Corium Experimental Thermodynamics: A Review and Some Perspectives

Abstract

More than 30 years ago a specialist meeting was held at Joint Research Center Ispra (Italy) from 15 to 17 January 1990 to review the current understanding of chemistry during severe accidents in light water reactors (LWR). Let us consider that, at the end of the 1980s, thermodynamics introduced in the severe accident codes was really poor. Only some equilibrium constants for a few simple reactions between stoichiometric compounds were used as well as some simple correlations giving estimates of solidus and liquidus temperatures. In the same time, the CALPHAD method was developed and was full of promise to approximate the thermodynamic properties of a complex thermochemical system by the way of a critical assessment of experimental data, a definition of a simple physical model and an optimisation procedure to define the values of the model parameters. It was evident that a nuclear thermodynamic database had to be developed with that new technique to obtain quite rapidly prominent progress in the knowledge of thermochemistry in the severe accident research area. Discussions focused on the important chemical phenomena that could occur across the wide range of conditions of a damaged nuclear plant. The most pressing need for improved chemical models is identified with condensed phase mixtures to model the corium progression. This paper reviews more than 30 years of experimental data production in the field of corium thermodynamics. This work has been conducted through multiple international programs (EURATOM, ISTC, OECD) as well as through more specific studies conducted at the national scale. This research has been capitalised in specific databases such as NUCLEA and TAF-ID, databases developed at IRSN and at CEA, respectively, and are now used in degradation models of the severe accident simulation codes. This research is presented in this paper. In the conclusion, we outline the research perspectives that need to be considered in order to address today’s and tomorrow’s issues.

1. Introduction

In order to understand and model all the physical phenomena that can occur during a severe accident, a good knowledge of the materials properties is essential. During such an accident, temperatures of more than 2750 °C can be reached. In these extreme conditions the various materials of the different core components (absorber rod, cladding, fuel, etc.) melt and interact to form complex mixtures (commonly called corium).

Corium is generally characterised by the presence of a large number of chemical elements and may present a multiphase aspect (e.g., a mixture of a liquid phase and solid phases, a mixture of two immiscible liquid phases, etc.). Therefore, the assessment of the properties must not only cover the materials constituting the individual core components but also the mixtures resulting from the interaction of these materials with each other over a temperature range theoretically from the nominal operating temperature of the reactor to temperatures up to fuel melting (2850 °C for UO₂). It is easy to understand the difficulty of the task both experimentally and in terms of modelling.

For more than 30 years, numerous programmes have made it possible to make progress in this undertaking. In the framework of the European Commission EURATOM Framework Programmes (FPs) [1,2,3,4,5,6,7], the International Science and Technology Centre (ISTC) Programmes [8,9], the SARNET Networks of Excellence [10,11] and the Organisation for Economic Cooperation and Development (OECD) Programmes [12,13], severe accident experts have been interested in the production and the assessment of thermodynamic data for a number of compounds of reactor materials and fission products and complex phases mixing a large number of chemical elements. Using the CALPHAD method, thermodynamic databases for collecting all this knowledge in a consistent way have been developed [14,15,16]. Thanks to previously mentioned international programmes, in particular to the European Commission EURATOM Programmes, the European tool NUCLEA [14], has been developed for in- and ex-vessel corium applications, and intensively and continuously validated at IRSN [10,11], until now, with the technical support of the SIMAP Laboratory (Grenoble, France) and the contributions from EDF and CEA. Such a database is much more than a compilation of thermodynamic data from various sources. Its constitution needs considerable analysis for self-consistency, to ensure that all the available experimental information is satisfactorily reproduced. It is used today in the interpretation of experiments simulating specific sequences of the accident as well as in the severe accident modelling (e.g., ASTEC code).

During a severe accident sequence in light water reactors (LWRs), implying partial or complete core melting, thermodynamic models are required to predict the behaviour of the melts formed from the degradation of the core materials. Data such as the composition of the phases present in the corium and their properties (solidus and liquidus temperatures, heat capacities, enthalpies, etc.) are key parameters for modelling, among other things, of the corium flow properties and then for modelling of the progression of the accident. Of particular importance is the determination of “critical” (in terms of importance for the accident progression) temperatures, above which significant amounts of liquid phase form as a result of chemical interactions between some core components or by reaching a melting point of one material.

According to the general understanding of the phenomena occurring during a severe accident [17,18] and on the basis of the experimental results and thermodynamic considerations, it is possible to roughly distinguish, in a typical accident sequence, four different temperature regimes in which liquid phases of different nature may be formed in the reactor, leading to substantial material relocations and different degrees of core damage, from limited degradations in the core to formation of a large molten pool in the bottom of the reactor vessel and possible ex-vessel progression involving relocation of molten core debris into the reactor cavity (Figure 1):

• The first regime is characterised by the melting of the absorber rods and the eutectic reaction between some metallic components in the core. The upper temperature of this regime approximately corresponds to the melting point of stainless steel (around 1450 °C) while the lower temperature around 800 °C is linked to the liquefaction of the Ag-Cd-In absorber alloy.
• In the so-called intermediate regime, which extends to 2300 °C, the fuel liquefaction due to its interaction with molten Zircaloy takes place and constitutes the main degradation process occurring in the core. Formation of local pools may form in the core.
• At temperature above 2300 °C (some papers mentioned temperatures slightly below 2300 °C [19,20]), a (partial) relocation of the fuel rod materials occurs resulting in the formation of a more or less large molten pool. This is the third regime. It is usually characterised by an evolution of the corium composition from the metal-oxide region of the U-O-Zr-stainless steel system towards the fully oxide one, depending on available water and the oxidation process.
• The vessel rupture and the ex-vessel progression of a severe accident in a PWR involve the relocation of molten core debris into the reactor cavity. The molten materials are able to interact with the concrete of the basemat resulting in ablation and release of species by vaporisation. The composition of the melt changes progressively as the basemat decomposition products are incorporated into the melt during the molten core–concrete interaction.

In this paper, we propose to review the experimental results obtained for these different regimes in the field of corium thermodynamics by trying to relate the data obtained with the issues of the severe accident progression. The paper is divided in four parts, reflecting the temperature scale previously described.

2. Low Temperature Regime (below 1450 °C)

In light water reactors (LWR), boron carbide (B₄C) and silver-indium-cadmium (SIC) alloy are the most widely used neutron absorber materials in absorber rods and blades. In a severe accident situation, the decay heat in the core is no longer dissipated sufficiently to avoid the increase of temperatures in the core. These absorber rods are, then, the first components of the core to degrade in such uncontrolled situation.

For the SIC alloy, this temperature increase causes the absorber alloy (usual composition is 80 wt.% Ag, 15 wt.% In, 5 wt.% Cd, solid solution so-called SIC) to “melt” at a temperature of 800 ± 10 °C [21]. It should be noted that this is the material with the lowest melting point in the reactor core. This alloy does not react with the stainless steel cladding where SIC alloy is encapsulated so that the cladding retains its integrity. The reason is that stainless steel components of the cladding are thermodynamically stable versus the chemical elements of the absorber materials, Ag and In, until practically the melting temperature of stainless steel. Stainless steel components do not mix easily with SIC elements even at high temperature (see the references Ag-Fe [22] Ag-Cr [23] Ag-Ni [24] In-Fe [25], and In-Cr [26] for the systems of interest). At the same time, with increasing temperature, the internal pressure of the absorber rod gradually increases. This is because the pressure of the filling gas increases proportionally with increasing temperature. To a lesser extent, the volatility of the constituent elements of the absorber alloy, in particular cadmium, also contributes to the pressure increase. The nature of the degradation mode of the absorber rod (Figure 2) depends on the pressure of the primary circuit at the time of the accident. Depending on the accident scenario, the absorber rod may be either over-pressurised or depressurised with respect to the primary circuit.

