Thermodynamic modelling assessment of the ternary system Cs-Mo-O

This work reports the thermodynamic modelling assessment of the rather complex Cs-Mo-O system, which is key for the understanding of fission products chemistry in oxide fuelled Light Water Reactors (LWRs) and next generation Sodium-cooled and Lead-cooled Fast Reactors (SFRs and LFRs). The model accounts for the existence of the ternary molybdates Cs 2 MoO 4 ( 𝛼 and 𝛽 ), Cs 2 Mo 2 O 7 ( 𝛼 and 𝛽 ), Cs 2 Mo 3 O 10 , Cs 2 Mo 4 O 13 , Cs 2 Mo 5 O 16 , and Cs 2 Mo 7 O 22 , for which sufficient structural and thermodynamic information are available in the literature. These phases are treated as stoichiometric in the model. The liquid phase is described with an ionic two-sublattice model, and the gas phase as an ideal mixture. The optimized Gibbs energies are assessed with respect to the known thermodynamic and phase equilibrium data in the Cs 2 MoO 4 -MoO 3 pseudo-binary section. A good agreement is generally obtained within experimental uncertainties. The calculated vapour pressures above Cs 2 MoO 4 (solid and liquid) are also compared to the available experimental data. Finally, isotherms of the Cs-Mo-O ternary phase diagram are calculated at relevant temperatures for the assessment of the fuel pin behaviour in LWRs, SFRs and LFRs.


Introduction
The safety assessment of nuclear fuel behaviour in a nuclear fission reactor requires the development of models and simulation codes of the complex chemistry of the numerous fission products generated during irradiation.The chemical elements generated inside the oxide fuel matrix (U, Pu)O 2 of Light Water Reactors (LWRs) and next generation Sodium-cooled and Lead-cooled Fast Reactors (SFRs and LFRs) form gaseous or volatile species, metallic precipitates, oxide precipitates, or constitute soluble species according to the classification of Kleykamp [1].The exact speciation depends on the specific physico-chemical properties of the elements, and the conditions on burnup (as well as isotopic composition of the fuel and neutron flux spectrum), temperature, and oxygen potential under normal operation and accidental conditions.Among those fission products, the speciation of cesium and molybdenum is of particular interest.Cs and Mo are firstly generated with a high fission yield (e.g.∼20 and 21% in the fast reactor Phénix fuel pin (U 0.77 Pu 0.23 O 2− ) at 10 at.% burnup [2]).Moreover, cesium belongs to the class of volatile products [3], and the potential release of 135 Cs and 137 Cs to the coolant and subsequently to the environment in a severe accident scenario should be assessed carefully for the protection of the general public.
The chemical form of cesium varies with the value of the oxygen potential that increases during irradiation.For low oxygen potential values, e.g.around − 500 kJ⋅mol −1 in hypostoichiometric oxide fuels, the formation of CsI, Cs 2 Te, Cs 2 UO 4 and Cs 2 MoO 4 is expected from thermodynamic calculations in increasing order of abundance [2].For higher oxygen potential values, e.g.above − 400 kJ⋅mol −1 , CsI and Cs 2 MoO 4 become the most stable compounds (again in this increasing order of abundance as the yield of iodine, ∼ 9%, is much lower than that of molybdenum) [2].The formation of Cs 2 MoO 4 is thus expected to be rather significant, especially at high burnups, as is the case in fast neutron reactors such as in SFRs and LFRs.
A phenomenon very specific to fast reactor oxide fuel pin is in fact observed at the (U, Pu)O 2 fuel periphery, namely the formation of a socalled JOG (Joint-Oxyde-Gaine, a French term that corresponds to the oxide-cladding joint) layer, at high burn-up (above 7%-8% fission per initial metal atom), in between fuel and cladding.The volatile fission products mentioned earlier (Cs but also I, Te, Mo) migrate radially due to the high thermal gradients in this type of fuel (∼973 K at the https://doi.org/10.1016/j.calphad.2021.102350Received 13 July 2021; Received in revised form 20 August 2021; Accepted 2 September 2021 periphery and ∼2273 K at the centre), and build up in the cooler rim region in the JOG layer of thickness 150-300 μm [2].
The JOG layer was found to have a porous and highly heterogeneous structure, and was reported to include the fission products (Cs, Mo, Te, I, Zr, Ba) and cladding components (Fe, Cr) [4].From the combination of post-irradiation examinations (PIE) and thermodynamic calculations, the JOG layer was shown to be made of Cs 2 MoO 4 (main constituent), CsI, Cs 2 Te and Cs 2 UO 4 [4][5][6][7][8][9][10].The presence of higher polymolybdates was also reported in localized areas by Cappia et al. [4], in particular Cs 2 Mo 3 O 10 .The authors also reported the signature of a structure with monoclinic  2 1 ∕ symmetry, which they attributed to Cs 2 Ba 2 O 3 (following Cs decay into Ba), but could also be interpreted as -Cs 2 Mo 2 O 7 .From these findings, it is clear that a thorough knowledge of the thermochemistry of the Cs-Mo-O system, and of the thermochemical and thermophysical properties of its constituting cesium polymolybdates is essential for the assessment of the fuel behaviour.It is in particular worth mentioning that Cs 2 MoO 4 has a thermal conductivity lower than the fuel by about one order of magnitude [11,12].It also shows a strong and anisotropic thermal expansion upon increasing temperature at the expected operating temperatures [13].All these data are necessary to feed so-called Fuel Performance Codes (FPCs) that are able to predict fuel pin behaviour at the engineering scale.
This work reports a thermodynamic modelling assessment of the key Cs-Mo-O system, based on the CALPHAD methodology, and with descriptions compatible with the formalisms used in the TAF-ID database (Thermodynamics of Advanced Fuels -International Database) of the OECD/NEA [14].The available literature data, including structural, thermodynamic, phase diagram and vapour pressure data, are first critically reviewed, after which the models used are described in detail, and benchmarked against the experimental information.

