High temperature oxidation of SiC fibers under low oxygen partial
pressure
Hun Nicolas, Brissonneau Laurent,
CEA, DEN, Cadarache DTN\STPA\LIPC, F-13108 Saint-Paul-lez-Durance, France
Rebillat Francis,
Université de Bordeaux, Laboratoire des Composites Thermostructuraux (LCTS),
France
Summary
Gas Fast Reactor (GFR) is one of the different Generation IV concepts under investigation for energy production. SiC/SiC composites are candidates of primary interest
for a GFR fuel cladding use, thanks to good corrosion resistance among other properties.
The mechanisms and kinetics of SiC oxidation under operating conditions have to be
identified and quantified as the corrosion could decrease the mechanical properties
of the composite. An experimental device has been developed to study the oxidation
of silicon carbide under high temperature and low oxygen partial pressure. The results pointed out that not only parabolic oxidation, but also interfacial reactions and
volatilization occur under such conditions. After determining the kinetics of each
mechanism, as functions of oxygen partial pressure and temperature, the data are
used for the modeling of the composites oxidation. The model will be used to predict
the lifetime of the composite in operating conditions.
This paper details the experimental methodology. The results obtained on Tyranno
SA3 fibers are discussed.
Keywords: SiC oxidation, diffusion, interfacial reaction, volatilization.
1
Introduction
During service in GFR, SiC/SiC composites are exposed to high temperatures (between 800 and 1200°C) and to a low amount of oxidizing species (a few ppm). The
oxidation of the composite could decrease its mechanical properties and therefore,
the mechanisms and kinetics of oxidation have to be determined.
An experimental device combining measurements of mass variation and oxygen
concentration has been developed to study the oxidation of Tyranno SA3 fibers in
operating Ar/O2 conditions. The experimental results showed that silica growth and
SiC volatilization occur simultaneously at 1200°C between 5 and 500 Pascal of oxygen. Very few papers have been devoted to the oxidation/volatilization of SiC in such
a low oxidant atmosphere. A few studies have been performed in Ar/O 2/H2O [1, 2],
but nothing was found under pure Ar/O2 atmospheres. Based on the experiments, a
model describing the key steps of SiO and SiO2 formation is put forward in this paper.
The method to interpret the experimental results and to extract kinetic data is described in addition.
1
2
Materials and experiment
The materials used are the commercial stoechiometric Tyranno SA3 fibers supplied
in yarns of 500 fibers. The average diameter of a single fiber is 7,5 µm. The samples
are previously desized in air at 600°C and set in an alumina crucible (≈45 mg). The
experimental techniques used are thermogravimetry (TGA, Mettler Toledo
TGA/SDTA 851) coupled with micro gas chromatography (µGC, Agilent G2891A),
and SEM observations (FEI quanta 400 FEG). Moisture traps and a chilled mirror
(Michell S4000) are used to control the absence of water that would modify the kinetics. The flowing atmosphere (9 l/h) constituted of Ar/O2 (5 to 500 Pa) is set at room
temperature in a mixing bay. The sample is heated at 20°C/min up to 1200°C under
flowing argon, the oxidizing atmosphere is then introduced in the furnace and the
samples are aged between 100 and 300 hours. The TGA is modeled with Ansys Fluent software to ensure that the kinetic regime is reaction controlled and not limited by
the flow conditions in the furnace.
3
Experimental Results
3.1 Typical results
The thermogravimetric curves reveal a continuous weight gain (fig.1a) and the µGC
measures the oxygen consumption (by difference with the previously performed
blank tests) at the outlet of the furnace (fig.1b). The quantity of CO and CO2 species
is too low to be detected by the µGC. The mass change is not important enough
compared to the oxygen consumption attributed to SiO2 formation. As confirmed by
active to passive transition studies [3-5] and thermochemical calculations (performed
with HSC 4.1 software), SiO volatilization has to be taken into account in the composition/temperature range of this study. The global reactions describing the system are
given below:
(I)
SiC  3 / 2 O2  SiO2  CO
(II)
SiC  O2  SiO  CO
The mass variation due to the formation of SiO2 and SiO is respectively 20g/mol and
-40g/mol. Considering that CO and SiO issued from reactions (I) and (II) oxidize in
the gas phase far from the crucible, a system is obtained:
m  20  nO 2

n SiO2 


m

20

n

40

n


60
SiO2
SiO

(1)

