Thermodynamic assessment of the PdRhRu system using calphad and first-principles methods
Introduction
Uranium oxide is the most common fuel of Light Water Reactors (LWR). During burnup, many fission products form and among them Pd, Rh and Ru are very abundant. According to Guillaumont [1], the fission yields of these fission products (in grams per ton of fissile uranium) are about 1245 g of Pd, 487 g of Rh and 2157 g of Ru for an UOX1 spent fuel 3.5% enriched in 235U with a burnup of 33GWj t−1. In this framework, numerous studies were undertaken to point out the chemical interactions between platinoids and fuel materials [2], [3], [4] or under waste disposal conditions [5], [6].
During reactor operation, the evolution of these platinoid based phases is of major importance. Pd, Rh and Ru fission products exhibit no solubility in the fluorite structure of the oxide fuel [2], [3]. They mainly form metallic precipitates revealed by post irradiation examination of the fuels. These so-called “white inclusions” are constituted of PdRhRu generally alloyed with two other fission products: Mo and Tc [2], [7]. If chalcogen fission products (Se,Te) are present, these PGMs may also form chalcogenide rich solid solutions or intermetallic phases. The white inclusions can be single-phase or two-phase constituted; their compositions depend mainly on burnup, temperature gradient and oxygen potential of the oxide fuel [2].
In the glass matrix of high level nuclear wastes, these fission products partly precipitate either as metal or oxide phases as function of the oxygen potential [6], [8], [9], [10]. Palladium and rhodium preferentially react with chalcogen elements (Se,Te) to form complex intermetallic phases [11], [12], [13], [14], [15] whereas ruthenium forms both metallic Ru or RuO2 particles and/or RuO2 needles [9], [10], [11], [12], [13], [14], [15], [16]. But, in case of the occurrence of rhodium, a mixed solid solution of rhodium and ruthenium dioxide: (Rh,Ru)O2 can precipitate [6], [8], [17]. In order to predict the formation of these different phases, the description of the thermodynamic properties of all the competing phases is needed.
The thermodynamic and phase diagram data of the ternary system PdRhRu were thus reviewed and a description of the stable phases was proposed in the present work. New Differential Thermal Analysis (DTA) experiments were performed to provide additional phase diagram data. Furthermore, the mixing enthalpies of the FCC and HCP solid solutions were calculated using the Special Quasirandom Structures (SQS) methodology coupled with Density Functional Theory (DFT) calculations to compensate the lack of experimental thermodynamic data for most of the systems under consideration. Using the Calphad method, all these results were used to describe thermodynamically the binary systems PdRh, PdRu and RhRu as well as the ternary system PdRhRu.
Section snippets
Bibliography
As far as the authors know, no intermetallics form in any of the three binary systems. The solid phases are the solid solutions based on Ru (HCP) and Pd and Rh (FCC). To make the paper clearer these ternary extension of the solutions (Pd,Rh,Ru)-FCC and (Pd,Rh,Ru)-HCP solid solutions are merely noted FCC and HCP.
The three binary systems have been already reviewed by Tripathi et al. [18], [19], [20] and by Okamoto [21], [22], [23]. All these binary systems were thermodynamically assessed by
DFT and SQS methodologies
The SQS methodology [48] has been coupled with DFT calculations [49] in order to estimate the mixing enthalpy of binary and ternary solid solutions. The solid solutions have been treated by the SQS method: i.e. a random-like distribution of atoms into a given lattice is considered at a given composition and with a finite number of total atoms in a cell.
All SQS structures have been calculated in the frame of the DFT within a pseudo-potential approach using the VASP package within projector
DTA experiments
Differential Thermal Analysis (DTA) analyses were performed using a Setaram Setsys device calibrated using the melting point of pure gold, nickel and palladium. From this calibration, the temperature uncertainty is estimated to be ±3 K.
Due to temperature limitations, these DTA experiments were performed only in the Pd rich domain of the PdRh system. Several heating and cooling ramps were performed at: 20 K/min, 10 K/min, 5 K/min and 3 K/min. In all cases, the samples were produced in situ by
Conclusion
A thermodynamic assessment of the PdRhRu system was performed to better predict and understand the formation of the metallic fission product precipitates observed in post-irradiation examinations in oxide fuels. A literature review was carried out on the PdRh, PdRu and RhRu binary systems and on the PdRhRu ternary system.
As experimental thermodynamic data are scarce on these systems, DFT-SQS calculations were performed to determine binary mixing enthalpy data for the FCC and HCP phases and
Acknowledgments
DFT calculations were performed using HPC resources from GENCI-CINES (Grant 2015-096175).
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