## 8 Phase-Contrast X-ray Imaging in Various Thermal Environments
The black-spotted areas have the lowest density, indicating ice (density: 0.917 g/cm\({}^{3}\) at 273 K), and the gray areas have a higher density, indicating THF hydrates (density: 0.967 g/cm\({}^{3}\) at 273 K). THF hydrates co-existing with ice can be visualized even within the bead material. At 276 K, the white-spotted areas have a higher density, indicating liquid water (density: 1.00 g/cm\({}^{3}\) at 273 K) formed by melting ice. The CXI methods are limited by sample outlining arising from a large phase shift caused by the difference in density between the samples (THF hydrate, water, and ice) and the beads. Polyethylene beads were used to perform the X-ray CT measurements because the small difference in density between the beads and THF hydrate results in good contrast. A comparison of the two images in Figure 14 shows that the multiple phases of the icy materials can be clearly visualized using in situ CXI. The high-energy CXI method enables fine observation of complex materials. The final examples are a CH\({}_{4}\) hydrate (Figure 15a) and a natural gas hydrate (Figure 15b). Both are icy crystals composed of water and natural gas, consisting primarily of CH\({}_{4}\), which is considered an unconventional natural gas [58]. Comparison of the X-ray phase shift between the hexagonal ice and the CH\({}_{4}\) hydrate revealed that the density of the CH\({}_{4}\) hydrate was 0.007 \(\pm\) 0.003 g/cm\({}^{3}\) greater than that of hexagonal ice (0.927 g/cm\({}^{3}\)) at 193 K. The density of the CH\({}_{4}\) hydrate was thus estimated to be 0.934 \(\pm\) 0.003 g/cm\({}^{3}\) at 193 K, which is equivalent to that obtained from powder diffraction structure analysis (0.936 g/cm\({}^{3}\)) at the same temperature [65]. For natural gas hydrates with a density of 0.944 g/cm\({}^{3}\) at 193 K, obtained from powder diffraction structure analysis, identification with ice has been made [66]. Figure 14: X-ray images of THF hydrates: (**a**) THF hydrate with ice at 253 K and (**b**) THF hydrate with water at 276 K at interparticle pore spaces obtained by CXI [63]. Densities of ice, CH4, and air hydrates are the values at 233 K, and those of THF hydrate and water are the values at 273 K. HDPE denotes high-density polyethylene. (**c**) Absorption contrast image of THF hydrate and ice in a polypropylene (PP) tube at 123 K measured by monochromatic X-rays of 8 keV using synchrotron radiation, where the two cannot be distinguished [64]. Accordingly, the density resolution of the CXI method is approximately several mg/cm\({}^{3}\), even under low temperature conditions. Thus, by using ice as a reference for density, CXI measurements can be used to analyze the three-dimensional distribution of density. High temperature stability during measurement is of great importance because the thermal expansion and contraction of materials arising from a temperature change are not negligible. For instance, the linear thermal expansion of hexagonal ice at 253 K is estimated to be 0.005%/K, which corresponds to an approximate deviation of 0.5 \(\upmu\)m for a 10-mm sample. The estimated density of the sample will thus change by approximately 0.14 mg/cm\({}^{3}\) owing to a temperature change of only 1 K. Controlling the sample temperature with high precision is also important for analyzing the three-dimensional distribution of density with high accuracy. The sensitivity of CXI for light elements is more than several hundred times that of conventional absorption X-ray imaging in principle although the actual sensitivity greatly depends on the phase detection method. For example, the PI has been used to determine the microstructure of ice cream under negative temperature conditions [67]. However, neither PI nor absorption contrast methods were not successful for CH\({}_{4}\) hydrate imaging [64] because they are less sensitive than CXI. In contrast, the air hydrates in the Antarctic ice core and CH\({}_{4}\) hydrate were successfully visualized using CXI, not only by CXI but also by DEI [57, 65].