Thorium Monocarbide Research Articles

First-Principle Studies on Local Lattice Distortions and Thermodynamic Properties in Non-Stoichiometric Thorium Monocarbide

Thorium monocarbide (ThC) is interesting as an alternative fertile material to be used in nuclear breeder systems and thorium molten salt reactors because of its high thermal conductivity, good irradiation performance, and wide homogeneous composition range. Here, the influence of carbon vacancy site and concentration on lattice distortions in non-stoichiometric ThC1−x (x = 0, 0.03125, 0.0625, 0.125, 0.1875, 0.25, or 0.3125) is systematically investigated using first-principle calculations by the projector augmented wave (PAW) method. The energy, mechanical parameters, and thermodynamic properties of the ThC1-x system are calculated. The results show that vacancy disordering has little influence on the total energy of the system at a constant carbon vacancy concentration using the random substitution method. As the concentration of carbon vacancies increases, significant lattice distortion occurs, leading to poor structural stability in ThC1−x systems. The changes in lattice constant and volume indicate that ThC0.75 and ThC0.96875 represent the boundaries between two-phase and single-phase regions, which is consistent with our experiments. Furthermore, the structural phase of ThC1−x (x = 0.25–0.3125) transforms from a cubic to a tetragonal structure due to its ‘over-deficient’ composition. In addition, the elastic moduli, Poisson’s ratio, Zener anisotropic factor, and Debye temperature of ThC1-x approximately exhibit a linear downward trend as x increases. The thermal expansion coefficient of ThC1−x (x = 0–0.3125) exhibits an obvious ‘size effect’ and follows the same trend at high temperatures, except for x = 0.03125. Heat capacity and Helmholtz free energy were also calculated using the Debye model; the results showed the C vacancy defect has the greatest influence on non-stoichiometric ThC1−x. Our results can serve as a theoretical basis for studying the radiation damage behavior of ThC and other thorium-based nuclear fuels in reactors.

Lattice dynamics and thermal properties of thorium metal and thorium monocarbide

Thorium is a chemical element that is beginning to attract attention because of its potential use as a nuclear fuel. It is not easy to carry out experiments because of its radioactive nature, and therefore theoretical works are highly appreciated. Thorium contains only a small number of the $5f$ states, and it is generally accepted that these states are itinerant, that they form a chemical bond, and that their nature does not need to be corrected with the Hubbard model. On the other hand, there is a well-known problem with the description of the $6{p}_{1/2}$ states when the spin-orbit coupling is added as the perturbation to a scalar-relativistic calculation. Electronic, elastic, phonon, and thermodynamic properties are analyzed in terms of the importance of the spin-orbit coupling acting on the $6d$ and $5f$ states. The importance of the spin-orbit coupling acting on the semicore $6p$ states is discussed. The same properties are analyzed for thorium monocarbide, and a difference caused by adding a carbon atom into the structure is discussed. Detailed analysis of the thermal conductivity (both phonon and electronic contributions) is also included. We have given extra attention to the thermal conductivity of ThC to explain why the optical phonon modes account only for approximately 6% of the phonon thermal conductivity.

Electronic structure, elastic and thermal transport properties of thorium monocarbide based on first-principles study

We investigate the electronic structure, mechanical properties and thermal transport properties of ThC based on density functional theory. We find that thorium monocarbide shows metallic and mechanically stable at ground state, and the 5f-orbital and 6d-orbital electrons of Th atoms do not exhibit strong correlation properties. The Debye temperature obtained from the elastic constant is also in good agreement with the results of others. The thermal transport properties of ThC were discussed with the Boltzmann transport equation. It is found that the thermal conductivity of the lattice comes from the contribution of the acoustic support, and the optical branch has a lower thermal conductivity because of the suppression of the anharmonicity. The Seebeck coefficient and the power factor of ThC have a maximum at the valence band and increase with the increasing temperature, while the conductivity is less affected by the temperature. The electronic thermal conductivity increases with the increasing temperature, and at high temperatures, Widman-Franz law is ineffective. At low temperatures, the total thermal conductivity mainly comes from the lattice thermal conductivity; electrons occupy a major role at high temperatures. The thermoelectric figure of ThC is close to 0 at room temperature and cannot be used as a good thermoelectric material.