Review of literature data
Cs-Mo-O is a rather complex system, with a number of ternary cesium molybdate phases reported: Cs   = 0.13) [15].A comprehensive literature review of this system has been reported by Fabrichnaya [16] and more recently by Smith et al. [17].Its key features are detailed hereafter, including reported phase diagram data, thermodynamic and vapour pressure data.The thermodynamic assessment reported herein accounts for the following ternary phases, for which sufficient structural and thermodynamic information is available: Cs  The knowledge on the other phases is too limited to this date to include them in the thermodynamic model.

Constituting binary systems
The phase diagrams of the three binary sub-systems constituting this ternary system are shown in Figs.1(a [19], and the liquid phase parameters were re-assessed by Kauric [20] so as to suppress the appearance of a miscibility gap towards high MoO 3 content in several ternary systems such as Na-Mo-O and Ba-Mo-O [21].The full list of optimized parameters are given in [21].The Cs-Mo system is characterized by a low reciprocal solubility of the elements.The available experimental data are scarce.The model for this binary system was optimized in the framework of the Fuelbase project (2011) [22].The assessed parameters are listed in Appendix.

Structural data
The crystal structures of the aforementioned ternary phases is summarized in Table 1.Note that two polymorphs have been reported for the Cs 2 MoO 4 and Cs 2 Mo 2 O 7 intermediates, with transition temperatures at   (Cs 2 MoO 4 , -) = (841.3± 1.0) K [23] and   (Cs 2 Mo 2 O 7 , -) = (650 ± 5) K [17], respectively.Two structures have also been reported for Cs 2 Mo 4 O 13 , one triclinic, in space group  − 1 (supposedly the phase stable at room temperature) [24], and one monoclinic, in space group 2∕ (supposedly a phase stable at high temperatures).However, the exact transition temperature and nature of the transition between these two modifications is not known with certainty.The phase diagram studies of Hoekstra [25] and Spitsyn and Kuleshov [26], discussed in the next section, suggested the existence of a metastable phase, formed when quenching the melt at room temperature.The authors observed exothermic events in their thermal analysis measurements around 608 K and 643 K, respectively, which Hoekstra interpreted as the transformation from the metastable form to the stable phase of Cs 2 Mo 4 O 13 upon heating.The polymorphism of Cs 2 Mo 4 O 13 thus still needs to be clarified.We have included only one modification in the present thermodynamic model.

