L. Leibowitz

Thermodynamics of the uranium-zirconium system

Abstract Renewed interest in metallic fuel for nuclear reactors has prompted new studies of the thermodynamics and phase equilibria in binary alloys containing uranium, plutonium, and zirconium so that the ternary phase diagram might be calculated. An analysis of the uranium-zirconium alloy system has been performed. Thermodynamic functions for all existing uranium-zirconium phases have been derived and a phase diagram was calculated. These results are compared with the available thermodynamic data and accepted phase diagrams and general agreement was found. Disagreements generally occurred where experimental data were sparse and when previously drawn phase boundaries were found to be inconsistent with theory.

Solidus and liquidus temperatures in the uranium-plutonium-zirconium system☆

Abstract Renewed interest in metallic fuel for nuclear reactions has prompted study of the solidus and liquidus for the uranium- plutonium-zirconium system. These temperatures are of importance in assessing the possibility of fuel melting during abnormal reactor conditions. Data obtained in previous work in this area were found to be inadequate for the needs of the current reactor development effort. A dual effort was undertaken to provide the needed data: (1) thermodynamic phase diagram analysis and calculation of the ternary solidus and liquidus surfaces and (2) experimental determination of solidus and liquidus temper- atures for selected alloys. The methods used and results obtained are described.

Thermal conductivity of zirconium

Abstract A correlation for the thermal conductivity of zirconium as a function of temperature has been developed from a statistical analysis of zirconium thermal conductivity and thermal diffusivity measurements from 1951 to present. The recommended equation for the thermal conductivity of zirconium in W m−1 K−1 from 298 through 2000 K is: k = 8.8527 + 7.0820 x 10 −3 T+ 2.5329 X 10 −6 T 2 + 2.9918 x 10 3 T −1 . One standard deviation uncertainties of this fit to the data range from 5 to 9.5%, depending on temperature.

Vapor pressures and vapor compositions in equilibrium with hypostoichiometric uranium dioxide at high temperatures

Abstract Thermodynamic functions of the gaseous species, thermodynamic functions of the condensed phase, and an oxygen-potential model have been combined to calculate the vapor pressures and vapor compositions in equilibrium with condensed-phase UO 2-x for 1500⩽T⩽6000 K and 0⩽ x ⩽0.5 . A method for extending the oxygen-potential model of Blackburn to the liquid region has been derived and evaluated. Results of these calculations show that the oxygen-to-uranium ratio of the vapor is larger than that of the condensed phase with which it is in equilibrium for most of the ranges of T and x of interest. Near 6000 K the vapor is very oxygen-rich so that the composition of the condensed phase would be changed considerably by even a few percent vaporization. In general, the vapor in equilibrium with UO 2-x is poorly approximated at UO2(g); the species U, UO, UO3, O2, and O each have higher partial pressures than UO2 for some conditions. The calculated total pressures at high temperatures are in good agreement with those recommended by the International Working Group on Fast Reactors (IWGFR).

Thermodynamic analysis of phase equilibria in the iron—zirconium system

Continuing interest in development of metallic fuels for nuclear reactors has prompted an examination of the phase relations of many of the relevant binary and ternary systems of interest. We performed a thermodynamic analysis and optimization of the Fe-Zr system. Overall reasonably good agreement was found with published diagrams, but some significant changes were required to ensure thermodynamic consistency.

Enthalpies of thoria-urania from 2300 to 3400 K

Abstract The enthalpies of some thoria-urania solid solutions — (Th0.70U0.30)O2, (Th0.85U0.15)O2, and (Th0.92U0.08)O2 — were measured from 2300 to 3400 K, using an induction-heated drop-calorimeter system. The enthalpy measurements from this work were compared with other reported lower-temperature data, analyzed, and fitted to equations. Discontinuities in the slopes of the enthalpy-temperature curves were found for the various thoria-urania solid solutions at temperatures, Tr, equal to about 0.8 of the melting temperature. This behavior is consistent with that observed for both ThO2 and UO2. Heat capacities below the transition temperature, Tr, derived from the enthalpy equations were as predicted from mole averages calculated from ThO2 and UO2 data.

Thermodynamics and phase equilibria of the iron—uranium system☆

Abstract Interest in metallic fuel for nuclear reactors has prompted studies of the thermodynamics and phase equilibria of several binary and ternary fuel alloys. Of particular interest are systems involving uranium-plutonium-zirconium alloy fuel and components of the stainless steel cladding. An experimental study and phase diagram calculation of the iron-uranium alloy system were performed. Thermodynamic functions for the existing phases were derived and a phase diagram was calculated that agrees reasonably with published diagrams.

Thermodynamic modeling of the phase equilibria of the plutonium-uranium system

Abstract Interest in metallic fuel for nuclear reactors has prompted studies of the thermodynamics and phase equilibria of binary alloys containing uranium, plutonium, and zirconium. An analysis and phase diagram calculation of the plutonium-uranium alloy system were performed. Thermodynamic functions for all existing phases were derived and a phase diagram was calculated. The results generally agreed with the accepted phase diagram. Regions of disagreement are discussed.

High temperature physical properties of fast reactor materials

Abstract Physical properties of materials of interest in fast reactor safety are presented. These include enthalpy and heat capacity, vapor pressure, density, surface tension, speed of sound, viscosity, and thermal conductivity. The emphasis is on saturated fuel materials and coolant. Much of the data is the result of direct experimental measurement while the remainder was obtained by extrapolative techniques from data at lower temperatures.

Analytical expressions for enthalpy and heat capacity for uranium-- plutonium oxide

Abstract Enthalpy data which have been reported for UO 2 -(20–25)wt% PuO 2 in the range from room temperature to ≈ 3000K were fitted through non-linear regression analysis to an Einstein function modified with a defect formation energy term. An expression for heat capacity was derived by differentiating the enthalpy function with respect to temperature. The fitted parameters in the modified Einstein functions are compared with theoretical values calculated for the UO 2 -PuO 2 lattice. Polynomial temperature functions were determined using the smoothed values for enthalpy and heat capacity given by the Einstein functions, thus providing simpler alternate expressions for these two properties.