Chemical thermodynamic representations of 〈PuO2−x〉 and 〈U1−zPuzOw〉

All available oxygen potential-temperature-composition data for the calcium fluorite-structure 〈PuO_2?x〉^★★ phase were retrieved from the literature and utilized in the development of a binary solid solution representation of the phase. The data and phase relations are found to be best described by a solution of [Pu_{$\text{4}\text{3}$}O₂] and [PuO₂] with a temperature dependent interaction energy. The fluorite-structure 〈U_1?zPu_zO_w〉 is assumed to be represented by a combination of the binaries 〈PuO_2?x〉 and 〈UO₂ ± x〉, and thus treated as a solution of [$\text{Pu}{}_{\mathrm{<mtext>4</mtext><mtext>3</mtext>}}\text{O}{}_2$], [PuO₂], [UO₂], and either [U₂O_4.5] or [U₃O₇]. The resulting equations well reproduce the large amount of oxygen potential-temperature-composition data for the mixed oxide system, all of which were also retrieved from the literature. These models are the first that appear to display the appropriate oxygen potential-temperature-composition and phase relation behavior over the entire range of existence for the phases.     

Study of homogenisation and cation interdiffusion in mixed UO2-PuO2 compacts by X-ray diffraction

Homogenisation in mixed UO₂-PuO₂ compacts has been studied by X-ray diffraction. It is observed that the homogenisation proceeds, mainly, by the assimilation of UO₂ into PuO₂. This near one-way flow of material, from UO₂ to PuO₂, is shown to be due to high activity (large BET surface area) of the PuO₂ powder as compared with that of the UO₂ powder.An X-ray line profile analysis method of determining various mixed composition fractions in sintered mixed compacts has been used to evaluate homogeneity in terms of the fraction of UO₂ that has gone into PuO₂. A concentric core-shell diffusion model, in which UO₂ forms a solute core and PuO₂ forms a solvent shell, was used to determine cation interdiffusion coefficients from the homogenisation data. The temperature dependence of cation diffusivity in the range 1573–1873 K is obtained as $\text{D = 2.55 × 10}{}^{\mathrm{?11}}\text{exp(?2.22 × 10}{}^5\text{/8.31 T)}$ m²/s. The low value (222 kJ/mole) of activation energy for cation interdiffusion is attributed to the hypostoichiometry of the mixed compacts studied.The diffusivity values at 1573 and 1673 K separately give an activation energy of 126 kJ/mole, which suggests grain-boundary diffusion as the primary mechanism of homogenisation in this temperature range.     

Effect of sintering atmosphere on the density of uranium dioxide pellets

$\text{UO}{}_2$ pellets were sintered in flowing H₂-N₂-H₂O gas mixtures at temperatures between 1000 and 1300°C. Sintered density increased with increasing ratio $\text{R =}\text{partial pressure}\text{H}{}_2\text{O/partial pressure}$$\text{H}{}_2$. The results provide a method of produ dense stoichiometric $\text{UO}{}_2$ pellets by means of a single-stage sintering process.     

Phase relation and defect structures of nonstoichiometric U4O9±y and UO2+x at high temperatures

Phase relations in the composition range from $\text{UO}{}_{\mathrm{2+x}}$ to $\text{U}{}_3\text{O}{}_{\mathrm{8?z}}$ were studied by electrical-conductivity measurements and X-ray diffraction in the ranges $\text{1025°C ? T ? 1140°C}$ and . The plot of log σ versus log showed straight lines with distinct slopes, which corresponded to four regions ($\text{UO}{}_{\mathrm{2+x}}$, $\text{U}{}_4\text{O}{}_{\mathrm{9?y}}$, $\text{U}{}_4\text{O}{}_{\mathrm{9+y}}$ and $\text{U}{}_3\text{O}{}_{\mathrm{8?z}}$). The existence of the hyperstoichiometric $\text{U}{}_4\text{O}{}_{\mathrm{9+y}}$ phase was suggested in the temperature range from 1025 to 1126°C. The peritectoid temperature ($\text{U}{}_4\text{O}{}_{\mathrm{9\pm y}}\text{= UO}{}_{\mathrm{2+x}}\text{+ U}{}_3\text{O}{}_{\mathrm{8?z}}$) was estimated to be present between 1126 and 1131°C. The partial free enthalpies and entropies for the two-phase equilibrium ($\text{U}{}_4\text{O}{}_{\mathrm{9+y}}\text{+ U}{}_3\text{O}{}_{\mathrm{8?z}}$, and $\text{U}{}_4\text{O}{}_{\mathrm{9?y}}\text{+ UO}{}_{\mathrm{2+x}}$) were calculated and compared with previous results. From the dependence of the electrical conductivity on the oxygen partial pressure the nonstoichiometric defect structures of $\text{UO}{}_{\mathrm{2+x}}$ and $\text{U}{}_4\text{O}{}_{\mathrm{9\pm y}}$ were interpreted as consisting of doubly charged oxygen interstitials (O_i'') and doubly charged oxygen vacancies (V_O''). At room temperature, the homogeneity range of the U₄O₉ phase was investigated with a Debye-Scherrer camera.     