Phase diagram data
A number of phase equilibria studies have been reported in the pseudo-binary section between Cs 2 MoO 4 and MoO 3 : by Spitsyn and Kuleshov1 [26], Salmon and Caillet2 [29], Hoekstra3 [25], and Bazarova et al. 4 [30].Some discrepancies exist between those studies, however.According to the review of Fabrichnaya in 2007 [16], the data of Hoekstra [25] are believed to be most reliable.Smith et al. [17] very recently re-investigated the Cs 2 MoO 4 -MoO 3 pseudo-binary phase diagram using Differential Scanning Calorimetry (DSC) and coupled Thermogravimetry-Differential Scanning Calorimetry (TG-DSC) to solve some of these discrepancies.The most important outcomes are summarized below: • the existence of a phase transition in the Cs 2 Mo 2 O 7 compound was confirmed, and measured at   = (650 ± 5) K. • the melting temperature of Cs 2 Mo 2 O 7 was measured at    = (725 ± 5) K, in good agreement with the data reported previously by Smith et al. [27] (720.2 ± 5.0 K).It should be noted that the other sources report higher values: 737 K for Hoekstra [25], 749 K for Salmon and Caillet [29], and 767 K for Spitsyn and Kuleshov [26].• the (congruent) melting temperature of Cs 2 Mo 3 O 10 was found at    = (806 ± 5) K, which is ∼15 K lower than reported by Hoekstra [25] (820 K), Salmon and Caillet [29] (823 K), and Spitsyn and Kuleshov [26] (818 K).It should be noted that the onset temperature of the heat flow curve was selected for the analysis.The extremum temperature of the same heat flow signal yielded (825 ± 5) K, in closer agreement with the other data.

Table 1
Structural data for the ternary phases in the Cs-Mo-O system (1 Å = 0.1 nm).Uncertainties relative to the last digits are given in parenthesis.a Data measured at  = 948 K.
The collected data by Smith et al. [17] are found generally lower than Hoekstra [25].It is not clear, however, how the thermal analysis data were treated in the work of Hoekstra with respect to temperature calibration and choice of the offset or onset temperature of the signals, as reported by [17].The most recent phase equilibrium data by Smith et al. [17] have been selected for the re-assessment of the Cs-Mo-O system as the temperature calibration of the DSC and TG-DSC measurements was carefully checked with the measurement of the well-known three phase transitions and melting temperatures of the Na 2 MoO 4 compound [17].

Thermodynamic data
The standard enthalpies of formation of -Cs  [31,32], Smith et al. [17,33] and Benigni et al. [34].The latter data are summarized in Table 2.A very good agreement is seen between the various studies.
The enthalpies of formation listed in Table 2 were derived using a thermochemical cycle involving the enthalpy of formation of MoO 3 (cr), i.e. −(745.0 ± 1.0) kJ⋅mol −1 (value selected in the review by Cordfunke and Konings [23]).The reported uncertainty ± 1 kJ⋅mol −1 is most probably largely underestimated, however, as stressed by [17].This value  was derived from the average of the measurements of Staskiewicz et al.
(−744.65 ± 0.40 kJ⋅mol −1 ) [36] and Mah (−745.4±0.5 kJ⋅mol −1 ) [37].However, the latter data were derived from the incomplete combustion of molybdenum and MoO 2 to MoO 3 (it reached only 70%-93%).Even if corrections were made to account for this, we believe that the quoted final uncertainties amounting to less than 0.07% are largely underestimated.The review by Cordfunke and Konings [23] assigning an uncertainty of 0.1% is already more conservative.But in the present work, the uncertainties on the enthalpies of formation have been recalculated considering an uncertainty of 1% (± 7.45 kJ⋅mol −1 ) on the enthalpy of formation of MoO 3 , which is believed to be more realistic as reported already in [17].The newly assessed uncertainties are listed in Table 3.Moreover, the weighted average of the latter values has been calculated for each composition, and is selected for the present thermodynamic assessment. 5he standard entropies of -Cs 2 MoO 4 and -Cs 2 Mo 2 O 7 were obtained from low-temperature heat capacity measurements using adiabatic calorimetry [35] and thermal-relaxation calorimetry [27], respectively.The measured data are listed in Table 2 and selected for the present assessment.
The uncertainty was calculated using the formula: Fredrickson and Chasanov [39], Konings and Cordfunke [40], and Denielou et al. [41] reported high temperature enthalpy increment measurements for Cs 2 MoO 4 in the temperature ranges (845-1191 K), (415-700 K), and (1232-1500 K), respectively.The review of Cordfunke and Konings [23] discards the data of Fredrickson and Chasanov because of discrepancies with the other sets of data.Kohli and Lacom [42] reported heat capacity measurements in the range 300-800 K using differential scanning calorimetry (DSC).The high temperature heat capacity equations selected in the review by Cordfunke and Konings [23] for -Cs 2 MoO 4 (orthorhombic in space group  ) and -Cs 2 MoO 4 (hexagonal in space group  6 3 ∕) are those of Konings and Cordfunke [40].The data of Denielou et al. [41] were adopted for the liquid phase in [23].The heat capacity function of Cs 2 MoO 4 was optimized as part of this assessment based on the low-temperature heat capacity data of Osborne et al. [35], high temperature heat capacity data of Kohli and Lacom [42], and enthalpy increment data of Konings and Cordfunke [40].
The high temperature heat capacity of Cs 2 Mo 2 O 7 was measured in the range (310-700 K) by Kohli [43] based on DSC measurements and the step method, but found in poor agreement with the lowtemperature heat capacity data of Smith et al. [27].In their work, Smith et al. [27] suggested an estimation of the high-temperature heat capacity by combining their measured low-temperature heat capacity data in the range (248.7-313.2K) with data estimated above  = 500 K using the Neumann-Kopp approximation applied to the heat capacity functions of Cs 2 MoO 4 [23,35] and MoO 3 [23,44].The latter function was retained for the present assessment of the Cs-Mo-O system.(See Table 4.) The reported phase transition temperatures for the cesium polymolybdates are summarized in Table 7 together with the optimized values in the present CALPHAD model.The associated transition enthalpies were determined by Konings and Cordfunke [40], Fredrickson and Chasanov [39], Denielou et al. [41], and Smith et al. [17].They are also listed in Table 7, where they are compared to the optimized values.
Thi-Mai-Dung Do et al. [52] investigated the vaporization of Cs 2 Mo 2 O 7 by combining thermogravimetry with a transpiration method.The authors suggested a congruent vaporization for Cs 2 Mo 2 O 7 (l) and The authors suggest the formation of Cs 2 Mo 2 O 7 (g) based on Raman spectra of deposits collected on platinum sheets in the downstream of a transpiration set-up.
We have accounted for Cs 2 MoO 4 (g) in the description of the gas phase in the present model.However, we have not included Cs 2 Mo 2 O 7 (g) at this stage.We recommend to first confirm the formation and stability of such a heavy molecule as Cs 2 Mo 2 O 7 (g) (molar weight 569.7 g⋅mol −1 ) by analysis directly the gas phase itself using mass spectrometry, and to proceed to the determination of all necessary thermodynamic functions (enthalpy of formation and standard entropy at 298.15 K as well as heat capacity at high temperatures).

