Bredig Transition Research Articles

Thermodynamic and thermoelastic properties of hypostoichiometric MOX fuels with molecular dynamics simulations

Employing the Cooper-Rushton-Grimes (CRG) interatomic empirical potential with new parameters for U3+ interactions in U1-y,PuyO2-x, classical Molecular Dynamics simulations were carried out for the first time to compute the enthalpy, the lattice parameter, the elastic constants and derived properties of hypostoichiometric U1-y,PuyO2-x compounds (with y in the range 0-1, x between 1.92-2.0, and from 1000 K to melting points). As hypostoichiometry results from adding oxygen vacancies to U1-y,PuyO2, this study investigates how oxygen vacancies affect the thermodynamic and thermomechanical properties of MOX compounds. The most pronounced effect appears at high temperatures, where the so-called Bredig transition occurs. We observed that the effects of this transition on the properties are softened by the presence of oxygen vacancies. The analytical law of the heat capacity for stoichiometric mixed-oxide fuels U1-y,PuyO2 developed by Bathellier et al. [9] was modified by introducing the deviation from stoichiometry as a variable. It was fitted on Molecular Dynamics data of heat capacity and linear thermal expansion coefficient and a good agreement was found. To model the thermal evolution of mechanical properties up to the melting point, a new law was developed. The laws may be used in Fuel Performance Codes.

A science‐based mixed oxide property model for developing advanced oxide nuclear fuels

AbstractHerein, a science‐based uranium and plutonium mixed oxide (MOX) property model is derived for determining the properties of MOX fuel and analyzing their performance as functions of Pu content, minor‐actinide content, oxygen‐to‐metal ratio, and temperature. The property model is constructed by evaluating the effect of phonons and electronic defects on the heat capacity and thermal conductivity of MOX fuels. The effect of phonons was evaluated based on experimental datasets related to lattice parameters, thermal expansion, and sound speeds. Moreover, the effect of electronic defects was determined by analyzing oxygen‐potential data based on defect chemistry. Furthermore, the model evaluated the effect of the Bredig transition on the thermal properties of MOX fuel by analyzing the irradiation test results. The derived property model is applied to the performance code to analyze fast reactor fuel pins.

The Heat Capacity of PuO2 at High Temperature: Molecular Dynamics Calculations

Abstract A new generation of fast breeder reactors (FBRs) is under development with the objective of making nuclear energy more sustainable. Most promising reactor designs are loaded, at least during their early phase of deployment, with UO2–PuO2 mixed oxide fuel (MOX). Concentrations of plutonium dioxide that are foreseen for FBRs range up to 30 mol%. This highlights the need for a sound and deep knowledge of the thermophysical properties of PuO2. This statement is valid in the case of heat capacity, as evaluations on MOX fuel are usually carried out by using the Neumann–Kopp rule. Heat capacity is relevant for thermal conductivity and performance under transient conditions. However, measurements on the heat capacity of plutonium dioxide are scarce or even lacking at high temperature. Numerical methodologies such as molecular dynamics (MD) calculations have been employed to overcome the difficulties encountered in experimental measurements. Besides numerical also theoretical models have been applied as valuable tools for interpretation of enthalpy measurements. Nevertheless, due to the mentioned lack of experimental measurement issues such as the existence of the Bredig transition and the formation of defects at high temperatures are still debated in nuclear fuel research. Excess enthalpy seen in measurements of actinides oxides has been explained by means of either electronic disorder or anion disorder. In the case of plutonium dioxide, a common consensus has been reached on the hypothesis that anion disorder leads to a significant increase in heat capacity at high temperature. Konings and Beneš have developed a model that accounts for this phenomenon. Their correlation has been often included in models of heat capacity and employed for recommendations. However, in the high-temperature region, MD calculations showed an underestimation of model predictions that was not compensated by the presence of a peak of heat capacity that has been interpreted as the Bredig transition. Based on these observations, this paper presents MD evaluations on the heat capacity of PuO2 at high temperature that are mostly focused on the formation energy of oxygen Frenkel pairs (OFPs) and its correlation with the model proposed by Konings and Beneš. Besides an interatomic potential published in the open literature and developed in compliance with the experimental thermal expansion of PuO2, a second interatomic potential has been applied in calculations. This latter is featured by a lower formation energy of OFP. The contribution due to defects formation was calculated by means of a simplified theoretical model of heat capacity. Results of calculations in the very high-temperature domain showed an increase in the contribution due to OFP defects consistent with the model by Konings and Beneš. Predictions suggest the onset of a premelting transition around 85% of melting temperature without the presence of a peak of heat capacity. Major deviations from the recommended model have been noted in the intermediate temperature region where the effect of clustering of defects should play a significant role. Therefore, the value of formation energy of OFP proposed by Konings and Beneš could be interpreted as an effective value that accounts for the two processes (defects clustering and premelting transition) that could contribute, according to our results, to the heat capacity of plutonium dioxide at high temperature. This conclusion is consistent with the numerical evaluations of OFP formation energy that are in general higher than proposed by Konings and Beneš.