If the pressure in the primary circuit is higher than the pressure inside the absorber rod, the geometry of the absorber rod does not change until it ruptures at 1450 °C due to the “melting” of the stainless steel cladding, followed by the dissolution of the Zircaloy guide tube by the absorber alloy and the molten stainless steel. All the elements in (partially) liquid form then relocate by flowing along the absorber rod to the lower parts of the vessel.

If the pressure in the primary circuit is lower than that in the absorber rod, the absorber rod cladding will deform by creep and will come into contact with the Zircaloy guide tube (Figure 2b). In practice, this occurs in the hottest regions of the core, usually around the mid-plane of the core. Chemical interactions between steel and Zircaloy lead to the formation of liquids resulting from eutectic reactions between iron and zirconium, between nickel and zirconium and between chromium and zirconium. The Fe-Zr [27], Cr-Zr [28], and Ni-Zr [29] systems exhibit eutectic reactions occurring at 928 °C, 1332 °C and 960 °C respectively for the lowest ones. Rupture of the absorber rod effectively occurs at temperatures of around 1220 °C. Due to the difference of pressure between the one inside the absorber rod and the one in the primary circuit, the molten absorber alloy is ejected more or less abruptly (schematically shown in Figure 2c). These ejections of absorber material can deposit on the Zircaloy claddings of neighbouring fuel rods and can initiate their dissolution, while the majority of the SIC alloy flows along the guide tube dissolving it and gradually relocates to the bottom of the vessel (Figure 2d) [21,30]. The whole scenario of the degradation of the absorber rod described above is schematised in Figure 2.

The degradation of the absorber rod in B₄C (boron carbide) proceeds from a different phenomenology. The steel of the absorber rod cladding reacts with boron carbide between 1260 and 1350 °C [31,32] with as consequence its degradation. The interaction between B₄C and Zircaloy of the guide tube with liquid phase formation is visible at a higher temperature around 1650 °C, i.e., close to the eutectic invariant transformation of the Zr-B phase diagram [33]. The combined ruptures of the absorber rod and its guide tube allow the passage of water vapour and the oxidation of boron carbide into boron sesquioxide (B₂O₃) [34,35]. This oxide can vaporise (above 1500 °C) but also in its turn react, with steam to form, according to the conditions of temperatures and steam partial pressure, various boric acids (HBO₂, H₃BO₃ and (HBO₂)₃). B₂O₃ can also interact with fuel rods and contribute to their degradation. There were some indications in the Phébus FPT3 test (performed with a B₄C rod) of an early but limited degradation of fuel rods [36]. The chemical system between boron sesquioxide and refractory oxides (UO₂, ZrO₂) are poorly known. Nevertheless, the EC ENTHALPY Project [37,38,39] put in evidence that boron sesquioxide could lower the liquidus temperatures of the above-mentioned refractory oxides and thus potentially provoke an earlier destruction of fuel elements.

Depending on the accident scenario, the boron species (in the case of B₄C) and the species vaporising from the SIC-containing melts can react with fission products (gas, vapour and/or aerosols) and consequently affect the source term (defined as the magnitude, the chemical and physical form of the fission product source distribution in the containment atmosphere, during severe accident conditions). Boron plays a role in the formation of gaseous iodine because it can form caesium polyborates and then may prevent CsI aerosol formation. Its influence on the fraction of iodine gas (which is a major contributor to the short-to-mid-term gaseous source term to environment) has been observed experimentally [40]. Silver (and cadmium) is known to have also an impact on the iodine chemistry [41] (e.g., by possibly forming AgI and CdI₂ aerosols or by modifying the molybdenum chemistry which in turn impacts that of caesium) such as the vaporisation of the different elements of the Ag-In-Cd mixtures at the initiation of the absorber rod rupture, and of the Ag-In-Zr-(O-H) mixtures (once the interaction between the guide tube and the absorber rod takes place) are key points to investigate.

The release mass rate of species i from the Ag-In-Cd melt (or any melt) by evaporation can be estimated as:

$$\frac{d{m}_i}{dt}=S{\beta }_i{M}_i\left({\rho }_i^S-{\rho }_i^{\infty }\right)$$

(1)

where ${\rho }_i^S$ and ${\rho }_i^{\infty }$ are the mole concentrations of species i in the gas near the evaporating surface and in the bulk, S the evaporating surface, M_i the molar mass of species i and β_i (m/s) the mass transfer coefficient of species i. In reactor conditions, ${\rho }_i^{\infty }$ can be neglected in comparison with ${\rho }_i^S$. The previous equation can be then formulated as:

$$\frac{d{m}_i}{dt}=S{\beta }_i{M}_i\frac{P_i}{RT}$$

(2)

where P_i is the partial pressure of species i in the gas at the vicinity of the evaporating surface, T the gas temperature and R the ideal gas constant. P_i are functions of the concentration (X_i) of the chemical elements (i) in the mixture and the activity coefficients (γ_ι) of (i) in the mixture.

A very important work on the determination of the Ag-Cd-In system was recently undertaken at IRSN in collaboration with IM2NP (Marseille, France) [42,43,44,45] for the experimental part and with SIMAP (Grenoble, France) [45] for the Calphad modelling part, with a particular focus on the phase equilibria with the liquid phase and the determination of the mixing enthalpy in liquid phase. All these works are reported in

Table 1. Main thermodynamics information in the Ag-In-Cd ternary system.

Authors	Compositions and Temperatures	Data	Technique
Experimental Data
Snyder [48]	Rich-silver corner at 20 °C and 315 °C	Stability of the fcc solid solution	XRD (3) and metallography
Horrocks [46] Bowsher et al. [47] Steinbruck et al. [21]	SIC nominal composition	Melting range Liquidus temperature Melting range	DSC (2) Not reported DSC (2)
Horrocks [46]	Isopleth sections xIn = 0.6 and xIn/xCd = 3	Liquidus temperature	Smith analysis technique
Bénigni et al. [42]	Isopleth sections xCd/xIn = 1, ¼, 1/9 and xAg/xIn = 1/4, 1/19 at 450 °C	Enthalpy of mixing of liquid	Drop calorimetry
Decreton [43] Gajavalli et al. [44] Fischer et al. [45]	Different compositions	Liquidus temperature	DTA (4)
Phase diagram modelling
Horrocks [46] Desgranges [49] Fischer et al. [45]	All temperatures and compositions	Gibbs energy of all phases (1)	Modelling

⁽¹⁾ Gibbs energy parameters unpublished for [46], and [49]. ⁽²⁾ DSC: differential scanning calorimetry. ⁽³⁾ XRD: X-ray diffraction. ⁽⁴⁾ DTA: differential thermal analysis.