Extension of vapour pressure measurements of nuclear fuels (U,Pu)O2 and UO2 to 7000 K for fast reactor safety analysis

A new high-energy laser technique, including fast temperature recording in the microsecond range, was developed for measuring the vapour pressure of fast breeder uranium-plutonium oxide fuels up to 7000 K. In the ternary system, the pressure of uranium-plutonium oxide above its melting point was determined to be $\text{log p (atm) = 7.966 ? (28137/T)}$, yielding a high-temperature heat of evaporation of $\text{ΔH}{}_{\mathrm{evap}}\text{= 128.7 kcal/mol}$. Measurement of the UO₂ partial pressure over the solid gave $\text{log p (atm) = 9.365 ? (32436/T)}$, resulting in a heat of sublimation of $\text{ΔH}{}_{\mathrm{sub}}\text{= 148.4 kcal/mol}$. The difference of these heats yields the heat of fusion $\text{ΔH}{}_{\mathrm{f}}\text{= 19.7 kcal/mol}$, which is in good agreement with the literature value of 19.4 kcal/mol. In the binary UO₂ system, the pressure above the melting point was determined to be $\text{log p (atm) = 7.7 ? (27900/T)}$,giving a heat of evaporation of $\text{ΔH}{}_{\mathrm{evap}}\text{= 127.6 kcal/mol}$. An assessment of literature data for below the melting point yielded $\text{log p (atm) = 8.846 ? (31506/T)}$, and a heat of sublimation of $\text{ΔH}{}_{\mathrm{sub}}\text{= 144.1 kcal/mol}$. The resulting heat of fusion, $\text{ΔH}{}_{\mathrm{f}}\text{= 16.5 kcal/mol}$, is only slightly below the published value of $\text{ΔH}{}_{\mathrm{f}}\text{= 17.7 kcal/mol}$.     

Equi-chemical-potential curves in ternary uranium oxides MyU1−yO2+x

Using Schuhmann's method the chemical potentials of three components in nonstoichiometric ternary uranium oxides $\text{M}{}_{\mathrm{y}}\text{U}{}_{\mathrm{1?y}}\text{O}{}_{\mathrm{2+x}}$(M = Mg and Pu) have been calculated. The obtained results are shown in the form of equi-chemical-potential curves (surface of partial molar free energy) in the composition triangle. In the hypostoichiometric region the contour lines of the surface are dense and run parallel with each other. Taking account of this fact the difficulty in attainment of homogeneity in the fabrication of mixed oxide fuel is discussed.     

Electrical conductivity of UO2-ThO2 solid solutions

The electrical conductivities of UO_2+x. ThO₂ and their solid solutions, in thermodynamic equilibrium with the gas phase, were measured as a function of temperature, and of oxygen partial pressure in the temperatnre range 800 to 1200°C. The slope of the plot log α versus 1/$\text{T}$ for UO_2+x and UO₂-rich solid solutions exhibits a single region, whereas in the ThO₂-rich solid solutions it exhibits two regions. The pressure dependence of the conductivity (σ) in the UO₂-rich solid solutions can be represented by σ ∝ [O_i] ∝ in the range of $\text{0.01 < x < 0.1}$. Here, O_i is an interstitial oxygen and the partial pressure of oxygen, and it varies with the ThO₂ content. At greater deviation from stoichiometry ($\text{x ? 0.1}$) the presence of U₄O₉ or (Th U)₄O₉ phases influences the conductivity data. In ThO$\text{2}$ or ThO₂-rich solid solutions. P-type conduction at high oxygen pressures is interpreted as arising from the incorporation of excess oxygen into oxygen vacancies.     

