transformation studies of Zr alloys in service and LOCA conditions - - PowerPoint PPT Presentation

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transformation studies of Zr alloys in service and LOCA conditions - - PowerPoint PPT Presentation

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Development of thermokinetic tools for phase transformation studies of Zr alloys in service and LOCA conditions C. TOFFOLON-MASCLET, L. MARTINELLI, C. DESGRANGES, P. LAFAYE, J.-C. BRACHET, F. LEGENDRE, J.-C. CRIVELLO, J.-M. JOUBERT, D.

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SLIDE 1

Development of thermokinetic tools for phase transformation studies of Zr alloys in service and LOCA conditions

  • C. TOFFOLON-MASCLET, L. MARTINELLI,
  • C. DESGRANGES, P. LAFAYE, J.-C. BRACHET,
  • F. LEGENDRE, J.-C. CRIVELLO, J.-M. JOUBERT,
  • D. MONCEAU

18 JUIN 2019 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK

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SLIDE 2

BACKGROUND

18 JUIN 2019 | PAGE 2 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK

As nuclear fluel cladding materials, Zr alloys are subjected to numerous solicitations both in:

service conditions

❑ Pressurized water: 155 bars ❑ Water temperature: 320-360°C ❑ Neutron irradiation ❑ Oxidation / hydriding

LOCA conditions

❑ Internal pressure: up to > 100 bars inducing creep/ballooning and burst ❑ Max (Peak Cladding) Temperature : 1200 °C ❑ Steam environment inducing High Temperature Oxidation and potential secondary hydriding

The development of thermokinetic tools enables the determination of:

  • phase transformation temperatures
  • phases chemical compositions
  • phases volume fractions
  • precipitation of more or less brittle phases
  • new alloy compositions
  • …

Considering the influence of microstructure on mechanical properties

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SLIDE 3

OVERVIEW

18 JUIN 2019 | PAGE 3 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK

New thermodynamic database for Zr alloys

Systematic use of Density Functional Theory (DFT) and Special Quasirandom Structure (SQS) calculations Phase diagram and thermodynamic data calculations Extended to Cr containing alloys for Cr-coated Zr EATF R&D

Numerical code Ekinox-Zr

Simulation of O concentration profiles and thickness evolution of the different phases appearing/developing during a LOCA transient

Thermodynamic tool Kinetic tool

Linked with Open Calphad/OCASI and thermodynamic database

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SLIDE 4

THERMODYNAMIC TOOL

18 JUIN 2019 | PAGE 4 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK

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SLIDE 5

18 JUIN 2019 | PAGE 5 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK

NEW THERMODYNAMIC DATABASE : Zr-Cr-Fe-Nb-Sn SYSTEM

Binary and ternary models are combined into a quinary database. 10 binary systems :

Cr-Nb Nb-Sn Cr-Sn Nb-Zr Cr-Zr Sn-Zr Cr-Fe Fe-Zr Fe-Sn Fe-Nb

10 ternary systems :

Cr-Fe-Nb Sn-Nb-Zr Cr-Fe-Zr Nb-Fe-Zr Cr-Nb-Zr Fe-Sn-Zr Cr-Fe-Sn Fe-Nb-Sn Cr-Sn-Zr Cr-Nb-Sn

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SLIDE 6

Calphad method

Solution (ex : A−B)

srfGϕ = xAGϕ (A) +xBGϕ (B) cnfGϕ = −T·cnfSϕ = −RT(xAlnxA +xBlnxB) exGϕ = xAxBLAB , où LAB =Ʃn i=0 iLϕ A,B(xA −xB)i

Stoichiometric compound (AB2) G (AB2) = GSER (A) +2GSER (B) + a + b.T + ... Non-Stoichiometric compound Sublattice model

THERMODYNAMIC MODELLING USING THE CALPHAD METHOD

Phase equilibria Crystallography Thermodynamic database Thermodynamic parameters DFT calculation of ΔHf DFT-SQS calculations of ΔHm

