# Weakly Bonded Water in Interstitial Sites: A Source of Inaccuracy in Rehydroxylation Dating
## 2 Materials and Methods
### Methods  
The samples were analyzed using thermogravimetric analysis (TGA). A thermogravimetric analyzer by Mettler Toledo (Greifensee, Switzerland) was used to perform the analysis in a dry-air atmosphere (temperature rate 10 \({}^{\circ}\)C / min, temperature range 25-1000 \({}^{\circ}\)C). The results were matched with literature data to determine the material components that evaporated during the analysis. RHX dating involves the measurement of very small mass variations (\(\sim\)10\({}^{-7}\) g) and requires an extremely precise device to maintain constant environmental conditions during the experiment. For this purpose, a dynamic vapor sorption analyzer (Aquadyne DVS2, AquaDyne, Kent, WA, USA) was used. The two balance plates in the device allow the weighing of two samples simultaneously. The plates are placed in a conditioned room with controlled temperature and relative humidity (RH). For the purpose of this study, RH was set to a stable value of 40%, while temperature was varied according to experimental conditions, as explained further. For this analysis, the samples were cut to a mass of \(\sim\)200-300 mg. Every experimental step involving recording of mass \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample ID** & **Paper Label** & **Expected Date** & **Experimental Date** \\ \hline PV18 & Brick\_1 & 1030 \(\pm\) 80 CE & 1842 \(\pm\) 200 BCE \\ D2500F & Brick\_2 & 1574 \(\pm\) 50 CE & 1639 \(\pm\) 60 CE \\ D2643A & Brick\_3 & 1110 \(\pm\) 90 CE & 1137 \(\pm\) 110 CE \\ \(L_{c}\) & Cer\_1 & 1380 \(\pm\) 60 CE & 188 \(\pm\) 140 CE \\ \(L_{k}\) & Cer\_2 & 1350 \(\pm\) 60 CE & 1486 \(\pm\) 140 CE \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Expected and experimental dates for the five samples analyzed. change was divided into two parts, following the explanation of Stage I and Stage II given in the Introduction. Stage I is transient and is not associated with any experimental effect. The data analysis focuses on the trend in Stage II mass values vs. time (see Figure 1). To study the effect of the preheating temperature on the reliability of the dating process, the commonly accepted dating procedure [6] was changed as follows:  
* A preliminary TGA spectrum was acquired for every sample; this provided general insight into the behavior of the material mass at different temperatures. The temperature range was set between 25 and 10,000 \({}^{\circ}\)C, with the region of interest between 25 and 600 \({}^{\circ}\)C; the curves were acquired in air, with a temperature-change rate of 100 \({}^{\circ}\)C/min. * The samples that showed a significant mass loss in the dehydration range (100-400 \({}^{\circ}\)C) were subjected to different preheating temperatures: the same samples were sequentially preheated at room temperature (RT), 105, 200, 300, and 400 \({}^{\circ}\)C for 12 h; after each heating, they were processed according to Step 3. * The samples that did not show a significant mass loss were processed following the commonly accepted procedure [14], skipping the multiple-preheatings sequence. * The samples were placed in the dynamic vapor sorption balance (DVS) at a constant temperature and relative humidity (200 \({}^{\circ}\)C, 40% RH). Once the mass variation recorded on the mass vs. time curve reached a value \(<\)10\({}^{-4}\) mg/min, meaning that there were no more significant changes in the mass loss, the mass vs. time data related to Stage II were used to generate linear regression parameters, with the mass \(m_{2}\) (see Equation (1)) as the intercept and the mass change (negligible) as the slope (Figure 1a). * All samples (both the ones that had been sequentially preheated and the ones that had been preheated only at 100 \({}^{\circ}\)C) were fired at 500 \({}^{\circ}\)C for 24 h. During this step, all the water fractions were released and the ceramic material returned to its original condition after the first firing. * The mass-gain data were acquired for every sample.