, together with the previous experimental [21,46,47,48] and modelling studies on this system [46,49]. It is important to note that a specific temperature cycling protocol, so-called Interrupted-Heating Differential Thermal Analysis (IHDTA) method [44] was used for the determination of liquidus temperatures in the Ag-Cd-In system [44,45]. In this thermal analysis protocol, interrupted-heating cycles are applied near the liquidus temperatures to better approach the thermodynamic equilibrium in the sample. Gajavalli et al. [44] demonstrates that this technique which operates closer to equilibrium conditions, significantly reduces the uncertainty in the liquidus determination. By taking into account these new experimental data and the past experiments, the Calphad modelling of the Ag-Cd-In ternary system was built [45]. In this modelling, the binary Ag-In, Ag-Cd and In-Cd subsystems and the ternary system, at high temperature, in composition domains where liquid phase is present are well reproduced. The modelled section at 350 °C [45] taking into account the new experimental data compared to the previous version from Desgranges [49] (Figure 3) shows that the liquid domain is less extended than previously modelled. Additional experimental investigations of the solid phases could allow to better characterize thermodynamics of the solid solutions, γ and α, of hexagonal compact and face-centered cubic structures respectively.

It will be very important to consider in future studies the assessment of the zirconium (and oxygen) impacts on the SIC absorber element vaporisation. Investigations of interaction between the SIC alloy and the Zircaloy of the guide tube [30] show that the guide tube can be liquefied as early as 1100 °C and that this reaction accelerates from 1200 °C. Thermodynamics of melts resulting from the absorber rod interaction with the Zircaloy guide tube needs be modelled. First the metallic chemical systems including zirconium, Ag-Zr [50], In-Zr [51,52] and Ag-Zr-In, as well as the In₂O₃-ZrO₂ oxide system [53], must be considered. Since the assessment of the Ag-Zr system by Karakaya [50] who highlighted the unresolved controversies about the transformations of the AgZr and AgZr₂ compounds, very few new data have been produced. Nevertheless, a recent investigation at IRSN with IM2NP (Marseille, France) and SYMME (Annecy, France) [43,54] established that AgZr and AgZr₂ decompose congruently and peritectically, respectively. In addition, no experimental thermodynamic property of any phase can be found in the literature, apart from the determination of the mixing enthalpies in the liquid phase performed by Fitzner and Kleppa [55]. In the same article, the standard enthalpies of formation of AgZr and AgZr₂ were determined by direct calorimetry but were called into question later, by Kleppa himself in [56]. The data reported on the In-Zr system are very poor [51,52] apart the stoichiometries of the stable compounds at room temperature (In/Zr = 3,2,1,1/2,1/3). The phase diagram is then largely unknown. Regarding the thermodynamic properties, only the standard enthalpy of formation of InZr₂ has been reported [57] and recently redetermined [58]. The two systems, Ag-Zr and In-Zr, as well as the oxide one, In₂O₃-ZrO₂, are currently under investigation at IRSN [43,58].

3. Intermediate Temperature Regime (1450–2200 °C)

In the temperature regime between 1450 and 2200 °C, the main process to be considered regarding the in-vessel core degradation is the fuel dissolution by Zircaloy cladding. Below the melting temperature of Zircaloy, the dissolution is very limited. In the temperature range above 1500 °C, the highly exothermic oxidation reaction of Zircaloy of fuel rod cladding with steam leads to a temperature escalation in the upper parts of the core. Temperatures may then exceed the melting temperature of the oxygen-stabilised α-Zr(O) such as interaction between α-Zr(O) and UO₂ fuel may locally produce liquid mixtures. The fuel elements can be subjected to different gaseous environments (steam and hydrogen) which determine the extent of the interaction between the cladding and the fuel and the temperature at which the cladding loses its integrity. This topic has been largely discussed in [59] and the analysis showed that the failure temperature is strongly dependent on the heat-up rate.

The UO₂/liquid cladding interaction in detail analysed in [60,61], now well understood, can be described as a succession of two distinct periods. During the first one, the fuel dissolution is a relatively quick process governed by natural convection driven by the uranium and zirconium density difference in the fully liquid melt. During the second period, the dissolution process continues but much more slowly due to the fact that the composition of the melt moves within the biphasic (U,Zr)O_2-x solid + (U,Zr,O) liquid (L) region of the O-U-Zr phase diagram. To model such a process in a simulation severe accident code, detailed knowledge of the O-U-Zr system is required, in particular the position of the liquidus line at the different temperatures which determines when solid phases begin to precipitate in the melt and then the slowing down of the dissolution process as well as the orientation of the tie-lines in the biphasic (U,Zr)O_2-x + L region which gives the composition of the precipitates.

The thermodynamic Calphad modelling of the U-O-Zr phase diagram is available in different papers [19,62,63]. An important conclusion of these works is that the overall topology of the phase diagram is thermodynamically assessed over the whole temperature range 1000–2800 °C in the hypo-stoichiometric region. In particular, the modelling reported in [62] is shown to be consistent with the experimental liquidus temperatures determined by Farmer et al. [64,65] for U-O-Zr compositions representative of PWR and BWR coriums with different oxidation rates and with experimental data obtained later by Asmolov et al. [66,67,68,69] in the framework of the OECD MASCA Project. All these compositions are located in the composition region (x(O) > 50 mol%), corresponding, for most of them, to relatively high liquidus temperatures (>2300 °C). A strong recommendation made in [62] was then to focus the efforts on the production of new experimental data in the UO₂-ZrO₂-Zr composition region between 1700 and 2200 °C, which is obviously important for the modelling of the UO₂/Zr interaction, as previously mentioned.

In the framework of the ISTC CORPHAD Project, Khabensky et al. [70] and Bottomley et al. [71] determined solidus and liquidus temperatures for compositions less rich in oxygen by visual polythermal analysis (VPA) and by differential thermal analysis (DTA) and simple thermal arrest technique (laser flash heating), respectively. The comparison between these new experimental data and the O-U-Zr modelling [62] seems to indicate that the liquidus temperatures in the Zr-rich region of the UO₂-ZrO₂-Zr composition domain (x(O) < 50 mol%) are slightly too low (between 50 and 100 °C).

They could lead into a moderation of the curvature of the liquidus line in the Zr rich region between 1800 and 2200 °C (Figure 4). This curvature is linked to liquidus temperatures interpreted from UO₂/Zr dissolutions tests performed by Hayward et al. [72,73] and later by Hofmann et al. [74,75,76] in the EURATOM COLOSS Project as well as to Farmer’s DTA liquidus determinations [64,65]. It must be noted that this curvature could be more precisely obtained with the experimental determination of the shape of the liquidus in the Zr-O system (this experiment is likely very difficult to perform), in the hypo-stoichiometric region ZrO_2-x, which remains today insufficiently known. Some very recent data from Quaini et al. [63] and Almjashev et al. [77] should be also considered to improve the modelling of the U-O-Zr system below 2200 °C. The most recent experimental data with their characteristics are summarised in

Table 2. More recent thermodynamic data related to the O-U-Zr ternary system at high temperature.