18 JUIN 2019 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK 6

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SLIDE 7

18 JUIN 2019 | PAGE 7 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK

(Nb)8:(Fe)16 (Fe)8:(Nb)16 (Zr)8:(Nb)16 (Nb)8:(Zr)16 (Zr)8:(Fe)16 (Fe)8:(Zr)16 (Zr)8:(Zr)16 (Fe)8:(Fe)16 (Nb)8:(Nb)16 (Zr)8:(Fe)16 (Fe)8:(Zr)16 (Zr)8:(Zr)16

(Fe)8:(Fe)16

Structure Intermetallic compound Wyckoff position Space group

C15 ZrFe2 8a (Zr) 16d (Fe) Fd-3m (227) 22 = 4 end-members for a binary system 32 = 9 end-members for a ternary system

C36

site 8a 100 site 16d 100 (Zr)8:(Zr)16 (Zr)8:(Fe)16 (Fe)8:(Zr)16

(Fe)8:(Fe)16

WHY SYSTEMATIC USE OF DFT AND SQS CALCULATIONS ? → SUBLATTICE MODEL

(Zr)8:(Fe)16 (Fe)8:(Zr)16 (Fe)8:(Fe)16 (Zr)8:(Zr)16 (Zr)8:(Fe,Zr)16 (Fe,Zr)8:(Fe)16

End-members Hf calculated by DFT

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SLIDE 8

APPLICATION TO THE BINARY SYSTEM Fe-Nb : DFT and SQS calculations

18 JUIN 2019 | PAGE 8 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK

FeNb binary system from Pavlu et al.*

* J. Pavlu, J. Vrest ’al, M. Sob, Stability of Laves phases in the Cr- Zr system, Calphad-Comput. Coupling Phase Diagr. Thermochem. 33 (2009) 382-387

The calculated ground-state confirms the stability of Fe2Nb (C14) and Fe7Nb6 (µ) phases

Fe2Nb Fe7Nb6

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SLIDE 9

18 JUIN 2019 | PAGE 9 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK

New assessment of the FeNb system Validation of the optimisation by comparison with exp. data: Fe activity at 1600°C Mixing enthalpy of the liquid phase at 1762°C

Fe activity

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SLIDE 10

18 JUIN 2019 | PAGE 10 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK

Mixing binary systems enables extrapolation towards ternary systems DFT SQS-DFT EXP DFT SQS-DFT EXP DFT SQS-DFT EXP

EXTRAPOLATION TO THE Fe-Nb-Zr TERNARY SYSTEM

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SLIDE 11

EXISTENCE OF THE Fe2(Nb,Zr) (C36 LAVES PHASE) INTERMETALLIC PHASE?

18 JUIN 2019 | PAGE 11 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK

Experimental verification : Alloy fabrication Fe2Nb0,5Zr0,5 → 3 weeks annealing at 800°C → Analysis by :

  • X-ray diffraction
  • EPMA

2 experimentally observed phases : Fe2Nb (C14) and Fe2Zr (C15) Non existence of the Fe2(Nb,Zr) (C36) confirmed by DFT calculations

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SLIDE 12

THERMODYNAMIC ASSESSMENT OF THE Fe-Nb-Zr SYSTEM

18 JUIN 2019 | PAGE 12 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK

800°C 900°C Nb Nb Zr Zr Fe Fe

Good agreement between experimental and calculated data The whole database has been created applying the same methodology

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SLIDE 13

APPLICATION ON INDUSTRIAL ALLOYS

18 JUIN 2019 | PAGE 13 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK

Zr-0,7%Nb-0,3%Sn-0,35%Fe-0,25%Cr

annealing at 675 °C EDS analysis→ quaternary equilibria : α-Zr + β-Zr + LAVES + LAVES

Zr0.7Nb0.3Sn0.35Fe0.25Cr

Zr Nb Fe Cr Zr(Nb,Fe,Cr)2 33.8 20.2 29.2 16.8 Zr(Fe,Cr)2 33.0 4.6 29.5 32.9 Zircobase