nO 2  2  nSiO  2nSiO2
n  m  10  nO 2
SiO
60

with:
- m : the total mass variation (g.m-2.s-1),
- n SiO : the molar amount of SiO volatilized (mol.m-2.s-1),
- nSiO2 : the molar amount of SiO2 remaining at the surface of the fibers (mol.m-2.s-1),
- nO 2 : the molar amount of O2 consumed during oxidation (mol.m-2.s-1).
nSiO2 is correlated to the thickness of silica (  in m) remaining on the fibers. The circular geometry of the fibers is taken into account to calculate  . However, because
the ratio silica layer / fiber radius is very small, there is no big difference between the
calculations for a circular and a plane geometry. The calculated values (fig.2a) of 
are compared and validated with the measured ones by SEM (fig.2b).
2
The amount of silica formed reported to the amount of Si reacted gives the ratio  .
After a transient period,  is stabilized around 76%. It means that 24% of the reacted
Si formed SiO and 76% formed SiO2.
The shapes of the figures presented below (1200°C, 5 Pa O2) are representative of
all the tests for this study.
6E-3
10
9
PO2 (Pa)
Blanc
8
7
4E-3
PO2 (Pa)
m/S (mg/cm²)
5E-3
3E-3
2E-3
6
5
4
3
2
1E-3
1
0E+0
0
0
50
Figure 1a:
100
150
t (h)
200
250
300
0
50
100
150
200
250
t (h)
m / S at 5Pa O2 and 1200°C
Figure 1b: O2 measurement (5Pa O2 and 1200°C)
100
90
80
 (nm)
70
60
50
40
30
20
10
0
0
50
100
150
200
250
300
t (h)
Figure 2a:
4

calculated (5Pa – 1200°C) : 87nm
Figure 2b:

measured by SEM (5Pa O2 and
1200°C) : 85±12 nm
Kinetic model
4.1 Kinetic regime
11 tests were performed at 1200°C between 5 and 500 Pa and exploited as presented before.
The results pointed out that volatilization of SiC is not negligible for the test conditions. Opila et al. [1, 2] used Tedmon’s approach [6] to describe the simultaneous
silica formation and its volatilization in moist atmospheres. In Opila’s approach, SiO2
parabolic growth is limited by the diffusion of the oxidizing species through the silica
layer, while it reacts in surface with H2O to form hydroxygenated species such as
Si(OH)4. Thermodynamical studies allowed the calculation of the partial pressure of
equilibrium at the surface of SiO2 and for reaction (III), depending on the oxygen partial pressure. Assuming that the convective flux of argon in the furnace controls the
kinetics of SiO evacuation, a theoretical flux of SiO can be calculated. It appears that
these calculated fluxes are far from the values obtained during the experiments.
(III)
SiC  2SiO2  3SiO  CO
Opila’s approach is therefore not applicable to our experimental conditions.
In our experimental conditions, the SiO2 growth is rather paralinear (fig 2a) as described by Deal and Grove [7] and other authors [8, 9]. The SiO2 growth is controlled
3
by diffusion of O2 through the silica layer and reaction of O2 at the SiC/SiO2 interface.
The thinner the silica layer is, the more linear the growth is. The reaction at the interface is the limiting step as the silica layer is not thick enough to act as a diffusion barrier for O2.
4.2 Oxidation mechanisms
Deal and Grove’s approach fits the experimental evolutions of  , but Opila’s approach is insufficient to explain the volatilization of SiO 2. In order to take the volatilisation and the paralinear growth of SiO2, a new approach for the SiC oxidation is
suggested:
SiO2 formation results from two key reactions:
(IV)
SiC  O2  SiO  CO
(V)
SiO  1 / 2 O2  SiO2
A fraction  of SiO is oxidized in the silica layer by reaction of the counter flux of O 2.
 can depend either on the diffusion coefficient of O 2 in SiO2 (D(O2-SiO2)) or SiO in
SiO2 (D(SiO-SiO2)).
Deak et al. [10] studied by first thermodynamic principle calculations the reactions of
O2 with an initially perfect SiC/SiO2 interface. Even if it is not the less energetic route,
SiO2 formation via SiO production (as proposed in this paper) is one of the possible
reaction calculated.
Assuming that a fraction  of SiO is oxidized at the interface SiC/SiO2, the different
steps of the SiC oxidation are described in figure 3:
And:
With:
- 
1
O2
-  SiO the SiO flux for the reaction IV,
1
the oxygen flux through the gas boundary
-  SiO the SiO flux for the reaction V,
2
layer,
-  O 2 the oxygen flux through the silica layer,
2
- 
3
O2
the oxygen flux for the reaction V,
- 
4
O2
the oxygen flux for the reaction IV
-  SiO the SiO flux through the silica layer
3
Figure 3: description of O2 and SiO fluxes at the surface of SiC
4.3 Modeling
Assuming a steady state, the different fluxes expressed before can be related together. The fluxes  are expressed in mol.m-2.s-1.
(2)
 1O 2 =  O2 2 =  3O 2 +  O4 2
1
2
3
(3)
 SiO =  SiO +  SiO
4
 O4 2 =  1SiO
Considering the stoechiometry of reaction (II),
2 3O 2 =  2SiO
(4)
(5)
The oxygen flux through the gas boundary layer  1O 2 is:
 1O 2  k D C e  C s 
(6)
with:
- k D : the transfer coefficient in the gas boundary layer (m.s-1),
- C e : the external oxygen concentration (mol.m-3),
- C s : the concentration of O2 at the SiO2 surface (mol.m-3).
The oxygen flux through the silica layer  O2 2 can be expressed by Fick’s first law:
dC
 O2 2   DO 2  SiO2
(7)
d
with:
- DO 2 SiO2 : the diffusion coefficient of O2 in SiO2 (m2.s-1),
-  : the thickness of SiO2 formed (m).
Considering a steady state, there is no O2 retention in the SiO2 layer. The variation of
O2 concentration in the layer is linear [7]:
C  Cs
 O2 2   DO 2 SiO2 i
(8)