Authors	Year	Compositions and Temperatures	Data	Technique
Experimental data related to the UO2-ZrO2-Zr composition domain
Farmer et al. [64,65]	1998	UO2-ZrO2-Zr compositions with x(O) > 50 mol%	Solidus/liquidus temperatures	DTA (2)
Asmolov et al. [66,67,68,69]	2001–2004	UO2-ZrO2-Zr compositions with x(O) > 50 mol%	Liquidus temperatures	Visual technique
Khabensky et al. [70]	2006	UO2-ZrO2-Zr compositions	Solidus/liquidus temperatures	VPA (1) and DTA (2)
Bottomley et al. [71]	2008	UO2-ZrO2-Zr compositions	Liquidus temperatures	Thermal arrest
Quaini et al. [63]	2018	Miscibility gap at liquid state, 2294 °C	Tie-lines	Equilibrium + quenching
Hayward et al. [72,73]	1996	UO2-ZrO2-Zr compositions, 2000–2500 °C	Liquidus	Indirect determination based on dissolution kinetics change
Hofmann et al. [74,75,76]	1997	UO2-ZrO2-Zr compositions with x(O) > 50 mol%	Liquidus	Indirect determination based on dissolution kinetics change
Almjashev et al. [77]	2021	Miscibility gap at liquid state	Tie-lines	Equilibrium + quenching
Bechta et al. [78]	2008	Miscibility gap at liquid state, 2370 °C, 2480 °C	Tie-lines	Equilibrium + quenching
Guéneau et al. [79]	1998	Miscibility gap at liquid state, 2950 °C	Tie-lines	Equilibrium + quenching
Experimental data related to the UO2-ZrO2-O2 composition domain
Ronchi et al. [80]	2002	UO2-ZrO2	Solidus temperatures	Thermal arrest
Punni et al. [81]	2001	UO2-ZrO2-(O2)	Solidus/liquidus temperatures	Thermal arrest
Manara et al. [82]	2008	UO2-ZrO2	Solidus/liquidus temperatures	Thermal arrest
Mastromarino et al. [83]	2017	UO2-ZrO2-O2	Solidus/liquidus temperatures	Thermal arrest
Phase diagram modelling
P.Y. Chevalier et al. [19,62] A. Quaini et al. [63]	2004–2008 2018	All temperatures and compositions	Gibbs energy of all phases (1)	Modelling

⁽¹⁾ VPA: visual polythermal analysis ⁽²⁾ DTA: differential thermal analysis.

.

The main difficulty to overcome in obtaining some data in the rich-zirconium region at high temperature is to prevent any contamination of the melt by the crucible. The high affinity of metallic zirconium with oxygen and with carbon prevents most oxides and carbides from use as containers. Metallic refractory metals as W [84] or C, are also known to pollute the U-Zr-O samples. Nevertheless, some alternative exist. Thoria [85] and sub-stoichiometric yttria [86] (stoichiometric Y₂O₃ possibly reacts with metallic zirconium [87]) have been tested with success with melts containing metallic zirconium. Regarding carbide-made crucibles, Farmer et al. [64,65] used TiC, TaC and ZrC and concluded about the superiority of TaC (also recommended in [85]) for DTA experiments for sub-oxidised U-O-Zr melts up to very high temperature (2500 °C) while McDeavitt et al. [87] successfully tested ZrC but only up to 2000 °C with pure metallic zirconium. Nevertheless, some alternatives exist. Today, in most experiments devoted to this topic, self-crucibles (with a laser heating mode) and cold crucibles are used. If these techniques allow to prevent the sample to be contaminated, they have also potentially some drawbacks. With the cold crucible technique, the existence of a temperature gradient within the sample is inevitable and leads to a composition gradient in the melted material and does not allow a full control of the composition. The other drawback for the experiments where equilibrium is quenched from high temperature can be linked to the too slow quenching process which may induce a redistribution of the species between phases during cooling. For the laser flash technique, one of the main arguments developed in [88,89] against the employed methodology is the possible formation of metastable phases due to the large quenching speed (about 10,000 °C/s). Nevertheless, it is rather well established today that these techniques allow to give important insights at high temperature on the chemical systems of interest for severe accident phenomenology.

4. High Temperature Regime (above 2200 °C)

The destruction of fuel rods and melting of materials lead to the accumulation of core materials, commonly called “debris”, in the lower plenum of the reactor vessel. The debris may be partially solid and liquid, with a molten pool surrounded by solid particles. This usually occurs at temperatures above 2200 °C (but could be below according some observations [90]). The melt can be held in core as in the Phebus FPT0 [91] or FPT1 tests [92]. The liquefaction temperature range of such a melt is an important input to predict the behaviour of the molten pool in the lower head of the reactor vessel and the potential damages of this one. The composition of the molten pool in the FPT1 test as well as in the FPT0 one corresponded to the atomic composition of (U_0.50, Zr_0.47, Fe_0.02, Y_0.01)O₂.

The melting temperature of FPT1 corium samples (liquidus) was measured at 2487 ± 25 °C by means of the laser flash technique [80], consistently with [81,82,93] considering the impact of small amount of iron oxide. Using the same technique, a similar result was obtained for the FPT0 corium. In an accident situation as TMI-2, large amount of debris (among this part, 20 tons was liquefied) was found onto the lower part of the vessel. Simulated fuel debris samples having a similar chemical composition (in wt.%: 72.1 UO₂, 20.5 ZrO₂, 3.4 Fe₃O₄, 1.3 Cr₂O₃, 1.0 NiO, 1.7 Ag) to TMI-2 debris were fabricated in order to obtain data on melting temperature [94,95]. The melting temperature measured by thermal arrest technique was estimated to be about 2557 ± 50 °C, i.e., consistently with the Phebus FP tests.

The debris could interact with the steel of the bottom of the reactor pressure vessel and then threaten the integrity of the primary containment vessel. The heat fluxes received by the vessel are key quantities to identify the scenario (in particular time and location) of an eventual rupture of the vessel. In the previous different examples (Phébus FP or TMI-2), the molten pools were fully oxidized at the end of the accident sequences. In the general case, the U-O-Zr-Fe pool compositions may be not fully oxidized depending on the kinetics of oxidation process and the steam availability such as the molten pool in the lower part of the reactor vessel may include both oxide and metallic materials. In these particular conditions, a metal layer located above the oxide corium is considered as a potential cause for vessel failure because the vessel wall adjacent to the metal layer would be subjected to important heat fluxes (Figure 5). Calculations indicate that the upper metal layer may receive up to 50% of the thermal power released by the corium, this power being transferred by convection to the vessel walls. The thinner this layer is (for small masses of steel) the higher the flux, "focused" at the interface with the vessel. A thermal flux of 2 megawatts per square meter can be reached or exceeded where the metal layer is only 10 cm thick. This so-called focussing effect [96,97,98], particularly during transient phases, can lead to critical and dangerous situations, capable of rapidly melting the vessel wall locally. Some actual reactor designs include a system able to mitigate this risk by injecting water around the vessel to cool the outer wall (Figure 5) and prevent it from breaking through. This strategy—known as IVR for in-vessel retention—which is currently attracting a lot of attention was introduced about 20 years ago [99,100] and first applied to two reactor designs, AP600 [101] (later replaced by the AP1000 design but keeping the IVR option) and VVER-440, this last case leading to practical application at the Lovisa Plant (Finland) [102]. Some studies are still ongoing on the extension of this strategy to high power reactors [97,98].

