C interaction by high-temperature mass spectrometry

Nuclear Engineering and Design 238 (2008) 2866–2876

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Kinetic study of the UO2 /C interaction by high-temperature mass spectrometry a ´ S. Gosse´ a,∗ , C. Gueneau , T. Alpettaz a , S. Chatain a , C. Chatillon b , F. Le Guyadec c a

CEA Saclay – DEN/DANS/DPC/SCP/LM2T, 91191 Gif-sur-Yvette Cedex, France SIMAP/LTPCM, ENSEEG BP 75 Grenoble, 38402 Saint-Martin d’H`eres Cedex, France c CEA Pierrelatte – VRH/DTEC/STCF/LMAC, BP 111 – 26700 Pierrelatte, France b

a r t i c l e

i n f o

Article history: Received 6 April 2007 Received in revised form 17 January 2008 Accepted 23 January 2008

a b s t r a c t For very high-temperature reactors (V)-HTR, one of Generation IV future systems, the high-level operating temperature of the fuel materials in normal and accidental conditions requires the prediction of the possible chemical interactions between the fuel component (UO2±x ) and the structural materials (C, SiC). To predict the thermo-mechanical behaviour of the TRi-ISOtropic (TRISO) particle, it is necessary to better understand the gaseous carbon oxides formation at the fuel–buffer interface that leads to the build up of the internal pressure. High equilibrium CO(g) pressures resulting from the UO2±x /C reaction are predicted using thermodynamic calculations. The kinetic mechanisms involved in this reaction that limit this pressure increase have to be determined by convenient experiments and associated models. Some of the reported data on the kinetics of CO(g) formation due to the UO2±x and carbon interaction have been reviewed. The discrepancies between the reaction mechanisms can be explained (i) by the different geometries and sample types and (ii) by the oxide stoichiometry and the flowing gas used during the experiments. Depending on these characteristics, the phenomena involved in CO(g) formation can be of three different origins: interface, surface or diffusion. Using high-temperature mass spectrometry (HTMS), kinetic measurements of the CO(g) and CO2(g) species evolved during the interaction between UO2±x and carbon were performed. The samples are pressed pellets consisting of a mixture of UO2±x (60% molar) and carbon black (40% molar) powders. CO(g) is the major product above 1200 K. Rates of the CO(g) formation have been established taking into account the oxygen composition of the non-stoichiometric uranium dioxide and temperature. Results underline the upmost importance of kinetic factors for studying the CO(g) pressure variation inside the TRISO particle. © 2008 S. Gossé. Published by Elsevier B.V. All rights reserved.

1. Introduction The TRi-ISOtropic (TRISO) coated fuel particle is one of the retained fuels for the Generation IV very high-temperature reactors (V)-HTR. The integrity of this particle with respect to fission products is a key point of the inherent safety features of the (V)-HTR. This study deals with the chemical interaction between the UO2±x fuel kernel and its surrounding pyrolytic carbon matrix which has to accommodate noble fission products and CO(g) and CO2(g) gas releases. During the fission process of the UO2 kernel, gaseous fission products (He, Xe and Kr) are directly formed whereas carbon oxides are produced by excess oxygen released during fission reacting with carbon from the low-density buffer. Both these phenomena must be taken into account to establish the thermo-mechanical fuel behaviour. The maximum internal pressure of the TRISO particle

∗ Corresponding author. Tel.: +33 1 69 08 97 39; fax: +33 1 69 08 92 21. ´ E-mail address: [email protected] (S. Gosse).

is defined by a value of approximately 1000 atm before overpressurization failure of the SiC coating. Under nominal operating conditions, the TRISO particle can be considered as a closed system in which the formation of gaseous products generates an increase of its internal pressure. In case of a failure of the SiC coating, the TRISO particle can be considered as an open system. The release of gaseous products generates an inner CO(g) pressure drop. This may move equilibrium and generate the formation of uranium carbide phases. A previous work was undertaken on the thermodynamic properties of the uranium–carbon–oxygen ternary system (Gosse´ et al., ´ 2006) and on the CO(g) associated equilibrium pressures (Gueneau et al., 2005). In fact, it is important to establish the maximum CO(g) and CO2(g) gas pressures produced inside the fuel particle due to the interaction between the UO2±x kernel and the carbon buffer (Fig. 1). When estimated by using thermodynamic calculations, the pressure values are largely higher than those observed. Thus, it is also necessary to determine the formation rates of CO(g) and CO2(g) which will be used as input data for calculation codes that model the thermo-mechanical behaviour of the fuel particles. A thorough

0029-5493/$ – see front matter © 2008 S. Gossé. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2008.01.019

S. Goss´e et al. / Nuclear Engineering and Design 238 (2008) 2866–2876

Nomenclature C D fi G Ie− Ii k K kD m m Mi pi r R s Si t T V0

clausing coefficient diffusion coefficient isotopic abundance ratio geometric factor of the mass spectrometer, independent of the ionized vapour specie intensity of the electron beam measured ionic intensity of the i species reaction rate constant Jander’s proportionality rate constant Lindemer’s diffusion rate constant (cm2 /s) sample mass mass loss of the sample molar mass of the i species partial pressure of the i species UO2 particle radius perfect gas constant surface sensitivity of spectrometer for the i species time (0 = initial, f = final) temperature (K) initial volume of the fuel particle

Greek symbols ˇ integration constant I detector yield i mass spectrometer transmission  degree of conversion I electron ionization cross-section of the original molecule

study of the high-temperature behaviour of a mixture of UO2 and carbon is then necessary in order to establish the kinetics of the interaction between both materials. The objectives are (i) to predict the possible formation of carbide phases and (ii) to establish the controlling mechanisms of the UO2±x /C interaction kinetics (in a more practical way, UO2±x will further be written UO2 ). Furthermore, in case of “UCO” kernels manufacturing by solgel processes, the knowledge of (i) the equilibrium CO(g) pressure inside the U–C–O ternary system and (ii) the kinetics of the interaction between UO2 and carbon may also constitute useful data.

