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

doi:10.1016/j.calphad.2018.11.002

Calphad

Volume 64, March 2019, Pages 43-54

https://doi.org/10.1016/j.calphad.2018.11.002 Get rights and content

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.

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. These elements allow the stabilization of Zr(Cr,Fe)₂ precipitates (Zircaloy-4) or β-Nb solid solution (M5^®) which improve the mechanical strength as well as the corrosion resistance of the alloys [3], [4]. 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 Cr–Nb–Sn–Zr quaternary system. In a previous paper [5], we have already presented the thermodynamic modelling of the Cr–Nb–Sn ternary system based on new experimental and calculated data, reassessing the Cr–Nb, Cr–Sn and Nb–Sn binary systems. The Calphad modelling of the Cr–Nb–Sn ternary system and of the Cr–Nb and Nb–Sn binary systems is adopted from Ref. [5] but a new description of the Cr–Sn system is given in the present paper. Moreover, in the present study, a partial isothermal section of the Cr–Sn–Zr system was determined at 1173 K. Note that, to our knowledge, no experimental data had been previously determined for this ternary system before the present work. This isothermal section exhibits a ternary C14 phase on the Sn-poor region. In 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 ZrSn₂ 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 [6] is available in the literature. Unfortunately, Perez et al. [6] used the formation enthalpies measured by Meschel et al. [7] that exhibit very large deviations from publications [8], [9], [10] and from our own DFT calculations. For the Nb–Zr system, a very thorough description is available in the literature [11]. 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 [12] shows important gap with the optimized one. At last, many researchers have performed thermodynamic modelling of the Cr–Zr system [13], [14], [15], [16] but the assessments were obtained without DFT calculations and the resulting formation enthalpies exhibit large deviations from the DFT ones. A very careful and recent publication dedicated to the Calphad modelling of the Cr–Zr system [17] is available in the literature. Unfortunately, Lu et al. [17] used a two-sublattice model for the description of the C14 and C36 Laves phases that is not compatible with our database.

Thus, the Cr–Zr, Nb–Zr and Sn–Zr 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.

Section snippets

Experimental data

The Cr–Zr system has been studied by many researchers [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30]. This system includes three intermetallic phases, the C15, C36 and C14 Laves phases, ordered at Cr₂Zr stoichiometry. This system presents two eutectic reactions, one eutectoid reaction and two metatectic reactions.

Domagala et al. [20], Gebhardt et al. [21] and Rumball et al. [24] determined the solubility of the terminal solid solutions on the Zr–rich side. In

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” (55 ppm 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 weight losses were not significant. The samples were then wrapped in molybdenum sheets (less reactive than Ta with the possible presence of liquid Sn) and placed in a silica tube sealed under argon. After annealing,

Calphad assessment

The thermodynamic assessment of Cr–Sn system published in Ref [5] has been revised to avoid excessively large excess entropic parameters for the liquid and the bcc phases. This could be achieved only by introducing third order non-temperature dependent parameters for this phase. The list of updated parameters can be found in Table 2.

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,

Conclusions

The thermodynamic modelling of the Cr–Nb–Sn–Zr quaternary system has been performed using the Calphad approach according to our new experimental and calculated data and the combination of the assessed ternary sub-systems. Note that the thermodynamic modelling of the Cr–Nb–Sn system was presented in a previous paper [5] and the assessment of the Cr–Sn has since been slightly modified.

The experimental study has been carried out in order to determine several phase equilibria in the isothermal

Acknowledgements

Eric Bouaravong and Didier Hamon are acknowledged for the synthesis and EPMA measurements, respectively. SQS and DFT calculations were performed using HPC resources from GENCI–CINES (Grant 2017-096175 and den0006). The authors wish to thank the GDR CNRS no 3584 TherMatHT for fruitful discussions and collaborative work on the present project. This work was conducted and funded within the framework of the French Tripartite Institute CEA/EDF/Framatome [Projet Gaine].