Oxygen pressures over fast breeder reactor fuel (I) A model for UO2±x

A model has been developed for calculating oxygen pressures for uranium oxide compositions in the range from the $\text{UO}{}_{\mathrm{2?x}}$ metal-rich boundary to UO_2,1. The model is based on the law of mass action, the free energy of formation of UO₂ and U₄O₉, and phase boundary data. Oxygen pressures calculated with the model are in excellent agreement with experimental observations.     

Chemical thermodynamic representation of 〈UO2 ± x〉

The entire $\text{〈UO}{}_{\mathrm{2\; \pm \; x}}\text{〉}$★★ data base for the dependence of the nonstoichiometry, $\text{x}$, on temperature and chemical potential of oxygen (oxygen potential) was retrieved from the literature and represented. This data base was interpreted by least-squares analysis using equations derived from the classical thermodynamic theory for the solid solution of a solute in a solvent. For hyperstoichiometric oxide at oxygen potentials more positive than $\text{?266700 + 16.5T J/mol}$, the data were best represented by a $\text{[UO}{}_2\text{]-[U}{}_3\text{O}{}_7\text{]}$ solution. For O/U ratios above 2 and oxygen potentials below this boundary, a $\text{[UO}{}_2\text{]-[U}{}_2\text{O}{}_{4.5}\text{]}$ solution represented the data. The $\text{〈UO}{}_{\mathrm{2?x}}\text{〉}$ data were represented by a $\text{[UO}{}_2\text{]-[U}{}_{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{]}$ solution. The resulting equations represent the experimental behavior and can be used in thermodynamic calculations to predict phase boundary compositions consistent with the literature. Collectively, the present analysis permits, for the first time, a mathematical representation of the behavior of the total data base.     

Existence of hypostoichiometric chromium sesquioxide at low oxygen partial pressures

The nonstoichiometric composition of $\text{Cr}{}_2\text{O}{}_{\mathrm{3\pm x}}$ was measured by means of thermogravimetry in the range of $\text{1173 ≦ T/K ≦ 1318}$ and . The compositional deviation from stoichiometry, $\text{x}$, in the hyperstoichiometric Cr₂O_3+x phase was observed to be smaller than 2 × 10^?4, irrespective of temperatures, provided that the hyperstoichiometric Cr₂O_3+x exists. The existence of the hypostoichiometric Cr₂O_3?x phase was first established in this study in the region of low oxygen partial pressure below 10^?5 Pa. From the oxygen partial pressure dependence of $\text{x}$ in Cr₂O_3?x, the defect structure was discussed with the neutral chromium interstitials in the composition near stoichiometry and with the triply charged ones far from stoichiometry. The partial molar enthalpy and entropy of oxygen of Cr₂O_3?x showed the complex compositional dependences, suggesting the change of the type of the predominant defect.     

Electrical conductivity measurement and thermogravimetric study of pure and niobium-doped uranium dioxide

The electrical conductivity and nonstoichiometric composition of UO_2+x and (U_1?yNb_y)O_2+x (y = 0.01, 0.05 and 0.10) were measured in the range $\text{1282 ≦ T ≦ 1373}$ K and Pa by tie four inserted wires method and thermogravimetry, respectively. The electrical conductivity of (U_1?yNb_y)O_2+x plotted against the oxygen partial pressure indicated a minimum corresponding to the transition between $\text{n}$- and $\text{p-}\text{type}$ cone uction. The band-gap energy of (U_1?yNb_y)O_2+x was calculated to be $\text{(248 ± 12)}$ kJmol.^?1, independent of niobium content, which is nearly the same as that of UO_2+x. From the oxygen partial pressure dependences of both the electrical conductivity and the deviation $\text{x}$ of UO_2+x and (U_1?yNb_y)O_2+x, the defect structures in these oxides were discussed with the complex defect model consisting of oxygen vacancies and two kinds of interstitial oxygens.     

The oxygen potential of near- and non-stoichiometric urania-25 mol% plutonia solid solutions: A comparison of thermogravimetric and galvanic cell measurements

To resolve discrepancies between the existing low temperature data for solid solution mixed (U, Pu)-oxide nuclear fuel material, additional measurements have been performed on $\text{U}{}_{0.75}\text{Pu}{}_{0.25}\text{O}{}_2\text{±x}$ employing a combined thermogravimetric (TGA) and solid-electrolyte galvanic cell technique. These measurements, which were performed at temperatures between 800 and 1000°C, and for O : M ratios in the range 1.940 to 2.028, are reasonably self-consistent and show good agreement with the results of previous TGA measurements. However, they do not corroborate the earlier EMF cell measurements of Markin and McIver. Possible explanations for errors in these earlier EMF cell results are examined. The new results indicate that the of stoichiometric mixed oxide at typical outer surface fuel temperatures is close to ?100 kcal/mol O₂ ($\text{?419 kJ/mol O}{}_2$). Attempts have been made to fit the new data to two equations derived from recent defect models, and it is shown that neither equation accurately represents the experimental $\text{po}{}_2\text{?x}$ data over more than a short range of $\text{x}$.     