Fig. 1. TRISO particle for high-temperature reactor. (1) Graphite buffer (accomodates noble fission products and CO(g) , CO2(g) gas release), (2) inner PyC (protects the SiC layer), (3) SiC (decreases fission products diffusion and enhances mechanical strength) and (4) outer SiC (barrier for fission products and protects the SiC layer and contributes to the particle mechanical strength).

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Thermodynamic knowledge of the U–C–O ternary system can help to determine the final relative amounts of carbide and oxide phases inside the kernels as a function of the initial carbon amount in the uranyl nitrate solution. Kinetics will help to optimize the experimental conditions of both calcination and sintering heat treatments during the synthesis route (temperature, duration and atmosphere). The origin of this interaction can be explained by phenomena occurring at surface, interface or by diffusion. The first part of the present work is a review of several kinetic models in the literature. Initially, the experimental methods used to establish the kinetics of interaction are described. Then, the second part deals with the experimental results obtained by high-temperature mass spectrometry (HTMS). These first kinetic results, coupled with metallographic analyses of the samples make it possible to validate some assumptions on the reactional mechanisms. 2. Review of the kinetic of the (UO2 + C) interaction Several studies relate to the kinetics of interaction between UO2 and carbon. The primary reason for these studies is that these compounds are reagents of the carbothermic reaction which remains an important synthesis route of uranium carbide. It is thus to increase the reaction yield and to favor selective syntheses of the uranium dicarbide that the following reaction was specifically studied. UO2 + 4C = UC2 + 2CO(g) Therefore, these studies were mainly carried out with the aim of establishing the kinetics of formation of carbide and not that of the formation of CO(g) and/or CO2(g) . They consider that the CO(g) formation is inevitably associated with that of an uranium carbide, assumption which corresponds to be located in a monovariant equilibrium inside the U–C–O ternary system (Fig. 2). Interest in this reaction also comes from the fact that interaction between UO2 and the graphite buffer could lead to a carbide formation in TRISO fuels. As this reaction is reversible, various projects plan to introduce a mixture of UO2 and UC2 as an “UCO” fuel, in order to maintain a low initial value of CO(g) pressure inside the particle which tends to increase with irradiation time (Petti et al., 2002). However, in the case of an UO2 fuel (which excluded the UO2 + UC2 mixtures), the

Fig. 2. Calculated phase diagram of the uranium–carbon–oxygen system at 1273 K ´ showing the three monovariant equilibriums (Gueneau et al., 2005): UO2 + C + U2 C3 , UO2 + UC(O) + U2 C3 , UO2 + UC(O) + Uliquid .

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equilibrium is not monovariant but bivariant (Fig. 2). CO(g) pressures depend not only on the temperature but also on the chemical composition of the system. These kinetics are difficult to establish, on one hand because they are solid–solid and heterogeneous solid–gas reactions, and on the other hand, because many parameters must be considered in this study. The relative quantities of the reagents as well as the geometry and the particle size of the components have a significant influence on measured reactional rates. Several models, which are valid in the case of spherical symmetry of the reagents and the products, deal with interaction kinetics between two solid phases. Among them, some models consider that kinetics are limited by diffusion (Valensi–Carter, Ginstling, Jander) or interface (Spencer and Topley) phenomena, as shown in the case of the UO2 /C interaction (Danger and Besson, 1974; Mukerjee et al., 1990, 1994). 2.1. Danger kinetic models (Danger and Besson, 1974)

Fig. 3. Linear transform of several kinetic models (diffusion, surface and interface) by Lindemer et al. (1969).

The main product of the reaction between UO2 and carbon, leading to uranium carbides production is CO(g) . It is therefore possible to follow the evolution of this system and the kinetics of the UO2 + C interaction by measurement of the mass loss of the sample by thermogravimetric analysis (TGA). According to Danger and Besson (1974), the reaction begins to be significant at 1773 K. The reaction products always consist of a mixture of uranium monocarbide (UC) flakes inside a uranium dicarbide (UC2 ) matrix. The Valensi–Carter (Carter, 1961) model for powder reactions was used to describe this reaction between UO2 spherical particles and powdered graphite. In the case of a parabolic shape of the reaction curve, it is possible to establish the kinetic law from the degree of conversion () using the Valensi–Carter function F(). When the expansion coefficient between the reactant and the product is close to unity, the following linear function of time is obtained (Eq. (1)). This relationship is equivalent to the Ginstling’s model (Ginstling and Brounshtein, 1950) used by Lindemer (Lindemer et al., 1969) and described subsequently. The rate constant (K) is the product of two components; the first is a function of the diffusion processes and of the interfacial equilibrium constants, and the second is a function of the experimental conditions (Danger and Besson, 1974). F() = 1 −

2 2/3 = Kt  − (1 − ) 3

(1)

where m0 − mt = m0

(2)

