Volumen II - SAM

Table 2: Interface equilibrium concentration in different Zr alloys at [1100, 1200, 1250]°C
C β/β+α β/β+α β/β+α β/β+α
Cα/α+β α/α+β
Cα/α+ α/α+ox α/α+
T°C
Zy-4
(wt frac) (at. frac)
Zr-O
((((wt frac)
Zy-4
(wt frac) (at. frac)
Zr-O
(wt frac)
Zy-4
(wt frac) (at.frac)
Zr-O
(wt frac)
1100
TC
C-K
0.0031
0.0038
0.0174
0.0213
0.0040 0.0162
0.0212
0.0854
0.1099
0.0152 0.0684 0.2943 0.0702
1200
TC
C-K
0.0048
0.0057
0.0279
0.0316
0.0061 0.0209
0.0248
0.1086
0.1267
0.0198 0.0698 0.2998 0.0715
1250
TC
C-K
0.0058
0.0068
0.0322
0.0376
0.0071 0.0228
0.0265
0.1175
0.1344
0.0218 0.0705 0.3021 0.0721
Kinetic data set
Experimental diffusion profiles from [1], determined by microprobe analysis, allow to locate with adequate
precision the α/β interface at different temperatures. Then, an adequate set of input kinetic parameters for
Zy-4 has been chosen in the [1100-1250]°C temperature range in order to reproduce the α/β interface
position at each diffusion time (Table 3).
Table 3: Diffusion coefficients in αZr, βZr and ZrO2 at 1100, 1200, 1250°C
T°C Dα (cm 2 /s) Dβ (cm 2 /s) Dox (cm 2 /s)
1100 2.48x10 -8 8.44x10 -7 3.99x10 -7
1200 8.50x10 -8 1.55x10 -6 9.21x10 -7
1250 1.48x10 -7 2.05x10 -6 1.35x10 -6
Comparison of EKINOX simulations with experimental oxygen profiles
The diffusion profiles in α and β phases of Zy-4 are presented in the [1100-1250]°C temperatures range
(Fig.4.) These profiles have been simulated using EKINOX and TC for Zy-4 values from Table 2 and
kinetics parameters given in Table 3. The experimental data are partially taken from [1].
The simulation profiles are in the experimental quoted errors (around 1x10 -2 atomic fraction). The shape of
the experimental oxygen diffusion profile obtained at 1200°C for the longest oxidation times is due to α(o)
incursions in prior-β. Additionally, the determination of the experimental equilibrium concentration at the
α/ox interface is quite difficult. Considering these points, simulations are in good agreement with
experimental data.
Oxygen concentration (at. fraction)
0,3
0,25
0,2
0,15
0,1
0,05
1100°C
0
0 100 200 300 400 500 600
Distance (µm)
467s - Experimental
467s - Simulation
117s - Experimental
117s - Simulation
Oxygen concentration (at.fraction)
0,30
0,25
0,20
0,15
0,10
0,05
0,00
0 100 200 300 400 500 600
Fig. 4. Comparison of experimental and calculated O diffusion profiles in Zy-4 at 1100, 1200 and 1250°C.
The choice of adequate kinetic variables in α phase is significant for the simulation. Finally, the Arrhenius
plot presented in Fig.5, determined from adjusted EKINOX diffusion parameters (Table 3), can be expressed
T[K]
as follows:
D [cm 2 /s]
1E-6
1E-7
1E-8
1200°C
Distance (µm)
1520 1480 1440 1400 1360
0,00066 0,00069 0,00072
1 / T [K -1 ]
1429s - Simulation
1500s - Experimental
520s - Simulation
500-600s - Experimental
187s - Simulation
~ 200s - Experimental
55s - Simulation
~ 50-60s - Experimental
Fig.5. Arrhenius diagram of O diffusion in αZr
1320
Oxygen concentration (at. fraction)
0,3
0,25
0,2
0,15
0,1
0,05
1250°C
0
0 100 200 300 400 500 600
Distance (µm)
120s - Experimental
120s - Simulation
309s - Experimental
309s - Simulation