Volumen II - SAM

Concerning oxygen diffusion inside the cladding tubes (Zr base alloys) an adaptation of the EKINOX code
has been performed. First a non-null oxygen equilibrium concentration in the substrate has been added.
Second, a new interface in the substrate has been added in order to simulate the α→β phase transformation.
Fig.3. Schematic representation of the concentration profile in the Zircobase-TQ-EKINOX
simulations.
The substrate of metal M extends from Ns to NM+1 β(O)Zr and from NM to NI+1 (α(O)Zr).The oxide scale
extends from the layer NI to the layer number 1. In the oxide, two sub-lattices are considered for the cations
and for the anions. Only one lattice is considered in the metal. Each sublattice is occupied either by the
corresponding chemical species (metal M, oxygen O) or by the corresponding vacancies (VM , VO). Species
transport is calculated slab to slab with the explicit treatment of vacancy fluxes following Fick’s first law.
ThermoCalc-Zircobase. ThermoCalc [6] is a software able to calculate (with the system appropriated
information) different thermodynamic parameters in alloyed materials. During the past few years, CEA
(Commissariat à l'Energie Atomique) has been involved in the development of computer tools able to predict
metallurgical and thermomechanical behaviour of Zr alloys in normal and accidental conditions. In this
frame, a thermodynamic database named "Zircobase" [7] has been developed using ThermoCalc software. In
the present version of the EKINOX model the equilibrium concentrations at each interface are calculated
using an interface program ThermoCalc (TQ) from ZIRCOBASE.
3. RESULTS
Surface Interface
Gas Oxide Metal
Cφ/G Cφ/α ZrO2
(φ)
α(O)Zr
C α/φ
1 2 … N i +1
Cβ/α NM NM+1
N i … N s
Thermodynamic data set
Chung and Kassner [8] investigated the zirconium-rich portion of the pseudobinary Zy-4/oxygen phase
diagram. At T>1280K this work expressed the equilibrium concentrations between β and α phases as:
8220
ln C = 5.
02 −
β / β +α
(1) ln C = −2.
28 + 0.
535 ⋅ln(
T − 1083 ) (2)
α / α + β
T
where Cβ/β+α and Cα/α+β are the oxygen concentration in wt% at the β and α-phase boundaries respectively at
a given temperature T in Kelvin.
Equilibrium values can also be calculated from the Zircobase-ThermoCalc database [7]. They have been
calculated for both Zr-O system and taking into account the nominal composition of Zy alloy in the
temperature range [1100-1250]°C. The nominal composition of Zy-4 alloy considered for the calculation is
reported in Table 1.
Table 1. Typical chemical composition of Zy-4 alloys
Alloying elements Sn Fe Cr O
Weight % 1.30 0.20 0.09 0.138
Table 2 summarizes the equilibrium concentration values calculated from Chung-Kassner (C-K) expression
and from the ThermoCalc Zircobase (TC).
p n
C α/β
1319
Interface
β(O)Zr