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 As nuclear fluel cladding materials, Zr alloys are subjected to numerous solicitations both in: service conditions LOCA conditions ❑ Internal pressure: up to > 100 bars inducing ❑ Pressurized water: 155 bars creep/ballooning and burst ❑ Water temperature: 320-360 ° C ❑ Max (Peak Cladding) Temperature : 1200 ° C ❑ Neutron irradiation ❑ Steam environment inducing High Temperature ❑ Oxidation / hydriding Oxidation and potential secondary hydriding Considering the influence of microstructure on mechanical properties 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 - … 18 JUIN 2019 | PAGE 2 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK
OVERVIEW Thermodynamic tool Kinetic tool New thermodynamic Numerical code Ekinox-Zr database for Zr alloys Systematic use of D ensity F unctional T heory ( DFT) and Linked with Open Calphad/OCASI and S pecial Q uasirandom S tructure ( SQS) thermodynamic database calculations Phase diagram and thermodynamic data Simulation of O concentration profiles and thickness evolution of the different calculations phases appearing/developing during a Extended to Cr containing alloys for Cr-coated Zr EATF R&D LOCA transient 18 JUIN 2019 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK | PAGE 3
THERMODYNAMIC TOOL 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK | PAGE 4 18 JUIN 2019
NEW THERMODYNAMIC DATABASE : Zr-Cr-Fe-Nb-Sn SYSTEM 10 binary systems : 10 ternary systems : Cr-Nb Nb-Sn Cr-Fe-Nb Sn-Nb-Zr Cr-Sn Nb-Zr Cr-Fe-Zr Nb-Fe-Zr Cr-Zr Sn-Zr Cr-Nb-Zr Fe-Sn-Zr Cr-Fe Fe-Zr Cr-Fe-Sn Fe-Nb-Sn Fe-Sn Fe-Nb Cr-Sn-Zr Cr-Nb-Sn Binary and ternary models are combined into a quinary database. 18 JUIN 2019 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK | PAGE 5
THERMODYNAMIC MODELLING USING THE CALPHAD METHOD DFT-SQS calculations of ΔH m Phase equilibria Calphad method Solution (ex : A−B) srf G ϕ = x A G ϕ (A) +x B G ϕ (B) Crystallography cnf G ϕ = −T· cnf S ϕ = −RT(x A lnx A +x B lnx B ) ex G ϕ = x A x B L AB , où L AB =Ʃ n A,B (x A −x B ) i i L ϕ Thermodynamic i=0 database Stoichiometric compound (AB 2 ) G (AB 2 ) = G SER (A) +2G SER (B) + a + b.T + ... Non-Stoichiometric compound Sublattice model Thermodynamic parameters DFT calculation of ΔH f 18 JUIN 2019 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK 6
WHY SYSTEMATIC USE OF DFT AND SQS CALCULATIONS ? → SUBLATTICE MODEL (Fe) 8 :(Zr) 16 (Zr) 8 :(Zr) 16 100 site 16 d C 36 (Zr) 8 :(Fe,Zr) 16 (Fe,Zr) 8 :(Fe) 16 site 8 a 0 100 (Zr) 8 :(Fe) 16 (Fe) 8 :(Fe) 16 2 2 = 4 end-members for a binary system (Zr) 8 :(Zr) 16 (Fe) 8 :(Fe) 16 (Zr) 8 :(Fe) 16 (Fe) 8 :(Zr) 16 3 2 = 9 end-members for a ternary system (Nb) 8 :(Nb) 16 (Zr) 8 :(Zr) 16 (Zr) 8 :(Fe) 16 (Fe) 8 :(Zr) 16 (Fe) 8 :(Fe) 16 Wyckoff (Zr) 8 :(Nb) 16 Structure Intermetallic Space (Fe) 8 :(Nb) 16 position compound group 8 a (Zr) Fd- 3 m (Nb) 8 :(Zr) 16 (Nb) 8 :(Fe) 16 C 15 ZrFe 2 16 d (Fe) (227) (Fe) 8 :(Fe) 16 (Zr) 8 :(Zr) 16 End-members Hf calculated by DFT 18 JUIN 2019 (Zr) 8 :(Fe) 16 (Fe) 8 :(Zr) 16 | PAGE 7 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK
APPLICATION TO THE BINARY SYSTEM Fe-Nb : DFT and SQS calculations Fe 7 Nb 6 FeNb binary system from Pavlu et al.* Fe 2 Nb The calculated ground-state confirms the stability of Fe 2 Nb (C14) and Fe 7 Nb 6 (µ) phases * J. Pavlu, J. Vrest ’al, M. Sob, Stability of Laves phases in the Cr- 18 JUIN 2019 Zr system, Calphad-Comput. Coupling Phase Diagr. Thermochem. | PAGE 8 33 (2009) 382-387 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 18 JUIN 2019 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK | PAGE 9