In order to establish the rate-controlling step of the interaction between UO2 and carbon, Lindemer et al. (1969) have studied the behaviour of spherical UO2 particles coated with graphite in the 1673–1879 K temperature range. This spherical geometry has the advantage of simulating perfectly the expected behaviour of TRISO particles. In order to highlight the involved kinetic phenomena in this interaction (interface, surface, diffusion), the degree of conversion was determined by metallographic methods and two sample configurations (particles and pellets) were produced and studied. The model used by Lindemer et al. is that of Ginstling (Eq. (3)) developed for diffusion kinetics (Ginstling and Brounshtein, 1950). It makes it possible to assess growth kinetics of the product layer according to the temporal decrease of the UO2 radius r(t) inside the particle and knowing this radius (r0 ) at t0 : 1 − 3

 r(t) 2 r0



× 1−

2r(t) 3r0



=

kD t r02

(3)

2.2. Lindemer kinetic models The case of kinetics controlled by surface or interface phenomena have also been studied by Lindemer et al., using all the previously quoted models to treat their experimental data. After a series of experiments performed at constant temperature, the phenomena controlling the kinetics can be represented as a linear function of time. This interpretation makes it possible to consolidate the assumption of a kinetic control by a diffusion phenomenon (Fig. 3). Indeed, among the kinetic models applied to the experimental measurements, Ginstling’s model (Eq. (3)) is the only one passing by the origin (Ginstling and Brounshtein, 1950). This characteristic makes it possible to eliminate the surface and interface kinetic models. However, the graphic interpretations seem in all cases not very robust because of the lack of experimental data and of the poor regression coefficients. The diffusion model is thus only retained as being the determining reaction step. A post-mortem observation of the particles makes it possible to highlight two distinct reactional mechanisms according to the heat treatments. The first configuration shows a UO2 kernel surrounded by a UC2 layer of uniform thickness. It was obtained after a fast heating to 1273 K in less than 2 min followed by a 15 min temperature plateau (during which no carbide was yet formed). The sample was then heated to the final temperature (between 1673 K and 1829 K) at a heating rate of 25 ◦ C/min and finally cooled at −50 ◦ C/min to prevent any risk of cracking of the particle. The second configuration was obtained when the particles were submitted to high heating rates ranging between 50 ◦ C/min and 100 ◦ C/min. These high heating rates induce the existence of strong thermal gradients inside a particle, in spite of their small diameter (500 ␮m). The sample profiles have a non-uniform shape where UO2 occupies the central part of the sphere and overflows partially towards external surface of the particle. There is a noticeable difference between reaction rates of these two mechanisms. In the second case, the reaction rate of conversion is between two and five times faster than the first one. Logically, this difference in the rate is attributed to a kinetic control by different reactional steps. The comparison of the experimental results according to each protocol makes it possible for Lindemer et al. to propose two distinct reactional mechanisms. The “uniform” kinetic scheme establishes the oxygen diffusion – starting from the interface between oxide and carbide through carbide and towards the surface of the particle – as the controlling step. On the contrary, in the case of the “non-uniform” reaction, it is supposed that the CO(g) diffusion controls the kinetics.

S. Goss´e et al. / Nuclear Engineering and Design 238 (2008) 2866–2876

The review of this study makes it possible to state that: • the uranium carbide formation due to the reaction between UO2 and C is controlled by the diffusion, • the diffusion of [O]UO through UC2 controls the kinetics when 2 UC2 encloses the UO2 kernel completely, • the reaction rate increases in the case of a “non-uniform” reaction related to a fast increase of the sample temperature, • the geometrical form and the physical contact of the reagents during conversion have a significant effect on the composition of the solid phase. Nevertheless, these two mechanisms do not consider the interaction step between UO2+x and carbon, during which, in a first step, uranium dioxide is reduced without carbide formation. It is thus also necessary to establish the behaviour of the interaction between UO2 and carbon before the formation of a carbide phase. 2.3. Mukerjee’s kinetic models Mukerjee et al. studies (Mukerjee et al., 1990, 1994) deal with the carbothermic conversion of UO2 + C mixture to carbides under both vacuum and flowing argon. They are a good complement to Lindemer et al studies. Indeed, in this case, the kinetics are determined from both CO(g) concentration measurements in an inert flowing gas or from manometric measurements under vacuum. Furthermore, the samples are mixed powders instead of coated particles. Thus, the experimental conditions are close to those used within our experimental measurements by HTMS. According to the experimental conditions, two distinct behaviours were highlighted: (i) under vacuum, the UO2 reduction is controlled by reagent–product interface reactions, whereas (ii) under a neutral gas flow, the CO(g) diffusion through the layer of carbide is the controlling step. Stinton et al. (1979) postulated that during the carbothermic reaction performed on microspheres, surface nucleation is extremely fast and the particle is instantaneously covered by a thin carbide layer. In this case, the determining step becomes the propagation of the reactional interface towards the particle core controlled either by diffusion, surface or interface reactions. Mukerjee’s reaction route is based on Stinton’s (Stinton et al., 1979), in which UC2 dicarbide was substituted by UC monocarbide. In these experiments, the carbothermic steps are interface or diffusion reactions. When diffusion through the products layer is so fast that the reagents cannot combine till equilibrium at the interface, the reaction rate is controlled by interface phenomena. By assuming that nucleation occurs instantaneously and that the reaction rate is proportional to the reagent surface which has not yet reacted (St ), the equation rate is written as follows: d kSt = V0 dt

(4)

