Liquid UO2 Research Articles

Thermophysical properties of liquid UO2, ZrO2 and corium by molecular dynamics and predictive models

Predicting the fate of accident-melted nuclear fuel-cladding requires the understanding of the thermophysical properties which are lacking or have large scatter due to high-temperature experimental challenges. Using equilibrium classical molecular dynamics (MD), we predict the properties of melted UO2 and ZrO2 and compare them with the available experimental data and the predictive models. The existing interatomic potential models have been developed mainly for the polymorphic solid phases of these oxides, so they cannot be used to predict all the properties accurately. We compare and decipher the distinctions of those MD predictions using the specific property-related autocorrelation decays. The predicted properties are density, specific heat, heat of fusion, compressibility, viscosity, surface tension, and the molecular and electronic thermal conductivities. After the comparisons, we provide readily usable temperature-dependent correlations (including UO2-ZrO2 compounds, i.e. corium melt).

The structure of liquid UO2−x in reducing gas atmospheres

High energy X-ray diffraction experiments performed on hypostoichiometric UO2−x liquids in reducing gas mixtures of 95%Ar:5%CO and 95%Ar:5%H2 are compared to that conducted in a pure Ar atmosphere [Skinner et al., Science 346, 984 (2014)]. The measurements are pertinent to severe accident scenarios at nuclear reactors, where core melts can encounter reducing conditions and further shed light on the oxide chemistry of the low valence states of uranium, particularly U(III), which become stable only at very high temperatures and low oxygen potentials. The radioactive samples were melted by floating small spheres of material using an aerodynamic levitator and heating with a laser beam. In the more reducing environments, a 1.7% shift to lower Q-values is observed in the position of the principal peak of the measured X-ray structure factors, compared to the more oxidizing Ar environment. This corresponds to an equivalent elongation in the U-U nearest neighbor distances and the U-U periodicity. The U-O peak (modal) bond-length, as measured from the real-space total correlation functions, is also observed to expand by 0.9–1.6% under reducing conditions, consistent with the presence of 15–27% U3+ cations, assuming constant U-O coordination number. The slightly larger U-U elongation, as compared to the U-O elongation, is interpreted as a slight increase in U-O-U bond angles. Difficulties concerning the determination of the hypostoichiometry, x, are discussed, along with the future directions for related research.

Topological ordering in liquid UO2

A molecular dynamics model of liquid UO2 that is in good agreement with recent high-energy x-ray diffraction data has been analyzed using the Bhatia–Thornton formalism. A pre-peak appears in the topological structure factor SNN(Q) at Q = 1.85(1)Å−1 which is not present in the more common, element specific Faber–Ziman partial structure factors. A radical Voronoi tessellation of the 3D molecular dynamics model shows the presence of a wide distribution of clusters, consistent with presence of highly mobile oxygen atoms. However, 4-fold Voronoi polyhedra (n4) are found to dominate the structure and the majority of clusters can be described by the distribution n3 ⩽ n4 ⩾ n5. It is argued that an open network of 4-fold Voronoi polyhedra could explain the origin of the pre-peak in SNN(Q) and the topological ordering observed in liquid UO2.

Molecular dynamics simulation of premelting and melting phase transitions in stoichiometric uranium dioxide

Results of molecular dynamics (MD) simulation of UO2 in a wide temperature range are presented and discussed. A new approach to the calibration of a partly ionic Busing-Ida-type model is proposed. A potential parameter set is obtained reproducing the experimental density of solid UO2 in a wide range of temperatures. A conventional simulation of the high-temperature stoichiometric UO2 on large MD cells, based on a novel fast method of computation of Coulomb forces, reveals characteristic features of a premelting lambda transition at a temperature near to that experimentally observed (T(lambda)=2670 K). A strong deviation from the Arrhenius behavior of the oxygen self-diffusion coefficient was found in the vicinity of the transition point. Predictions for liquid UO2, based on the same potential parameter set, are in good agreement with existing experimental data and theoretical calculations.

Experimental determination of the thermal conductivity of liquid UO2 near the melting point

The article gives an account of measurements of the thermal conductivity of liquid UO2. The sample was heated up to above the melting point by a laser pulse of a controlled shape, and the produced thermogram of temperature history was measured by a fast and accurate pyrometer with a time resolution of 10 μs. The experiment shows that the rate of temperature increase during the ascending part of the pulse changes moderately across the melting point. Due to the high power input, this effect cannot be explained in terms of the sole intake of latent heat of fusion. By solving the related heat transfer equation with a 2D-axisymmetric numerical model, it is demonstrated that this feature depends principally on heat conduction in the sample, and proves that the thermal conductivities of solid and liquid are not very different. A theoretical sensitivity study assessing the influence of the liquid thermal conductivity on the pulse temperature evolution showed that the conductivity of the liquid can be deduced from the fitting of the thermograms with a numerical precision of the order of 1%. The analysis reveals that the thermal conductivity is weakly correlated with the effective heat losses during the pulse and to the melting enthalpy, so that the uncertainty in its evaluation by fitting the experimental thermograms with model predictions is satisfactory. The value of the thermal conductivity of liquid UO2 near the melting point resulted to be 2.6±0.35 W m−1 K−1, where the magnitude of the uncertainty is much lower than the scatter of the previously published, discordant measurements.