EXTRAPOLATION TO THE Fe-Nb-Zr TERNARY SYSTEM Mixing binary systems enables extrapolation towards ternary systems DFT SQS-DFT EXP DFT SQS-DFT EXP DFT SQS-DFT EXP 18 JUIN 2019 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK | PAGE 10
EXISTENCE OF THE Fe 2 (Nb,Zr) ( C 36 LAVES PHASE) INTERMETALLIC PHASE? Experimental verification : Analysis by : - X-ray diffraction Alloy fabrication Fe 2 Nb 0,5 Zr 0,5 → 3 weeks annealing at 800°C → - EPMA 2 experimentally observed phases : Fe 2 Nb ( C 14) and Fe 2 Zr ( C 15) Non existence of the Fe 2 (Nb,Zr) ( C 36) confirmed by DFT calculations 18 JUIN 2019 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK | PAGE 11
THERMODYNAMIC ASSESSMENT OF THE Fe-Nb-Zr SYSTEM Nb Nb Fe Fe Zr Zr 900°C 800°C Good agreement between experimental and calculated data The whole database has been created applying the same methodology 18 JUIN 2019 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK | PAGE 12
APPLICATION ON INDUSTRIAL ALLOYS 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 Zr Nb Fe Cr Zr0.7Nb0.3Sn0.35Fe0.25Cr 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 • α -Zr + β -Zr + C14 + C15 • α -Zr + β -Zr + LAVES • Modification of the nominal Zr Nb Fe Cr composition C14 34.2 24.6 38.4 2.7 α -Zr + β -Zr + C14 + C14 C15 32.0 3.8 33.0 31.1 18 JUIN 2019 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK | PAGE 13 *Barberis et al., 17th Int. Symp. Zr Nucl. Indust, STP1543, Hyderabad, India, 2015
KINETIC TOOL 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK | PAGE 14 18 JUIN 2019
CONTEXT: MICROSTRUCTURAL EVOLUTIONS DURING LOCA HIGH INFLUENCE ON THE MECHANICAL PROPERTIES: BALLONING & BURST, WATER QUENCHING AND POST-QUENCHING RESISTANCE/DUCTILITY …) Loss Of Coolant Zr β Zr α Zr (O) ZrO 2 Oxygen content Zr Accident (LOCA) (hcp) ~25 wt.% (cc) ~66 at.% 2-7 wt.% ZrO2 Steam 10-29 at.% ZrO 2 (tetra.) β Zr α ZrO2 0.14-0.9 wt.% ZrO 2 1-5 at.% (mono.) Distance from the outer surface Zr O Zr (O) β Zr Ex.: Single-side oxidation Temperature of the cladding at a given axial position (°C) Steam 1200 Prior- β Zr ZrO 2 JAEA, A 3-1 800 ZrO 2 ZrO 2 α Zr (O) 400 Prior- β Zr Example of Large Break LOCA transient Zr Zr (O) CEA <900s (+ H) Time Zr + 2H 2 O → 2H 2 + ZrO 2 ANL, ICL#2 18 JUIN 2019 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK | PAGE 15
CONSEQUENCES OF HIGH TEMPERATURE OXIDATION ON POST-QUENCH MECHANICAL BEHAVIOR OF THE CLADDING [O] External surface External surface α Zr (O) prior- β Zr ZrO 2 C ox/vap Nuclear fuel C α /ox C ox/ α C α / β C β / α O O C 0 diffusion diffusion e α e ox profile profile x Brittle Ductile Ductile Brittle At Room-Temperature (RT): Brittle Brittle [O] Remaining ductility at RT only in the prior- Zr layer C β / α for [O] < 0.4wt% O O diffusion diffusion Otherwise ductile → brittle 0.4 wt% profile profile x 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) J.-C. Brachet et al . Journal of ASTM 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK | PAGE 16 international , 5 , n°5 (2008), Paper ID JAI101116
Numerical code EKINOX-Zr (E STIMATION KIN ETICS Ox IDATION MODEL FOR Z R - BASED ALLOYS ) Initially developped for Ni base alloys » Chemical species and atomic defects transport via atomic solid diffusion » Intermediate scale » Interface reaction • system is described by "slabs" of constant concentration : [O] in the metal layers local thermodynamic equilibrium [V O ] in the oxyde phase 1st and 2nd Fick‘s law » Moving boundaries algorithm for interfaces motion » growth kinetics » Numerical time integration » Diffusion of chemical species and vacancies concentration profiles in the oxide scale Model enables calculation of in the metal 18 JUIN 2019 19th International Symposium on Zr in the Nuclear Industry, May 20-23 2019, Manchester, UK | PAGE 17
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