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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. 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
| PAGE 519th 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-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
| PAGE 719th 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
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
| PAGE 819th 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
18 JUIN 2019
| PAGE 919th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK
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
| PAGE 1019th 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
EXISTENCE OF THE Fe2(Nb,Zr) (C36 LAVES
PHASE) INTERMETALLIC PHASE?
18 JUIN 2019
| PAGE 1119th 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
THERMODYNAMIC ASSESSMENT OF THE
Fe-Nb-Zr SYSTEM
18 JUIN 2019
| PAGE 1219th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK
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
18 JUIN 2019 | PAGE 1319th 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%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
19th International Symposium on Zr in the
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
| PAGE 1519th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK
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):
18 JUIN 2019 | PAGE 1719th 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
NUMERICAL CODE EKINOX-ZR
(ESTIMATION KINETICS OXIDATION MODEL FOR ZR-BASED ALLOYS)
18 JUIN 2019
| PAGE 1819th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK
Interface
OCASI
𝐶𝛼/𝛽, 𝐶𝛽/𝛼
EKINOX numerical resolution
of diffusion equations
OPENCALPHAD + Zircobase
(thermodynamic calculations)
18 JUIN 2019
| PAGE 1919th 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 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
| PAGE 2019th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK
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
18 JUIN 2019 | PAGE 2119th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK
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
18 JUIN 2019 | PAGE 2219th 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 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
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
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
ICMPE | 27 OCTOBRE 2017| PAGE 8
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
18/06/2019
TECHNIQUES DE CALCULS
ICMPE | 27 OCTOBRE 2017| PAGE 9
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
| PAGE 2819th 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
18 JUIN 2019 | PAGE 2919th 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
18 JUIN 2019 | PAGE 3019th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK