Oxidation kinetic analysis of a mixed uranium dicarbide and graphite
compound
M. Marchand a,*, O. Fiquet a and M. Brothier a
a Commissariat à l’Energie Atomique et aux énergies alternatives, CEA, CADARACHE, DEN, DEC, SPUA/Laboratoire des
Combustibles Uranium, 13108 Saint Paul-lez-Durance Cedex, France.
ABSTRACT
Oxidation of a mixed uranium dicarbide and graphite powder has been investigated by simultaneous
thermal gravimetric (TGA) and differential thermal (DTA) analyses coupled with gas phase
chromatography. For isothermal oxidation conditions with temperatures below 330°C, UC2 only
chemical phase is progressively oxidised into oxides form U3O8. Parabolic weight gain curves as a
function of the oxidation on time were obtained. A detailed kinetic study is proposed to establish a
pseudo stationary state during the oxidation process. Using an experimental method based on the
jumps of temperature, a single rate limiting step has been validated and then modelled by a three
dimensional diffusion law. An apparent activation energy calculated from the Arrhenius representation
has been evaluated to -35 kJ/mol describing the diffusion of oxygen through the oxide layer.
1.
INTRODUCTION
Context of the study The development of the new superconducting linear accelerator SPIRAL
2/GANIL [1] facility will use an UCx target assembly in order to generate high energy heavy ions. The
target material could be chemically defined by a mixed of Uranium dicarbide and free graphite [2].
After use, the potential pyrophoric behaviour of Uranium Carbide do not allow a direct storage as
Nuclear Waste. Used material has to be first stabilized and therefore requires the development of a
chemical process to guarantee safety handling conditions. One possible process pathway consists on
a selective isothermal oxidation of UCx into uranium oxides (UOx) at a given oxygen partial pressure.
The understanding of the oxidation kinetic mechanism of Uranium Carbides is essential to avoid a
hazard ignition in air and to optimize oxidation process parameters.
State of art Few studies only have been reported on Uranium dicarbide oxidation. Rado et al. [3]
showed that exothermic ignition corresponding to the transformation of UC2 into UO2/U3O8 could occur
from 230°C depending of specific conditions (sample grain size, heating rate, initial mass, etc.). The
oxidation reaction with uranium dicarbide in oxygen partial pressure atmospheres leads to the final
formation of uranium oxide form U3O8 [4]. The reaction enthalpy from UC2 into U3O8 has been
evaluated to -1400 kJ/mol [5]. A detailed study including the identification of intermediate oxidation
products of UC2 has been exposed by Nawada et al. [6]. The experimental data’s were obtained with
simultaneous non isothermal and isothermal conditions by thermal gravimetric, evolved gas detection,
X ray diffraction and chemical analysis. Four oxidation intermediate steps are proposed for the
formation of U3O8 from UC2; (1) the first oxidation step gives to -UO3 with the release of chemically
*
Corresponding author. Tel : +33 04 42 25 49 39 ; fax : +33 04 42 25 48 86
E-mail address : mickael.marchand@cea.fr
bound carbon, then (2) the oxidation of chemically bound carbon to CO2, (3) the oxidation of -UO3 to
U3O8 and finally (4) the residual free carbon oxidation to CO2. No kinetic analysis has been achieved
to understand the oxidation mechanism of uranium dicarbide. The authors noted however that carbon
release could be the rate limiting step.
The only Uranium single carbide chemical structure has been studied on kinetic aspect in according
with the development of the advanced fast nuclear reactor and its use as potential fuel. In a study on
UC microspheres oxidation kinetic with variable oxygen partial pressure, Mukerjee et al. [7] observed
for a partial pressure higher than 20 kPa the formation of U3O8 powder with a release of CO2.
Intermediate oxidation products may be formed and depend on the experimental conditions such as
temperatures and oxygen partial pressures. First, a layer of UC1-xOx may appear during oxidation
before the formation of an UO2 layer and the final U3O8 product [8]. By studying the time dependent
evolution of the average thickness oxide layers exposed to air at ambient temperature, Matzke et al [9]
concluded that the oxidation kinetic on UC single crystals is controlled by a volume diffusion process.