Data statement

All data generated or analysed during this study are included in this published article

References (65)

P. Lafaye et al.
Thermodynamic modelling of the Cr-Nb-Sn system
Calphad
(2017)
S.V. Meschel et al.
Standard enthalpies of formation of some 3d, 4d and 5d transition-metal stannides by direct synthesis calorimetry
Thermochim. Acta
(1998)
V.I. Baykov et al.
Structural stability of intermetallic phases in the Zr-Sn system
Scr. Mater.
(2006)
S.C. Lumley et al.
The stability of alloying additions in Zirconium
J. Nucl. Mater.
(2013)
S. Liu et al.
Insight into structural, mechanical, electronic and thermodynamic properties of intermetallic phases in Zr-Sn system from first-principles calculations
J. Phys. Chem. Solids
(2015)
H.-G. Kim et al.
Phase boundary of the Zr-rich region in commercial grade Zr–Nb alloys
J. Nucl. Mater.
(2005)
T. Chart et al.
Thermodynamically calculated phase-diagram for the Co-Cr-Zr system
Calphad
(1979)
H.-J. Lu et al.
Thermodynamic modeling of Cr–Nb and Zr–Cr with extension to the ternary Zr–Nb–Cr system
Calphad
(2015)
J. Pavlu et al.
Stability of Laves phases in the Cr-Zr system
Calphad
(2009)
K. Zeng et al.
Thermodynamic modeling of the laves phases in the Cr-Zr system
Calphad
(1993)

W. Rumball et al.

Phase equilibria in zirconium-rich zirconium-chromium-oxygen alloys

J. Less-Common Met.

(1969)

A. Knapton

Niobium and tantalum alloys

J. Less-Common Met.

(1960)

H. Richter et al.

Constitution of zirconium-niobium alloys

J. Less-Common Met.

(1962)

A.R. Miedema et al.

Cohesion in alloys — fundamentals of a semi-empirical model

Phys. Bc.

(1980)

C. Colinet et al.

Trends in cohesive energy of transition metal alloys

Calphad

(1985)

G. Carpenter et al.

The aging response of zirconium-tin alloys

J. Nucl. Mater.

(1981)

D. Arias et al.

The solubility of tin in alpha-zirconium and beta-zirconium below 1000-Degrees-C

J. Nucl. Mater.

(1983)

N. Subasic

Thermodynamic evaluation of Sn-Zr phase diagram

Calphad

(1998)

N. Dupin et al.

A thermodynamic database for zirconium alloys

J. Nucl. Mater.

(1999)

W.Y. Kim et al.

Laves phase fields in Cr-Zr-Nb and Cr-Zr-Hf alloy systems

Scr. Mater.

(2003)

W.-B. Wang et al.

Experimental investigation of phase equilibria in the Zr-Nb-Cr system at 1573 K and 1373 K

J. Nucl. Mater.

(2015)

J.-C. Crivello et al.

ZenGen, a tool to generate ordered configurations for systematic first-principles calculations: the Cr–Mo–Ni–Re system as a case study

Calphad

(2015)

S.C. Lumley et al.

The stability of alloying additions in zirconium

J. Nucl. Mater.

(2013)

C. Lemaignan, A.T. Motta, Zirconium alloys in nuclear applications, in: Mater. Sci. Technol., Wiley-VCH Verlag GmbH &...

J.-P. Mardon, Matériaux des tubes de gainage pour réacteurs à eau pressurisée, Techniques de l’ingénieur, bn3700,...

P. Barberis et al.

Role of the second-phase particles in zirconium binary alloys

J.-.P. Mardon, D. Charquet, J. Senevat, Influence of composition and fabrication process on out-of-pile and in-pile...

R.J. Perez et al.

The Zr-Sn binary system: new experimental results and thermodynamic assessment

Calphad

(2008)

A. Guillermet

Thermodynamic analysis of the stable phases in the Zr-Nb system and calculation of the phase-diagram

Z. Met.

(1991)

L. Kaufman, H. Nesor, The Cr-Zr system, Air Force Mater. Lab. Tech. Rep. AFML-TR-73-36,...

L. Kaufman et al.

Treatise on Solid State Chemistry

(1975)

K. Zeng et al.

A thermodynamic assessment of the Cr-Zr system

Z. Met.

(1993)

Cited by (23)