Mechanical stability and superconductivity of PbO-type phase of thorium monocarbide at high pressure

As a potential nuclear fuel for the next generation of nuclear reactors, the structural and physical properties of thorium monocarbide (ThC) under high pressure have attracted a wide range of research interest. Here, the mechanical, electronic, dynamical, and superconducting properties of PbO-type ThC have been systematically investigated through first-principles calculations, which established the thermodynamic and mechanical stability of this phase within the pressure range of 60–140GPa. Moreover, it is found that pressure significantly affected the electronic states near the Fermi level and superconductivity. The superconducting transition temperature Tc first increases, and then decreases with increasing pressure. The maximal value of Tc reaches 4.64K at 80GPa. This phenomenon is a representation of the reconstruction of the Fermi surface and phonon hardening under compression.

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.

Defect stability in thorium monocarbide: An ab initio study**Project supported by the International S&T Cooperation Program of China (Grant No. 2014DFG60230), the National Natural Science Foundation of China (Grant No. 91326105), the National Basic Research Program of China (Grant No. 2010CB934504), and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDA02040104).

The elastic properties and point defects of thorium monocarbide (ThC) have been studied by means of density functional theory based on the projector-augmented-wave method. The calculated electronic and elastic properties of ThC are in good agreement with experimental data and previous theoretical results. Five types of point defects have been considered in our study, including the vacancy defect, interstitial defect, antisite defect, schottky defect, and composition-conserving defect. Among these defects, the carbon vacancy defect has the lowest formation energy of 0.29 eV. The second most stable defect (0.49 eV) is one of composition-conserving defects in which one carbon is removed to another carbon site forming a C2 dimer. In addition, we also discuss several kinds of carbon interstitial defects, and predict that the carbon trimer configuration may be a transition state for a carbon dimer diffusion in ThC.

Prediction of new high pressure structural sequence in thorium carbide: A first principles study

In the present work, we report the detailed electronic band structure calculations on thorium monocarbide. The comparison of enthalpies, derived for various phases using evolutionary structure search method in conjunction with first principles total energy calculations at several hydrostatic compressions, yielded a high pressure structural sequence of NaCl type (B1) → Pnma → Cmcm → CsCl type (B2) at hydrostatic pressures of ∼19 GPa, 36 GPa, and 200 GPa, respectively. However, the two high pressure experimental studies by Gerward et al. [J. Appl. Crystallogr. 19, 308 (1986); J. Less-Common Met. 161, L11 (1990)] one up to 36 GPa and other up to 50 GPa, on substoichiometric thorium carbide samples with carbon deficiency of ∼20%, do not report any structural transition. The discrepancy between theory and experiment could be due to the non-stoichiometry of thorium carbide samples used in the experiment. Further, in order to substantiate the results of our static lattice calculations, we have determined the phonon dispersion relations for these structures from lattice dynamic calculations. The theoretically calculated phonon spectrum reveal that the B1 phase fails dynamically at ∼33.8 GPa whereas the Pnma phase appears as dynamically stable structure around the B1 to Pnma transition pressure. Similarly, the Cmcm structure also displays dynamic stability in the regime of its structural stability. The B2 phase becomes dynamically stable much below the Cmcm to B2 transition pressure. Additionally, we have derived various thermophysical properties such as zero pressure equilibrium volume, bulk modulus, its pressure derivative, Debye temperature, thermal expansion coefficient and Gruneisen parameter at 300 K and compared these with available experimental data. Further, the behavior of zero pressure bulk modulus, heat capacity and Helmholtz free energy has been examined as a function temperature and compared with the experimental data of Danan [J. Nucl. Mater. 57, 280 (1975)].

A new phase of ThC at high pressure predicted from a first-principles study

The phase transition of thorium monocarbide (ThC) at high pressure has been studied by means of density functional theory. Through structure search, a new phase with space group P4/nmm has been predicted. The calculated phonons demonstrate that this new phase and the previous B2 phase are dynamically stable as the external pressure is greater than 60 GPa and 120 GPa, respectively. The transformation from B1 to P4/nmm is predicted to be a first-order transition, while that from P4/nmm to B2 is found to be a second-order transition.

