing temperature and sand proportion

The impact of two key ceramic production parameters on the
robustness of our method was assessed: the firing temperature and the
proportion of sandy fraction. These parameters exhibit significant
archaeological variability: ceramics may contain varying amounts of
sand, and firing temperatures range from 700 to 1200 °C, the temper-
ature being a parameter that cannot be reliably assessed. It is therefore
critical that the proposed method remains insensitive to these variations
to avoid significant bias in its application.

However, LIBS raw signal showed a strong dependence on firing
temperature, the same commercial clay fired at 850° and 1000 °C
providing a mean raw spectrum higher for most of elemental lines with
the highest temperature (see SFig. 13). It results on intensity elemental
images misleading to actual relative concentration. This phenomenon

arises from the transformations induced during firing: temperature
directly affects densification, hardness, and mineralogical changes in the
ceramic matrix. These modifications, in turn, influence ablation effi-
ciency and plasma parameters (e.g., electronic density, temperature,
emission duration, etc.), which consists in LIBS matrix effects. Similarly,
the distinct matrices of sandy and clayey materials suggest that their
relative proportions could disrupt calibration, potentially compromising
the accuracy of the method in determining the composition of the clay
fraction.

4.3.1. *Influence of firing temperature*

The effect of firing temperature on our methodology was assessed on briquettes tempered with the same sand ratio (11.7 %) and fired at 850° and 1000 °C. The result of clay fraction composition obtained through the protocol is compared to XRF reference measurement of clay, as displayed on log-scale in Fig. 6a. All elements provide similar concentrations across samples, with no visible effect of temperature affecting clay matrix composition determination, except for one element, the sodium. NaO₂ concentration is more important in the briquette fired at very high temperature, which may be linked to Na spreading from grains into clay fraction during firing as well as mineralogical transformation of sodic feldspars grains.

This phenomenon can be evidenced on the merged elemental images
shown on Fig. 7, where some sodo-alkali feldspars show a light rim of Na
around their boundaries, in the clay fraction for briquette fired at
1000 °C (b and c), while no such diffusion is apparent on briquette fired
at 850 °C (a and d). The mask definition could be thus adapted to fit the
most possible grains with these spread zones without removing other
part of clay fraction. Such an effect may be also expected for elements

<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Comparison of firing temperature (a) and non-plastic proportion (b) impacts on the clay LIBS quantitative methodology. Error bars are: for XRF clay the same as on Fig. 5; for quantitative LIBS results uncertainties evaluated as in section 4.2.4.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>**Fig. 7.** µ-LIBS multielemental image (Na–K–Si–Ca–Fe–Mn) of briquettes fired at 850 (a & d) and 1000 °C (b & c). Spreading of Na at high temperature is visible with reddish pixels, around alkali felsic grains (Na brightness/contrast are identical: between 0.1 and 1.5 wt %).</figcaption></figure>

from minerals of less durability like plagioclase feldspars or calcite that get transformed at high temperature. Therefore, Ca might be affected but there is neither obvious Ca rims on images (Fig. 7) nor significant change in clay final Ca concentrations. Presence or absence of such rims are also directly noticeable on semi-quantitative elemental maps on Fig. 3 and on S.Figs. 6–8.

### 4.3.2. Influence of non-plastic proportion

Furthermore, for assessing the impact of increasing sand proportion on our methodology, we focused on the results on the three reference briquettes fired at 1000 °C with increasing temper ratio of 5.9, 11.7 and 22.9 %. The composition of their clay fraction we determined through our protocol is compared to actual clay composition (Fig. 6b). Consistency in elemental concentrations is generally maintained, with no significant variations observed across samples. However, minor deviations are detectable for certain elements, which correlate with increasing sand content.

The most striking deviation occurs for Na, once again. This trend is logically attributed to the quantity of sodic grains amplifying previous discussed deviation due to firing, since the more the Na-alkali feldspar on the sample, the more Na spreads in clay through high temperature-firing. In addition, some other elements as Al, K, Mg, Mn, Rb or Si exhibit subtle, linear-like deviations, though these remain largely within the range of analytical uncertainty. Specifically, higher sand content leads to a slight overestimation of silicon, while the concentrations of other elements are correspondingly underestimated. This effect may stem from limitations in mask definition: fine quartz grains might occasionally be overlooked, contributing to the observed deviation, though its magnitude remains negligible. Such a discrepancy could arise from minor inconsistencies in the mask delineation, or from the resolution limit of the imaging system, which may be unable to detect the finest quartz grains.

### 4.4. Archaeological application: *Lugdunum calcareous coarse ware*

Our main purpose is to verify whether the same raw clay material was used for both La Muette B Terra sigillata and coarse ware (amphorae and other) produced in *Lugdunum* during the Augustan period. While earlier archaeometric studies [12,13] suggested this interpretation, our work seeks to validate it through robust geochemical evidence, further contextualized by comparisons with two other sigillata productions from the same period.

