Development of thermokinetic tools for phase ... 36 Development of...thermokinetic tools for phase transformation studies of Zr alloys in service and LOCA conditions C. TOFFOLON-MASCLET,

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

BACKGROUND

18 JUIN 2019

| PAGE 219th 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

OVERVIEW

18 JUIN 2019 | PAGE 319th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK

New thermodynamicdatabase for Zr alloys

Systematic use of Density Functional Theory (DFT) and Special Quasirandom Structure (SQS)

calculations

Phase diagram and thermodynamic data calculationsExtended to Cr containing alloys for Cr-coatedZr EATF R&D

Numerical code Ekinox-Zr

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

Thermodynamic tool Kinetic tool

Linked with Open Calphad/OCASI and thermodynamic database

THERMODYNAMIC TOOL

18 JUIN 2019

| PAGE 4

19th International Symposium on Zr in the

Nuclear Industry, May 20-23 2019, Manchester,

UK

18 JUIN 2019


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-SnCr-Sn Nb-ZrCr-Zr Sn-ZrCr-Fe Fe-ZrFe-Sn Fe-Nb

10 ternary systems :

Cr-Fe-Nb Sn-Nb-ZrCr-Fe-Zr Nb-Fe-ZrCr-Nb-Zr Fe-Sn-ZrCr-Fe-Sn Fe-Nb-SnCr-Sn-Zr Cr-Nb-Sn

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

18 JUIN 2019


(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

positionSpace

group

C15 ZrFe28a (Zr)

16d (Fe)

Fd-3m

(227)

22 = 4 end-members for a binary system

32 = 9 end-members for a ternary system

C36

site 8a0 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

APPLICATION TO THE BINARY SYSTEM Fe-Nb :

DFT and SQS calculations

18 JUIN 2019


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

18 JUIN 2019


New assessment of the FeNb system

Validation of the optimisationby comparison with exp. data:

Fe activity at 1600°C Mixing enthalpy of the liquid phase at 1762°C

Fe

ac

tivit

y

18 JUIN 2019


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

EXISTENCE OF THE Fe2(Nb,Zr) (C36 LAVES

PHASE) INTERMETALLIC PHASE?

18 JUIN 2019


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

THERMODYNAMIC ASSESSMENT OF THE

Fe-Nb-Zr SYSTEM

18 JUIN 2019


800°C 900°C

Nb Nb

ZrZrFeFe

Good agreement between experimental and calculated data

The whole database has been created applying the same methodology

APPLICATION ON INDUSTRIAL ALLOYS


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

KINETIC TOOL

18 JUIN 2019

| PAGE 14


Nuclear Industry, May 20-23 2019, Manchester,

UK

CONTEXT: MICROSTRUCTURAL EVOLUTIONS DURING LOCA HIGH

INFLUENCE ON THE MECHANICAL PROPERTIES: BALLONING & BURST, WATER

QUENCHING AND POST-QUENCHING RESISTANCE/DUCTILITY…)

18 JUIN 2019


Steam

<900s

Time

Te

mp

era

ture

of th

e c

lad

din

g

at a

giv

en

axia

l p

ositio

n (

°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

Ste

am

ZrO2

Oxyge

n

co

nte

nt

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)

CONSEQUENCES OF HIGH TEMPERATURE OXIDATION ON

POST-QUENCH MECHANICAL BEHAVIOR OF THE CLADDING

| PAGE 1619th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UKJ.-C. Brachet et al. Journal of ASTM

international, 5, n°5 (2008), Paper ID JAI101116

[O]

x

C0

Cox/αCα/ox

C β /α

Cα/β

Cox/vap

Ex

tern

al

surf

ace

Ex

tern

al

surf

ace

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 layerfor [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):


» 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

NUMERICAL CODE EKINOX-ZR

(ESTIMATION KINETICS OXIDATION MODEL FOR ZR-BASED ALLOYS)

18 JUIN 2019


Interface

OCASI

𝐶𝛼/𝛽, 𝐶𝛽/𝛼

EKINOX numerical resolution

of diffusion equations

OPENCALPHAD + Zircobase

(thermodynamic calculations)

18 JUIN 2019


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 effectof 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 oxidation) transients

18 JUIN 2019


2°C.min-1 20°C.min-1

Comparison betweencalculated and

experimental (TGA) anisothermal weight

gain variation of Zircaloy-4 upon heating

under O2+He environment

at 2°C/min and 20°C/min


Calculated O concentration profiles in Zircaloy-4 alloy for anisothermaloxidation 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


CONCLUSIONS

Development of a new thermodynamic database for Zr alloys including systematicand 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 calculationsof the HT phase thicknesses and associated oxygen concentration profiles inducedby 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

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 01918 JUIN 2019


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

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

positionSpace

group

C15 ZrFe28a (Zr)

16d (Fe)

Fd-3m

(227)

22 = 4 end-members for a binary system

32 = 9 end-members for a ternary system

C36

site 8a0

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

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


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.


18/06/2019

TECHNIQUES DE CALCULS


Calculs DFT-SQS des ΔHm

Calculs DFT des ΔHf

C15 C14 C36

0 20 40 60 80 1000

2

4

6

8

10

12

Cr-Fe system

SQS-ferromagnetic

SQS-parramagnetic

experiments

H

mix (

kJ/m

ol. a

t.)

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

SnCr XSn

NUMERICAL CODE EKINOX-Zr

(ESTIMATION KINETICS OXIDATION MODEL FOR ZR-BASED ALLOYS)

18 JUIN 2019


Interfaces conditions : 1st and 2nd Fick’s law :

Moving interfaces O flux at the different interfaces :

OpenCalphad

/OCASI +

Zircobase


Zy4 + [H] = 150 ppm mass. –oxydation – 1200°C – 190s

EPMA profil

EKINOX-Zr profil


Development of thermokinetic tools for phase ... 36 Development of...thermokinetic tools for phase transformation studies of Zr alloys in service and LOCA conditions C. TOFFOLON-MASCLET,

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