After several operations (Mukerjee et al., 1990; Spencer and Topley, 1929), the previous equation can be put in a form highlighting the dependence of  with the initial radius of the particle (r0 ): 1 − (1 − )

1/3

=

kt r0

(5)

On the contrary, when the penetration of one of the reagents through the layer of products separating the two reactive phases is the determining step, the temporal dependence of the progressive accumulation of the product layer is inversely proportional to its thickness, y: dy k = y dt

(6)

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After integration, this relation provides a parabolic equation which can be then written according to the  parameter. Jander (1927) applied this equation to packed powders; he deduced the following law (Eq. (7)) which is a function of a proportionality constant, K, and a diffusion coefficient, D: [1 − (1 − )

1/3 2

] =

2KDt r02

(7)

This last equation was modified by Zhuravlev et al. (1948) by assuming that the activity of the reagent is proportional to the unreacted fraction (Eq. (8)). They obtain:



2

1 (1 − )

1/3

−1

=

2KDt r02

(8)

Valensi and Carter’s model takes into account the difference between the product and the reagent densities consumed during the interaction. The assumption is made that the diffusion proceeds through a layer of constant composition. After a valid first order approximation, Mukerjee simplifies this model into the form (Eq. (9)): ln(1 − ) =

kt r02

(9)

Under flowing gas experiments, the degree of conversion of the reaction is determined by measuring the quantity of CO(g) formed. For the experiments carried out under vacuum, the measurement is only manometric. The realistic assumption is made that the gas is mainly made of CO(g) . This assumption has been confirmed by performing isothermal thermodynamic calculations of the CO(g) and CO2(g) pressures as a function of the O/U ratio in ´ the uranium–carbon–oxygen system (Gueneau et al., 2003). For the experiments performed under a gas flow, CO(g) formed is oxidized into CO2(g) by passing through a copper catalyst. The quantities of CO2(g) are then determined by titration by a NaOH solution. The rate curves are characterized by a maximum of formation followed by a decrease of the reaction rate. At 1723 K, the rate becomes very slow for a value of  higher than 0.98. For lower temperatures, the reaction rate tends quickly to a plateau. Each kinetic model was used to treat Mukerjee’s experimental data. For data under vacuum, the best plots are obtained by fitting the results with the Spencer and Topley’s relation (Eq. (5)) (Spencer and Topley, 1929). In this case, the limiting step is the UO2 /UC2 interface reaction. In the case of the experiments performed under gaseous flow, the reaction rate is much slower than in the case of those performed under vacuum and whatever the temperature, the reactional rate increases proportionally with the gaseous flow. Experimental data are interpreted using Valensi and Carter’s relation (Eq. (9)), which indicates that in this case, the kinetics are controlled by diffusion phenomena. Mukerjee et al. (1994) also investigated the reactional mechanisms of the UO2 + C interaction using two types of samples. The first particle batch is made of UO2 + C mixed powders, as in the previous study. New microspheres were also synthesized, made up only of uranium dioxide dispersed in excess carbon black powder. Under vacuum, the kinetics are much slower, in case of the UO2 microspheres dispersed in carbon black, than in the case of (UO2 + C) microspheres. In this last case, the value of the C/UO2 ratio has an effect on the composition of the products. For a ratio equal to 3, the carbide formed is UC and for a value of 4, the carbide formed is UC2 . In case of an intermediate value, the products consist of a mixture of these two carbides. This result reveals the influence of the proportions of the reagents on the nature of the products, related to the reaction trajectory inside the U–C–O system. This new interpretation of the reactional mechanisms supplements Muker-

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jee’s first reactional mechanism (Mukerjee et al., 1990) which only considered the UC carbide formation. As in his first study, Mukerjee deduced a kinetic mechanism according to interface phenomena for experiments performed under vacuum. The interpretation confirms that the CO(g) release is fast, which does not make it possible to clearly define the determining step among the proposed reaction mechanism:

Under vacuum, carbon diffusion is the limiting step of the carbide formation in UO2 + C microspheres. The assumed mechanism follows the same route as the previous one. But, since there is no intermediate product, and the quantity of available carbon is sufficient to convert all the UO2 into UC/UC2 without leaving a core in the centre of the particle, the steps 7–12 should not occur. 3. Experimental study

1. C(gr) → [C]UC 2. Diffusion from the surface towards the UO2 –UC interface C(gr) → [C]UC 3. [C]UC + UO2 → UC + 2[O]UC 4. [O]UC diffusion towards the microsphere surface 5. 2[O]UC + 2C(gr) → 2CO(g) at the surface Two steps seem to be the determining steps: (i) the diffusion of carbon or oxygen in the solid phase, and (ii) diffusion through the product layer. The lack of carbide of a higher degree (U2 C3 , UC2 ) during the intermediate steps of the UO2 + C conversion into UC indicates that a phenomenon of carbon diffusion could be the determining step when the experiments are performed under vacuum. On the contrary, under gas flow, the kinetics of CO(g) formation are controlled by the CO(g) diffusion through the layer of products formed. Moreover, the kinetics are dependent on the initial C/UO2 ratio of the samples. For a given temperature, the time necessary for a complete reaction increases as a function of the obtained products: UC2 , UC + UC2 and finally UC. To explain these different rates, a new mechanism is proposed by Mukerjee including additional steps to the previous ones: 6. CO(g) diffusion towards the UC2 layer 7. 3UC2 + UO2 → 4UC + 2CO(g) 8. [C]UC2 → [C]UC Dissolution of C from UC2 towards UC at the UC–UC2 interface 9. Diffusion of [C]UC at the UC–UC2 interface towards the UO2 –UC interface 10. [C]UC + UO2 → UC + 2[O]UC