Thermodynamic reassessment of Sn–Zr system assisted by DFT phonon calculations
2024, Calphad: Computer Coupling of Phase Diagrams and Thermochemistry
The Sn–Zr system was re-assessed thermodynamically. Gibbs free energies of the intermetallic compounds of this system were calculated by DFT phonon calculations which can give more reliable information owing to considering the contributions of lattice vibration and electric thermal excitation. Newly published valuable experimental data of liquidus, solidus and invariant reactions of this system were used for the first time in the optimization of the model parameters. It is shown that the previous thermodynamic models, where the Gibbs free energies of formation at different temperatures were replaced by energies of formation at 0 K, overestimated obviously the stability of all the compounds of this system. The thermodynamic model for the Sn–Zr system established in this work would give more solid prediction of phase structures and thermodynamic properties for materials containing Sn–Zr system.
Experimental investigation and CALPHAD modeling of the Mo-Nb-Zr system
2024, International Journal of Refractory Metals and Hard Materials
To accelerate the design of novel nuclear fuel cladding materials for applications, the phase equilibria of the Mo-Nb-Zr system at 1223 K and 1773 K have been experimentally investigated by a combination of scanning electron microscopy, energy dispersive spectroscopy, electron probe microanalysis with wavelength dispersive spectrometer. In addition, the liquidus of the vertical sections at x(Mo) + x(Nb) = 0.67, x(Zr) + x(Nb) = 0.60 were also studied in this work utilizing an in-situ high-speed pyrometer. The thermodynamic assessment of the Mo-Nb-Zr system was carried out by the CALPHAD method based on the experimental data available in the present work and literature. A set of self-consistent thermodynamic parameters of the Mo-Nb-Zr system was obtained. The calculated liquidus projection of the Mo-Nb-Zr system over the whole composition was also presented.
Vacuum brazing of medical TA9 alloy to ZrO<inf>2</inf> bioceramics using a biocompatible filler: Interfacial microstructure, mechanical properties and biocompatibility
2024, Ceramics International
Based on the principle of developing new biocompatible fillers, the Sn–Zr + AuSn20 filler system was designed. Firstly, the surface of ZrO₂ ceramics was metallized by biocompatible Sn-xZr filler at 900 °C for 20 min. The interfacial microstructure of the Sn–Zr metallization layer/ZrO₂ consisted of β-Sn + Sn₂Zr/m-ZrO₂/t-ZrO₂. Then the pre-metallized ZrO₂ ceramics were brazed to TA9 alloys by AuSn20 metal foil at 550 °C for 30 min. The typical interfacial microstructure of the TA9/ZrO₂ joint is TA9/AuTi₅Sn₃+Sn–Zr/AuSn₄+AuSn₂+Au–Sn–Zr + ZrSn₂/AuSn₄+m-ZrO₂/t-ZrO₂. With the increase of Zr content, the Sn₂Zr phase gradually increases in the metallized layer, the thickness of the AuTi₅Sn₃ layer decreases, the AuSn₄ phase gradually decreases, and the AuSn₂ phase gradually increases in the TA9/ZrO₂ joint. Besides, the optimal shear strength of 46.5 MPa is obtained at 550 °C for 30 min with 6 at.% Zr content. At this point, the joint fractures at the interface of the AuTi₅Sn₃ and AuSn₄ layers, which is a weak area of the joint. Only a little amount of m-ZrO₂ is changed from t-ZrO₂ inside the t-ZrO₂ substrate; the majority of m-ZrO₂ grows directly on the t-ZrO₂ substrate surface. All materials have no cytotoxicity, and even the Sn–Zr metallization layer can promote cell proliferation.
Experimental measurement and modeling of lattice thermal expansion and specific heat capacity of C15-Cr<inf>2</inf>Nb Laves phase intermetallic compound
2024, Journal of Alloys and Compounds
