Development of EKINOX Model for the Prediction of Development of EKINOX Model for the Prediction of

Microstructural Evolutions in Zr Alloys during OxydationMicrostructural Evolutions in Zr Alloys during Oxydation

L. Anagonou, C. Desgranges, C. Toffolon-Masclet, S. Poissonnet and J.C. BrachetCEA, 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 ZrO2 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/

C0

0

gas

l

C ZrO2

(O)Zr

xx1

Moving interface

//

111

1

)()(

CCPBR

x

CD

x

CD

dt

dx xxxx

(O)Zr(O)Zr

Conclusions

Fig. 1: Schematic representation of the “1D” system with Ns contiguousslabs of thickness en.

1 2 … Ni N N+1 Ns1 2 … Ni +1 NiNi … Ns

OxideGas

ene

Metal

InterfaceSurface

C/G C/

C/

C0

()

CN

(O)ZrZrO2

Numerical solution calculated from time integration by 1D explicit finite differencies algorithm

The EKINOX model enables calculation of :

the growth kinetics

chemical species and vacancies concentration profiles in the oxide and in the metal

/

21

CC

JJeNiNiNNi

ni

l

/

i1-

ox Ω t

Interfaces motion (oxide referential), example for oxide growth at metal/oxide interface :

)2

(1 1

0/

0

tD

xxerf

CC

CC

Analytical solution for oxygen concentration profile Cα 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

121

1~

nn

n

kV

n

kV

Vee

XXDJ

Ω

1 1nn

kV

sinks

n

VM

n

1nn

Vi

n1n

Vinn

Vin

Vi )X(e

JJ Ω

t

XX

In the substrate

sinks

n

VM

n

1nn

Vi

n1n

Vinn

Vin

Vi )X(e

JJ Ω

t

XX

In the substrate

sinks

n

VM

n

1nn

Vi

n1n

Vinn

Vin

Vi )X(e

JJ Ω

t

XX

In the substrate

Fick’s Laws using 1D description (Fig.1)

Initial and Boundary Conditions

t=0t>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 ZrO2, 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 ZrO2 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 : ZrO2/(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)

C0 (at.%) C/(at.%) D(cm2.s-1)

0.7 28.4 1.53 1010

Table. 1: Parameters used for calculated profile

x

CDJ

Jx

C

EKINOX simulationAnalytical solution EPMA Analysis Nanohardness measurements

Fig. 3: Electron micrograph showing the two phase layers, ZrO2 oxide and (O)Zr, in a Zy-4 alloy oxidized at 800°C and the nanohardness measurements.

(O)Zr ZrO2

0

5

10

15

20

25

30

0 5 10 15 20

Distance (from the moving metal/oxide interface) (µm)

Oxy

gen

co

nce

ntr

atio

n (

at.%

)

2,5

8

13,5

Nan

o h

ardn

ess (GP

a)

t = 481s

(a) (b)

0

5

10

15

20

25

30

0 10 20 30 40 50 60

Distance (from the moving metal/oxide interface) (µm)

Oxy

gen

co

nce

ntr

atio

n (

at.%

)

2,5

8

13,5

Nan

o h

ardn

ess (GP

a)

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.