The oxygen diffusion through the oxide layer may be the limiting stage. UC powders isothermal
oxidation under different oxygen partial pressures have been also studied by Naito et al. [10]. They
defined three distinct regimes depending on oxidation temperatures from 400 and 1400°C and
calculated several apparent activation energies ranging from 6 to 96 kJ/mol. In opposite to Matzke et
al., they observed at the initial stage, constant oxidation rates for all case studied suggesting a surface
controlled reaction. A comparison of the thermal gravimetric analyses revealed different oxidation
behaviors depending experimental conditions. For example, Peakall [11] and Herrmann et al. [12]
obtained constant oxidation rates whereas Moreau and Philipport [13] measured parabolic mass
curves in similar conditions. Results have been obtained with different oxidizing conditions
(temperature range and heating rate, material composition and form, etc). These conditions clearly
influence the oxidation kinetic. Moreover these results are relative to the stoichiometric UC
composition and may differ from a biphasic material in UC2 and graphite. In the present work, we
propose to study the oxidation behavior of this compound – mixed of graphite and uranium dicarbide
powder - combined with a detailed kinetic analysis.
2.
EXPERIMENTAL METHOD
Manufacturing and characteristic of the UCx powder
UCx compound was prepared by carbothermic reduction from Uranium dioxide following the
experimental procedure proposed by IPNO (Institut Physique Nucléaire Orsay) in the development of
UCx targets for heavy ion accelerator [14]. A stoichiometric mixture of UO2 and graphite was pelletized
then heated until 2000°C for 6 hours under vacuum. The global carbothermic reduction reaction is
defined by:
UO2  6C  UC2  2C  2CO


UCx
Équation 1
Mixed UC2 and graphite pellets were crushed and saved with a sieve of 100 µm in order to get a
narrow grain size powder for oxidation experiments. It should be noted that in practise, the perfect
stoechiometry C/U=4 defining the UCx mixture was difficult to satisfy.
Oxidation study: material set up and parametric field
Oxidation tests were performed by thermal gravimetric and thermal differential analyses in a
SETARAM SetSys Evolution DTA/TGA thermal balance. The differential thermal signal (DTA) has
been preliminary calibrated from several standard materials in similar experimental conditions used for
the oxidation of UCx. A gas chromatograph SRA-A300 analyser has been coupled on the gas output
line of the thermal balance to monitor the gas evolution during the oxidation cycles. The balance was
located in a glove box under nitrogen atmosphere. UCx samples mass for DTA/TGA tests was about
(50.0+/-0.8) mg. We used a 100 µL cylindrical platinum crucible. Samples were first heated to desired
oxidation temperature (rate 10°C/mn) under argon (gas flow rate 50 mL/mn Patm). Oxidation
experiments were performed under 1 bar absolute pressure and with an oxygen concentration of [O2]
=10.3%. After a stabilisation step of 30 minutes, a mixture argon-air gas mixture (ratio 0.5/0.5, total
gas flow: 32 mL/mn) was introduced. Mass variation and heatflow were recorded with Calisto
software. Temperatures in isothermal regime varied from 240 to 700°C. After the isothermal oxidation
treatment, an additional oxidation cycle (rate 10°C/mn, TMAX = 800°C) was optionally programmed.
This additional step is useful to quantify the complete oxidation and obtain a final U3O8 product without
any carbon residues.
Identification of chemical phases from partial oxidised UCx samples at different oxidation conversion
rates was carried out by a Brucker D8 Advance X-ray diffractometer (XRD). For this purpose,
oxidation was stopped at specific time and the samples were cooled down in pure Argon.
Kinetics analysis and methodology
Basic kinetic equation and hypotheses
In most kinetics studies, we use the assumption that the fractional conversion α follows equation
 Ea
d
 k T (T ) f ( )  A exp(
) f ( )
dt
RT
Équation 2
Where kT(T) is the activation kinetic with Ea called an effective or apparent activation energy
(Joules/mol), R the ideal gas constant, A the preexponential factor and f(α) an analytical function
which depends in particular on the sample shape and the step controlling the growth [15].