Our database

Zr Nb Fe Cr C14 34.2 24.6 38.4 2.7 C15 32.0 3.8 33.0 31.1

  • α-Zr + β-Zr + LAVES
  • Modification of the nominal

composition α-Zr + β-Zr + C14 + C14

  • α-Zr + β-Zr + C14 + C15

*Barberis et al., 17th Int. Symp. Zr Nucl. Indust, STP1543, Hyderabad, India, 2015

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SLIDE 14

KINETIC TOOL

18 JUIN 2019 | PAGE 14 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK

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SLIDE 15

CONTEXT: MICROSTRUCTURAL EVOLUTIONS DURING LOCA  HIGH INFLUENCE ON THE MECHANICAL PROPERTIES: BALLONING & BURST, WATER QUENCHING AND POST-QUENCHING RESISTANCE/DUCTILITY…)

18 JUIN 2019 | PAGE 15 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK

Steam

<900s Time Temperature of the cladding at a given axial position (°C) 400 800 1200

ANL, ICL#2 JAEA, A 3-1

Example of Large Break LOCA transient

CEA

Prior-βZr αZr(O) ZrO2

Zr (+ H)

ZrO2

Ex.: Single-side oxidation

Prior-βZr Zr(O)

ZrO2

Zr + 2H2O → 2H2 + ZrO2

Zr

(cc)

Zr

(hcp)

ZrO2

(tetra.)

αZrO2

(mono.)

Zr O

βZr

ZrO2

βZr Zr(O)

ZrO2 αZr(O) βZr

Steam

ZrO2

Oxygen content

0.14-0.9 wt.% 1-5 at.%

2-7 wt.% 10-29 at.%

~25 wt.% ~66 at.%

Distance from the outer surface

Loss Of Coolant Accident (LOCA)

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SLIDE 16

CONSEQUENCES OF HIGH TEMPERATURE OXIDATION ON POST-QUENCH MECHANICAL BEHAVIOR OF THE CLADDING

| PAGE 16 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK J.-C. Brachet et al. Journal of ASTM international, 5, n°5 (2008), Paper ID JAI101116

[O] x C0 Cox/α Cα/ox C β /α Cα/β Cox/vap External surface External surface

Brittle Brittle

[O] x

O diffusion profile O diffusion profile

C β /α

0.4 wt%

Brittle Ductile

ZrO2 αZr(O) prior-βZr eox eα

O diffusion profile O diffusion profile

Brittle Ductile

Remaining ductility at RT only in the prior-Zr layer for [O] < 0.4wt% Otherwise ductile → brittle

Nuclear fuel

Create a tool able to forecast thicknesses of brittle and ductile phases, O diffusion profiles (and weight gains) as a function of HT steam oxidation time and temperature (and able to take into account the additional effect of hydrogen)

At Room-Temperature (RT):

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SLIDE 17

18 JUIN 2019 | PAGE 17 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK

» Chemical species and atomic defects transport

 via atomic solid diffusion

» Interface reaction

 local thermodynamic equilibrium

» Intermediate scale

  • system is described by "slabs" of

constant concentration : [O] in the metal layers [VO] in the oxyde phase 1st and 2nd Fick‘s law

» Moving boundaries algorithm for interfaces motion » Numerical time integration » growth kinetics » Diffusion of chemical species and vacancies concentration profiles

 in the oxide scale  in the metal

Initially developped for Ni base alloys

Numerical code EKINOX-Zr (ESTIMATION KINETICS OxIDATION MODEL FOR ZR-BASED ALLOYS)

Model enables calculation of

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NUMERICAL CODE EKINOX-ZR (ESTIMATION KINETICS OXIDATION MODEL FOR ZR-BASED ALLOYS)

18 JUIN 2019 | PAGE 18 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK

Interface OCASI 𝐷𝛽/𝛾, 𝐷𝛾/𝛽 EKINOX numerical resolution

  • f diffusion equations

OPENCALPHAD + Zircobase (thermodynamic calculations)

