Phase relations and linear thermal expansion of cubic solid solutions in the Th1−xMxO2−x/2 (M = Eu, Gd, Dy) systems

Cell parameters and linear thermal expansion studies of the Th-M oxide systems with general compositions Th_1−xM_xO_2−x/2 (M = Eu³⁺, Gd³⁺ and Dy³⁺, 0.0 ? x ? 1.0) are reported. The XRD patterns of each product were refined to specify the solid solubility limits of MO_1.5 in the ThO₂ lattice. The upper solid solubility limits of EuO_1.5, GdO_1.5 and DyO_1.5 in the ThO₂ lattice under conditions of slow cooling from 1673 K are represented as Th_0.50Eu_0.50O_1.75, Th_0.60Gd_0.40O_1.80 and Th_0.85Dy_0.15O_1.925, respectively. The linear thermal expansion (293-1123 K) of MO_1.5 and their single-phase solid solutions with thoria were investigated by dilatometery. The average linear thermal expansion coefficients () of the compounds decrease on going from EuO_1.5 to DyO_1.5. The values of for EuO_1.5, GdO_1.5 and DyO_1.5 containing solid solutions showed a downward trend as a function of the dopant concentration. The linear thermal expansion (293-1473 K) of the solid solutions investigated by high-temperature XRD also showed a similar trend.     

Thermal conductivities of hypostoichiometric (U, Pu, Am)O2−x oxide

The thermal conductivities of (U_0.68Pu_0.30Am_0.02)O_2.00−x solid solutions (x = 0.00-0.08) were studied at temperatures from 900 to 1773 K. The thermal conductivities were obtained from the thermal diffusivities measured by the laser flash method. The thermal conductivities obtained experimentally up to about 1400 K could be expressed by a classical phonon transport model, λ = (A + BT)⁻¹, A(x) = 3.31 × x + 9.92 × 10⁻³ (mK/W) and B(x) = (−6.68 × x + 2.46) × 10⁻⁴ (m/W). The experimental A values showed a good agreement with theoretical predictions, but the experimental B values showed not so good agreement with the theoretical ones in the low O/M ratio region. From the comparison of A and B values obtained in this study with the ones of (U,Pu)O_2−x obtained by Duriez et al. [C. Duriez, J.P. Alessandri, T. Gervais, Y. Philipponneau, J. Nucl. Mater. 277 (2000) 143], the addition of Am into (U, Pu)O_2−x gave no significant effect on the O/M dependency of A and B values.     

Thermodynamic and composition changes in UO2±x (x< 0.005) at 1950 K

The composition of UO_2±x has been determined in a narrow range on either side of the stoichiometric composition, as a function of the equilibrium oxygen pressure at a single temperature, 1950 K. Samples of UO_2−x cooled rapidly from 1950 K to room temperature disproportionate to stoichiometric UO₂ and U metal. The significance of these results to the commercial sintering of UO₂ fuel pellets is discussed.     

Kinetic models for the synthesis of (U, Pu)O2−y by hydrogen-reduction and carbothermic techniques

Three models have been developed that permit the calculation of the time necessary for the synthesis of hypostoichiometric oxide from (U, Pu)O₂. The models are based on the interrelation between oxygen potential, valence of plutonium, and temperature determined by Rand and Markin and on the experimental conditions for reduction. Two reduction techniques are considered: the flowing hydrogen system and the C-CO-CO₂ system. At the usual temperatures for reduction, the partial pressure of water, the hydrogen flow, and the total weight of plutonia are the most important factors in the hydrogen system, while in the C.CO-CO₂ system the important factors are the weight of the plutonia in each oxide pellet, the partial pressure of carbon monoxide, the proximity of the oxide and the carbon used for reduction, and the oxygen-to-metal ratio possible at the oxygen potential of the C-CO-CO₂ equilibrium.     

Energy levels and classifications of doubly-excited states in two-electron systems with nuclear charge, Z = 1, 2, 3, 4, 5, below the N = 2 and N = 3 thresholds

Below the thresholds for production of He⁺ in the N = 2 and N = 3 states the doubly-excited states in isoelectronic helium (Z = 1, 2, 3, 4, 5) have been completely classified as to series and outer quantum number by means of calculations using the truncated diagonalization method with hydrogenic basis functions. The classifications, energy levels, and effective quantum numbers are tabulated here for all systems with total orbital angular momentum L = 0, 1, 2, 3.     