Équation 2 implies several hypotheses and in particular that kinetic is controlled by a rate limiting step
which follows an Arrhenius law. This rate limiting step can be analysed by a unique geometric reaction
model within the f(α) mathematical term. Using α which reflects the progress of the overall
transformation of a reactant to a final product, it is generally assumed that the chemical reaction is
perfectly identified. A wide variety of kinetic models are used to describe the conversion dependence
of the process rate [16,17]. In General, f(α) can be described by the Ginstling-Brounshtein diffusion
law of reactant trough an oxidised layer or by the Avrami-Erofeev law to model sigmoid experimental
curves.
The use of these models implies that the global process rate is constant during all the chemical
reaction. However, transformations often involve more than a single reaction step. Multiple steps with
specific conversion rates αi for a reaction i may appear during the entire oxidation reaction [18].
Moreover, nucleation and growth processes may be in competition and the specific surface changes
may vary during the oxidation. In general,
Équation 2 is not strictly valid in particular with
heterogeneous material. Then, it is assumed that the real mechanism involves several steps but only
one determines the overall kinetic.
Kinetic analysis for a biphasic material
In case of a mixed uranium dicarbide and graphite compound, several elementary oxidation steps may
exist to end finally with Uranium oxides and some remaining carbon. As way of consequences, it is
crucial to verify the existence of a single rate-limiting mechanism before modelling the oxidation of UCx
powder and in particular UC2 by a typical kinetic law. An experimental methodology proposed by
Soustelle et al. [19,20] can be used to verify two fundamental hypotheses in heterogeneous kinetic. It
consists to demonstrate:
-The existence of a pseudo-stationary state and a rate limiting step during complete isothermal
oxidation.
-The existence of a single rate-limiting step based on temperatures or pressures variations [19,21] and
given by:
d
  (T , P) E (t )  Ry
dt
Équation 3
In which
 (T , Pi )
is a function rate per unit area (mol.m -2.s-1) and
expressed in m2.mol-1.
The function
Équation 3 is only validated after the pseudo stationary regime is established.
 (T , P)
is correlated to the nature of the rate limiting step (interface reaction or
diffusion) and only depends of the partial pressure
The function
E(t ) a “space time function”
P
of the reacting gases and the temperature
T.
E(t ) corresponds to the extent of the reaction zone where the rate limiting step occurs.
In its kinetic formulation,
Ry is called the reactance.
Contrary to
Équation 2, no initial assumption is made concerning the nature and the spatial
localisation of the reaction step. This methodology experimentally described in detail in the following
paragraph has already been used with success to study the transformation kinetic of UO2 into U3O8 in
air by thermal gravimetric in isothermal conditions [23]. This method has never been applied for the
UCx system.
3.
RESULTS AND DISCUSSIONS
Description of a complete oxidation cycle – Identification of the main oxidation reaction at
300°C
Figure 1 : Superposition of thermal and differential gravimetric curves versus time coupled with gas
detected by gas phase chromatography. Oxidation of UCx powder at 300°C.
Figure 1 represents the mass variation (in %) and the associated Heatflow of UCx compound (in mW)
for an isothermal oxidation at 300°C. The test ends with a second non isothermal oxidation cycle at
800°C. Evolutions of chemical gas phases recorded by chromatography (O2, CO2 and CO) are also
represented. In isothermal regime, the sample mass increases of 14.9 % and stabilises. The DTA
signal (Heatflow) gives an oxidation heat of -207 Joules (-4120 J/g). No production of CO and CO2 is
recorded during the isothermal regime. The TGA weight gain is compatible with the following global
oxidation reaction:
UC2  1.8C  1.3O2  0.3U 3O8  2CUC2  1.8C
Équation 4
Therefore we postulate, in agreement with Nawada et al. [6], that uranium dicarbide is oxidised into
U3O8 with a simultaneous release of carbon. This reaction was also proposed by Berthinier et al. [22]
from UC oxidation studies at low temperature. We will note this carbon CUC2. Free graphite (noted C)
is not oxidised at these low temperatures.