High-temperature specific heat of UO2 ThO2, and A12O3

The high-temperature specific heat of solid UO₂, ThO₂, and Al₂O₃ can be represented by an equation of the form $\text{C}{}_{\mathrm{p(s)}}\text{= 3}{}_{\mathrm{n}}\text{RF(?}{}_{\mathrm{D}}\text{/T) + dT}{}^3$, (1) where ?_D is the Debye temperature, F(?_D/T) is the Debye function, $\text{d}$ represents contributions of the anharmonic vibrations within the lattice, and $\text{n}$ denotes the number of atoms per molecule. In the liquid the corresponding equation is $\text{C}{}_{\mathrm{p(1)}}\text{= 3}{}_{\mathrm{n}}\text{RF(?}{}_{\mathrm{D}}\text{/T) +}\text{h}\text{T}{}^2$, (2) where h is the anharmonic term. It is shown that for Al₂O₃ and UO₂, where experimental data for the liquid phase are also available, $\text{d}\text{h}$ has the same value, Indicating that both materials behave identically. If we compare the thermodynamic relationship $\text{C}{}_{\mathrm{p}}\text{? C}{}_{\mathrm{v}}\text{= Vα}{}^2\text{KT}$, (3) where V is the volume, $\text{α}$ the volume expansion coefficient, and $\text{K}$ the bulk modulus, with equation (1), It follows that d must be equal to $\text{Vα}{}^2\text{K}\text{T}{}^2$; the value of $\text{Vα}{}^2\text{K}\text{T}{}^2$ is calculated in the temperature region where d was obtained; within experimental error they are equal.     

Fabrication of high-density UO2 and (U0.75Pu0.25)O2 by hot pressing

The hot pressing behavior of hyperstoichiometric UO₂ and (U, Pu)O₂ powders has been evaluated. Specimens with densities in excess of 99% $\text{ρ}{}_{\mathrm{th}}$ can be fabricated with this technique at temperatures of 1000°C or less.     

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.     

Electrical conductivity of UO2+x

Isothermal and isobaric conductivities of UO_2+x nave been measured as a function of oxygen pressure and temperature. Intrinsic disorder predominates at low-oxygen pressures. The pressure dependence of the conductivity can be expressed as in the intermediate oxygen pressure range in which more than one type of charge carrier predominate. At high oxygen pressures, it has been proposed that oxygen vacancy-interstitial trios in association with U⁺⁵ ions faciliate the fast transport of oxygen interstitials in the region.     

Etude aux rayons X a haute temperature du systeme U-C-N en presence d'un exces de graphite et sous pression controlee d'azote

Pressed samples of initial compositions $\text{“UC}{}_2\text{” + 1 C}$ and $\text{“UC}{}_2\text{” + 2 C}$ were made to undergo progressive reaction under a gradually increasing pressure of nitrogen () in a high-temperature X-ray diffraction apparatus which operated in the range 800–2000°C. In this way, the various equilibrium domains [ α or β “UC₂”, C, N₂], [α or β “UC₂”, UC_yN_x, C, N₂] and [ UC_yN_x, C, N₂], were successively made manifest; this permitted the lattice parameters and equilibrium pressures of the carbonitrides to be determined, and also their standard free enthalpies of formation and compositions to be evaluated. It was established, in particular, that the “dicaibide” and the “monocarbonitride” in equilibrium on the monovariant “plateau” are hypostoichiometric and hyperstoichiometric, respectively; the stability of these compounds is enhanced by their large nitrogen contents, which increase with the temperature. It was also shown that above 1410°C, a temperature rise leads to a substantial drop in the nitrogen content of the virtually stoichiometric monocarbonitride which is in equilibrium with graphite under Torr. Between 800°C and 1410°C and Torr, an excess of carbon coexists with α “U₂N₃” and β “U₂N₃”, and the lattice parameters of these phases were likewise determined.