For sub-oxidised corium, the configuration of the molten pool strongly depends on the zirconium oxidation degree of the corium. The described configuration (with the top layer made of metallic components) can occur if, in particular, all zirconium is oxidised. Indeed, stainless steel of internal structures is known to form a non-miscible liquid with UO₂ oxide fuel [103,104] and zirconia [105]. Two liquids, one of metallic character (including steel components) and one oxide liquid (including mainly UO₂ and ZrO₂) can be consequently formed. Regarding the different densities of the two liquids, the metallic layer can separate from the oxide one and can position above the latter. In case of sub-oxidized corium, free metallic zirconium could chemically reduce core oxides and then could produce a denser metallic phase containing part of steel but also metallic uranium and metallic zirconium. Such chemical interaction may potentially lead to a molten pool having a three-layered morphology (bottom to top): denser liquid metallic phase, liquid oxide phase and lighter metallic liquid. The thickness of the latter layer can be smaller than in the situation of a two-layer molten pool since in this situation steel is distributed between both metallic layers. The three-layer molten pool may then increase the risk of heat-focusing effect. The main consequence is that interaction between species has to be taken into account if one wants to model the molten pool configuration evolution in severe accident sequences. To predict the morphology of the molten pool then requires to model the coupling between thermodynamics and thermal-hydraulics [106]. This approach is also necessary to predict the distribution of the fission products in the pool in order to calculate the decay heat associated to each phase.

During an accident sequence, compositions as well as temperatures of the molten pool can vary. The CALPHAD databases as NUCLEA [14] or TAF-ID [16], which models the corium chemistry in the entire composition region from metal to oxide, are used today in the severe accident codes to predict the phases as function of temperature and composition. Regarding more specifically the thermochemistry of the U-O-Zr-Fe system in reducing atmosphere conditions, the state of knowledge can be summarized as follows:

-

the U-O phase diagram exhibits a miscibility gap in the liquid state. The small solubility of oxygen in liquid uranium and then a wide liquid miscibility gap in U-O was reported in [79,107] and has been recently confirmed by new experimental data in the framework of the ISTC CORPHAD Project [78].

-

the miscibility gap in the liquid state is also present in the U-O-Zr system (Figure 6a). For a long time, there was a controversy about this extent into the ternary phase diagram since some authors mentioned its existence on the UO₂-Zr section [108], while others [109,110], as Politis, extended it to the α-Zr(O) section whereas finally other authors, as Hayward et al. [72,73], did not report it. This extension is modelled in [62,63] mainly by considering the experimental data related to the tie-line orientation at very high temperature (2950 °C) [79] and the measurement of oxygen solubility limit in U-Zr liquid at 2000 °C [105]. More data have been recently reported on the tie-line orientation in the miscibility gap [63,77]. They disagree with some experiments performed in the framework of the ISTC CORPHAD Project [78]. Even if this disagreement is not fully understood at this stage, different assumptions can be invoked to explain it, as a possible redistribution of some mobile species between the phases in case of insufficiently quick quenching or accuracy of the oxygen composition measurements. Regarding this latter item, the oxygen concentration measurement in the uranium–zirconium metallic alloys is a difficult task and a key point to determine the extension of the miscibility gap. It must be pointed out that more accurate techniques of oxygen measurement in metallic phases were tested during the ISTC CORPHAD Project [70] (as the carbon thermal reduction).

-

the ternary phase diagrams (Fe-O-Zr and Fe-O-U, Figure 6b,c, respectively) have been poorly investigated at high temperature in reducing conditions. Some data have been recently produced on the Fe-O-Zr system but remain preliminary or need to be confirmed [77,78]. For this system, the modelling is rather tricky in absence of data since on the one hand, metallic zirconium is known to dissolve zirconia [111] and on the other hand, iron is weakly miscible with zirconia [105]. The oxygen solubility in Fe-Zr liquids results from the competition between these two tendencies. For the Fe-O-U system, taking into account the experimentally proved immiscibility between UO₂ and U, and between UO₂ and Fe, a low oxygen solubility in Fe-U liquids until high temperature (>2500 °C) may be assumed.

Until the 2000s, the database of experiments performed within the quaternary U-O-Zr-Fe (or steel) system at high temperature in the metal-oxide composition region was relatively limited [112,113,114,115,116,117]. In Hofmann’s experiments [116] which are the more detailed of these past data, the reaction behaviour of the UO₂, Zircaloy-4 and austenitic steel core components was investigated as a function of temperature until complete melting under inert atmosphere, for component compositions representative of a PWR prototypical molten pool. They varied between that of corium named A1, assuming that the fuel rods, spacers and the core support plate were molten (~65 wt.% UO₂, ~18 wt.% Zry and ~17 wt.% steel) and that of corium named E2 for which additional structural elements were added (~35 wt.% UO₂, ~10 wt.% Zry and ~55 wt.% steel). For these two compositions A1 and E2, two immiscible liquids were obtained at temperatures above 2523 °C, one containing little oxygen (called metallic phase) and the other one much more oxidised.

Despite these initial data, it was considered that sufficient knowledge on chemical distribution in these different phases in prototypic segregated liquid corium was still lacking at the beginning of the 2000s. A more systematic experimental investigation of the interaction between molten sub-oxidised U-Zr-O melts and iron (and steel) was launched in the framework of the OECD MASCA and MASCA2 Projects [12,13,66,67,118,119,120,121,122,123]. The different compositions investigated in these Projects are reported in

Table 3. More recent experimental data related to the O-U-Zr-Fe(steel) system at high temperature in the metal-oxide composition range. (*) r = mass of iron/(mass of iron + mass of U-Zr-O).

Authors	Compositions and Temperatures		Data	Technique
MASCA1 and 2 Projects PWR Tests U/Zr = 1.2
U-O-Zr-Fe (2500 °C–2600 °C)
	Cn	r (*)
	32	0–29	Composition of metal and oxide phases	Equilibrium + quenching in cold crucible
	50	2.0
	70	2–10
	100	2.0
U-O-Zr-Steel
	32	9.1
MASCA1 and 2 Projects BWR Tests U/Zr = 0.9
U-O-Zr-Fe (2500 °C–2600 °C)
	32	0–20	Composition of metal and oxide phases	Equilibrium + quenching in cold crucible

. One of the specific objectives of these Projects was then to provide information on the compositions of the different phases in a situation of phase separation in the corium in order to be able, in detail, to predict the configuration the corium could exhibit in the lower head of the vessel. The impacts of different parameters, e.g., the amount of steel, the oxidation rate of the U-Zr-O melts (C_n = n_Zr/(n_Zr + n_ZrO2)), the U/Zr initial ratio in these melts (this value usually characterises the reactor type, PWR about 1.5 or BWR lower than 1), and temperature were investigated.

Figure 6. (a) O-U-Zr isothermal section modelled in NUCLEA [14] at 2873 K. (b) O-Fe-U isothermal section modelled in NUCLEA [14] at 2873 K. (c) O-Fe-Zr isothermal section modelled in NUCLEA [14] at 2873 K, NUCLEA Database 2014.

Figure 6. (a) O-U-Zr isothermal section modelled in NUCLEA [14] at 2873 K. (b) O-Fe-U isothermal section modelled in NUCLEA [14] at 2873 K. (c) O-Fe-Zr isothermal section modelled in NUCLEA [14] at 2873 K, NUCLEA Database 2014.

The following tendencies have been observed. The uranium and zirconium contents in the metallic phase decrease mainly by dilution effect when iron is progressively added in the melt. When the oxidation rate is augmented, which corresponds to a reduction of the initial metallic zirconium, a reduction of uranium amount transferred from the sub-oxidised corium to the metallic phase is observed. It tends to decrease the density of the metallic phase. The experimental results from the MASCA and MASCA2 Projects are satisfactorily reproduced by the NUCLEA database. An example of this agreement for the PWR C₃₂ corium is reported in Figure 7.