During the oxidation cycle at 800°C in non isothermal conditions, two weight losses are measured :
first weight loss of -6.76 % for a temperature of (315+-5) °C followed by a second of about -9% at
(560+-10)°C . Two consecutive CO2 gas releases are recorded (CO is also detected at 560°C). By
comparison, experiments performed on graphite in similar conditions showed that the second mass
loss and the simultaneous release of CO/CO2 gas can be attributed to the oxidation of free graphite of
UCx compound. We suppose that the first mass loss correspond to the oxidation of the release carbon
CUC2 into CO2 (or other residual oxidised product UC2-xOy containing carbon bond of UC2 phase). Thus
the carbon form issued from UC2 phase is more reactive compared to free graphite. Moreover, we do
not observe CO release during its oxidation contrary to free graphite. The carboneous phase issued
from UC2 is only observed temperatures below 330°C. For temperature above, carbon CUC2 is oxidised
and CO2 is released. Our results showed that another oxidation mechanism is involved [24].
The total mass variation observed (-1.32 %) in Figure
1 is compatible with Equation 5 :
UC2  1.8C  5.2O2  1 / 3U 3O8  3.8CO2
Equation 5
Sequential XRD analyses at different oxidation times have been achieved to identify the
crystallographic chemical phases and validate the different hypotheses. Results are shown in table 1.
Phase’s determinations are classified by order of peaks intensities. It should be noticed that X-ray
diagram are not well defined. Oxidised products are not well crystallized at these temperatures
(specifically at a short oxidation time t1). XRD analysis of the sample oxidised after t2=650 minutes and
corresponding to a stabilised mass gain with the TGA signal revealed U 3O8 and C as main phases.
Some partly ill defined peaks or present in minor quantity were also observed and could be attributed
to oxides forms as UOx
x=2-2.12
or UC2-xOy. XRD analyses performed at time (t3) (first mass loss) and at
t4 (after the second mass loss) reveal well-defined diffraction patterns and confirm the progressive
oxidation of free graphite and the presence of stable hexagonal U3O8 form as final residue.
Oxidation time on Figure 1
Identified Chemical phases
Comments
Isothermal oxidation –
t1=110 mn
C, UC2, U3O8, UOx x=2-2.12
conversion rate =0.5
Isothermal oxidation –
t2=650 mn
C, U3O8, (UOx x=2-2.12 , UC2-xOy)
conversion rate =1
Non isothermal oxidation – after
t3=805 mn
C, U3O8
the first mass loss
End of oxidation – after the
t4=900 mn
U3O8
second mass loss
Table 1 : Chemical phases detected by X ray diffraction for different oxidation times
Figure 2 : Isothermal weight gain curves versus time during oxidation of UC2
Kinetic analysis of UC2 oxidation
Isothermal oxidation profiles from UC2 into U3O8
Figure 2 shows conversion rates α as a function of time for isothermal oxidation experiments. α is a
dimensionless fractional extent of conversion defined by :
 (t ) 
(m(t ) / m0 )
(mF (t ) / m0 )
Equation 6
Where
(mF (t ) / m0 ) is the theoretical mass gain measured by thermal gravimetric at the end of
the isothermal oxidation cycle and corresponding to the reaction of UC2 into U3O8 according to
Équation 4 ( mF (t ) / m0
 14.98% ).
Six different isothermal oxidation cycles with
temperatures ranging from 240 to 330°C and [O2] concentration of 10.3% are represented. All
experiments performed at temperatures below 330°C give parabolic curves. No CO and CO2 release
is detected by µGC analyser.
Isothermal representation of the fractional conversion versus time (Figure 2) can be analysed by
testing a large variety of kinetic models. For this, it is essential to validate preliminary hypotheses of a
pseudo stationary regime and a single rate limiting state.
Verification of a pseudo-stationary state
Figure 3 : Experimental validation test of a pseudo-stationary system
The assumption of a pseudo-stationary regime during the complete oxidation of uranium di-carbide
into oxidised form can be justified by the measure of two extensive physical variables at different
fractional conversion α [21]. Using simultaneous DTA and TGA measurements, the pseudo-stationary
state assumption is validated when the rates of the derivate of weight gain and heat flow curves are
proportional in all extent of conversion α.