A theoretical study for thorium monocarbide (ThC)

The structural, mechanical, electronic and thermodynamic properties of thorium monocarbide (ThC) with NaCl-type structure have been investigated by using first-principles plane wave density functional calculations with GGA, LDA and LDA+U functionals. It is shown that calculated equilibrium structural parameters of ThC are in agreement with the experimental results. It is seen from calculated single-crystal elastic constants that ThC with NaCl-type structure is mechanically stable. And from calculated density of states and band structure, it is observed that ThC is metallic. After the properties at 0GPa are clarified, pressure dependency of the structural parameters, the elastic properties and related mechanical properties, density of states (DOS) and hardness are studied. Furthermore, the thermodynamic properties of ThC are obtained from the quasi-harmonic Debye model (QHM) over high pressure and temperature ranges for three functionals. The results are compared to each other, and the available experimental and theoretical data.

The influence of carbon non-stoichiometry on the electronic properties of thorium monocarbide ThC

The first-principle band structure calculations are employed to examine the influence of carbon non-stoichiometry on the structural and electronic properties of the cubic thorium monocarbide ThC. As a result, the equilibrium geometries, electronic bands, densities of states (DOS), Sommerfeld constants and Pauli paramagnetic susceptibility for ThC 1− x (where x = 0, 0.25 and 0.50) are obtained and analyzed in comparison with available experimental data. Additionally, the formation energies of carbon vacancies are theoretically estimated for ThC 1− x . The results obtained indicate that the introduction of carbon vacancies in ThC is accompanied by pronounced DOS changes due to the appearance of novel “vacancy states” in the near-Fermi region formed by comparable contributions of Th 6 d and 5 f states. The carbon deficiency strongly affects the structure and stability of thorium carbide. For example, for the hypothetical “over-deficient" composition ThC 0.50 the initial cubic structure undergoes significant tetragonal distortions. On the contrary, for ThC 0.75 the value of E vf is positive and the cubic structure of this phase is preserved.

First-principles study of structural, elastic and electronic properties of thorium dicarbide (ThC 2) polymorphs

The comparative study of the structural, elastic, cohesive and electronic properties of three polymorphs (α-monoclinic, β-tetragonal and γ-cubic) of thorium dicarbide ThC 2 is performed within the density-functional theory. The optimized atomic coordinates, lattice parameters, theoretical density ( ρ), bulk moduli ( B), compressibility ( β), as well as electronic densities of states, electronic heat capacity ( γ) and molar Pauli paramagnetic susceptibility ( χ) for all ThC 2 polymorphs are obtained and analyzed in comparison with available experimental data. The peculiarities of inter-atomic bonding for thorium dicarbide are discussed. Besides, we have evaluated the formation energies ( E f) of ThC 2 polymorphs for different possible preparation routes (namely for the reactions with the participation of simple substances (metallic Th and graphite) or thorium monocarbide ThC and graphite). The results show that the synthesis of the ThC 2 polymorphs from simple substances is more favorable – in comparison with the reactions with participation of Th monocarbide.

Thermodynamics of the vaporization of non-stoichiometric thorium monocarbide ThC 1 ± x

Vaporization thermodynamics of thorium monocarbide phase ThC 1 ± x was studied by mass spectrometric Knudsen effusion method at the compositions of ThC 0.891, ThC 0.975, ThC 1.007 and ThC 1.074. The partial vapor pressure of Th(g) and activities of Th and C in ThC 1 ± x were determined at 2060 to 2330 K. Gibbs energies of formation of ThC 1 ± x were also determined. Congruent vaporization composition of ThC 1 ± x was evaluated at 2300 K to be ThC 1.09. Congruent vaporization and congruent effusing compositions were defined explicitly and their characteristics brought out.

Electrical Properties of Thorium Carbonitrides

The electrical resistivity, Hall coefficient, and thermoelectric power of thorium carbonitride solid solutions ranging in composition from ThC0.778N0.108 to ThC0.029N0.937 were measured from 4.2°K to about 400°K. A maximum was observed in each property as nitrogen was substituted for carbon. The results were compared with results on nonstoichiometric thorium monocarbide and thorium mononitride.

On the free energy of formation of thorium monocarbide

An assessment of the free energies of formation of thorium monocarbide has been made from equilibria in the plutonium-thorium-carbon and thorium-carbon-oxygen systems for the temperature range 1373–1873°K. The data are consistent with a negative entropy of formation.

