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Journal ArticleDOI

Experimental investigations and thermodynamic modelling of the Cr–Nb–Sn–Zr system

TL;DR: In this article, the Calphad model of the Cr-Nb-Sn-Zr quaternary system was used to estimate the mixing enthalpies of the A2 and A3 binary solid solutions.
Abstract: This work reports the Calphad modelling of the Cr–Nb–Sn–Zr quaternary system. In a previous paper, the thermodynamic modelling of the Cr–Nb–Sn system was presented. Since no experimental data were available for the Cr–Sn–Zr ternary system, new experimental data are provided, within this study, on the isothermal section at 900 °C. A ternary C14 phase has been identified on the Sn-poor side of the phase diagram. In addition to these experimental data, Density Functional Theory (DFT) calculations are carried out in order to determine formation enthalpies of the stable and metastable compounds. At last, the Special Quasirandom Structures (SQS) method is jointly used with DFT calculations in order to estimate the mixing enthalpies of the A2 and A3 binary solid solutions. Finally, these experimental and calculated data in addition to those from the literature, are used as input data for the Calphad modelling of the Cr–Zr, Nb–Zr and Sn–Zr binary systems and the Cr–Nb–Zr, Cr–Sn–Zr and Nb–Sn–Zr ternary systems. A complete database for the Cr–Nb–Sn–Zr quaternary system is provided.

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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Experimental investigations and thermodynamic
modelling of the Cr-Nb-Sn-Zr system
P. Lafaye, C. Toolon-Masclet, J-C. Crivello, J-M. Joubert
To cite this version:
P. Lafaye, C. Toolon-Masclet, J-C. Crivello, J-M. Joubert. Experimental investigations and
thermodynamic modelling of the Cr-Nb-Sn-Zr system. Calphad, Elsevier, 2018, 64, pp.43-54.
�10.1016/j.calphad.2018.11.002�. �cea-02339676�

1
Experimental investigations and thermodynamic modelling of the CrNbSnZr system
Paul Lafaye
a,b
, Caroline Toffolon-Masclet
a
, Jean-Claude Crivello
b
, Jean-Marc Joubert
b*
a
DEN-Service de Recherches Métallurgiques Appliquées, CEA, Université Paris-Saclay,
F-91191 Gif-sur-Yvette, France
b
Université Paris Est, ICMPE (UMR 7182), CNRS, UPEC, F- 94320 THIAIS France
*
corresponding author
Tel.: +33 1 49 78 13 44; Fax: +33 1 49 78 12 03
E-mail address: joubert@icmpe.cnrs.fr
Abstract
This work reports the Calphad modelling of the CrNbSnZr quaternary system. In a
previous paper, the thermodynamic modelling of the CrNbSn system has been presented.
Since no experimental data were available for the CrSnZr ternary system, new experimental
data are provided, within this study, on the isothermal section at 900 °C. A ternary C14 phase
has been identified on the Sn-poor side of the phase diagram. In addition to these
experimental data, Density Functional Theory (DFT) calculations are carried out in order to
determine formation enthalpies of the stable and metastable phases. At last, the Special
Quasirandom Structures (SQS) method is jointly used with DFT calculations in order to
estimate the mixing enthalpies of the A2 and A3 binary solid solutions. Finally, these
experimental and calculated data in addition to those from the literature, are used as input data
for the Calphad modelling of the CrZr, NbZr and SnZr binary systems and the CrNbZr,
CrSnZr and NbSnZr ternary systems. A complete database for the CrNbSnZr
quaternary system is provided.

2
Keywords: CrNbSnZr; Calphad; DFT; SQS; thermodynamic databases; assessment; phase
equilibrium
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]. In order to improve significantly the behaviour of the
claddings, both in nominal and accidental conditions, it appears useful to have a better control
of the microstructure and phase transformations occurring in these alloys, as a function of
temperature and composition. In this frame, a new thermodynamic database dedicated to
Zirconium alloys is being developed using the Calphad approach, considering the five
following elements Zr, Cr, Fe, Nb, Sn. The novelty of this work relies on the systematic use
of the Density Functional Theory (DFT) calculations for the reassessment of the individual
binary and ternary subsystems.
This paper presents the Calphad modelling of the CrNbSnZr quaternary system. In a
previous paper [3], we have already presented the thermodynamic modelling of the CrNbSn
ternary system based on new experimental and calculated data, reassessing the CrNb, CrSn
and NbSn binary systems. The Calphad modelling of the Cr-Nb-Sn system is taken from this
paper [3], including a new description of the Cr-Sn system. In the present study, a partial
isothermal section of the CrSnZr system was determined at 1173 K. Note that, to our
knowledge, no previous experimental data was available for this ternary system before the
present work. This isothermal section exhibits a ternary C14 phase on the Sn-poor region. In