Figure 3 represents the variations of the TGA signal derivate (dm/dt) and heat flow DTA signal (dQ/dt)
versus time from an UCx isothermal oxidation at 300°C under an air-argon mixture (10.3% [O2]). Both
curves are well superimposed. Some minor differences appear at oxidation end corresponding to a
conversion factor α higher than 0.9. So we conclude that the isothermal oxidation of UCx powder into
oxide according to Équation
4 follows a pseudo-stationary regime.
Validation of a single rate-limiting step assumption
Figure 4 : Experimental validation test of a single rate limiting step
The validation of the existence of a single rate-limiting step can be experimentally verified with a
specific method. It consists to perform successive experiments introducing rapid change of one
extensive variable (typically temperature or partial pressure) at different oxidation times. This
approach is used by Rousseau et al [23] for the study of the oxidation kinetic of uranium dioxide UO2.
The experimental validation test of a single rate limiting step is represented with the
Figure 4 a-b
(inset). A first thermal gravimetric curve obtained with a temperature of 280°C is considered as the
reference curve and corresponds to the progressive oxidation of UCx into U3O8 powder during 14
hours (Cf. Équation 4). At two different oxidation times called tα=0.2 and tα=0.6 corresponding to different
fractional conversion α=0.2 and α=0.6, we suddenly raised the temperature to T1=300°C (heating rate
=10°C/mn - All other parameters set to constant). Masses variations after its rapid heating at 300°C
are recorded and then compared to the original curve (T=280°C). We calculate the rates before (RI)
and after (RF) the temperature change from slopes of thermal gravimetric curves.
If the pseudo-stationary state and the single rate limiting step assumption are verified, then the ratios
RF/RI are equal for any time t. If the ratios are not equal, there is no single rate limiting step and
Équation 3 previously defined in not valid.
According to this equation, rates (RI) and (RF) can be expressed by:
RI   (T0  280 C, Patm ) E (t 0.2 )
And
RF   (T1  300C, Patm ) E (t 0.2 ) For t 0.2
And
RI   (T0  280C, Patm ) E (t 0.6 ) And
RF   (T1  300C, Patm ) E (t 0.6 ) For t 0.6
All experiments were achieved at the same partial pressure Patm. Therefore, temperatures changes
occurred at the same oxidation time to evaluate RI and RF. As a result,
rates (=0.2 and =0.6) are equal.
E (t  ) terms for each oxidation
By comparison ratios of RI and RF terms (also called reactance in
heterogeneous kinetic) at two different oxidation times tα=0.2 and tα=0.6, we obtain the following
expressions:
RF
RI
RF
RI

 (T1  300C , Patm ) E (t 0.2 )  (T1  300C )

 (T0  280C , Patm ) E (t 0.2 )  (T0  280C )

 (T1  300C )
 (T0  280C )
 0.2
 0.6
Calculations
RF
RI
 0.6
give
ratios
of
For =0.2 and
For =0.6
RF
RI
  0.2
1.386.103

7.892.104
 1.757  0.042
for
α=0.2
and
  0.2
4.522.104

 1.759  0.043 for α=0.6.
2.570.104  0.6
We got identical numerical ratios which validate the existence of a single rate-limiting reaction step.
Chemically speaking, it means that no intermediate species accumulation occurs. Each UC2 mole is
entirely converted into oxide mole. The physical
 (T , P) term, which defines the oxide path growth,
is independent with the time.
It should be noticed that all thermal gravimetric curves are perfectly reproducible for this test. The ratio
RF/RI has been calculated for two oxidation rates α=0.2 and 0.6. It corresponds to the maximal Heat
Flow during oxidation (for =0.2) and a Heat Flow four times lower (for =0.6) (see
Figure 3). We
have reproduced the same experimental test from isothermal oxidation curve obtained at 300°C. We
have got for calculated ratios RF/RI at =0.2 and =0.6 again similar results.
These results valid hypothesis of a pseudo-stationary state and a single rate-limiting reaction step in
order to describe the isothermal oxidation of UCx at temperatures until 330°C.
For higher oxidation temperatures (T> 350°C), sigmoid shapes mass curves are obtained [24]. A
release of CO2 is then observed during the isothermal treatment. The pseudo stationary state is no
more valid.
