# Weakly Bonded Water in Interstitial Sites: A Source of Inaccuracy in Rehydroxylation Dating
## 1 Introduction
The rate at which rehydroxylation occurs has been described by a well-defined equation, as a function of \(time^{1/4}\)[7]. It is assumed that reheating the ceramic to a sufficiently high temperature (typically \(>500\)\({}^{\circ}\)C) for a sufficient duration will dehydroxylate the ceramic and that any subsequent mass gain will replicate the original mass gain following firing, provided the environmental conditions, mainly the temperature, are the same. Dating by RHX requires the acquisition of the initial mass of the sample (\(m_{2}\)), which is the sum of the ceramic mass, the masses associated with the three types of water adsorbed during the sample lifetime (\(m_{w0}\), \(m_{w1}\), \(m_{a}\), see below) and that masses of possible nonrefractory components. Here, we use the same terms as in [6], as follows:  
\[m_{2}=m_{car}+m_{w0}+m_{w1}+m_{nrc}+m_{a} \tag{1}\]  
where \(m_{car}\) is the mass of the total inorganic mineral assemblage; \(m_{nrc}\) is the mass of the non-refractory components, including any substances other than water present in the as-received sample; \(m_{a}\) is the mass of water gained during RHX; \(m_{w0}\) is the physisorbed water, i.e., water molecules easily eliminated by heating at 105-110 \({}^{\circ}\)C; and \(m_{w1}\) represents all the remaining water molecules present in the ceramic in interstitial positions, which also should be partly eliminated by the lower-temperature heating, although this often does not happen [12], as it will be discussed below. This lower-temperature drying procedure is generally carried out for a period that varies in length from a few hours to several days. After the lower-temperature heating step at 105-110 \({}^{\circ}\)C, \(m_{2}\) is measured (see Figure 1). Then, after the material has been heated at 500 \({}^{\circ}\)C, the amount of absorbed water in the sample structure (\(m_{w0}\), \(m_{w1}\), \(m_{a}\)) is reset, as is \(m_{nrc}\), the non-refractory fraction; the mass-gain curve is acquired, and from this curve, a dry-mass value (\(m_{4}\)) and a growth rate \(\alpha\) are derived. These are the parameters required for dating a sample following the equation below:  
\[Age=\left(\frac{m_{2}-m_{4}}{\alpha}\right)^{4} \tag{2}\]  
Since the first works by [PERSON] et al. [5; 7], the complexity of the molecular-diffusion processes that influence RH/RHX have been evident. Figure 1: (**a**) Brick_1 \(m_{2}\) mass evaluation; blue curve represents the experimental data, dotted green line represents the extrapolation of the mass value. (**b**) Brick_1 \(m_{4}\) mass and \(\alpha\) evaluation; blue curve represents the experimental data, dotted green lines represent the linear regression of the different steps. They underlined that the temperature at which an artefact was submitted in its life should be known: a mean temperature from tabulated values should be considered [13]. The effect of humidity on the instantaneous mass of the ceramic sample may be significant, but this point is still a matter of debate [14; 15]. RHX is also strongly affected by the mineralogical composition of the samples to be dated because the phenomenon is known to be differently important across different mineral components. It could be useful to determine the ceramic's composition [16]. The complex picture of DHX/RHX can be investigated using different techniques: infrared spectroscopy (IR) [12], nuclear magnetic resonance (NMR) [17], differential thermal analysis (DTA) and thermogravimetric analysis (TGA) [18]. It is clear that a single, simple mechanism cannot be established also because the RHX can be different in different mineral components. Of course, it is not always possible to investigate the mineralogical composition of ceramic samples to be dated. However, the behaviors of some minerals during hydroxylation have been studied, and some interesting results have been published [19]. The amounts of H\({}_{2}\)O and OH can be measured by IR spectroscopy, and changes in these values as a function of heating treatment can be measured by TGA.