Interaction between point defects in nonstoichiometric compounds

The variation in thermodynamic activity as a function of nonstoichiometry was derived for binary compounds exhibiting large deviations from stoichiometry. The assumptions were made that only one type of point defect is present in high concentrations, and that there are pair-wise interactions among the randomly distributed defects. It is shown that comparisons of experimentally determined activities with the theoretically derived relations may be used to deduce the type of point defect which is predominantly responsible for the nonstoichiometry, and to determine the free energy of interaction between the defects. Experimental hydrogen activities in yttrium and cerium hydrides, and thorium activities in thorium monocarbide are analyzed in this manner.

Chemical Bonding of Thorium Monocarbide

The magnetic susceptibility of non-stoichiometric thorium monocarbide having compositions between ThC0.72 and ThC0.96 was measured at various temperatures. The susceptibility showed weak paramagnetism independent of temperature, which increased with decreasing carbon content (χmole=6.0×10−5 emu for Th0.72 4.1×10−5emu for Th0.96). The bonding of Th-Th, Th-C and C-C is discussed with the aid of a metallic bonding model applied to the compound. The bond energies of Th-Th and Th-C have been analyzed on the basis of Pauling's scheme, and evaluated to be −51 kcal/mole and −271 kcal/mole respectively, at a composition of ThC0.95. The narrow band of ThC is examined from measured results of magnetic susceptibility.

Chemical Bonding of Thorium Monocarbide

The magnetic susceptibility of non-stoichiometric thorium monocarbide having compositions between ThC0.72 and ThC0.96 was measured at various temperatures. The susceptibility showed weak paramagnetism independent of temperature, which increased with decreasing carbon content (χmole=6.0 X10-5 emu for ThC0.72, 4.1X10-5 emu for ThC0.96). The bonding of Th-Th, Th-C and C-C is discussed with the aid of a metallic bonding model applied to the compound. The bond energies of Th-Th and Th-C have been analyzed on the basis of Pauling's scheme, and evaluat-ed to be -51 kcal/mole and -271 kcal/mole respectively, at a composition of ThC0.95. The narrow band of ThC is examined from measured results of magnetic susceptibility.

Reactions of uranium mononitride, thorium monocarbide and uranium monocarbide with nitric acid and other aqueous reagents

Uranium mononitride was inert at 80° in water, 3–12 M HCl, 1 M H 2SO 4, 1 M NaOH, 1 M NaNO 3, and 5 M NH 4NO 3; however, it did react in 1–2·5 M Al(NO 3) 3. The nitride reacted with 0·5–15·8 M HNO 3 to give gaseous mixtures of N 2, N 2O, NO, and NO 2 (NO 2 was produced only when the acid concentration was 6 M or higher). In reactions of thorium monocarbide with 0·1 to 1 M HNO 3 at 90°, both hydrolysis (yielding mainly methane) and oxidation (yielding CO 2, N 2, and nitrogen oxides) of the carbide took place; at higher HNO 3 concentrations, only oxidation occurred. The principal reaction of UC or ThC with 4 and 6 M NH 4F at 80° was: ▪

Preparation of Thorium Carbides

Some factors influencing the formation of thorium carbide from a mixture of thorium dioxide and graphite powder were studied. The effects of the molecular ratio of the reactants, reaction temperature, extrinsic properties (such as surface area, defects, and crystallinity of the materials), and the ambient pressure were examined. The molecular ratio of the reactants gave the most important effect on the composition of the final products. Thorium dicarbide was formed from a mixture having a molecular ratio (C/ThO2) of more than three and the reaction rate then obeyed the parabolic rate equation. To form thorium monocarbide, it is necessary to use a mixture having a ratio less than four. A tentative explanation of the reaction mechanism of ThC formation is given.

Thermodynamic properties and nonstoichiometry of thorium monocarbide

The values of emf in the cell W/Th, ThF 4/CaF 2/ThF 4, ThC x / W were measured at the temperatures of 720° to 950° C and at the compositions of 0.13 ⩽ x ⩽ 1.60. Thermodynamic informations of nonstoichiometric thorium monocarbide were obtained. Lattice parameters and densities of thorium monocarbides were measured. Phase boundaries and lattice defects of this compound were discussed from these results. The anomaly at about 830° C of the sample of ThC 0.76 observed in the temperature dependences of emf is discussed on the basis of superlattice formation of carbon atoms and vacancies.