3.1. High-temperature mass spectrometry principles High-temperature mass spectrometry (HTMS), coupled with Knudsen effusion cells, is a well-established partial pressure measurement method (Ba¨ıchi et al., 2001; Chatillon et al., 1979; Chatillon, 1998; Drowart et al., 2005). It is also used to perform kinetic studies in which gaseous species are formed from chemical interactions between solid phases. In this method, a material is heated to a high temperature in a Knudsen cell in which a condensed phase (solid or liquid) is in equilibrium with a gas phase. A hole, whose dimensions are small with respect to the surface of the sample, in the lid of the cell allows sampling of a very small part of the vapour that forms a molecular beam. The mean free path of the molecules in this molecular beam is such that there are no collisions between the molecules during their sampling. The rarefied gas flow or molecular beam passes without collision through a diaphragm directly in the ionization chamber of a mass spectrometer maintained under high vacuum (Fig. 4). The gaseous species are ionized by an electron beam, and the generated positive ions which are then extracted from the ionization chamber, accelerated by an electric field, and then separated according to their mass/charge ratio by a high-frequency electric field (quadrupole mass spectrometer in the present case). The Beer-Lambert law, applied to the absorption of the electrons in a diluted medium, leads to the basic mass spectrometric relation between the vapour pressures and the measured ionic intensities/temperature product (Chatillon et al., 1979; Chatillon, 1998): pi Si = Ii T

(10)

3.2. Coupling of the Knudsen cell and mass spectrometric methods

Reaction between [C]UC and UO2 at the UO2 –UC interface 11. Diffusion of [O]UC formed at the UC–UO2 interface towards the UC–UC2 interface 12. [O]UC + UC2 → UC + CO(g) Reaction between [O]UC and UC2 at the UC–UC2 interface. During this process, two interfaces must be considered: UC–UC2 and UC2 –(UO2 + C). The reactional steps involved at the UC2 –(UO2 + C) interface are reactions 1–5, and the step 6 corresponds to the CO(g) diffusion. In case of a total consumption of the free carbon at the external surface of the UC2 layer, the interaction between trapped UO2 and UC2 proceeds according to the reaction 7. This leads to the formation of a thin layer of UC between the UO2 and UC2 layers. The mechanism of interaction is described according to the steps 8–12. The conversion of the UO2 + C microspheres into UC2 proceeds according to a succession of steps during which the layer of dicarbide grows and generates a UC2 microsphere. In this case, the reaction occurs according to steps 1–6. The slower formation rate of UC could be due to the implications of reactions 7–12. When conversion occurs according to reactions 1–12, the final size of the UO2 core after the carbon disappearance determines the global reaction rate. The larger the size of the UO2 core, the slower are reactions 8–12.

The flow of gaseous molecules from a surface s, is the same as the rarefied gas effusion flow resulting from a sufficiently large container (isotropy condition) by a same hole of cross-section s with ideally thin wall. The essential condition to be preserved is that the mean free path of the molecules in the gas is higher than the dimensions of the lid orifice (Gosse´ et al., 2006). The flow of gaseous molecules, in moles per unit of time, is obtained by integration of all the half space above the hole leading to the Hertz–Knudsen relation (Carlson, 1967): dni = dt

pi sC



2Mi RT

(11)

In case of the UO2 + C interaction, the composition of the result´ ing gaseous phase is known (Gosse´ et al., 2006; Gueneau et al., 2003). In the U–C–O system, at least concerning the framework of TRISO fuel particles under nominal or accidental conditions, it is composed mainly of CO(g) , but can sometimes be supplemented by a few percent of CO2(g) . The CO(g) and CO2(g) ionic intensity measurements allow their respective partial pressures to be determined, and subsequently the vapour phase composition. Measurements versus time lead to the kinetics of formation of the gaseous phase. From the total mass loss of the sample during the experiment, the final overall composition of the sample can

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Fig. 4. High-temperature mass spectrometer (HTMS) with multiple Knudsen effusion cells.

be determined in the U–C–O system. The phase compositions are measured using post-mortem analyses (SEM, XRD). These kinetic experiments do not require any additional calibration of the spectrometer since the mass loss (m) of the sample is known, which is then correlated with the released gas. For each gaseous species (i), it is possible to calculate the molecular flow by associating the mass spectrometric and the Knudsen–Hertz relations (Eqs. (10) and (11)): √ sCIi T

dni =  dt Si 2Mi R

Si



sC

2Mi R



ni (t) = ˇi

(12)

(13)

t

√ Ii T dt

(14)

0

At the end of the experiment, the total amount of gas corresponds to the mass loss of the sample: ˇi =

In this equation, the molecular flow of a gaseous species is proportional to the product of the measured ionic intensities and the squared root of the temperature. For a defined geometry and single vapour specie, all the parameters can be considered as a single constant ˇi , specific to the measuring device. The integral of the last relation represents the amount of evaporated moles and so the mass loss of the sample due to the formation of the i specie: ˇi =

Then, the total amount of gas (moles) is determined by integration of the molecular flow with time.

m

MCO

 tf √ 0

Ii T dt

(15)

Then, the quantity of CO(g) (moles) at any time can be written as follows: t √ m 0 ICO T dt  (16) nCO (t) = √ MCO tf ICO T dt 0 In case of several gaseous species in the vapour composition, the mass spectrometer sensitivities (Si ) for each gaseous species (e.g. CO(g) and CO2(g) ) are obtained by an appropriate calibration of the mass spectrometer (Heyrman, 2004). The sensitivity factor of the mass spectrometer (Si ) is a function of numerous parameters (Eq. (17)): Si = Ie− Gi i i fi

(17)

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Fig. 5. Ionization cross-sections of CO+ and CO2 + ions by Freund et al. (1990).