For BWR-type reactors, the potential effect of B₄C (absorber material) on the composition of the metallic phase has to be additionally considered. Fischer et al. [124] by repeating the same experiments with two BWR corium compositions (U/Zr = 0.83, same C_n, without and with 1.4 wt.% B₄C) put in evidence in the post-test analyses, the zirconium diboride as the phase trapping boron. The presence of ZrB₂ in the metallic phase was also reported in An et al. [125] and Song et al. [126]. From these observations, it can be expected that the effect of boron is to decrease the metallic zirconium amount previously available for the reduction of the UO₂ and ZrO₂ oxides since one part is chemically associated to boron to form zirconium diboride. The consequence is a decrease of uranium amount transferred from UO₂ to the metallic phase and then a reduction of the density of the metallic phase with a lower possibility of a 3-layer corium morphology. An important remaining issue to be solved is to be able to estimate the boron amount entering the corium, strongly dependent on the B₄C absorber rod degradation scenario.

Not only knowledge of the distribution of the main elements between these phases but also the repartition of the most important heat-producing fission products [127] is required to properly evaluate the heat removal capabilities of a potential safety system. Fischer et al. [112] studied the distribution of the more important heat-producing fission products between molten UO₂ and liquid iron in inert atmosphere. It was found that yttrium (Y), lanthanum (La), strontium (Sr), barium (Ba), zirconium (Zr), praseodymium (Pr) and cerium (Ce) were mostly located in the oxide phase whereas molybdenum (Mo) and ruthenium (Ru) were distributed in the metallic phase. No accurate value of fission product partitioning coefficient between oxide and metallic phases was available in the literature until the realisation of the STFM-FP tests in the framework of the OECD MASCA and MASCA2 Projects [119]. The main objective of these tests was to determine the distribution of the fission products between the oxide and metallic phases after equilibration of the liquid phases of U-Zr-O-Fe melts. The experimental results are in agreement with the conclusions of the previous work of Fischer et al. [112], i.e., barium and strontium as well as the lanthanides La and Ce predominantly in the oxide phase whereas most of Mo and Ru are trapped in the metallic phase. The fission products I, Cs, Kr, Xe, Sb and Te were not considered since these elements in their stable form of oxides or elements have high vapour pressures and are consequently largely released before the formation of the molten pool in the vessel lower head and do not contribute to the decay heat.

5. Ex-Vessel Corium Progression

The ex-vessel progression of a severe accident in a nuclear reactor involves the relocation of molten core debris into the reactor cavity. The molten materials are able to interact with the concrete of the basemat resulting in ablation and release of concrete species by vaporisation and of combustible gases. The composition of the melt changes progressively as the basemat decomposition products are incorporated into the melt during the molten core–concrete interaction (MCCI). In order to estimate the consequences of this interaction, models are required to simulate the thermalhydraulic and chemical behaviour of the melt during the interaction.

In the molten core–concrete interaction modelling, obtaining accurate thermochemical data for an oxide/metal corium mixture is of prime importance for evaluating the pool temperatures and material transport properties, which strongly influence heat transfer distribution within the corium pool. In particular, large uncertainties are still existing on modelling of solidification at the interfaces of a corium pool submitted to concrete material and gas incorporation. It has been considered that heat convection occurs if the pool temperature was above a mobility threshold value characterised by a solidification temperature, usually chosen between solidus and liquidus temperatures at the pool composition. A crust may appear at the pool/concrete interface if the interface temperature lies below this solidification temperature. This solidification temperature is usually defined by fixing a threshold corium molten fraction, which is calculated by using a thermodynamic database, as e.g., NUCLEA for the ASTEC code.

Additionally, in the different chemical processes usually taken into account in the numerical simulations of MCCI, concrete “ablation” is an important concept. Even if this concept has no meaning from the point of view of thermodynamics (and this a real difficulty), it is usually defined in the scientific literature as the process at the concrete interface in which the decomposition products of concrete become incorporated into the core melt or debris. It is expected that this process is characterised by a temperature at which material detaches from the concrete surface. This temperature is generally called “ablation temperature”. As a corollary, the ablation enthalpy, associated to the ablation process, is defined as the heat required to raise the concrete temperature from ambient temperature to the ablation temperature. These quantities, if they are introduced in the MCCI simulation codes as computational conveniences in order to reproduce experimental results, are expected to approximate the thermodynamic behaviour of concrete at high temperature. For this reason, the ablation temperature is defined from a liquid fraction threshold and differs from one concrete to another. Investigations were performed to assess the effect of the rebars present in the concrete. Interpretation of some MCCI tests [128] seems to show that the rebars in the concrete tend to elevate the melt/concrete interface temperature up to the melting temperature of the reinforcing steel, i.e., 1526 °C. One must keep in mind that the ablation temperature is a notional temperature used for numerical modelling although concrete ablation is not a process that occurs uniformly at the interface and at a fixed temperature, as a congruent phase change would.

The chemical approach involving modelling and critical assessment of experimental data for corium-concrete chemical systems plays an increasing role as the simulation codes are more advanced. For the modelling of the thermodynamics of corium–concrete mixtures the CALPHAD approach consists in the mathematical description of the Gibbs energy of each phase of the O-U-Zr-Fe-Cr-Si-Al-Ca-Mg complex system, based on a phenomenological model in such a way that the model parameters are adjusted to allow to reproduce the available experimental thermochemical information in the different oxide sub-systems.

The first study by Chevalier [129] aiming to illustrate the practical application of thermodynamics for nuclear safety codes was based on the optimisation on the limiting binary systems containing UO₂ and/or ZrO₂ coming from the works of Relave et al. [130] and Gisby [131]. A second thermodynamic study was later published by Ball et al. [132] who drew important conclusions about the limitations of the model which did not include data for systems with MgO and FeO_x and possible ternary interactions in the CaO-UO₂-SiO₂ and CaO-SiO₂-ZrO₂ systems. Since these initial studies which were performed at the very beginning of the development of the corium databases, a huge experimental and assessment work was undertaken to improve the description of the chemical sub-systems governing the corium-concrete melt thermodynamics. First an important work was performed by AEA Technology (UK) during the European Commission Fourth Framework Programme (1994–1998), the THMO Project focussed on thermochemical data and modelling of ex-vessel corium behaviour [133]. A critical data assessment on the binary systems of interest for corium–concrete mixtures commonly led by THERMODATA and AEA-T was then performed during the ENTHALPY Project of the European Commission Fifth Framework Programme (1994–1998) [3], leading to the European NUCLEA thermodynamic database first version for corium applications.

Since this work, a number of key oxide systems were investigated, e.g., FeO_x-UO₂ [134,135], FeO_x-ZrO₂ [136,137], FeO_x-UO_2+x-ZrO₂ [138,139,140,141], and Fe₂O₃-SiO₂ [142] within the framework of the ISTC CORPHAD and PRECOS Projects and other international Projects [10,11].