with C i : the oxygen concentration at the SiO2/SiC interface (mol.m-3)
The oxygen flux for the reaction with SiC (reaction IV) is  O4 2 :
n
(9)
 O4 2  k l Ci l
with:
- k l : the linear constant of reaction (IV) (m.s-1 if nl =1),
- nl : the order of reaction (IV).
 is described as the fraction of SiO that reacted to form SiO2 :  2SiO   1SiO . Thanks
to relations (4) and (5) a relation between  O2 2 and  3O 2 is established:
 3O 2 

(10)
 O4 2 2
Equations (2), (6) and (9) give:
1 
2 k C nl
(11)
Ce  C s 
l i
kD
Equations (2), (6), (8) and (9) give:
1  
2 k C nl
(12)
C s  Ci 
l i
DO 2  SiO2
Dividing eq (12) by eq (11), the ratio Ce/Cs is obtained:
1  
2 k C nl 1
1
l i
Ce
DO 2  SiO2

(13)
Cs
 1  

1 

 nl 1
2
2
1 
kl 
k l C i
kD
 DO 2  SiO2



1
Introducing eq (13) in eq (6) the expression of  O 2 is:







5

 C
 1O 2  k D C e  C s   k D C e 1  s
 Ce
1   2 k C
1   2  1   2 k
l

Ci
1 nl




e
kl 
(14)
l
DO 2  SiO2
kD
The expression of the flux  is obtained with eqs (2), (10) and (14):
kl Ce
 O4 2 
1  
1 
(15)
1 nl
2
2 k
Ci

kl 
l
DO 2  SiO2
kD
The values of C e ,  and  are known from the experiment. k D is calculated from
the Fick diffusion coefficient [11] and the gas flow characteristics ( Re , Sc ) in the TGA.
Depending on the limiting step of reaction (II), nl can take different values:
- nl =0,5:
dissociation of O2 and adsorption of O2- at the interface SiC/SiO2 [12],
- nl =1:
reaction (II), stoechiometry controls the reaction order.
Parameters calculations have been done in both cases in order to determine the reaction order. The experimental curves are fitted with a strong accuracy in both cases.
As Trimaille et al. [13] observed a linear dependence with O2 for the silica growth until  <180nm at 1100°C, the following expressions are then written assuming that the
kinetics are limited by the reaction of O2 with SiC.
Considering a plane geometry, the expression of the SiO2 thickness is:
4
d    O 2 M SiO2