Inclusion of pre-compound scattering in evaluation formulae for σn, 2n(E) and σn, 3n(E)

This paper is a sequel to an article describing a simple procedure for the evaluation of heavy-mass (n, 2n) and (n, 3n) cross-sections. The neglect of pre-compound effects in the energy range above the (n, 3n) threshold leads to an overestimation of σ_{n, 3n}(E), at the expense of σ_{n, 2n}(E). Pre-compound effects on σ_{n, 2n}(E) and σ_{n, 3n}(E) can be estimated through the use of simple evaluation formulae, derived from basic, more involved integrals. Agreement between evaluation and experiment is much improved in the energy range above the (n, 3n) threshold.     

Thermodynamic properties of the O-U system. II - Critical assessment of the stability and composition range of the oxides UO2+x, U4O9−y and U3O8−z

The published data concerned with the determination of the composition ranges of uranium oxides, UO_2+x, U₄O_9−y and U₃O_8−z, which have been determined using thermogravimetric, X-ray diffraction and electrochemical techniques are critically assessed. U₄O₉ and U₃O₈ have quite small domains of composition and the assessment of such data has carefully considered the uncertainties in the experimental determinations. In addition, the thermodynamic properties of U₄O₉ and U₃O₈, enthalpies of formation and transformation, entropies, and thermal capacities are analyzed and selected to build a primary data base for compounds.     

Influence on the structural characteristic of defect solid solution GdxZr1−xO2−x/2 with 0.18 ? x ? 0.62 under longer term annealing studied by Gd Mössbauer spectroscopy

Three kinds of defect solid solution Gd_xZr_1−xO_2−x/2 with 0.18 ? x ? 0.62, including the three single crystal samples with x = 0.21, 0.26 and 0.30, were investigated by ¹⁵⁵Gd Mössbauer spectroscopy at 12 K. Difference in the structural characteristic under longer term annealing were confirmed by comparing the ¹⁵⁵Gd Mössbauer parameters of the polycrystalline samples sintered one time and twice at 1773 K for 16 h in air, respectively. The results indicated that the polycrystalline samples sintered twice have relatively equilibrated structure by comparing with the three single crystal samples. After being sintered twice, basically the local structure around the Gd³⁺ ions does not change, but the degree of the displacements of the six 48f oxygen ions from positions of cubic symmetry becomes slightly smaller, and distribution of the Gd³⁺ ions in the system becomes more homogeneous.     

Oxygen potentials of (U,Gd)O2 ± x solid solutions in the temperature range 1000–1500°C

Oxygen potentials of U_0.86Gd_0.14O_{2 ± x} and U_0.73Gd_0.27O_{2 ± x} solid solutions, together with UO_{2 ± x}, have been measured at 1000, 1300 and 1500°C by using a thermogravimetric technique. The results at 1000°C show good agreement with the results of a previous solid electrolyte galvanic cell measurement. The oxygen potentials for the solid solutions increase positively with increasing Gd content. Stable hypostoichiometric phases are seen at the oxygen potentials below ?65 and ?50 kcal/mol between 1000 and 1500°C for U_0.86Gd_0.14O₂ and U_0.73Gd_0.27O₂, respectively. From the oxygen partial pressure dependence of x, models for the defect structure in hyper- and hypostoichiometric solid solutions are suggested.     

Relative intensities for Li (i = 1-3) and Mi (i = 1-5) subshell X-rays

The intensities for L_i (i = 1-3) subshell X-ray lines have been computed relative to the most intense line in each series, for elements with 30 ? Z ? 92, from published X-ray emission rates based on the Dirac-Fock (DF) model. In the case of M_i (i = 1-5) subshell X-ray lines, complete sets of emission rates based on both the Dirac-Hartree-Slater and the DF models have been generated for elements with 65 ? Z ? 92 by logarithmic interpolation of the data available for a limited number of elements. The intensities for different M X-ray lines have been computed relative to the most intense line in each series using these two sets of emission rates. The L_i (i = 1-3) and M_i (i = 1-5) subshell X-ray relative intensities computed from the DF model based emission rates have been least-squares-fitted to polynomials in the atomic number for use in software packages for quantitative elemental analysis using X-ray emission techniques and for other applications.     

