# Pore Structure and Water Transfer in _Pietra d'Aspra_ Limestone: A Neutronographic Study
## 2 Materials and Methods
### Neutron Radiography Analysis
Accordingly, neutron radiographs of the dry (\(I_{(d)}\)) and wet (\(I_{(w)}\)) stone were corrected to both \(I_{(df)}\) and \(I_{(ob)}\) using the following relationships:  
\[I_{(w,corr)}=C\frac{I_{(w)}-I_{(df)}}{I_{(ob)}-I_{(df)}}, \tag{1}\]  
\[I_{(d,corr)}=C\frac{I_{(d)}-I_{(df)}}{I_{(ob)}-I_{(df)}}, \tag{2}\]  
where \(C\) is a rescaling factor accounting for the neutron beam fluctuations. The removal of unwanted bright pixels coming from scattered \(\gamma\)-rays was achieved by encountering the obtained images through a median filter. The procedure adopted to follow the water content from transmission radiographs consisted of normalizing wet images with respect to dry ones taken prior to the manual addition of water into the aluminum basement. In this way, the contribution of the stone is removed, and the obtained transmitted intensity can be directly related to the amount of water within the stone [32]. However, in order to get quantitative information on the amount of water contained within the material, a calibration of the collected neutron transmission values was necessary. Accordingly, a staircase-like sample holder, containing 12 different water contents with standardized thickness (ranging from 0.09 mm up to 5.00 mm), was used to evaluate the neutron transmission vs. water thickness plot. The obtained calibration curve (see Figure 2) follows a logarithmic behavior in the whole range of standardized water thickness used. From the fitting procedure, the value of the water attenuation coefficient was achieved and then used to correctly evaluate the amount of absorbed water within the structure of the investigated limestones, for all the water absorption images. The analysis of the neutron radiographs was carried out using the Fiji ImageJ software (Fiji is just ImageJ, Image Processing and Analysis in Java, open source), Version 1.53a, National Institutes of Health and Laboratory for Optical and Computational Instrumentation (University of Wisconsin), Madison, WI, US [49]. Following the procedure described by [PERSON] et al. [50], the water content distribution was computed by dividing the obtained wet image (\(I_{(w,corr)}\)) by the corresponding dry one (\(I_{(d,corr)}\)); then, the 2D distribution of the water thickness (\(\theta_{w}(x,y)\)) could be calculated as follows:  
\[\theta_{w}(x,y)=-\frac{ln\left[\frac{I_{(w,corr)}(x,y)}{I_{(d,corr)}(x,y)} \right]}{\mu_{w}}, \tag{3}\]  
where \(I_{(w,corr)}(x,y)=I_{0}(x,y)e^{-(\mu_{s}\theta_{s}+\mu_{w}\sigma_{w})}\) and \(I_{(d,corr)}(x,y)=I_{0}(x,y)e^{-\mu_{s}\theta_{s}}\), in which \(I_{0}(x,y)\) indicates the intensity of the incoming neutron beam, \(\mu_{s}\) and \(\mu_{w}\) are the stone and water attenuation coefficients, and \(\theta_{s}\) and \(\theta_{w}\) are the thickness of the stone and the equivalent water thickness. Since the thickness of the stone is known, the mean moisture content (MC) was firstly evaluated as  
\[MC=\frac{\theta_{w}\cdot\rho_{w}}{\theta_{s}}, \tag{4}\]  
where \(\rho_{w}\) represents the density of water. Then, by dividing the MC by the density of the stone \(\rho_{s}\), the water content (WC), expressed as a weight percentage (%), could be easily calculated as  
\[WC=\frac{MC}{\rho_{s}}. \tag{5}\]  
As the investigated stone was mostly composed of calcite (90% of CaCO\({}_{3}\)), \(\rho_{s}\) was taken to be almost equal to 2.69 g/cm\({}^{3}\). Figure 2: Calibration curve for water transmission values using different water contents with standardized thickness.