The consistency of the CALPHAD approach for corium–concrete mixtures can be validated through comparisons between thermodynamic database calculations and experimental results obtained on prototypical complex mixtures. For this purpose, the experimental data of Roche et al. [143] who measured liquidus and solidus temperatures by a combination of differential thermal analysis and rotational viscometry for three types of concrete (limestone, limestone sand, and siliceous) and for mixtures with urania and zirconia can be used. The compositions of the different corium-concrete melts are mainly in the UO₂-ZrO₂-CaO-SiO₂ phase diagram domain. More analytical tests where the minor compounds of the concrete were not considered in the mixtures have been performed within the UO₂-ZrO₂-CaO-SiO₂ system in the EC ENTHALPY Project [144]. From a general point of view, the liquidus shape in the UO₂-ZrO₂-CaO-SiO₂ phase diagram is mainly governed by the composition CaO/(CaO + SiO₂) ratio in the melt:

• when the CaO/(CaO + SiO₂) ratio is low (case of siliceous concrete), the thermodynamics of the corium–concrete mixtures mainly depends on the UO₂-ZrO₂-SiO₂ ternary phase diagram. At high temperature, this chemical system presents a tendency to immiscibility which results from the thermodynamic behaviours observed in the UO₂-SiO₂ [145,146] and ZrO₂-SiO₂ [147,148] systems in which immiscibility at the liquid state was also observed. In the UO₂-SiO₂ system, the miscibility gap which is today rather well established (even if it is in contradiction with previous data published by [149] or rejected in [150]) is positioned by Lungu et al. [145,146] at the monotectic temperature of 2090 °C between 29 and 70 wt.% UO₂. New experimental results have been produced within the Severe Accident NETwork (SARNET) of the European Commission [151] and within the ISTC CORPHAD Project [152], confirming the existence of the two-phase liquid region in this system. Positive deviations to the ideal behaviour were also measured in the UO₂-ZrO₂ phase diagram at high temperature [153]. Considering the repulsive interaction between both UO₂ and ZrO₂ and SiO₂, the miscibility gap between a urania-zirconia corium and a silica enriched liquid should be approximately located at 2150 °C between 30 and 70 wt.% of corium. As a consequence, the liquidus temperatures of the siliceous concrete-corium melts should not vary with the amount of concrete in the mixture for quantities of concrete between 30% and 80% wt. The liquidus temperatures measured by Roche et al. [143] are consistent with this description (

  Table 4. Corium–siliceous concrete compositions and measured solidus and liquidus temperatures [143].

  	Composition (wt. %)							Solidus (°C)	Liquidus (°C)
  	UO2	ZrO2	CaO	SiO2	Al2O3	MgO	Fe2O3
  Concrete (80%)–Corium (20%)	15.6	4.4	12.0	62.4	4.0	0.8	0.8	-	2170
  Concrete (27.5%)–Corium (72.5%)	56.5	16.0	4.1	21.5	1.4	0.275	0.275	1134–1322	2094/2276
  Concrete (10%)–Corium (90%)	70.2	19.8	1.5	7.8	0.5	0.1	0.1	1610	-
  Corium (100%)	78.0	22.0	-	-	-	-	-	-	-

  ).
• when the ratio CaO/(CaO + SiO₂) tends to 1 (case of limestone concrete), the UO₂-ZrO₂-CaO-SiO₂ phase diagram is expected to tend to an eutectic behaviour which results from the eutectic thermodynamic behaviours observed in the UO₂-CaO [154,155] and ZrO₂-CaO [156,157] systems. This behaviour should induce variations of liquidus temperatures with the amount of concrete in the mixture. The liquidus temperatures measured by Roche et al. [143] are not in agreement with this description since they are practically constant between 27.5% and 60% wt. of concrete. In the framework of the EC ENTHALPY Project, Hellmann et al. [144] determined, in inert atmosphere, liquidus and solidus temperatures by applying two methods of visual polythermal analysis (VPA) and of more classical differential thermal analysis. The composition Enthalpy n°8 (

  Table 5. Corium–limestone concrete compositions and measured solidus and liquidus temperatures [143,144].

  	Composition (wt. %)							Solidus (°C)	Liquidus (°C)
  	UO2	ZrO2	CaO	SiO2	Al2O3	MgO	Fe2O3
  Roche et al. [143]
  Concrete (60%)–Corium (40%)	31.2	8.8	42.6	7.2	1.8	7.8	0.6	1300	> 2577
  Concrete (36.2%)–Corium (63.8%)	49.8	14.0	25.7	4.3	1.1	4.7	0.4	-	> 2577
  Concrete (27.5%)–Corium (72.5%)	56.6	15.9	19.5	3.3	0.8	3.6	0.3	1247	> 2577
  Concrete (10%)–Corium (90%)	70.2	19.8	7.1	1.2	0.3	1.3	0.1	1615	-
  Hellmann et al. [144]
  Enthalpy n°8	61.9	14.9	23.2	-	-	-	-	1865 ± 5	1935 ± 45
  Enthalpy n°4	33.6	13.5	26.4	-	26.5	-	-	1340 ± 20	1760 ± 20

  ) can be compared to the Roche’s one with 27.5% limestone concrete and 72.5% corium. The liquidus temperature (Table 5) consistently measured by using the different techniques, around 2200 K, is about 600 K lower than the Roche’s data which appears as doubtful for these compositions.
• finally, when the CaO/(CaO + SiO₂) is between 0 and 1 (case of the limestone-sand concrete–corium mixtures), the prediction of the thermodynamic behaviour is more complex since there is a competition between the eutectic phase diagrams, CaO-UO₂ and CaO-ZrO₂, and the immiscible chemical systems, SiO₂-UO₂ and SiO₂-ZrO₂. Some data obtained by Roche et al. [143] and Hellmann et al. [144] reported in

  Table 6. Corium–“limestone common sand concrete” compositions and measured solidus and liquidus temperatures [143,144].

  	Composition (wt. %)							Solidus (°C)	Liquidus (°C)
  	UO2	ZrO2	CaO	SiO2	Al2O3	MgO	Fe2O3
  Roche et al. [143]
  Corium 1	92.0	8.0	-	-	-	-	-	-	-
  Concrete (60.4%)–Corium 1 (39.6%)	36.4	3.2	23.0	24.8	3.0	8.4	1.2	-	> 2304
  Concrete (47%)–Corium 1 (53%)	48.8	4.2	17.9	19.3	2.3	6.6	0.9	1175	> 2450
  Corium 2	78.0	22.0	-	-	-	-	-	-	-
  Concrete (80%)–Corium 2 (20%)	15.6	4.4	30.4	32.8	4.0	11.2	1.6	1245	-
  Concrete (27.5%)–Corium 2 (72.5%)	56.5	16.0	10.4	11.3	1.4	3.9	0.5	1087	2365/2577
  Concrete (10%)–Corium 2 (90%)	70.2	19.8	3.8	4.1	0.5	1.4	0.2	1575	-
  Hellmann et al. [144]
  Enthalpy n°9	31.5	9.5	33.5	25.5	-	-	-	1490 ± 30	1630–1830

  allow to validate the thermodynamic modelling of the databases.

6. Conclusions and Perspectives

This paper synthesises more than 30 years of effort conducted with the objective of advancing the knowledge of corium thermodynamics. If we chose to undertake a review as exhaustive as possible of the important chemical systems to be considered to simulate the progression of the corium in a severe accident situation and of the data obtained by experiment, a not lesser effort has been made to develop databases from the CALPHAD approach allowing to capitalise this knowledge in a self-consistent way and in the severe accident codes. NUCLEA and TAF-ID are the best examples of this capitalisation.

If we can consider that the acquired knowledge allows today to contribute to a relatively precise description of the thermodynamics of the corium, some points remain to be consolidated.