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SLIDE 19

18 JUIN 2019 | PAGE 19 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK

Ekinox-Zr has already demonstrated its ability at:

Simulating O diffusion profiles in Zr(O) and Zr

[1]

Taking into account the influence of H[2] Taking into account the effect

  • f a pre-oxide layer on the O

concentration profile [3]

During isothermal HT oxidation (1100 < T < 1250°C)

[1] C. Corvalan et al., JNM, 400, 3 (2010) 196-204 [2] B. Mazères et al., Oxid. Met., 79 (2013) 1-2 [3] B. Mazères et al., Corros. Sci., 103 (2016) 10-19

New development: simulation of anisothermal (HT

  • xidation) transients
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SLIDE 20

18 JUIN 2019 | PAGE 20 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK

2°C.min-1 20°C.min-1

Comparison between calculated and experimental (TGA) anisothermal weight gain variation of Zircaloy-4 upon heating under O2+He environment at 2°C/min and 20°C/min

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SLIDE 21

18 JUIN 2019 | PAGE 21 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK

Calculated O concentration profiles in Zircaloy-4 alloy for anisothermal

  • xidation at two different heating rates (2 and 20°C/min) at t = 200s

Similar ECR can be reached by different LOCA type anisothermal transients : the resulting O concentration profiles can potentially be very different

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SLIDE 22

18 JUIN 2019 | PAGE 22 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK

CONCLUSIONS

Development of a new thermodynamic database for Zr alloys including systematic and massive use of DFT and SQS calculations Consistency of the database: very good agreement of thermodynamic computations with experimental data Improvement of the Ekinox-Zr numerical code: enabling anisothermal calculations

  • f the HT phase thicknesses and associated oxygen concentration profiles induced

by HT steam oxidation typical of LOCA Include H and O in the thermodynamic database : « work in progress! » Ekinox-Zr :

  • Extend anisothermal calculations from room temperature to high

temperature

  • Adaptation of the code for the simulation of HT oxidation of Cr-

coated EATF claddings

FURTHER WORK

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SLIDE 23

Direction de l’Énergie Nucléaire Département des Matériaux pour le Nucléaire Service de Recherche de Métallurgie Appliquée Commissariat à l’énergie atomique et aux énergies alternatives Centre de Saclay | 91191 Gif-sur-Yvette Cedex

  • T. +33 (0)1 69 08 21 39

Etablissement public à caractère industriel et commercial | RCS Paris B 775 685 019

18 JUIN 2019 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK | PAGE 23

This work is funded by the project GAINE from the French Nuclear tripartite Institute CEA – EDF - FRAMATOME

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SLIDE 24

100

(Nb)8:(Fe)16 (Zr)8:(Nb)16 (Nb)8:(Zr)16 (Zr)8:(Fe)16 (Fe)8:(Zr)16 (Zr)8:(Zr)16 (Fe)8:(Fe)16 (Nb)8:(Nb)16

(Fe)8:(Fe)16

Structure Intermetallic compound Wyckoff position Space group

C15 ZrFe2 8a (Zr) 16d (Fe) Fd-3m (227) 22 = 4 end-members for a binary system 32 = 9 end-members for a ternary system