Ie− is the intensity of the electron beam, G a geometric factor independent of the ionized vapour specie, i the mass spectrometer transmission,  i the ionization cross-section of the ionized molecule, fi the isotopic abundance ratio and  i is the detector yield. In the case of the study of the UO2 + C interaction, the vapour composition is made of CO(g) and CO2(g) , for which almost all of these parameters are identical. Hence, the only parameter to be considered to evaluate a specific sensitivity for CO(g) and CO2(g) is the ionization cross-section,  i . Some data on the partial ionization cross-sections of CO(g) and CO2(g) into CO+ and CO2 + ions are available in literature Freund et al. (1990). For an ionization energy of 38.6 eV, they are respectively equal to 1.35 and 1.51 (Fig. 5). The ratio of these ionization cross-sections is used to normalize the spectrometer response ratio according to the CO(g) signal (Eq. (18)): SCO2 =

CO2 CO

SCO

(18)

Thus, it becomes possible to treat simultaneous data for CO(g) and CO2(g) and to calculate their respective amounts by using the two following relations (Eqs. (19) and (20)): t √ m × 0 ICO T dt  t (19) nCO (t) = √ √ t MCO 0 f ICO T dt + MCO2 (CO2 /CO ) 0 f ICO2 T dt

t √ m × CO2 /CO 0 ICO2 T dt  tf √ t nCO2 (t) = √ MCO 0 ICO T dt + MCO2 (CO2 /CO ) 0 f ICO2 T dt

(20)

From these relations and from the final mass loss of the sample, both partial pressures and produced amounts (moles) of each gaseous species can be calculated versus time during the experiment. It also allows an evaluation of the variation in the total composition of the condensed phase versus time in the uranium–carbon–oxygen ternary system. 3.3. Material preparation The samples were manufactured from carbon black and UO2+x powders (initial analysed O/U ratio of 2.06) with respective molar proportions of 40% and 60% (2.5 g of UO2+x and 0.075 g of carbon). After mixing, these powders were compacted in a pellet with a manual press in a glove box. The obtained green pellets are dense but remain brittle and occasionally show some cracks up to their surfaces. The composition of the pellets, in particular the stoichiometry of uranium dioxide, has to be well controlled because

this parameter determines the oxygen potential in the ternary uranium–carbon–oxygen system at the beginning of the experiment, influences the kinetics of formation of the gaseous phase and determines the global composition of the sample at the beginning of the experiment. O/U ratio determinations were performed on UO2+x green pellets issued from the same batch, using thermogravimetric analysis (TGA) according to an oxidation protocol of the dioxide UO2+x into U3 O8 . This cycle results from the literature critical analysis of the various calcination protocols of UO2±x into U3 O8 . Indeed, in this case, the main uncertainty in the measurement of the O/U ratio of UO2±x samples comes from the formation of hypostoichiometric U3 O8−z when performed at too high temperatures ´ (Gueneau et al., 2002; Labroche et al., 2003). Measurements were performed with an oxidizing gas flow (Ar + 20%O2 ) discarding airflow to avoid any formation of uranium oxy-nitrides which could alter the results (Labroche et al., 2003). Knowing the exact composition of the final oxidation product (stoichiometric U3 O8 ) and by measuring the mass gain of the sample, the initial stoichiometry of UO2+x is obtained. The test proceeds according to a heating rate of 10 K/min followed by a 35 min plateau at 1073 K during which UO2+x oxidation occurs. Then, the sample is cooled in order to stabilize the temperature to 873 K. This second plateau is necessary to obtain U3 O8 stoichiometric composition. For some of the pellets, the stoichiometry of uranium dioxide which was initially equal to 2.06, quickly increased to 2.15, in spite of the storage of the samples inside a glove box under nitrogen atmosphere. These unintentionally oxidized samples gave the opportunity to study the effect of the initial O/U ratio on the kinetics, but no real effect has been found.

4. Results 4.1. Kinetic interpretation HTMS experiments were performed on UO2+x + C pellets of known initial composition and UO2+x stoichiometry (O/U = 2.06). The experimental approach consists of highlighting the formation of CO(g) and eventually CO2(g) and to quantify their partial pressure from ionic intensity measurements. Moreover, as indicated in the previous section, the composition of the sample can be deduced from the calculation of its mass loss. The temperature range of interest is above 1273 K, corresponding to the nominal operating temperature of (V)-HTR fuels. Several experiments were performed between 1523 K and 1673 K. Measurements were also performed for the uranium gaseous species (UO(g) , UO2(g) , UO3(g) ): none of these species were detected. The first experiments consisted of a gradual heating of the samples in order to detect the threshold temperatures from which CO2(g) and CO(g) begin to appear, which are equal to, respectively, ≈1000 K and ≈1200 K. During these first heat treatments, ionic intensity measurements appear in the form of gaseous puffs from which it is difficult to predict kinetic behaviour. However, the ionic intensity curves confirm the preferential formation of CO2(g) (i) during the heating from 1000 K to 1400 K and (ii) at the beginning of the reaction when the uranium dioxide is still hyper-stoichiometric in oxygen. On the contrary, CO(g) is formed throughout the experiment with a formation rate strongly related to the temperature. In the next experiment, heat treatment was performed at a fixed temperature to determine the kinetic rate. The UO2 + C pellet was quickly heated to reach the 1573 K plateau during 10 h. During heating, CO(g) and CO2(g) signals appeared under the form of simultaneous significant puffs. After these CO(g) and CO2(g) peaks, the CO2(g) ionic intensity remained low and close to the background of the spectrometer, and so can be neglected. On the contrary, CO(g) ionic intensity was plainly detected and measured (Fig. 6).