Oxidation kinetic law of UC2 phase at low temperatures (below 330°C)
In the domain of single rate-limiting step mechanism below 330°C, we have tested different sort of
kinetic models [16-18].
Figure 5 : Ginstling dependence during isothermal oxidation of UC2 below 330°C
The most appropriate model to describe UC2 oxidation behaviour is a D4 Ginstring-Brounshtein three
dimensional diffusion model defined as:

g ( ) D 4  
0
d
2
1
 (1   ) 2 / 3  kT t
f D 4 ( )
3
Équation 7
Where g(α) is the integral form of the analytical function f(α) defined in
activation kinetic. Figure 5 represents the evolution of
g ( ) D 4 as
Équation 2 and kT the
a function of time from six
isothermal oxidation temperatures. Curves obtained are linear with time in particular at low
temperatures. In these experimental conditions, it implies that oxidation of the UC2 phase located into
UCx compound follows a diffusion-controlled mechanism. As a result, the activation constant kT
defined from equation
Équation 7 can be evaluated from the slopes of the curves plotted in Figure
5. Evolution of kT versus oxidation temperatures is then represented from an Arrhenius plot (see
Figure 6) in order to calculate the apparent activation energy of the mechanism. Slope of the curve
gives a constant energy of
E a  (34.8  3.1)kJ / mol .
This value indicates that the
conversion of UC2 into oxide is a low thermally activated reaction and reflects the major role of gas
transport. The apparent activation energy calculated is close to one reported by Murbach for UC [25]
and by Mazaudier et al. for (U,Pu)C fuels [26]. The validation of a pseudo-stationary state and a single
rate limiting step during the oxidation of UC 2 suggest that the oxidation is governed by the diffusion of
oxygen within the oxide U3O8 layer growing on each grain of UC2. It also means that the
nucleation/precipitation of oxygen at the UC2 surface is very quick in particular at the early step of
oxidation. A possible oxidation path mechanism as proposed by LeGuyadec et al [8] may occur.
Oxygen would enrich on the UCx surface and react with UC2 phase to form rapidly a layer of UC2-yOy
until saturation. The nucleation of U3O8 would be easier and could form a layer which extends during
oxidation by progressive consuming of UC2 kernel. Contrary to LeGuyadec, because of different initial
experimental conditions, we do not observe brutal ignition by working at low oxidation temperatures.
We suppose that the oxide layer does not break down due to a local stress. The UC2 conversion
shows a steady rate during the all oxidation cycle. No new activated surface is created and it does not
lead to a rapid elevation of heat flow as observed by LeGuyadec.
Figure 6 : Arrhenius plot of kinetic constant kT
4.
CONCLUSION
The behaviour of a mixed uranium dicarbide and free graphite compound has been studied by thermal
gravimetric (TGA) and thermal differential (DTA) analyses coupled with gas phase chromatography
analyser at low temperatures in isothermal conditions. Solids phases have been characterized by
XRD. Results showed that UC2 issued from UCx powder is progressively oxidised into oxide forms
(mainly into U3O8) in isothermal oxidation for temperatures below 330°C. Carbon in dicarbide remains
in the oxidised solid because no CO/CO2 gas release is detected. Free graphite located into initial UCx
powder is not oxidised at these temperatures. The simultaneous measures of parabolic curves
obtained by TGA and the resulting heatflow measured by differential thermal analysis (DTA) allow
validating a pseudo stationary state for the entire reaction. From a general formulation based on the
separation of the kinetic variables, a unique single rate limiting step has been also determined to
describe the overall oxidation of uranium di carbide into oxide and the modelling by a diffusion
controlled mechanism with a Ginstling Brouhnstein law. Low apparent activation energy (-34.8 kJ/mol)
revealed an oxidation process weakly thermally activated. The mechanism can be interpreted by to
the diffusion of oxygen through the oxide layer. Other experiments will be program to describe the UCx
powder oxidation behaviour with kinetic analyses at higher temperatures. These results may be used
for the validation for safety analysis of the UCx reprocessing process.
Acknowledgements
The authors wish to thank the Institut Physique Nucléaire d’Orsay (IPNO) for the furniture of UC x
pellets.
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