Thermodynamic properties of ThxU1−xO2 (0 < x < 1) based on quantum-mechanical calculations and Monte-Carlo simulations

Th_xU_1−xO_2+y binary compositions occur in nature, uranothorianite, and as a mixed oxide nuclear fuel. As a nuclear fuel, important properties, such as the melting point, thermal conductivity, and the thermal expansion coefficient change as a function of composition. Additionally, for direct disposal of Th_xU_1−xO₂, the chemical durability changes as a function of composition, with the dissolution rate decreasing with increasing thoria content. UO₂ and ThO₂ have the same isometric structure, and the ionic radii of 8-fold coordinated U⁴⁺ and Th⁴⁺ are similar (1.14 nm and 1.19 nm, respectively). Thus, this binary is expected to form a complete solid solution. However, atomic-scale measurements or simulations of cation ordering and the associated thermodynamic properties of the Th_xU_1−xO₂ system have yet to be determined. A combination of density-functional theory, Monte-Carlo methods, and thermodynamic integration are used to calculate thermodynamic properties of the Th_xU_1−xO₂ binary (ΔH_mix, ΔG_mix, ΔS_mix, phase diagram). The Gibbs free energy of mixing (ΔG_mix) shows a miscibility gap at equilibration temperatures below 1000 K (e.g., E_exsoln = 0.13 kJ/(mol cations) at 750 K). Such a miscibility gap may indicate possible exsolution (i.e., phase separation upon cooling). A unique approach to evaluate the likelihood and kinetics of forming interfaces between U-rich and Th-rich has been chosen that compares the energy gain of forming separate phases with estimated energy losses of forming necessary interfaces. The result of such an approach is that the thermodynamic gain of phase separation does not overcome the increase in interface energy between exsolution lamellae for thin exsolution lamellae (10 Å). Lamella formation becomes energetically favorable with a reduction of the interface area and, thus, an increase in lamella thickness to >45 Å. However, this increase in lamellae thickness may be diffusion limited. Monte-Carlo simulations converge to an exsolved structure [lamellae || ] only for very low equilibration temperatures (below room temperature). In addition to the weak tendency to exsolve, there is an ordered arrangement of Th and U in the solid solution [alternating U and Th layers || {1 0 0}] that is energetically favored for the homogeneously mixed 50% Th configurations. Still, this tendency to order is so weak that ordering is seldom reached due to kinetic hindrances. The configurational entropy of mixing (ΔS_mix) is approximately equal to the point entropy at all temperatures, indicating that the system is not ordered.     

Light ion irradiation effects on stuffed Lu2(Ti2−xLux)O7−x/2 (x = 0, 0.4 and 0.67) structures

We have recently synthesized “stuffed” (i.e., excess Lu) Lu₂(Ti_2−xLu_x)O_7−x/2 (x = 0, 0.4 and 0.67) compounds using conventional ceramic processing. X-ray diffraction measurements indicate that stuffing more Lu³⁺ cations into the oxide structure leads eventually to an order-to-disorder (O-D) transition, from an ordered pyrochlore to a disordered fluorite crystal structure. At the maximum deviation in stoichiometry (x = 0.67), the Lu³⁺ and Ti⁴⁺ ions become completely randomized on the cation sublattices, and the oxygen “vacancies” are randomized on the anion sublattice. Samples were irradiated with 400 keV Ne²⁺ ions to fluences ranging from 1 × 10¹⁵ to 1 × 10¹⁶ ions/cm² at cryogenic temperatures (∼77 K). Ion irradiation effects in these samples were examined by using grazing incident X-ray diffraction. The results show that the ion irradiation tolerance increases with disordering extent in the non-stoichiometric Lu₂(Ti_2−xLu_x)O_7−x/2.     

Structural study of Pu1−xAmxO2 (x = 0.2; 0.5; 0.8) obtained by oxalate co-conversion

This study describes the synthesis and the characterisation of Pu_1−xAm_xO₂ (x = 0.2; 0.5; 0.8) mixed oxides obtained by oxalate co-conversion. We studied the self-irradiation effect in these compounds at the structural scale. We determined, for each composition, the initial lattice parameter and the equation describing its variation versus time and displacements per atom. Similarly to other α emitting compounds, it was observed a fast lattice parameter expansion rate, followed by a stabilisation at a maximum value. The observations also showed that the initial expansion rate varies according to the Am content and the maximum value to the Pu content. However, for all compositions, the lattice parameter relative variations are the same.     

An experimental study on linear differential scattering coefficients of the radioactive compounds UO2(C2H3O2)2 · 2H2O and Th(NO3)4 · 5H2O at 60 keV

The linear differential scattering coefficients at 60 keV have been measured for UO₂(C₂H₃O₂)₂ · 2H₂O (uranyl-acetate) and Th(NO₃)₄ · 5H₂O (thorium-nitrate) radioactive compounds at seven angles ranging from 60° to 120° at intervals 10°. The obtained results have been compared with relativistic and non-relativistic theoretical values.     