A new heat capacity law for UO2, PuO2 and (U,Pu)O2 derived from molecular dynamics simulations and useable in fuel performance codes

In this work, a computationally efficient law of a nuclear fuel property obtained from molecular dynamics calculations is implemented in a fuel performance code, bridging the gap between atomic and pellet scales. The Cooper-Rushton-Grimes potential is employed through molecular dynamics simulations to compute the heat capacity of stoichiometric mixed-oxide fuels U1-yPuyO2 from 1000 K to the melting temperature, and over the whole range of plutonium content from pure UO2 (y=0) to pure PuO2 (y=1). The heat capacity is found to exhibit a peak at the temperature TB = 0.84 Tm, with Tm the melting temperature, for all the compounds with a significant effect of the plutonium content solely at high temperatures (T > 1800 K), i.e. around the peak. This peak is related to the so-called Bredig transition known to occur around 0.8 Tm. An analytical law of heat capacity Cp(T,y) has been established from our molecular dynamics data, and is valid from 700 K to the melting temperature and for the entire range of plutonium content. Concerning UO2, a good agreement is found between our calculations and the most recent experimental measurements. The law we propose in the present study has been implemented in GERMINAL V2, the fuel performance code developed by CEA to predict the in-pile behavior of mixed-oxide fuel in sodium-cooled fast reactors, and tested through the simulations of transient power test operated in the CABRI reactor. The results show that our law yields a lower margin to melting in the case of Reactivity-Initiated Accident, but throughout power ramp transient tests, the results obtained with our new law are very consistent with the reference heat capacity law currently used in GERMINAL.

The high-temperature heat capacity of the (Th,U)O2 and (U,Pu)O2 solid solutions

The enthalpy increment data for the (Th,U)O2 and (U,Pu)O2 solid solutions are reviewed and complemented with new experimental data (400–1773 K) and many-body potential model simulations. The results of the review show that from room temperature up to about 2000 K the enthalpy data are in agreement with the additivity rule (Neumann-Kopp) in the whole composition range. Above 2000 K the effect of Oxygen Frenkel Pair (OFP) formation leads to an excess enthalpy (heat capacity) that is modeled using the enthalpy and entropy of OFP formation from the end-members. A good agreement with existing experimental work is observed, and a reasonable agreement with the results of the many-body potential model, which indicate the presence of the diffuse Bredig (superionic) transition that is not found in the experimental enthalpy increment data.

High-temperature properties of thorium dioxide: A first-principles molecular dynamics study

Thorium has been considered a potential nuclear fuel for decades. To develop evaluation method for high-temperature properties of thorium dioxide as a candidate nuclear fuel, we perform first-principles molecular dynamics. The calculated enthalpy and thermal expansion agree well with the observed data. The Bredig transition temperature also coincides with experiments. Our results indicate that this method can provide reliable data of thermal properties of nuclear fuels.