First, it would be necessary to better specify the Fe-O-Zr and Fe-O-U systems at high temperature in the metal-oxide composition range to further improve the predictions of the phases present in a corium pool at the bottom of the vessel. In addition, it must be also mentioned that most of the experiments in the OCED MASCA and MASCA2 Programs were performed for PWR compositions. Much less data are available for typical BWR compositions, i.e., with an initial U/Zr around 0.9. In this framework, the experimental work in the rich-zirconium region of the U-O-Zr system should be continued although, as mentioned, experiments in this range of composition at high temperatures are extremely difficult.

From a general point of view, specific data should be produced to have a more reliable description of the corium progression in BWR geometries and designs. Since the Fukushima Daichi accident, a large effort has been undertaken to fill the gaps. Some recent tests in the more specific BWR geometry [158,159] in conditions representative of the Fukushima Daichi accidents allows also to have a better overview of the phases which can be formed, resulting of the different material interactions and of the impact of the metallic phases on the degradation process. From a more analytical point of view, a systematic identification of chemical systems requiring new experiments has been performed within the OECD TCOFF Project [160] on the basis of the phases identified in different interaction tests [161,162,163,164]. The ternary boron-oxygen based system as B-Fe-O, B-Zr-O, B-Cr-O and B-Ni-O have been considered as the first priority, not only for the oxide part (B₂O₃-MxO_y) for which few data have been reported but also for the metallic-oxide part of these systems. Such data could improve the description of the distribution of the elements between the metallic and the oxide phase in the molten pool in the presence of a significant amount of boron [126].

Regarding the ex-vessel phenomenology, the main challenge would be to evaluate the impact of the stainless steel components on the thermochemistry of the corium–concrete mixtures, firstly in terms of identification of the mechanisms involved in the oxidation of them [165] and secondly regarding the impact of their oxides on liquefaction curve of the corium–concrete mixtures. Few data were reported in the ISTC CORPHAD and PRECOS Projects and they need to be completed. The future studies should also focus on the interaction between corium and basaltic concrete, employed for the basemats of the units of the Fukushima Daichi site [166].

The development of accident-tolerant fuel cladding (ATF) which is a way of improving the safety of light water reactors will require the acquisition of data in chemical systems that have not been explored to date. Among the most promising avenues of research, the chromium-coated zirconium alloys will need to be assessed in severe accident conditions. In the past, the analyses of behaviour of the “standard” fuel bundles (UO₂ cladded with Zircaloy cladding) in these conditions showed that the oxide scale failure (ZrO₂) has a large impact on the accident progression. At present, in the majority of the severe accident codes, simple parametric models based on user-defined values are available to deal with the cladding failure mechanisms. The most widely used assumption is that the ZrO₂ layer fails when a certain temperature limit (typically 2000–2300 °C) is exceeded and when its thickness is less than a limiting value (the oxide shell is assumed not to break until typically 60% of the original cladding wall has been completely oxidised). It is certain that these criteria should be revised for Cr-coated claddings, and probably not in simple manner since the previous ones were not built following a mechanistic approach. Nevertheless, a very simple way to proceed would be the definition of some criteria from the solidus/liquidus of the Zr-Cr-O compositions, making a very simplified assumption of a full interdiffusion of the chemical elements of the coating layer and the zirconium-based substrate. Experimental data available on the ternary Zr-Cr-O system in the metal-oxide part are very limited. Only Rhee et al. [167] presented three isothermal sections experimental at 1200, 1773 and 1973 °C with the existence of a ternary compound of Zr₃Cr₃O stoichiometry. These sections were constructed from measurements made in tungsten crucibles for which it is now proven that interaction with zirconium is unavoidable. The ZrO₂-Cr₂O₃ pseudo-binary section proposed by Jerebstov et al. [168] is the only thermodynamic study available in the oxide part. It reports the temperature evolution of the respective solubilities of the constituents. Unfortunately, all the elaborations having been carried out in crucible of molybdenum, with contamination of up to 5% at of this metallic element in the samples, the uncertainty on the proposed values is such that they are suffering from questionable credibility. In any case there is a crucial need of experimental information to have an accurate description of the Zr-Cr-O system.

Other concepts of ATF cladding more revolutionary have been developed. Numerous compositions of FeCrAl alloys with varying Cr and Al contents have been studied. Along with the FeCrAl alloy composition modification, the introduction of dispersed oxide particles within FeCrAl alloys [169] has been also investigated as an improvement to its mechanical and/or oxidation properties. Critical parameters such as melting temperature, since they partially determine the onset of relocation in the core, are dependent on the composition. Studies until recently have had to utilise assumptions regarding the melting point for the FeCrAl cladding and its oxide for analysis of severe accident scenarios. The recommended melting temperature of FeCrAl by ORNL [170] is about 1427 °C, and the melting temperature of FeCrAl oxides is up to 1627 °C. Recent experimental studies [171] provide more precise information about the transition temperatures in the Fe-Cr-Al phase diagram. There is apparently no experimental data related to oxidation in steam at temperatures higher than the melting point. Regarding the interaction with fuel, it is well established that there is an interaction between liquid iron oxide and UO₂ at rather low temperature [134], compared to the melting temperature of the fuel. In the TMI-2 post-accident analysis framework, the interaction between stainless steel oxides (from the absorber rod cladding) and refractory compounds (UO₂ and ZrO₂) was the subject of important investigations in the context of understanding the degradation of the core after the accident at TMI-2. In TMI-2, Strain et al. [172] observed presence of eutectic oxide phase of Fe-Cr-O/(U,Zr)O₂ at the grain boundaries of the refractory matrix. Such penetrations were also seen in the Phebus PF test post-irradiation examinations [90]. Such penetrations have been also observed in preliminary tests of interaction between Fe-Cr-Al cladding and UO₂ fuel under oxidising conditions [173].

Silicon carbide SiC is often considered as an alternative material to metals or metal alloys for fuel rod cladding. The main objective is to reduce the oxidation of the material by steam and the associated hydriding. This mainly concerns nominal operation (primary hydriding) and design basis accidents, in particular of the LOCA type (secondary hydriding). In the latter case, the objective would be to make the cladding less fragile and to gain margins with respect to safety criteria. In case of complete oxidation of this type of cladding, the UO₂-SiO₂ phase diagram, based on Lungu’s measurements [145,146] indicates that from 2087 °C, liquid phase is able to be formed. Then, liquid SiO₂ is likely to interact with UO₂ to form liquid mixtures at temperatures well below that of fuel melting. In the other direction, the phase diagram in the silica-rich region is of monotectic type, indicating that urania and silica are poorly miscible. It could have some consequences in terms of degradation and corium morphology with a separation between the silica-rich and urania-rich phases. It could favour occurrence of a solid fuel slumping degradation scenario.

Regarding more conventional fuel, if the interaction between the cladding in liquid state and UO₂ has been the subject of many investigations, for the MOX fuel, only a few qualitative data are available [5,174,175]. For the interactions with other structural materials (especially steels and their oxides), experimental data are almost inexistent.

As it has been indicated in the introduction, specific non-ideal thermodynamic databases for corium applications, as NUCLEA, have been developed from the assessment of experimental information and keep improving by taking into account the new data. Today the challenge is clearly to integrate this knowledge in the severe accident simulation code. In this direction, considerable progress has been made at IRSN by integrating the NUCLEA database more closely the ASTEC code, for example in the model used to predict the behaviour of corium at the bottom of the reactor vessel [106] or in the corium–concrete interaction model [176].