C36

site 8a site 16d (Zr)8:(Fe)16 (Fe)8:(Zr)16

WHY SYSTEMATIC USE OF DFT AND SQS CALCULATIONS ? → SUBLATTICE MODEL

(Zr)8:(Fe)16 (Fe)8:(Zr)16 (Fe)8:(Fe)16 (Zr)8:(Zr)16 (Fe)8:(Nb)16

ICMPE | 27 OCTOBRE 2017| PAGE 7

(Zr)8:(Fe,Zr)16 (Fe,Zr)8:(Fe)16

(Zr)8:(Zr)16 100

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SLIDE 25

MODÈLE EN SOUS-RÉSEAUX

Phase

Groupe d’espace Wyckoff (CN) Configurations Système Nombre de sous- réseaux Modèle en sous-réseaux C15 Fd-3m (227) 8a (16); 16d (12) 25 Système quinaire 2 (Cr,Nb,Fe,Sn,Zr)1 (Cr,Nb,Fe,Sn,Zr)2 C14 P63/mmc (194) 2a (12); 4f (16); 6h (12) 125 Système quinaire 3 (Cr,Nb,Fe,Sn,Zr)2 (Cr,Nb,Fe,Sn,Zr)4 (Cr,Nb,Fe,Sn,Zr)6 C36 P63/mmc (194) 4e (16); 4f (16); 4f (12); 6g (12); 6h (12) 125 Système quinaire 3 (Cr,Nb,Fe,Sn,Zr)4 (Cr,Nb,Fe,Sn,Zr)4 (Cr,Nb,Fe,Sn,Zr)16

C15 C14 C36

ICMPE | 27 OCTOBRE 2017| PAGE 8

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SLIDE 26

MODÈLE EN SOUS-RÉSEAUX

Phase

Groupe d’espace Wyckoff (CN) Prototype Système Nbre de sous- réseaux Modèle en sous-réseaux C15 Fd-3m (227) 8a (16); 16d (12) MgCu2 Système quinaire 2 (Cr,Nb,Fe,Sn,Zr)1 (Cr,Nb,Fe,Sn,Zr)2 C14 P63/mmc (194) 2a (12); 4f (16); 6h (12) MgZn2 Système quinaire 3 (Cr,Nb,Fe,Sn,Zr)4 (Cr,Nb,Fe,Sn,Zr)2 (Cr,Nb,Fe,Sn,Zr)6 C36 P63/mmc (194) 4e (16); 4f (16); 4f (12); 6g (12); 6h (12) MgNi2 Système quinaire 3 (Cr,Nb,Fe,Sn,Zr)4 (Cr,Nb,Fe,Sn,Zr)4 (Cr,Nb,Fe,Sn,Zr)16 μ* R-3m (166) 3a (12) ; 6c (15); 6c (16); 6c (14); 18h (12) W6Fe7 Cr-Fe-Nb 4 (Cr,Fe,Nb)1 (Nb)4 (Cr,Fe,Nb)2 (Cr,Fe,Nb)6 σ* P42/mnm (136) 2a (12); 8i (12); 4f (15); 8i (14); 8j (14) Cr0.49Fe0.51 Cr-Fe-Nb 2 (Cr,Fe,Nb)1 (Cr,Fe,Nb)2

* J.-M. Joubert et al. “Mixed site occupancies in the μ phase” Intermetallics 12 (2004) 1373–1380 * J.M. Joubert, “Crystal chemistry and Calphad modeling of the σ phase”, Prog. Mater. Sci. 53 (2008)

528–583.

ICMPE | 27 OCTOBRE 2017| PAGE 9

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SLIDE 27

18/06/2019

TECHNIQUES DE CALCULS

ICMPE | 27 OCTOBRE 2017| PAGE 9

Calculs DFT-SQS des ΔHm Calculs DFT des ΔHf

C15 C14 C36

20 40 60 80 100 2 4 6 8 10 12

Cr-Fe system

SQS-ferromagnetic SQS-parramagnetic experiments

Hmix (kJ/mol. at.)

Composition (at. % Fe)

Consistance de la description !

Solutions solides peu étendues

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 500 750 1000 1250 1500 1750 2000 2250

[STE61] [PRE69] [DAR69] This work

Sn Cr XSn

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SLIDE 28

NUMERICAL CODE EKINOX-Zr (ESTIMATION KINETICS OXIDATION MODEL FOR ZR-BASED ALLOYS)

18 JUIN 2019 | PAGE 28 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK

Interfaces conditions : 1st and 2nd Fick’s law : Moving interfaces O flux at the different interfaces :

OpenCalphad /OCASI + Zircobase

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SLIDE 29

18 JUIN 2019 | PAGE 29 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK

Zy4 + [H] = 150 ppm mass. –oxydation – 1200°C – 190s EPMA profil EKINOX-Zr profil

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SLIDE 30

18 JUIN 2019 | PAGE 30 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK