Structural Phase Transition of ThC Under High Pressure

Thorium monocarbide (ThC) as a potential fuel for next generation nuclear reactor has been subjected to its structural stability investigation under high pressure, and so far no one reported the observation of structure phase transition induced by pressure. Here, utilizing the synchrotron X-ray diffraction technique, we for the first time, experimentally revealed the phase transition of ThC from B1 to P4/nmm at pressure of ~58 GPa at ambient temperature. A volume collapse of 10.2% was estimated during the phase transition. A modulus of 147 GPa for ThC at ambient pressure was obtained and the stoichiometry was attributed to the discrepancy of this value to the previous reports.

at diffraction curves at top 3 pressure points, where on each curve a strong peak appears at a lower angle next to the (111) peak of B1 ThC. One can even trace the origin of this peak back to 53.2 GPa. It is identified as (110) of the P4/nmm phase. The Rietveld refinement of high pressure (71 GPa) diffraction pattern is shown in Fig. S1. Even though from our data we can see the coexistence of the B1 and P4/nmm phase of ThC between 53.2 and 71.0 GPa, which are attributed to the pressure gradient in the sample chamber, the new phase of P4/nmm is undoubtedly discovered. Hence we conclude that ThC has a phase transition at around 58 GPa from B1 to P4/nmm. This is the first time ever that the high pressure transition of ThC has been experimentally reported. Our results agree well with the prediction by Guo et al. 5 . After the pressure was released, the sample returned back to the ambient phase B1, as the top curve shows in Fig. 2. Compared to the 1.2 GPa B1 phase, its peaks shift to the smaller angles as d space slightly increases under ambient condition, and become much broader as a result of many crystalline defects produced during the high pressure compression.
The phase transition of ThC under high pressure was previously studied through a first principle calculation 4 , and they found a high pressure structural transition sequence of NaCl type (B1) → Pnma → Cmcm → CsCl type (B2) at hydrostatic pressures of ~19 GPa, 36 GPa, and 200 Gpa, respectively. We checked our experimental data from 1.2 GPa to 53.2 Gpa and found no new peaks. Then we compared the experimental results obtained at higher pressures (>58.3 GPa) with the calculated phases including P4/nmm 5 , Pnma and Cmcm 4 , respectively, it was found that only P4/nmm phase agreed well with our experimental results (refer to Fig. S1 and R1). To compare the difference of these three phases, we calculated the atomic densities of P4/nmm, Pnma and Cmcm, which are 70.2%, 35.3% and 25.8% respectively. Among them, P4/nmm is the densest and would remain the best structural integrity under high pressure.
As mentioned previously, our ThC sample was mixed with small amount of ThC 2 , whose characteristic signals are weak yet visible. Its several peaks appearing on the lower pressure curves were identified to originate from the ambient monoclinic phase (space group C2/c), based on another work of our high pressure experiments on pure ThC 2 7 . The high pressure phase of ThC 2 can be seen at the top few pressure points, as marked in Fig. S1. It is worthy to point out that this new high pressure structure of ThC 2 has never been reported before, experimentally or theoretically as to our best knowledge. The details of the structural information of ThC 2 would be discussed in another article 7 .
The unit cell volumes of ThC were calculated based on the Rietveld refinement results at entire pressure range as shown in Fig. 3. The abrupt drop of volume at ~58 GPa clearly separates the data into two groups, undoubtedly suggesting the occurrence of a first order phase transition. The data can be fitted with the third-order Birch-Murnaghan equation of state (EOS) 8 for B1 (before transition) and P4/nmm (after transition) phase separately: where v/v 0 is the ratio of unit cell volume at pressure p to that at ambient pressure. B 0 is the bulk modulus at ambient condition, and B 0 ′ is its pressure derivative. The least-square fittings yield B 0 = (147 ± 3) GPa, and B 0 ′ = (4.6 ± 0.1) for B1 phase between 1.  In Table 1, we summarize and compare the lattice parameters and compressibility of ThC from present study and previous experimental and theoretical results [2][3][4][5][9][10][11][12][13] . It is worthy to note that the bulk modulus (147 GPa) of B1 phase in our study is much higher than the reported value (109 GPa 2, 3 ). The discrepancy is possibly due to the difference of stoichiometry as suggested by J. Staun Olsen et al. 14 . In Gerward's study 2 , they estimated that their sample should have a composition corresponding to ThC 0.76 . Based on the work of Pialoux and Zaug 15 , the stoichiometry of our sample is estimated to be Th:C = 1:0.95, different from Gerward's. Furthermore, J. Staun Olsen et al. 14 summarized the results for the uranium and thorium compounds respectively and found that smaller lattice parameters generally lead to larger bulk moduli with same crystal structure. The lattice parameters of thorium nitrides (ThN) and thorium sulphides (ThS) are 5.1666 Å and 5.6851 Å, respectively. In the present study, this value for ThC is 5.3397 Å which lies between that of ThN and ThS. As the bulk moduli of ThN 16 and ThS 17 are reported to be 175 GPa and 145 GPa respectively, it is reasonable to conjecture that the bulk modulus of ThC would have the value that is smaller than 175 but larger than 145 GPa, exactly where our result (147 GPa) fits. (A full list of the obtained structural parameters for both the B1 and the high-pressure ThC (P4/nmm) phases is shown in Table S1). Another minor factor that might contribute to the discrepancy is the different degree of the hydrostaticity of the pressure medium.
In Table 1, we compare the major parameters of the dimensions and compressibility of ThC between our experimental results with previous reports. At ambient pressure, the lattice parameter of B1 phase measured in our study is slightly larger than the other experimental values which could be attributed to the compositions of the sample. In ref. 2, the stoichiometry of ThC was estimated to be Th:C = 1:0.76. In our study, we estimate that this ratio to be ~1:0.95. The excess carbon will lead to a larger lattice parameter. At elevated pressure where P4/nmm phase exists, there are two groups of values provided by Guo et al. One is obtained at zero pressure 5 , while the other is calculated at 58.3 GPa (marked as *), same as the experimental condition. The lattice parameter calculated at zero pressure are noticeably larger than the experimental values obtained at high pressure, which is reasonable. The theoretical values calculated at same pressure as the experimental values agree quite well with them within 2% difference. The discrepancy on unit cell volume between the experimental and theoretical values is about 13%, and around 4% on the bulk modulus.

Conclusion
The crystal structure of ThC under high pressure was studied up to 71.0 GPa with a diamond anvil cell and micro-focused X-ray beam. Diffraction patterns revealed a first order phase transition from B1 to P4/nmm in ThC at ~58 GPa as the pressure increased. The result validates the prediction based on the first principles calculation by Guo et al. The bulk modulus of B1 phase is found to be ~147 GPa and the volume collapse during phase transition was estimated to be 10.2%.

Methods
Thorium monocarbide (ThC) was synthesized using thorium dioxide powder and natural graphite powder as starting materials by carbon thermal reduction method (SDCTM). The ThO 2 and graphite powders were mixed with C/ThO 2 molar ratio of 3.0 and followed with ball-milling for 2 h in ethanol. After that, the slurry was dried at 100 °C for 48 h in a vacuum drier. Then the dried mixture was pressed into pellets with 5 mm in diameter and 10 mm in height. Finally, the green pellets were sintered at 1950 °C with the vacuum of 1.3 × 10 −3 Pa for 30 min. After cooling down, the sintered specimens were immersed in cyclohexane to prevent oxidizing and hydrolyzing.
In order to obtain fine powder for X-ray diffraction (XRD) characterization, the bulk sample was grinded into sub-micro sized particles (200-300 nm) within silicon oil to avoid deliquesce.
A Mao-Bell type symmetric diamond-anvil cell with a pair of 200 μm culets was used to generate high pressure environment for thorium monocarbide. A hole of 80 μm in diameter and 30 μm in thickness was drilled at the center of the pre-indented stainless steel gasket as the sample chamber. A small piece of sample was loaded in the center of the chamber with three small ruby spheres (3-5 μm in diameter) at different locations in the chamber for monitoring the pressure distribution inside the sample chamber. Silicon oil was used as pressure transmitting medium. In-situ high-pressure XRD measurements were carried out at BL15U station at Shanghai Synchrotron Radiation Facility (SSRF). The monochromatic x-ray beam with wavelength 0.6199 Å was focused to a rectangle of ~3 μm (vertical) × 2.5 μm (horizontal) measured by full width at half maximum (FWHM). The diffraction patterns were collected using a MarCCD 165 image plate, with typical exposure time of 20 to 60 seconds. Each diffraction pattern was collected after the pressure was adjusted and stabilized to ensure steady pressure during XRD measurements. The two-dimensional diffraction patterns were integrated into one dimensional profiles of intensity versus 2-theta with FIT2D program 18 , followed by the GSAS structural Rietveld refinement 19 .