Equation of State of UO2

An international project supported by INTAS (International Association for Promotion of Cooperation with Scientists from the New Independent States of the former Soviet Union) was started in 1994 with the intent of constructing an equation of state (EOS) for liquid and gaseous UO2, which fully reproduces the comprehensive thermodynamic database for this compound. The new equation of state was devised for applications encompassing hypo- and hyper-stoichiometric compositions. A so-called “chemical model” was used for the theoretical description of liquid urania. This model is based on the thermodynamic perturbation theory (TPT) modified in order to account for the specific properties of the system investigated. It describes, in a unified formalism, a multicomponent mixture of chemically reactive, strongly interacting neutral and charged molecules and atoms. Comparisons of the predicted equilibrium vapor pressures with literature data provided an initial validation of the model up to temperatures of the order of 5500 K. A further, positive result is the fairly good agreement of the predicted heat capacity with experimental values, which extend up to 8000 K. A characteristic feature of non-congruentvaporization in UO2±x is the production of a very high maximum vapor pressure (P max∼1 GPa) as well as a substantial oxygen enrichment of the vapor phase over boiling UO2 ((O/U)max∼7). The critical point of a truly non-congruent phase transition in UO2 was also calculated. This point essentially differs from that defined for a gas–liquid phase transition in simple liquids; in particular, the equation (∂P/∂V) c ∼(P/V)≠0 applies here. The predicted critical parameters are: T c≈10120 K, P c≈965 MPa, ρ c≈2.61 g·cm−3.

Laser-pulse vaporization of uranium dioxide and other refractory materials

The nature of the vapor produced by pulse surface heating of UO2 and several other materials was investigated using normal-mode laser pulses with peak power densities between 104 and 106 W/cm2. Maximum surface temperatures measured by optical pyrometry ranged from 1900 to 4200 K. At temperatures below ∼2400 K for UO2, the vapor pulse followed the Hertz–Langmiur vacuum vaporization theory. More energetic transients produced gasdynamic blowoffs accompanied by significant supersaturation in the expanding plume. Neutron activation analysis of the collected vapor indicated that the total quantity of liquid UO2 evaporated in the pulse followed the Hertz–Langmuir formula. However, mass spectrometric analysis of the emitted vapor showed large deviations in the quantity and waveform shape of the monomer species. These and other features of the blowoff were satisfactorily explained in terms of nucleation and growth of polymeric species. Although UO2 clusters were undetectable by the mass spectrometer, polymers of MgO and ZrO2 were observed.

Vapor Pressure Determination of Liquid UO2 Using a Boiling Point Technique

By analogy with the classic boiling point method, a quasi-stationary millisecond laser-heating technique was applied to measure the saturated vapor pressure curve of liquid UO2 in the temperature r...

Equation of state of uranium oxide

The experimental and theoretical efforts on the equation of state of UO2 are reviewed. An overview of the transient-type dynamic pulse heating techniques, using laser, electron and neutron pulse heating is given. Two complementary approaches for the calculation of the oxygen potential, described as the macroscopic ‘mixture’ model and the microscopic ‘defect’ model, lead to good agreement in their calculated pressures up to 5000 K. A combination of mass-spectrometric, Langmuir probe and high-voltage diode studies resolved previous discrepancies and revealed consistency between thermodynamic extrapolations and direct measurements. For the total equilibrium pressure over liquid UO2 log (p/MPa)=–2.717 – 201 31/T+ 1.925 log T, is recommended for the temperature range from the melting point at 3130 K up to 5000 K. The model predictions of the critical point data of UO2 are summarised.

Chemical Interactions Between UO2 and Zircaloy-4 from 1000 to 2000°C

The chemical interaction between solid and liquid Zircaloy-4 and solid UO2 was examined in the temperature region 1000 to 2000°C in argon. The solid/solid reaction experiments were performed with s...