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Fig. 6. Experimental molecular flows of CO(g) and CO2(g) vs. time.

The high-temperature mass spectrometer was calibrated by mass loss of the sample (Chatillon, 1998; Heyrman, 2004). The so obtained sensitivity of the mass spectrometer made it possible to calculate the evolution of CO(g) and CO2(g) pressures above the pellet (Fig. 7). Moreover, thermodynamic calculations provide the limit of the hypo-stoichiometric uranium dioxide (O/U = 1.998). From this value, uranium dioxide cannot be reduced farther and carbon consumption is necessary related to the formation of carbide phases. This transition illustrates the composition path from the UO2 + C two-phase domain towards the [UO2 + U2 C3 + C] threephase domain (Fig. 8). Thus, it becomes possible to compare the measured pressure value to the known equilibrium pressure of the [UO2 + U2 C3 + C] three-phase domain at the same temperature (Gosse´ et al., 2006). Moreover, this allows the investigation of the high temperature behaviour of the UO2 + C mixture and a prediction to be made, as to whether the interaction is preferentially governed by thermodynamics or kinetic phenomena. Initially, the increase in pressure seems to be exponential until the delimitation between the two-phase and the three-phase domains which shows a maximum of pressure. Then, the pressure decreases slowly towards a plateau which is still not reached after more than 10 h of heat treatment.

Fig. 8. Evolution of the total composition of the sample during the high-temperature mass spectrometric experiment on a UO2 + C pellet.

Two phenomena are then highlighted: • firstly, the shape of the curve of CO(g) pressure reveals that time necessary to obtain a steady-state regime seems long. To reach it, it would thus be necessary to increase the duration of the experiment. However, this suggestion would lead to an additional consumption of C via CO(g) losses and thus a displacement of the overall composition of the system U–C–O which would move towards the [UO2 + U2 C3 + UC] three-phase domain; • secondly, the pressure asymptote seems to tend towards pressure values slightly lower than the thermodynamic equilibrium pressure (56.4 Pa). As vaporizing is performed in an effusion cell – close to equilibrium at the surface of the sample – lower pressures means kinetic limitations (Heyrman et al., 2006a; Heyrman and Chatillon, 2006b). This behaviour highlights the role of the kinetics on the values of CO(g) pressure which are then different from the thermodynamic estimation concerning the UO2 + C interaction. To determine the type of kinetic process involved in this interaction, measurements of CO(g) and CO2(g) pressures were treated using the various models herein described (Zhuravlev, Spencer and Topley; Jander, Valensi and Carter). The mass variation of this interaction is only due to processes in which carbon is involved through CO(g) and CO2(g) gaseous effusion loss. For this reason, the selected reference used to define the degree of conversion of the reaction is the initial amount of the minor solid reactant related to the UO2 + 3C = UC + 2CO(g) equation. Then, the degree of conversion  C of the reaction will be defined as a function of the variation of carbon content in the sample (Eq. (21)), since the relative molar initial UO2 and carbon ratio is equal to 60–40%. C =

Fig. 7. O/U ratio in UO2±x and measurements of CO(g) and CO2(g) pressures vs. time compared to the equilibrium pressure (56.4 Pa) of the [UO2 + U2 C3 + C] three-phase domain.

mC0 − mCt mC0

(21)

These relations were applied in order to describe the variation of the CO(g) and CO2(g) formation versus time represented by the loss of mass of the sample (Figs. 9–12) to compare the consistency of each model with the experimental data. In parallel, the degree of conversion  versus time is also represented on the right axis of the graphs.

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Fig. 9. Processing of experimental measurements of CO(g) according to Spencer and Topley’s model (Eq. (5)). (Dashed line is degree of conversion).

Fig. 10. Processing of experimental measurements of CO(g) according to Jander’s model (Eq. (7)) (Dashed line is degree of conversion).

Among the various models, the results seem to be more consistent with relations (Eqs. (5) and (7)), respectively corresponding to Spencer and Topley’s and Jander’s models. Spencer and Topley’s model fits well the experimental data with a linear function for a degree of conversion lying between 0.08 and 0.30 (noted Step 1 in Fig. 9). This result is consistent with an

Fig. 12. Processing of experimental measurements of CO(g) according to Valensi and Carter’s model (Eq. (9)) (Dashed line is degree of conversion).