Modeling Superionic Behavior of Plutonium Dioxide

AbstractThe Bredig transition to the superionic phase indicated with the $$\lambda $$-peak in $${C_p}$$ was highly expected for plutonium dioxide ($${\rm{Pu}}{{\rm{O}}_2}$$) as other actinide dioxides. However, least-square fit and local smoothing techniques applied to the experimental enthalpy data of PuO2 in 1980s could not detect a $$\lambda $$-peak in specific heat that might be due to too scattered and insufficient experimental data. Therefore, this issue has not been yet put beyond the doubts. In the current article, a superionic model of $${\rm{Pu}}{{\rm{O}}_2}$$ is developed with partially ionic model of a rigid ion potential. Thermophysical properties were calculated in constant pressure–temperature ensemble using molecular dynamics simulation. The Bredig transition with vicinity of a $$\lambda $$-peak in specific heat was successfully observed for the model system at about 2,100 K. Moreover, the experimental enthalpy change was well reproduced before and after the estimated transition temperature.

Structure and Thermal Expansion of YSZ and La2Zr2O7 Above 1500°C from Neutron Diffraction on Levitated Samples

High‐temperature time‐of‐flight neutron diffraction experiments were performed on cubic yttria‐stabilized zirconia (YSZ, 10 mol% YO1.5) and lanthanum zirconate (LZ) prepared by laser melting. Three spheroids of each composition were aerodynamically levitated and rotated in argon flow and heated with a CO2 laser. Unit cell, positional and atomic displacement parameters were obtained by Rietveld analysis. Below ~1650°C the mean thermal expansion coefficient (TEC) for YSZ is higher than for LZ (13 ± 1 vs. 10.3 ± 0.6) × 10−6/K. From ~1650°C to the onset of melting of LZ at ~2250°C, TEC for YSZ and LZ are similar and within (7 ± 2) × 10−6/K. LZ retains the pyrochlore structure up to the melting temperature with Zr coordination becoming closer to perfectly octahedral. Congruently melting LZ is La deficient. The occurrence of thermal disordering of oxygen sublattice (Bredig transition) in defect fluorite structure was deduced from the rise in YSZ TEC to ~25 × 10−6/K at 2350°C–2550°C with oxygen displacement parameters (Uiso) reaching 0.1 Å2, similar to behavior observed in UO2. Acquisition of powder‐like high‐temperature neutron diffraction data from solid‐levitated samples is feasible and possible improvements are outlined. This methodology should be applicable to a wide range of materials for high‐temperature applications.

Modeling Superionic Behavior of Plutonium Dioxide

The Bredig transition to the superionic phase indicated with the lambda-peak in Cp was highly expected for PuO2 as other actinide dioxides. However, least-square fit and local smoothing techniques applied to the experimental enthalpy data of plutonium dioxide in 80's could not detect a lambda-peak in specific heat that might be due to too scattered and insufficient experimental data. Therefore, this issue has not been yet put beyond the doubts. In the current article, a superionic model of PuO2 is developed with partially ionic model of a rigid ion potential. Thermophysical properties were calculated in constant pressure-temperature ensemble using molecular dynamics simulation. The Bredig transition with vicinity of a lambda-peak in specific heat was a successfully observed for the model system at about 2100K. Moreover, the experimental enthalpy change was well reproduced before and after the estimated transition temperature.

THERMOPHYSICAL PROPERTIES OF URANIUM DIOXIDE: A MOLECULAR DYNAMICS STUDY OF SOLID AND LIQUID PHASES OF STOICHIOMETRIC UO2

Thermodynamic and transport properties of solid and liquid uranium dioxide were studied using classical molecular dynamics simulation, with a newly parametrized interionic model potential. In addition to the static and transport properties which have been previously reported by the authors, this study further confirms that temperature dependence of the calculated thermophysical properties of uranium dioxide are in agreement with the available experimental data at both solid and liquid phases in providing an alternative rigid ion potential to the other model potentials in literature. Although lattice parameter and density have been underestimated, overall results give a fairly good description of the UO 2 system for wide range of temperature (0–4000 K). The transition to the superionic phase, Bredig transition, was successfully observed as a distinct λ-peak in specific heats at about 400 K below the experimental value. The results presented in our previous article and here show that the introduced alternative model potential for uranium dioxide is very promising and we are confident in the success of its use in future studies.