Pressure generation due to a temperature discontinuity at a liquid-liquid plane interface

Using a simplified equation of state, an analytic solution for the temperature, pressure, velocity, and acceleration of two semi-infinite liquids initially at two distinct temperatures is obtained by ignoring the effects of the generated pressure on the temperature distribution. It is found that the pressure wave generated in the cooler medium by the temperature discontinuity develops into a shock after passing through the thermal boundary layer. The cooler material is initially accelerated into the hotter material and thus if the cooler material is lighter, the interface is Raleigh–Taylor unstable. The pressures and velocities at the interface relax with a characteristic time τ=α/c2, where α is the thermal diffusivity and c is the speed of sound. For the particular case of liquid Na in contact with liquid UO2 specific results are given. The linearized approximation is compared with exact numerical integration of the full hydrodynamic equations and reasonable agreement is found.

Partial structure factors of an ionic model of liquid UO2

Because of its interest for nuclear technology, we have studied the partial structure factors of liquid UO2 just above its melting-point. An ionic model has been adopted, and the detailed interactions have been approximated by replacing the ions by oppositely charged hard spheres. This model has then been solved in the mean-spherical approximation, using the procedure developed earlier for arbitrary diameter ratio by Abramo et al. The structure factors and the corresponding radial distribution functions obtained reveal the presence of considerable short-range order and most of the features we obtain are reflected in characteristic distances of crystalline UO2.

Structural differences between lonic and molecular fluid models of liquid UO2

Abstract Though present evidence favours an ionic model of liquid UO2, it seems of interest to compare and contrast structural predictions of such a model with those of a molecular fluid model. Therefore, in this paper, we present partial structure factors on the basis of the reference interaction site model for liquid UO2 just above its melting temperature. In this treatment, the “molecules” consist of rigid (linear) clusters of hard spheres. In the absence of experimental information on the structure of liquid UO2, comparison is made with the earlier work of Bhuiyan et al, for the mean spherical approximation (MSA) to the ionic model. Considerable resemblance with the MSA results appropriate to zero coupling constant is found.

Vapour Pressure Studies Over Liquid Uranium Oxide and Uranium Plutonium Oxide Up to 5000 K

AbstractThe estimation of the energy release in a hypothetical fast breeder reactor core meltdown accident requires a detailed analysis of the disassembly process. Since the vapour pressure presents the ultimate shut‐down mechanism, the required data are given by the equation of state of the irradiated fuel.The pressure over the ternary uranium‐plutonium oxide was determined to log p(atm) = 7.966 – 28,137/T, yielding a heat of evaporation of ΔHevap = 128.7 kcal/mol, fully consistent with the heat of sublimation of ΔHsub = 148.4 kcal/mol below the melting point, and the heat of fusion of 19.4 kcal/mol. The corresponding equation for liquid UO2 was determined as log p(atm) = 7.7 – 27,900/T, with a heat of evaporation of ΔHevap = 127.6 kcal/mol, again in consistency with the assessed data below the melting point of ΔHsub= 144.1 kcal/mol, and the heat of fusion of 17.7 kcal/mol. For this a new high‐energy laser technique, including fast temperature recording in the microsecond range, was developed. The first quantitative measurements on (U, Pu)O2 above 4000 K were reported to the IAEA Symposium on Thermodynamics of Nuclear Materials in Vienna.The investigation of the total temperature range from 3000 K to Te = 7560 K revealed two principle experimental difficulties, a liquid layer movement at temperatures below 4000 K, and optical absorption due to increasing thermal ionisation above 5000 K. A new double intensity laser pulse technique is presented, which allows the extension of measurements to below 4000 K. In addition a multi‐wavelength pyrometer technique has been developed to eliminate, and at a later stage to determine, spectral emissivities above the melting point, during laser heating within pulse times of micro and nanoseconds.

On the Mechanism of Uranium Dioxide-Sodium Explosive Interactions

A mechanism believed responsible for the explosive vapor growth observed in Armstrong’s experiment with LMFBR materials (liquid sodium injected into molten UO2) is discussed. Basically, liquid sodium globules can be entrained and wet the liquid UO2 surfaces. The lack of nucleation sites in the liquid-liquid-like system results in the overheating of the liquid sodium until homogeneous nucleation occurs. When the superheat limit is reached, vaporization is rapid enough to produce shock waves.The validity of the proposed entrainment-wetting-superheat mechanism to explain the observed UO2-Na explosions has been demonstrated by above surface injection of liquid Freon-11 (normal boiling point 23.8°C) into hot water (70 to 90°C). This liquid-liquid system is believed to simulate Armstrong’s UO2-Na system, since in the latter, the transition from film boiling to nucleate boiling based upon Henry’s film boiling correlation will take place at a temperature well above the melting temperature of UO2.Based upon this mechanism, large-scale coherent UO2-Na vapor explosions would appear impossible in a reactor environment. In a real reactor system, fission gases and fragments, as well as solid materials and gas bubbles entrained in the liquid sodium, would be present and would promote boiling prior to reaching the threshold for homogeneous nucleation in sodium, therefore resulting in mild interactions of the type observed in the TREAT in-pile experiments.