# Authentication of a Painting Attributed to the Rembrandt School
## 3 Archaeometric and Chemometric Dating Characteristics
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multicolumn{6}{c}{**Chemometric Characteristics**} \\ \cline{2-6}  & **S/C * & **Ca/Ba * & **Pb/Ba * & **Si/Al ** & **Zn/Pb ** \\ \hline S1 & 0.080 & - & - & - & 0.023 \\ (area with white pigment) & 0.167 & 3.423 & - & 0.876 & - \\ \hline S2b & 0.106 & 0.823 & 1.908 & 1.365 & - \\ (area towards the centre of the sample) & 0.047 & 0.803 & 5.048 & 1.231 & 0.082 \\ \hline S3b & 0.085 & 2.206 & - & 0.776 & - \\ (area towards the centre of the sample) & 0.146 & 0.491 & - & 1.053 & - \\ with pictorial material, preparation and anchored dirt & 0.089 & 1.104 & 3.547 & 0.669 & - \\ with preparation and traces of pictorial material) & 0.029 & 1.905 & 3.940 & 1.692 & 0.092 \\ with pictorial material, preparation and anchored dirt & 0.111 & 0.852 & 2.236 & 1.871 & - \\ with preparation and traces of pictorial material) & 0.126 & 1.340 & 5.259 & 0.944 & - \\ \hline S8 & 0.025 & - & - & 0.665 & - \\ (zone I, on the wooden chassis, with traces of preparation) & 0.692 & 2.047 & - & 0.725 & - \\ \hline \hline \end{tabular}  
* Valid chemometric characteristics; ** Partially valid characteristics.  
\end{table} 
Table 3: Chemometric characteristics (C.C.) of the areas analysed. Among the experimentally validated chemometric-derived archaeometric characteristics, S/C, Ca/Ba, Pb/Ba, Si/Al and Zn/Pb ratios are presented below (Table 3). Among the archaeometric characteristics, such as porosity gradient on the penetration from the surface into the volume phase of the white colour and the penetration of oxidative dirt into the structural depth of the surfaces, were evaluated, falling in the value range of an age of ca. 360 \(\pm\) 3 years. These were in agreement with the chemometric characteristics, which required experimental validation, such as elemental atomic ratios: S/C, Ca/Ba, Pb/Ba, Si/Al, and Zn/Pb, placing the painting in the period of execution around 1655-1660. The data in Table 3 show a good correlation between the archaeometric characteristics highlighted for the samples of white (white lead), anchored dirt and preparation (porosity gradient on the surface penetration in the volume phase of the white and preparation colour varying between 1.0 and 2.5 \(\upmu\)m, while the penetration of the surface structure of oxidatively anchored dirt at the varnish depth is between 0.5 and 1.2 \(\upmu\)m) and the chemometric samples (from columns 2-5, Table 3). The archaeometric characteristics correspond to an age of about 365 years (the evolution gradient of the thickness of the craquelure is about 0.0014-0.0019 \(\upmu\)m/year, the porosity of the pigments 0.5 \(\times\) 10\({}^{-5}\)-1.1 \(\times\) 10\({}^{-5}\)\(\upmu\)m/year (considering that the painting would have been preserved in constant conditions of conservation). The archaeometric characteristic related to the increase in porosity of the painting material and preparation (both on the front and on the back of the painting), as a result of the embrittlement of the binder by the penetration of CO\({}_{2}\) in the presence of hygroscopic humidity (carbonation process), given by the ratios of S/C, Ca/Ba, Pb/Ba, and Zn/Pb, except the latter, also shows an evolution rate within the limit of about 365 years. The S/C value decreases about 12 times compared to the reference (elemental composition values underlined in blue and green). For Ca/Ba ratios, the values decrease by about 2 times and for the Pb/Ba ratio, the values increased by 5 times compared to the same references (white lead, barium sulphate, and gypsum samples).