3
addition to the new experimental determination, we 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 ZrSn
2
in the Sn-
Zr system. DFT calculations on Special Quasirandom Structures (SQS) were performed to
determine the mixing enthalpies of the A2 and A3 binary solid solutions. As it will be
discussed in section 4.3.2, a recent publication dedicated to the Calphad modelling of the Sn
Zr system [4] is available in the literature. Unfortunately, Perez et al. [4] used the formation
enthalpies measured by Meschel et al. [5] that exhibit very large deviations from publications
[68] and from our own DFT calculations. For the NbZr system, a very thorough description
is available in the literature [9]. 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. Moreover, a recent measurement of the monotectoid reaction temperature [10]
shows important gap with the optimized one. At last, a very careful and recent publication
dedicated to the Calphad modelling of the CrZr system [11] is available in the literature.
Unfortunately, Lu et al. [11] used a two-sublattice model for the description of the C14 and
C36 Laves phases that is not compatible with our database.
Thus, the CrZr, NbZr and SnZr binary systems have been reassessed.
The first part of this paper is dedicated to the literature survey of the binary systems; the
second part is dedicated to the methodology of our approach and the third part to our results
and the Calphad modelling of the different sub-systems of the quaternary system.

4
2. Literature survey
2.1 The CrZr binary system
2.1.1 Experimental data
The CrZr system has been studied by many researchers [1124]. This system includes three
intermetallic phases, the C15, C36 and C14 Laves phases, ordered at Cr
2
Zr stoichiometry.
This system presents two eutectic reactions, one eutectoid reaction and two metatectic
reactions.
Domagala et al. [14], Gebhardt et al. [15] and Rumball et al. [18] determined the solubility of
the terminal solid solutions on the Zrrich side. In addition, Domagala et al. [14] and
Svechnikov et al. [19] measured the solidus on the Zr-rich side. The liquidus temperatures
were measured between the two eutectic reactions by Budberg et al. [17] and Petkov et al.
[20]. In addition, Petkov et al. [20], Shen et al. [16] and Nemoshkalenko et al. [21]
determined the homogeneity range of the Laves phases. Petkov et al. [20] measured the
temperatures of the two metatectic reactions. Moreover, these researchers have reported the
existence of the C36 phase. A detailed bibliographic review of this system was carried out by
Arias et al. [22]. More recently, Lu et al. [11] conducted new measurements of the Cr
solubility in the terminal solid solutions on the Zr-rich side and of the homogeneity range of
the C15 phase. In addition, Lu et al. [11] are the first authors to have published measurements
of the Zr solubility in Cr.
2.1.2 Thermodynamic data
Sun et al. [23], Chen et al. [24], Pavlu et al. [12] and Lu et al. [11] have calculated the
formation enthalpies of the end-members of the C15 Laves phase. Lu et al. [11] have also
calculated the formation enthalpies of the end-members of the C14 and C36 Laves phases. In

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Abstract: Generalized gradient approximations (GGA’s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. [S0031-9007(96)01479-2] PACS numbers: 71.15.Mb, 71.45.Gm Kohn-Sham density functional theory [1,2] is widely used for self-consistent-field electronic structure calculations of the ground-state properties of atoms, molecules, and solids. In this theory, only the exchange-correlation energy EXC › EX 1 EC as a functional of the electron spin densities n"srd and n#srd must be approximated. The most popular functionals have a form appropriate for slowly varying densities: the local spin density (LSD) approximation Z d 3 rn e unif

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Frequently Asked Questions (2)
Q1. What are the contributions in "Experimental investigations and thermodynamic modelling of the cr-nb-sn-zr system" ?

This work reports the Calphad modelling of the Cr–Nb–Sn–Zr quaternary system. Since no experimental data were available for the Cr–Sn–Zr ternary system, new experimental data are provided, within this study, on the isothermal section at 900 °C. A complete database for the Cr–Nb–Sn–Zr quaternary system is provided. 

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.