To achieve this, a careful macroscopic examination of the ceramic paste is essential to identify the materials to be compared. While the coarse ware exhibits a sandy fraction primarily composed of granitic and rhyolitic sand mixed with a fine clay containing silty grains, La Muette B sigillata features a very fine paste, almost entirely composed of clayey material with only rare silty inclusions, clearly resulting from decantation. Chemically (see Table 5), La Muette B sigillata displays a significantly higher calcium content, characteristic of its raw source, along with elevated concentrations of aluminium and iron and a lower silicon content. This composition is consistent with a highly purified clay, devoid of quartz grains and clearly enriched in clay minerals.

For the coarse ware analysed using our methodology (raw LIBS maps on SFigs. 14–17), it is therefore critical to define clay-fraction masks that exclude as many grains as possible, including any potential temper or natural aggregates removed during raw clay processing. Our multi-elemental mapping approach accounted for both bright pixels (representing >20 µm grains) and slightly less bright pixels; the latter are smaller grains embedded in the clay matrix, where LIBS signals may be intermediate due to laser overlapping.

We thus apply previous developed methodology on the amphorae and the mortar specimens, resulting in semi-quantitative images for the 14 elements of interest for each specimen (Fig. 8 and S.Figs. 18–20). Masks of clay fraction were defined based on multi-elemental images, with Na–K–Si–Ca–Fe–Mn–Ti, Ti being added (gray channel) because of
its notable presence in grains over LIBS images. As illustrated in SFig. 21, the masks generated for archaeological samples were less dense than those applied to experimental briquettes, reflecting the finer texture of the material of our context.

The masks allowed to calculate the clay fraction composition for all the 14 elements determined in this study, prior to comparison with reference groups. To achieve this, we employed both a detailed examination of the concentration table and multivariate statistical approaches. As shown in Table 5, the transition from total specimens used for the test to their derived clay fraction compositions shows strong alignment with reference values, as evidenced by comparisons between coarse ware and La Muette B sigillata. Notably, calcium is significantly enriched, with aluminium showing a minor increase, while silicon is markedly reduced. Although not all elemental transitions converge (sodium, zirconium, and barium), consistent increases are also observed for iron, magnesium, potassium, and strontium. These resulting concentrations thus appear to be a compelling match to the composition of La Muette B, whereas La Muette A and Loyasse sigillata remain distinct (for example, calcium content excludes them).

To confirm that, we applied principal component analysis (PCA). It is preceded by discarding elements that are concerned with pollution probably due to taphonomy, Na, P and Ba (elements with the most variation in each group, already identified as likely due to

postdepositional pollution), we then transformed by ALR (Additive Log Ratio) the 11 other elements (CaO, Fe₂O₃, TiO₂, K₂O, SiO₂, Al₂O₃, MgO, MnO, Zr, Sr and Rb), based on TiO₂ that is the less varying element, before looking at the distribution of specimens through PCA. The resulting biplot is exposed on Fig. 9 and shows that the coarse ware (orange points)—in which the total test specimens are visible (green points)—is mainly very close from Loyasse sigillata group (blue) and La Muette B sigillata (purple). Q-Method allows checking that clay fraction of test specimens (red) converge to this latter fine ware and get into its 95 %-confidence tolerance ellipse. AMT371, AMT372 and AMT896, that were right inside the amphorae group, stay together on the top of the group of La Muette B, whereas AMT673, quite deviating from the group, is still in the limit for its clay, close to purple outliers.

A conventional clustering approach is also tested, as traditionally used for ceramic geochemistry in Lyon's Ceramology Laboratory - ArAr, without log-ratio transformation, but with a standard scaling (μ = 0 and σ² = 1) for Hierarchical Ascendant Classification (HAC). The analysis is done by average linking on the same 11 elements, used for the calculation of Euclidian distances. The result presented on SFig. 22 exhibits four distinct clusters, in which we clearly see the clay compositions determined for coarse ware being into one of the subgroups of La Muette B sigillata or, for AMT673, on the edge of the group.

Nevertheless, both statistical approaches show that our clay fraction

<figure><img src="image_10.png" /><figcaption>**Fig. 8.** Semi-quantitative µ-LIBS images of 14 elements from Lyon's Roman amphora AMT673 (log-scaled and ordered by decreasing mean image concentration).</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>**Fig. 9.** Principal Component Analysis on ALR transformed (on TiO₂) data from *Lugdunum* calcareous coarse ware (triangles and diamonds) and several calcareous sigillata from Lyon (La Muette A & B and Loyasse; points). Distribution over PC1 and PC2, with 95 % tolerance ellipses, and correlation circle. Test specimens are diamonds, green for total XRF composition and red for composition determined from LIBS. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>

results fall into the edge of the sigillata group, not right in the middle. Even with masks removing the finest grain possible, it may not be possible to avoid all the finest siltic contribution to clay composition in the case where it was removed by potter decantation.

