## 3 Results and Discussion
### Neutron Tomography  
While neutron and X-ray diffraction was used to identify the phase composition of the studied mosaic stones, the spatial distribution of the phases was analyzed by neutron tomography. The several tomography transverse slices of reconstructed tree-dimension models of sample 5 and sample 6 are presented in Figures 7 and 8, respectively. A voxels distribution on the gray-level scale reflects a spatial distribution of values of the neutron absorption coefficients inside the studied mosaic fragments [51]. The attenuation of the neutron beam corresponds to the scattering and absorption losses inside the volume of the investigated samples [17; 51]. The attenuation coefficient of a neutron beam with an average neutron wavelength of \(\lambda\)\(\sim\)2 A for calcite is \(\Sigma\) = 0.17 cm\({}^{-1}\); this is slightly larger than the relevant parameters for quartz (\(\Sigma\) = 0.11 cm\({}^{-1}\)) [18]. Therefore, a spatial distribution of major phases is visible in the neutron tomography experiments (Figure 7). Interestingly, an area of high neutron beam attenuation was found on the surface of sample 5. This surface area can be attributed to some paint or decorated layer, which is possibly related to some hydrates or amorphous aluminosilicates that have been detected in neutron diffraction by the effect on the background shape (Figure 7). Figure 6: Neutron diffraction patterns of the mosaic fragments sample 5 (top) and sample 6 (bottom). The experimental points and calculated profile are shown. The Miller indices of major phases are labeled. Ticks below represent calculated positions of the Bragg peaks of the calcite and quartz phases. The corresponding diffraction peaks are marked. Figure 7: The reconstructed 3D model and several virtual slices of the mosaic fragment sample 5. It is assumed that the green areas correspond to the calcite phase, while the red regions are quartz areas. The rainbow-like coloring shows neutron absorption degree from low (blue) to high (red). The volume of the mosaic sample 5 is formed by 2,762,838 voxels, which corresponds to the volume of 388 mm\({}^{-1}\). The total three-dimension (3D) reconstructed volume of the sample 5 was divided into three separate volumes corresponding to the calcite, quartz and high absorption \"paint\" components. The quartz comprises 1,504,705 voxels or 211.6 (3) mm\({}^{3}\), the calcite phases consist of 1,217,788 voxels or 171.2 (3) mm\({}^{3}\), the \"paint\" layer formed by 40,345 voxels or 5.6 (3) mm\({}^{3}\). The volume ratio of the calcite and quartz phases is 0.81, which is well consistent with neutron diffraction data. The 3D imaging data of volume corresponding to the mosaic sample 6 are shown in Figure 8. In addition to the main phase of calcite, the well-distinguishable areas characterized by a high neutron attenuation coefficient are visible. According to neutron diffraction data, it can be assumed that these are residues of clay or corrosions based on silicates and iron hydrates. The presence of hydrogen, with a high incoherent neutron scattering length in these compounds, determines the high radiographic contrast between these grains and the main calcite matrix. The observed hydrogen-contained areas do not exceed a size of 5-7 mm. The average size of the visible grains is 6.1 (1) mm. Their volumes are formed 114,023 voxels or 16.1 mm\({}^{3}\). The grains occupy 7.1(3) % of total sample 6 volume (2,344,550 voxels of 330 mm\({}^{3}\)). For this research, quite complex objects of cultural heritage as the fragments of ancient mosaics were studied. The samples contain the main components, such as calcite and quartz, the colorant phases, the phases of decorative elements, the phases of clay, etc. For a comprehensive analysis of the samples, various methods were used. For color characteristics spectroscopy, phase analysis attracted X-ray diffraction.