# Pressure-Temperature Phase Diagram of Ta-H System up to 9 GPa and 600 \({}^{\circ}\)C
## 4 Discussion  
Figure 4 depicts the unit cell volume/f. u. of distorted bcc TaH and hcp TaH\({}_{-2}\), obtained during a cooling run at a pressure range of 9.35 GPa to 8.36 GPa. Figure 4 also shows the unit cell volume/f. u. of pure Ta, which was determined by another in situ synchrotron radiation X-ray diffraction measurement. Temperature dependences of unit cell volume/f. u. of both distorted bcc TaH and hcp TaH\({}_{-2}\) were within error bars in Figure 4, indicating that the hydrogen concentration of both distorted bcc TaH and hcp TaH\({}_{-2}\) was constant at the observed \(p\)-\(T\) conditions. Using the value of hydrogen-induced volume expansion \(\Delta V_{\rm H}=2.4\) A\({}^{3}\)/f. u. [10], the averaged hydrogen concentration of distorted bcc TaH was estimated to be TaH\({}_{\rm x}\) for \(x=0.99\pm 0.04\). The hydrogen concentration of hcp TaH\({}_{-2}\) cannot be calculated in the same way, because unit cell volumes of hcp Ta are not accessible. The temperature dependence of the unit cell volume of hcp TaH\({}_{-2}\), on the other hand, is within experimental error, indicating an almost constant hydrogen concentration of hcp TaH\({}_{-2}\). Figure 3: Pressure–temperature phase diagram of Ta–H system. Squares and circles denote the pressure–temperature conditions where the formation of hcp TaH\({}_{-2}\) and distorted bcc TaH detected during heating and cooling runs, respectively, were observed. The solid line indicates the experimentally determined phase boundary between distorted bcc TaH and hcp TaH\({}_{-2}\). Dotted and dashed lines depict calculated phase boundaries based on Clausius-Clapeyron equation for dehydrogenation reaction of TaH\({}_{2.0}\) and TaH\({}_{2.2}\), respectively. Open circle indicates the previously reported pressure–temperature conditions where TaH\({}_{2}\) transformed into TaH [10]. Finally, the phase boundary between TaH and TaH\({}_{-2}\) is analyzed based on the Clausius-Clapeyron equation and possibility of the overstoichiometric composition of H/M under high pressure. The slope of the phase boundary between TaH and TaH\({}_{-2}\) shown in Figure 3 can be calculated using the Clausius-Clapeyron equation:  
\[\frac{dT}{dp}=\frac{\Delta V}{\Delta S}, \tag{1}\]  
where \(T\), \(p\), \(\Delta V\), and \(\Delta S\) are temperature, pressure, volume change, and entropy change during the dehydrogenation reaction of TaH\({}_{2}\rightarrow\) TaH + 1/2 H\({}_{2}\). At 427 \({}^{\circ}\)C (=700 K), \(\Delta V\) was calculated to be 2.93 \(\times\) 10\({}^{-6}\) (m\({}^{3}\)) based on Figure 4, and the volume of H\({}_{2}\) tabulated in ref. [15]. \(\Delta\)S can be approximated to the entropy change caused by the evolution of hydrogen molecules (=30.3 (J/K)). The slope between the phase boundary was then calculated to be 7.19 \(\times\) 10\({}^{-8}\) (K/Pa). This value is comparable to the experimentally obtained value of 8.18 \(\times\) 10\({}^{-8}\) (K/Pa). Next, we consider the overstoichiometric composition of H/M = 2.2, reported by [PERSON] et al. [10]. \(\Delta V^{\prime}\) and \(\Delta S^{\prime}\) were calculated to be 2.93 \(\times\) 10\({}^{-6}\) (m\({}^{3}\)) and 36.9 (J/K), respectively, assuming the same hydride was formed under high pressure and high temperature. In this case, the slope of the boundary was calculated to be 7.94 \(\times\) 10\({}^{-8}\) (K/Pa), which is closer to the experimental value. It is likely that the formed Ta dihydride at high pressure and high temperature has an overstoichiometric hydrogen composition of H/M \(\sim\) 2.2. It is required to understand the hydrogenation behaviors of pure metals to explore the synthesis of pressure-temperature conditions of novel hydrides under high pressure. However, little effort has been put into the investigation of the hydrogenation reactions of pure metals.