## 5. Conclusion

The most significant advance of this study is to provide a quantitative methodology capable of isolating and comparing the clay fraction composition of archaeological ceramics, circumventing the issue of temper content. Through the integration of high-resolution µ-LIBS imaging combined with XRF calibration to deliver accurate and microscale clay compositions, it overcomes a long-standing limitation in ceramic provenance studies by enabling direct geochemical comparisons between coarse and fine wares.

The methodology demonstrated robust results for reference briquettes, yielding elemental concentrations for the clay fraction that align closely with the actual raw clay composition. This approach provides semi-quantitative images as a detailed geochemical framework for understanding ceramic mixtures and phase interactions, by combining µ-LIBS imaging with calibration through XRF measurements of the total ceramic composition. Importantly, it corrects for matrix effects linked to firing temperature observed on LIBS intensity maps. The experimental validation highlights that this methodology is applicable to archaeological contexts, for coarse and fine wares, produced through decantation, with a negligible impact from variations in sandy proportions.

When applied to *Lugdunum* Roman amphorae and common ware, the converging results reveal the effectiveness of the protocol in cases where the complexity of non-plastic fraction contributions in coarse ware complicates geochemical provenance studies. This study further supports the interpretation, first proposed by Schmitt in the 1990s, that a common raw clayey material was used for both the calcareous amphorae of Lyon and La Muette B sigillata.

Beyond provenance, this application also sheds light on technical processes. While it is well established that sigillata were produced using decanted clay, our findings highlight the extent of this processing. The removal of silty grains by our mask method was not completely sufficient to achieve the purity observed in the fine wares from La Muette B, suggesting that a fine decantation was likely employed, to remove even siltic particles under 10–20 µm. The degree of refinement thus raises

questions about our method's applicability to wares produced through extremely fine processing.

The primary limitation of this proposed approach lies in mask definition: inaccurate masks or missed grains can lead to approximations in the final clay composition. A thorough understanding of the non-plastic fraction is therefore essential. Macroscopic observations and elemental µ-LIBS images help distinguish which elements are associated with grains, clay, or both, ensuring the relevance of the compositional results obtained through this LIBS Q-Method. This step is also critical for identifying elements potentially influenced by moving through high-temperature firing, thereby preventing misinterpretations.

Additionally, it is essential to consider the nature of the clay or fine ware intended to match the coarse ware. Due to raw material preparation—including sieving and decantation—not only sandy fractions but also silt and coarser clay particles may be removed. These particles, often near or below the resolution limit of LIBS (~10 µm), risk being misclassified as part of the clay matrix. Consequently, the proposed methodology seems best suited for comparing tempered wares with natural clayey materials or fine wares containing thin macroscopic grains. However, it cannot reliably match the composition of fine wares subjected to ultra-advanced decantation, where the resulting clay material consists of sub-micrometric particles—particles that LIBS imaging cannot resolve.

Future work should extend this methodology to other archaeological contexts, such as architectural bricks or architectural backed clays. Furthermore, new wavelength ranges should be investigated for more trace elements, as well as higher spatial resolution (2 µm) µ-LIBS imaging systems that could improve results for fine, decanted wares by capturing smaller particles currently beyond the detection limit.

## CRediT authorship contribution statement

**Nicolas Herreyre:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Resources, Methodology, Investigation, Formal analysis, Data curation. **Valérie Thirion-Merle:** Writing – review & editing, Supervision, Resources, Funding acquisition, Conceptualization. **Loan Lemaître:** Visualization, Investigation, Formal analysis, Data curation. **Anne Schmitt:** Writing – review & editing, Supervision, Resources, Funding acquisition, Conceptualization. **Christine Oberlin:** Writing – review & editing, Supervision, Resources,
Funding acquisition, Conceptualization. Clothilde Comby-Zerbino: Writing – review & editing, Supervision, Resources, Funding acquisition, Conceptualization. Vincent Motto-Ros: Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Methodology, Investigation, Funding acquisition.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgements

This work was partially supported by the Auvergne-Rhône-Alpes Region through the Optolyte platform (CPER 2016) and by the French National Research Agency (ANR) under project ANR-22-CE27-0017 (MEMOar). Financial support from the CNRS MITI is also acknowledged through the 80'Prime CaPhyMOAr project and the NMI-CERAM project, which funded the development of clay quantification in archaeological ceramics.

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.talanta.2026.129452.

## Data availability

Data will be made available on request.

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