Evaluation of Phonon-level Density of UO2 by Molecular Dynamics Simulation

Molecular dynamics calculation of UO2 in a wide temperature range are presented and discussed. The calculated lattice parameters, mean square displacements, and dynamic property of phonon-level density of the velocity auto-correlation functions for UO2 are provided. The Morelon potential and the Basak potential are employed. It confirms that the calculated lattice parameters using the Basak potential are in nearly perfect agreement with the reported values. The models successfully predict mean square displacement and Bredig transition. Furthermore, the phonon-level density of uranium dioxide are discussed. The intensity of phonon-level density increases with temperature, and the properties of UO2 are characterized by large thermal vibrations rather than extensive disorder.

A classical molecular dynamics study of the correlation between the Bredig transition and thermal conductivity of stoichiometric uranium dioxide

Thermophysical properties of uranium dioxide are investigated by classical molecular dynamics for temperatures from 300 K to 3000 K. An increase of specific heat in the temperature range from 1300 K to 2500 K is noted. Comparison with a theoretical model shows that the origin of this behavior is only due to anharmonicity. Such characteristic features of the Bredig transition as the peak in specific heat and high ionic conductivity are investigated. We show that one more important feature was left unnoticed: the rise in the lattice contribution to thermal conductivity at high temperatures. An explanation is provided for this effect which is specific to superionic conductors. Reasonable agreement with experimental data up to 3000 K is obtained for thermal conductivity, even in the absence of electronic excitations.

MOLECULAR DYNAMICS SIMULATION OF UO2: AN ALTERNATIVE RIGID ION MODEL POTENTIAL

A semi-empirical effective interionic potential model has been parameterized to investigate UO 2 by molecular dynamics simulation technique. The simulations were performed in the constant pressure–temperature ensemble between 300 K–3200 K at 100 K intervals. The pair distribution functions and coordination numbers signal the onset of structural changes at temperatures in accord with the Bredig transition and melting. The oxygen ion diffusion coefficients calculated from the mean square displacements markedly increase the liquid like value at T > 2100 K . The transition to the superionic state and melting are well reproduced within the limitations of a rigid ion potential.

Classical molecular dynamics simulation of uranium monocarbide (UC)

Inter-atomic potential parameters of UC, for a partially ionic potential model, were found out by fitting method using experimental lattice parameter data in an improvised way. The inter-atomic potential used here is essentially a combined potential model that has earlier been used to simulate UO 2 system. The calculated lattice parameters, bulk modulus and coefficient of thermal expansion of UC, using the current potential parameters, are in good agreement with the experimental values. The model also shows that there is no Bredig transition in UC system as contrary to UO 2, where the same potential model was used.

Classical molecular dynamics simulation of UO 2 to predict thermophysical properties

Interatomic potential parameters of UO 2, for a partially ionic potential model, were found out by a fitting method using isothermal compressibility data up to 1600 K. The inter-atomic potential used here is essentially a combined potential model comprising of Bushing–Ida and Morse-type potential to simulate UO 2 system using classical molecular dynamics. It has been shown that the deviation in the estimated lattice parameter from the experimental data as reported in literature is due to the inadequacy of the potential parameter. The calculated deviations in lattice parameter, due to the generation of point defects, with variation of temperature have been discussed. The calculated lattice parameters, thermal expansivity, isothermal compressibility of UO 2, using the current potential parameters are in close agreement with the experimental values. The model also successfully predicts Bredig transition.

Molecular dynamics study of mixed oxide fuel

In order to develop new techniques to calculate the physicochemical properties of MOX fuel, molecular dynamics methods were applied to UO 2, PUO 2, and (U,Pu)O 2. These methods enabled us to obtain the heat capacity and thermal conductivity from basic properties, viz., the lattice parameter, linear thermal expansion coefficient, and compressibility. Results for UO 2 showed both the existence of a Bredig transition and a peak in the heat capacity at high temperature. The lattice parameter, heat capacity, and thermal conductivity of MOX fuel were calculated from basic properties of UO 2 and PuO 2. These results showed that molecular dynamics techniques can be usefully applied to determine physicochemical properties of MOX fuel.