In order to determine the lattice thermal expansion and specific heat capacity (C_p) of the C15-Cr₂Nb Laves phase, an experimental investigation and modeling were carried out in the present paper by employing high-temperature X-ray diffraction (HTXRD) and differential scanning calorimetry (DSC). A thorough analytical model was utilized to predict the temperature-dependent variations of enthalpy and specific heat, and the predicted findings were compared to the experimentally measured data. Arc melting was employed to synthesize Cr₂Nb samples with distinct hexagonal (C14/C36) and cubic (C15) Laves phase structures, which were then subjected to the appropriate heat treatment. Room temperature XRD patterns, SEM, and EDAX experiments on homogenized samples at 1273 K for 72 h validated the homogeneity and C15 (Fd-3 m) crystal structure of Cr₂Nb. Rietveld refinement was used to determine the lattice parameters and relative phase fractions of the constituent phases. The average thermal expansion coefficient was determined to be $α_{a}^{i}$ = 0.659 × 10⁻⁵ and $α_{V}^{i}$ = ¹.977 × 10⁻⁵ K⁻¹ respectively. The C_p of the C15-Cr₂Nb Laves phase intermetallic compound was measured employing heat flux DSC, utilizing conventional “three-step” procedures, and being reported for the first time. The measured C_p and enthalpy increment data (H_T – H_298.15) with varying temperatures reported in the present investigation are being correlated utilizing the theoretical model applying the quasi-harmonic Debye Grüneisen model in the temperature range 0–860 K and illustrated different contributions to the total heat capacity i.e., vibrational, anharmonic, and electronic.
Critical reassessment of the H–Nb system and experimental investigation and thermodynamic modeling of the H–Nb–Zr system
2023, Calphad: Computer Coupling of Phase Diagrams and Thermochemistry
The phase diagram and thermodynamic data of the H–Nb system are evaluated and re-assessed to improve the description of this system. This system is modeled up to a few MPa. Only the gas phase and the solid phases are considered in the present study. Since only a few data were available for the H–Nb–Zr ternary system, a new set of experimental data has been obtained in the present work. For the first time, the solubility of niobium into the ε-ZrH₂ phase is found. In addition, Density Functional Theory calculations and the Special Quasirandom Structures method are used to determine the formation enthalpies of all the compounds and the mixing enthalpies in the different phases, respectively. Finally, the literature data as well as our experimental and calculated data are used for the Calphad modeling of the H–Nb–Zr system.
Hybrid calphad DFT modelling of the Mg–Al–Ca system
2023, Calphad: Computer Coupling of Phase Diagrams and Thermochemistry
The Mg–Al–Ca system is an important system for Mg alloys. Al is the most common alloying element for Mg alloys, and additions of Ca can be used to produce ductile alloys and alloys with good creep properties. The Mg–Al–Ca system has been investigated extensively in the past, in particular the Mg-rich corner. Also, calculations using density functional theory (DFT) have been extensively applied in the past. DFT calculations generally show high accuracy and consistency in this system. The Mg–Al–Ca system contains all three Laves phases (C14, C15 and C36), but existing thermodynamic models of this system only contain rather simplified and limited models for the Laves phases. In this work, DFT calculations are used to provide energies of formation for all possible end-members of the Laves phases and the Mg₁₇Al₁₂ (A12) phase. This is combined with a thermodynamic modelling of the system to provide a thermodynamic description of the system where the Laves phases and the Mg₁₇Al₁₂ phase have reasonable Gibbs energies for the complete composition space. The new model description also provides a good representation of most existing experimental data, in particular in the important Mg-rich corner.

View all citing articles on Scopus

View full text

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

Abstract

Introduction

Section snippets

Experimental data

Experimental details

Calphad assessment

DFT results

Conclusions

Acknowledgements

Data statement

Calphad

Thermochim. Acta

Scr. Mater.

J. Nucl. Mater.

J. Phys. Chem. Solids

J. Nucl. Mater.

Calphad

Calphad

Calphad

Calphad

J. Less-Common Met.

J. Less-Common Met.

J. Less-Common Met.

Phys. Bc.

Calphad

J. Nucl. Mater.

J. Nucl. Mater.

Calphad

J. Nucl. Mater.

Scr. Mater.

J. Nucl. Mater.

Calphad

J. Nucl. Mater.

Role of the second-phase particles in zirconium binary alloys

The Zr-Sn binary system: new experimental results and thermodynamic assessment

Calphad

Thermodynamic analysis of the stable phases in the Zr-Nb system and calculation of the phase-diagram

Z. Met.

Treatise on Solid State Chemistry

A thermodynamic assessment of the Cr-Zr system

Z. Met.