(16)
dt
 SiO2
which becomes using eq 15:
  kl Ce
d M SiO2

dt
 SiO2
1  
1 
(17)
2
2 k
1
kl 
l
DO 2  SiO2
kD
4
O2








4.4 Values of the parameters
The values of k l and DO 2  SiO2 are determined by minimizing the least square sum of
the experimental measures and the calculated values. The values are summarized in
figure 4a and 4b:
1,00E-11
DO2-SiO2 (m²/s)
1,00E-05
kl (m/s)
1,00E-06
1,00E-07
1,00E-08
1,00E-12
1,00E-13
1,00E-14
0
100
200
300
400
500
0
PO2 (Pa)
100
200
300
400
500
PO2 (Pa)
Figure 4a: Values of kl at 1200°C
Figure 4b: Values of DO2-SiO2 at 1200°C
The calculated values of k l and DO 2  SiO2 are stabilized above 50 Pa of oxygen. The
dispersion at low O2 amount could be attributed to the kinetics of nucleation and other mechanisms.
6
Above 50 Pa, the mean values are:
- k l = 8,2x10-8 (m.s-1)
- DO 2  SiO2 = 1,3x10-13 (m2.s-1)
5
Discussion
5.1 Comparison with literature
The value of DO 2  SiO2 is 1,25x10-13 m2.s-1. This value is in the order of magnitude of
Zheng [14] and Rodriguez [15] for molecular diffusion below 1240°C (4,0x10-14 <
DO 2  SiO2 < 4,5x10-11 m2.s-1). Ionic diffusion is 4 to 5 orders of magnitude lower than
molecular diffusion [14, 16]. This validates that the diffusing species at 1200°C and
low PO2 in silica are O2 molecules.
Even no study was found on the kinetics of SiO formation at the SiC/SiO 2 interface,
the value of k l can be compared to the linear constants of volatilization determined
at very high temperatures (1600 to 1650°C) in Ar/O2 atmospheres. In this study, k l at
1200°C equals 8,2x10-8 m.s-1. This value is smaller than the values of Narushima [17,
18] and Schneider [19]: 2x10-7 < k L < 5x10-5 m.s-1 which have been determined at
1600-1650°C. Assuming the same reaction mechanisms and an Arrhenius type behavior, experimental and literature values of k l can be compared to estimate an activation energy E a with 51< E a <330 kJ/mol. The calculated values of E a are consistent with literature [8, 20].
Based on the experimental values of DO 2  SiO2 and k l , an extrapolation in time is calculated up to 10000 hours. The silica thickness increases with PO2. A transition between the reaction controlled rate and the diffusion controlled rate can be observed
as a function the thickness. Parabolic oxidation described in literature at higher pressures [21, 22] and linear oxidation at low partial pressures [13, 23] are correctly reproduced by this model.
Figure5: Evolution of

at 1200°C based on experimental values of
DO 2  SiO2 and k l
5.2 Compared effect of DO 2  SiO2 and k l
The effect of DO 2  SiO2 and k l values can be discussed on the graphs below. Simulations have been calculated at 1200°C, 50 Pa O2, changing respectively the values of
DO 2 SiO2 and k l to observe the influence of their values.
7
Figure6a: Effect of
Figure6b: Effect of k l value on  evolution at
1200°C and 50 Pa O2
DO 2 SiO2 value on  evolu-
tion at 1200°C and 50 Pa O2
The evolution of  tends to be parabolic when DO 2  SiO2 is small compared to k l value and is nearly linear when DO 2  SiO2 is high compared to k l . Above some
k l / DO 2  SiO2 ratio, kinetics are only limited by diffusion through the silica layer, and the
evolution of  is parabolic no matter the value of k l . Below an other value of this
ratio and a limit SiO2 thickness, kinetics are linear as they are only limited by reaction
with SiC.
5.3 Limits of the approach
As seen in §4.4, the constants k l and DO 2  SiO2 are satisfactorily determined between
50 and 500 Pa of oxygen. Under these partial pressures, the µGC is not efficient
enough to precisely measure the O2 consumption, and the calculated values might
be overestimated. It can also be possible that the silica layer is first whiskers-like before covering homogeneously the fibers as observed by Nanri [24]. The time to reach
the silica layer is longer at small PO2 and not negligible anymore.
A study with a better measurement and characterization of the samples should be
realized at shorter times to better understand this transient state.
6
Acknowledgement
The authors thank F. Huang for his help and remarks on the topic.
7
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9