Evaluation of thermal properties of mixed oxide fuel by molecular dynamics

The molar specific heat and the thermal conductivity of PuO 2 and (U, Pu)O 2 solid solution were evaluated by a molecular dynamics (MD) technique. The partially ionic model was used. The calculated molar specific heat of PuO 2 well agreed with the experimental data. The simulation results for the temperature dependence of thermal conductivity of PuO 2, obtained by the Green–Kubo technique, was in good agreement with the experimental data. The Bredig transition did not occur in the MD cell of PuO 2 at high temperature. The variation in the calculated lattice parameter of (U, Pu)O 2 with PuO 2 content closely followed Vegard’s law. The calculated specific heat and thermal conductivity of (U 0.8, Pu 0.2)O 2 were in good agreement with the experimental values. From the change in the thermal conductivity of (U, Pu)O 2 with Pu content, it was found that the simulated Pu ions mutually act as phonon scattering centers. The simulated (U, Pu)O 2 cell showed both the existence of the Bredig transition and a peak in the specific heat in the vicinity of 2350 K, and provided various information on the diffusion coefficients for anions and cations at high temperature.

Evaluation of thermal properties of uranium dioxide by molecular dynamics

The molar specific heat and the thermal conductivity of UO 2 were studied by a molecular dynamics (MD) technique. The partially ionic model was used. It was confirmed that the temperature dependence of the calculated lattice parameters well agreed with the reported values for UO 2. The calculated compressibility agreed with the experimental values up to 1600 K, and markedly increased at T>2000 K similar to the real material. The MD cell reproduced the Bredig transition at high temperature. The calculated molar specific heat of UO 2 at the constant pressure well agreed with the experimental data. At 2200 K, the calculated specific heat revealed a peak which is associated with the onset of superionic conduction. At low temperatures, the calculation without the quantum correction for the kinetic energy provided too high values of the specific heat. The variation of the calculated thermal conductivity with temperature, obtained by the Green–Kubo technique, agreed well with the experimental data.

High-temperature heat capacities of UO 2 and doped UO 2

The heat capacity of UO 2 fuel at high temperatures is one of the most important properties of the fuel materials for the evaluation of its thermal properties, and several investigators have revealed a pronounced increase in the heat capacity at high temperatures above around 1500 K. The heat capacity of gadolinia-doped UO 2 has been recently measured by the present author and collaborators, and the onset of anomalous increase in the heat capacity was observed at temperatures of 700 K and increased up to 1200 K according to doped gadolinium amounts 14.2 to 4.4 at%, respectively. The high temperature enthalpy data of UO 2 and other actinide oxides have been recently reanalyzed by some investigators, and weak peaks in the heat capacity curves have been reported, suggesting the existence of a Bredig transition near the melting temperature. In this paper. a brief review of the high temperature heat capacity of UO 2 is given and the heat capacities of doped UO 2 are compared with that of UO 2 and the origin of the excess heat capacity of UO 2 is discussed.

Specific heat of UO2, ThO2, PuO2and the mixed oxides (ThxU1 –x)O2and (Pu0.2U0.8)O1.97by enthalpy data analysis

A recent reanalysis of enthalpy data for UO2 using a local smoothing technique has revealed a weak sigmoidal structure in the data and a corresponding specific heat peak, indicating the existence of a Bredig transition occurring at ca. 2610 K (ca. 0.84Tm). The same smoother applied to ThO2, PuO2 and the mixed oxides (ThxU1 –x)O2 with x= 0.7, 0.85 and 0.92 and (Pu0.2U0.8)O1.97 reveals a similar structure in the enthalpy data for the oxide (Th0.7U0.3)O2 alone. Although the smoother does not detect enthalpy sigmoids (and thus specific heat peaks) in the data for the other oxides, this does not necessarily imply that Bredig transitions are not occurring; simulation studies show that it could be caused by insufficiently dense data in the vicinity of 0.8 of their absolute melting temperatures.