Thermodynamic assessments of the U–Nb–Mo and U–Nb–Cr ternary systems
Introduction
Nuclear energy has attracted more and more attentions owing to its low greenhouse gas emissions [1]. It has been widely considered that U-based nuclear fuels are good candidates for next-generation reactors due to their high thermal conductivity and high melting points [1,2]. The investigations of U-based nuclear fuels focus not only on the uranium ceramics, but also on the U-based metallic alloys [[3], [4], [5]]. Extensive studies of the U-X binary systems have been carried out for developing new nuclear materials which could have low-enriched uranium to achieve the decrease of proliferation risks [6,7]. U–Mo alloy is a promising alternative alloy due to the large solubility of Mo in (γU) phase, which has good irradiation properties for reactor fuel [[7], [8], [9], [10], [11]]. Moreover, it has been proved that Cr can stabilize the (βU) phase to a large extent and can improve the creep resistance of U [12]. Besides, U–Cr alloy performs better strength properties than pure U [12]. In the U–Nb binary system, (γU) and Nb can dissolve with each other and form a miscibility gap region (γU)+Nb [13,14]. Nb atom is a good stabilizer for (γU) phase and U–Nb alloy also has excellent irradiation properties [13,14]. However, the stable bcc phase regions of U–Cr, U–Nb and U–Mo binary alloy are small and not applicable for the development of high-performance nuclear fuels.
The knowledge of thermodynamic properties and phase diagrams is a vital prerequisite for the development of nuclear fuels [15,16]. The calculated sub-binary phase diagrams [[17], [18], [19], [20], [21], [22], [23]] and experimental phase diagrams of the U–Nb–Mo [[24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36]] and U–Nb–Cr [37] system have been reported [[17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37]]. Several discrepancies in the ternary diagram of the location and extent of phase regions have been assessed when compared with the binary diagrams [[24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37]]. Although these two systems have some information of experimental data, their thermodynamic calculation is very limited and thermodynamic optimization has not been completed. In particular, the thermodynamic properties of these two ternary systems have not been reported.
A thermodynamic modeling using the CALPHAD (Calculation of Phase Diagrams) can obtain the phase equilibria in the region where experimental information is unavailable or uncertain. The CALPHAD method is a powerful tool to evaluate phase diagrams and calculate thermodynamic properties based on the existing experimental data [16], which is essential for the design of metallic U-based nuclear fuels. Considering that there is no thermodynamic descriptions for the U–Nb–Mo and U–Nb–Cr system, the aims of the present work are to, 1) assess reliable thermodynamic parameters for the U–Nb–Mo and U–Nb–Cr ternary systems based on available experimental data up to now. 2) present calculated phase diagrams in this paper, such as isothermal and vertical sections, liquidus projection and reaction scheme, over an extensive composition and temperature range.
Section snippets
Evaluation of previous works
To facilitate reading, a summary of the crystal information of all phases in the U–Nb–Mo and U–Nb–Cr ternary system is listed in Table 1.
Thermodynamic model and optimization procedure
Different thermodynamic models are used to evaluate the solution phases and intermetallic compounds in the U–Nb–Mo and U–Nb–Cr ternary systems.
Optimized results and discussion
The thermodynamic parameters of each phase were optimized by using PARROT [42] module in the Thermo-calc software pakeage, the experimental data were used as input to the program. Each piece of selected experimental data was given a certain weight by the importance of data and the weight can be changed until most of the selected experimental information is reproduced within an acceptable deviation. A complete set of optimized thermodynamic parameters describing the Gibbs free energy of each
Conclusions
In the present work, a thermodynamic assessment is conducted on the U–Nb–Mo and U–Nb–Cr system based on critically experimental data available in the literature. Two sets of self-consistent thermodynamic parameters have been obtained. Phase diagrams over a vast temperature and composition range, including isothermal sections, vertical sections and liquidus projection are calculated in the U–Nb–Mo and U–Nb–Cr systems. The reliable experimental data are well accounted for by the present modeling
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The authors would like to thank the financial support for this research by National Key Research and Development Program of China (2017YFB0702401), Natural Science Foundation of Fujian Province of China (2019J01033) and the Fundamental Research Funds for the Central Universities (20720170038).
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