Vaporization study on UO2 and (U1−yNby)O2+x by mass-spectrometric method

The vapor pressures over UO_2.000 and (U_1?yNb_y)O_2+x (y = 0.01, 0.05, x = 0.000–0.022) were measured by the mass-spectrometric method in the temperature range 2025–2343 K. The main gas species over UO_2.000 were observed to be UO₃(g) and UO₂(g) and those over (U_1?yNb_y)O_2+x were NbO₂(g), NbO(g), UO₃(g) and UO₂(g). The partial vapor pressures of almost all gas species over (U_1?yNb_y)O_2+x increased with increasing O/M (M = U + Nb) ratio. With increasing Nb content in (U_1?yNb_y)O_2.000, the partial vapor pressures of UO₂(g) and UO₃(g) decreased and those of NbO(g) and NbO₂(g) increased. The congruently vaporizing composition in the (U_1?yNb_y)O_2+x phase was estimated to be ($\text{U}{}_{\mathrm{0.985\pm 0.005}}\text{Nb}{}_{\mathrm{0.015\pm 0.005}}\text{)O}{}_{2.000}$ from the compositional dependence of the total vapor pressures. The partial molar enthalpy and entropy of oxygen of (U_1?yNb_y)O_2+x calculated from the partial pressures of gaseous species NbO₂(g) and NbO(g) were in fairly good agreement with those previously obtained by the present authors with a thermobalance.     

Cross section measurements of the 23Na(n, 2n)22Na, 58Ni(n, 2n)57Ni and 115In(n,n′)115mIn reactions

Cross sections for two high energy threshold reactions ²³Na(n, 2n)²²Na and ⁵⁸Ni(n, 2n)⁵⁷Ni were measured by the activation method in the neutron energy range from 14 to 18 MeV. Inelastic scattering cross section for ¹¹⁵In was measured in the threshold region, i.e. from 0.5 to 1.3 MeV. The results of measurements are compared with scarce and divergent earlier data.     

Electrical conductivity and non-stoichiometry in the (U,Gd)O2±x system

The isothermal electrical conductivity and oxygen potential of the (U,Gd)O_2±x solid solution were measured in various oxygen partial pressure regions at 1200 °C and 1300 °C. The electrical conductivity gradually decreased with decreasing oxygen partial pressure even in the hypo-stoichiometric region. These findings were in contrast to the implication of a hypo-stoichiometry where the electrical conductivity is increased through the formation of oxygen vacancies. The (U_1−yGd_y)O_2−y/2 was defined as a new stoichiometric composition to determine the relationship between the deviation of the oxygen composition from stoichiometry and oxygen partial pressure. The dependence of the new oxygen deviation, z in (U_1−yGd_y)O_2−y/2+z, on the oxygen partial pressure corresponds to the dependence of the electrical conductivity, and thus a consistent defect structure model can be deduced from both the dependence curves. It suggests that the defect type is oxygen interstitial even below the oxygen composition of 2.     

Combustion synthesis and thermal expansion measurements of the rare earth–uranium ternary oxides RE6UO12 (RE=La, Nd and Sm)

Rare earth–uranium ternary oxides were synthesized by a solution combustion route. The starting materials were the corresponding metal nitrates and urea. In these preparations, the metal nitrates act as oxidizer and urea as fuel. Highly exothermic decomposition of the metal nitrate–urea complexes on heating at about 500 K leads to a combustion process yielding RE₆UO₁₂ fine powders. Thermal expansion measurements of these compounds were carried out in the temperature range of 298–1173 K by high temperature X-ray powder diffractometry. The observed axial thermal expansion behaviour is explained on the basis of the crystal chemistry of the compounds.     

Oxygen potential of (U0.88Pu0.12)O2±x and (U0.7Pu0.3)O2±x at high temperatures of 1673-1873 K

The oxygen potential of (U_0.88Pu_0.12)O_2±x (−0.0119 < x < 0.0408) and (U_0.7Pu_0.3)O_2±x (−0.0363 < x < 0.0288) was measured at high temperatures of 1673-1873 K using gas equilibrium method with thermo gravimeter. The measured data were analyzed by a defect chemistry model. Expressions were derived to represent the oxygen potential based on defect chemistry as functions of temperature and oxygen-to-metal ratio. The thermodynamic data, and , at stoichiometric composition were obtained. The expressions can be used for in situ determination of the oxygen-to-metal ratio by the gas-equilibration method. The calculation results were consistent with measured data. It was estimated that addition of 1 wt.% Pu content increased oxygen potential of uranium and plutonium mixed oxide by 2-5 kJ/mol.