interface-controlled mechanism initiating at the surface of the UO2 grains. For Jander’s model, two successive segments are observed on the linear transform of the mass spectrometric measurements (Fig. 10). They can be adjusted in two degrees of conversion ranges. The first  C domain lies between 0.1 and 0.35. The second one lies between 0.4 and 0.52 (noted Step 2 in Fig. 10) where the reaction stops due to heating switch off. The linearity of the Jander’s transform over the Step 2 range shows that the second step involved in the kinetics of the UO2 and carbon interaction may be controlled by a diffusion mechanism towards the uranium carbide layer, starting to grow when the UO2 grain surfaces are entirely covered by the carbide phase. This second diffusion process is more sluggish than the first interface step. The reacting process is probably made of two distinctive controlling steps as shown by a break of slope at the end of Mukerjee’s experiments performed under vacuum at 1450 ◦ C and 1500 ◦ C (Mukerjee et al., 1990, Fig. 5). Nevertheless, the currently available results do not allow a choice between these various possible diffusion or interface kinetic mechanisms; a wider temperature range has to be investigated. However, the models suggested by Spencer and by Jander seem to be more adapted to analyse the present data. This statement is undoubtedly related to the similarities of our experimental conditions using high-temperature mass spectrometry and those reported by Mukerjee under high vacuum (Mukerjee et al., 1990, 1994). 4.2. Analysis of the samples’ composition

Fig. 11. Processing of experimental measurements of CO(g) according to Zhuravlev’s model (Eq. (8)) (Dashed line is degree of conversion).

Concerning CO(g) and CO2(g) , the processing of the ionic intensity signals using the equations (Eqs. (19) and (20)) allows the number of gaseous moles formed during the interaction to be calculated. Thus, the variation of the overall composition of the sample can be represented inside the ternary U–C–O diagram calculated at the temperature of the experiment. The evolution of the UO2 + C interaction can be represented by a trajectory based on the loss of gaseous species (CO(g) and/or of CO2(g) ). Thanks to this representation, it is possible to predict the condensed phases normally expected by thermodynamics (Fig. 8). In this specific case, the final composition of the mixture is located inside the triangle corresponding to the three-phase domain equilibrium, formed of slightly hypo-stoichiometric uranium dioxide UO2 (UO1.998 ), of uranium sesquicarbide U2 C3 and

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Fig. 13. Optical microscopy on polished section of the pellet after heat treatment (bulk = UO2 , white phase = UC, black hole = pores, light gray = carbon).

Fig. 14. X-ray diffraction diagrams of the UO2 + C pellet after reaction—in green UO2 , in blue C, in red UC. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

of carbon C. Post-experimental analysis of the samples by optical microscopy on polished sections reveals an important proportion of a white phase located under the surface of the pellet (Fig. 13). This phase is mainly located inside the pores, which means that it is associated with the CO(g) formation. The core of the pellet does not present this shining aspect in such a proportion and contains less of this white phase, which is characteristic of the uranium carbides. This statement is confirmed by the X-rays diffraction (XRD) analysis (Fig. 14).

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of CO(g) which is a representative marker of what occurs in the Knudsen cell. The contribution of CO2(g) must be taken into account for a O/U ratio higher than 2 and decreases rapidly during the first heating ramp. CO(g) is preferentially formed at higher temperatures, CO2(g) is no more formed above 1300 K. This precursor phenomenon may mainly be due to a gaseous adsorption–desorption reaction as observed usually during heat treatments of carbon. Experimental results show first the reduction of UO2+x by the carbon which is accompagned by a gas pressure increase and the measured pressures are far from those calculated at equilibrium. Then, when the UO2 reaches a quite stoichiometric composition (O/U = 1.998), a carbide phase begins to form and a three-phase domain is reached. But, the pressure equilibrium of the system under monovariant conditions is not obtained. These two features emphasizes that thermodynamic equilibrium was not reached. It was possible to apply various kinetic models to analyse the experimental measurements of CO(g) formation by HTMS. Spencer’s and Jander’s models (Mukerjee et al., 1990, 1994) fit best the experimental results. In this case, it seems that the reactional mechanism is governed by successive interface and diffusion phenomena. The observation of the samples confirms the formation of uranium monocarbide UC. In the case of experiments above 1650 K, the carbide phase was UC2 . In this last case, as predicted by thermodynamics, the formation UC2 carbide consolidates the conclusions that this compound is a high temperature phase. This statement is corroborated by the most recent U–C assessed binary phase diagram (Chevalier and Fischer, 2001). Although the formation of sesquicarbure U2 C3 is theoretically considered by thermodynamics, this compound was not identified by post-mortem analysis. Other experimental observations have shown this compound to be “sluggish” and the still high content of oxygen in the samples at the end of the experiments is known to stabilize both uranium monocarbide UC(O) and uranium dicarbide UC2 (O). Also, these experiments show that the formed carbide is mainly located on the edges of pores related to CO(g) and/or CO2(g) gas releases. All these results confirm the importance of kinetic limitations concerning the UO2 + C interaction in the framework of the thermomechanical behaviour of TRISO fuel particles. The observed difference between calculated pressures from thermodynamics and experimental values can be made profitable to evaluate the lifetime of the fuel under nominal conditions. Further investigations will make it possible to assess the involved reactional limiting mechanisms: surface, interface or diffusion and the associated activation energies. Acknowledgments The authors thank EDF and Framatome-ANP for their financial support of the present study.

5. Conclusion References This review of the main studies within the framework of the interaction between UO2 and carbon highlights the various available kinetic models as well as the associated reactional mechanisms involved in this high temperature interaction. The different mechanisms are greatly influenced by the experimental conditions in terms of sample (particle size, geometry, relative amounts of the reactants) and environment (vacuum, flowing gas). HTMS experiments performed on the UO2 + C pellets confirm the strong interaction between these two compounds above 1000 K. As already mentioned (Lindemer et al., 1969), this interaction is characterized by the formation of a gaseous phase mainly consisting

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