1. Development of EKINOX Model for the Prediction of Microstructural Evolutions in Zr Alloys during Oxydation L. Anagonou, C. Desgranges, C. Toffolon-Masclet, S. Poissonnet and J.C. Brachet CEA, DEN F-91191 Gif-sur-Yvette, France References: [1] N. Bertrand, PhD Thesis 2006, INP Toulouse [2] N. Dupin, I. Ansara, C. Servant, C. Toffolon, C. Lemaignan, J.C. Brachet, Journal of Nuclear Materials, 275 (1999), pp. 287—295. Calculation of oxygen concentration profile in  Zr during ZrO 2 oxide scale growth at high temperature Fig. 2: Oxygen profile of Zy-4 oxidized at temperatures below the  /  transformation temperature (<820°C) C  /G C/C/ C/C/ C0C0 0 gas  ll C ZrO 2  (O) Zr x x1x1 Moving interface  (O) Zr Conclusions Fig. 1: Schematic representation of the “1D” system with Ns contiguous slabs of thickness e n. 1 2… N i N N+1 N s 1 2… N i +1N i N i … N s Oxide Gas e n e Metal InterfaceSurface C  /G C/C/ C/C/ C0C0 ()() C N  (O) Zr ZrO 2 Numerical solution calculated from time integration by 1D explicit finite differencies algorithm T he EKINOX model enables calculation of :  the growth kinetics  chemical species and vacancies concentration profiles in the oxide and in the metal Interfaces motion (oxide referential), example for oxide growth at metal/oxide interface : Analytical solution for oxygen concentration profile C α in the  (O) Zr Further Work Using 1D Numerical Model for the Oxide Scale Growth EstimationKINeticsOXidation Model [1] (without quasi-stationnary hypothesis) Using Analytical solution in semi-infinite system Fick’s Laws using 1D description (Fig.1) Initial and Boundary Conditions t=0 t>0 During some hypothetical Light Water Reactor accidental transients, the nuclear fuel claddings can be subjected to a high temperature oxidation caused by the interaction of the steam with the metallic cladding zirconium base material. This leads to the growth of brittle phase layers, such as  Zr(O) and ZrO 2, from the parent (ductile)  Zr phase. This phenomenon has been mainly studied experimentally; but, in modern fuel cladding alloys, there is still a need for a better quantification and modelisation of the related phenomena, that is ZrO 2 and  Zr(O) layers growth kinetics and especially the associated oxygen diffusion profiles within the suboxide metallic layer. Thus it appeared useful to develop a computational tool able to predict the evolution of the microstructure of low-tin Zy-4 during high temperature oxidation and also at intermediate oxidation temperatures. The final goal of this work is to extend the EKINOX model [1] to zirconium industrial alloys by coupling with the thermodynamic database Zircobase [2]. In a first step, the EKINOX model has been built to extend the Wagner’s model but without the pseudo-steady state hypothesis and with explicit calculations of vacancy profiles, as well as considering both the substrate and the oxide. Moreover, the case of mixed anionic- cationic transport mechanism can be considered. The model is based on an original numerical treatment to correctly and easily describe elimination of vacancies at the interface and within the metal and thus relative motion between the substrate lattice and the oxide lattice, even for non-stationary states (Fig.1). The second step of development has been to extend the EKINOX model to Zirconium alloys considering non-null oxygen solubility in the metal. Then, both analytical (semi-infinite system) and numerical (EKINOX) calculations have been performed and compared to experimental results obtained fater oxidation at 800°C in a steam environment. Context Objectives Results : Application to Zircaloy 4 alloys oxidized at 800°C  Good agreement between analytical solution, EKINOX and experimental data for oxygen concentration profiles in  (O) Zr at 800°C. However, the analytical calculations are only valid for short term oxidations, because they do not take into account the finite size of the sample (boundary conditions i.e. no oxygen flux at the inner surface.  Advantage of Numerical resolution with EKINOX model (without quasi- stationnary hypothesis): possibility to take into account - Finite size samples (any boundary conditions can be implemented) - Non isothermal conditions - Variation of concentration at moving boundaries interfaces - Possibility to begin the calculation with a pre-oxidized sample, etc…  Apply EKINOX model at T > 1000°C taking into account two moving interfaces that is : ZrO 2 /  (O) Zr and  (O) Zr /  (O) Zr  Coupling EKINOX with THERMOCALC Zircobase for a better set of thermodynamic parameters in the description of both equilibrium concentration at interfaces and calculation of fluxes from chemical potential, taking into account other alloying elements. Fick’s Laws Interface motion : Fig. 4: Experimental and calculated oxygen concentration profile in Zy-4  phase oxidized at 800°C during 431s (a) and 4330s (b) C 0 (at.%)C  /  (at.%)D  (cm 2.s -1 ) 0.728.41.53 10 10 Table. 1: Parameters used for calculated profile EKINOX simulationAnalytical solutionEPMA Analysis  Nanohardness measurements Fig. 3: Electron micrograph showing the two phase layers, ZrO 2 oxide and  (O) Zr, in a Zy-4 alloy oxidized at 800°C and the nanohardness measurements.  (O) Zr ZrO 2 t = 481s (a) (b) t = 4330s The samples studied are industrial Zy-4 cladding tubes (nominal composition (wt.%) Zr-1.3Sn-0.2Fe-0.1Cr-0.13O) oxidized at 800°C for 481s and 4330s respectively. The oxygen concentration profile within the suboxide metallic  Zr layer was measured using Electron Probe MicroAnalysis( ). Nano-hardness measurements (  ) were also performed on these samples, showing the hardening effect of O in solid solution. Fig. 4 shows a good agreement between the experimental data and the analytical and numerical calculations.