Experimental investigations and thermodynamic modelling of the Cr–Nb–Sn–Zr system
Summary (2 min read)
1. Introduction
- Zirconium alloys are mainly used as fuel cladding and structural materials in Light Water Reactors (LWR) because of their very low thermal neutron absorption coefficient, their excellent mechanical properties and corrosion resistance and the relative stability of their properties under irradiation [1,2].
- This paper presents the Calphad modelling of the Cr–Nb–Sn–Zr quaternary system.
- This isothermal section exhibits a ternary C14 phase on the Sn-poor region.
- In addition to the new experimental determination, the authors provide new DFT calculations of the formation enthalpies of all the quaternary end-members of the C14, C15 and C36 phases; of all the end-members of the A15 phase in the Nb-Sn-Zr system; and of η and ZrSn2 in the SnZr system.
- Nevertheless, their authors have rejected some measurements of the monotectoid reaction which appear to be reliable due to a lower oxygen contamination of the samples.
2. Literature survey
- The value calculated by Baykov et al. [6] strongly disagrees with the measurements of Meschel et al. [5].
- 4.3 Thermodynamic assessment The Cr–Nb–Zr system was recently modelled by Lu et al. [11].
3.1 Experimental details
- The samples were prepared from high purity metals (Cr from Alfa Aesar (99.99%), Sn from Alfa Aesar (99.8%) and Zr “Van Arkel” (55ppm of oxygen) from LTMEX-CEA) by arc melting under argon atmosphere.
- The alloys were melted five times and turned upside down between each melting.
- The diffractograms were measured on a Bruker D8-Advance equipped with a graphite monochromator in the diffracted beam working with the Cu Kα radiation (Bragg-Brentano geometry, 2 range: 10-120°, step: 0.04°, time per step: 20s).
- They were analyzed by the Rietveld method to characterize the different present phases (Fullprof program).
- The details of samples composition and heat treatment are given in Table 6.
3.2 DFT calculations
- The total energies of all the C14, C15, C36, A15, η and ZrSn2 structures have been calculated within the framework of the DFT.
- The C15 phase is modelled with two-sublattice (SL) yielding the generation of 4²=16 end-members.
- DFT calculations were done by using the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) [54] functional and with projector augmented wave (PAW) pseudo-potentials (PP).
- The formation enthalpy is obtained by subtracting the total energy of the structure calculated by DFT to the molar fraction weighted sum of the energies of the pure elements in their Stable Element Reference (SER, ground-state structures for Cr, Nb, Zr and Sn for Sn).
- This method consists in generating a series of "special" configurations that reproduces the random disorder of a solid solution at a given composition with a limited number of atoms per unit cell.
4. Results and discussion
- 1 The Cr–Zr binary system 4.1.1 DFT results Fig. 1 shows the 0 K calculated formation enthalpies of the end-members of the C14, C15 and C36 Laves phase as a function of the mole fraction of zirconium, compared to data from literature.
- In addition, no entropic term was used for the metastable endmembers.
- The formation enthalpies of the A15 and η phases as well as the binary interaction parameters of the A2 and A3 solid solutions were fixed to the values computed by DFT.
- All the parameters the authors used and optimized are summarized in Table 5.
- The authors thermodynamic modelling of the Nb–Sn–Zr system presents a reasonable agreement with the measurements of Ivanov et al. [48] and Korotkova [50] as shown in Fig. 11 and 12.
5. Conclusions
- The thermodynamic modelling of the Cr–Nb–Sn–Zr quaternary system has been performed using the Calphad approach according to their new experimental and calculated data.
- Note that the thermodynamic modelling of the Cr–Nb–Sn system was presented in a previous paper [3] and the assessment of the Cr-Sn has since been slightly modified.
- EDF and AREVA are acknowledged for their financial support.
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Cites methods or result from "Experimental investigations and the..."
...Contrary to expectations [19][20][21][28], the presence of Laves (intermetallic) phases Zr(Fe, Cr)2 (C14-hcp or C15-bcc) in Zircaloy-4 and Zr(Nb, Fe)2 in M5 is not clearly highlighted on diffraction patterns....
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...They are then compared with the thermodynamic predictions at equilibrium obtained using Thermo-Calc and the Zircobase database [20][21]....
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References
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Frequently Asked Questions (2)
Q2. What have the authors stated for future works in "Experimental investigations and thermodynamic modelling of the cr-nb-sn-zr system" ?
This is particularly important for extrapolation into higher order systems since it does not extend in any of the binary systems. No quaternary parameter is needed and the quaternary database can be constructed by a combination of the systems the authors have presented.