Thermodynamic model
The optimization was performed using the PARROT module of the Thermo-Calc software (Version 2016b) [54,55].The Gibbs energy functions in the model are referred to the enthalpy of the pure elements in their stable state at room temperature 298.15K and 1 bar ( o    (298.15K)).The optimized parameters are listed in Table 6.

Pure elements
The Gibbs energy function of the pure element  at temperature  and in its state  is given by: where  is an integer (2, 3, −1 …) and , , , and   are parameters assessed based on experimental and theoretical information.The parameters reported by Dinsdale are used in this work for pure cesium, molybdenum, and oxygen [56].

Binary oxides
The binary oxides Cs where    is the number of atoms of the element  in the oxide formula.These are taken from the TAF-ID database [14].

Hexavalent ternary molybdates
Considering the available structural and thermodynamic data in the literature, the present model considers only the existence of the following ternary phases: Cs The Gibbs energies of the ternary molybdates is given by: where    is the number of atoms of the element  in the oxide formula.

Liquid phase
The liquid phase is described using an ionic two-sublattice model, with Cs + and Mo 4+ cations on the first sublattice, and MoO 2− 4 , O 2− anions, charged vacancies Va − , neutral MoO 3 , and neutral oxygen O on the second sublattice: and  are equal to the average charge of the opposite sublattice: where   is the site fraction for species  in the sublattice considered. and  vary with composition via the site fractions so as to keep the phase electrically neutral.

Gas phase
The gas phase is described as an ideal mixture of the gaseous species Cs, Cs where   is the fraction of the species  in the gas phase, o    the standard Gibbs energy of the gaseous species , and  o the standard pressure.The thermodynamic functions of the gaseous species were not optimized in this work.In particular, the Gibbs energy function of Cs 2 MoO 4 (g) was taken from [51].[17].The congruent melting of the same compound is calculated at 732.5 K, in between the data of Smith et al. [17] (i.e.725 ± 5 K), and the data of Hoekstra [25] (737 K), Salmon and Caillet [29] (749 K), and Spitsyn and Kuleshov [26] (767 K).Note that the nature of the thermal decomposition of -Cs 2 Mo 2 O 7 (congruent melting or peritectic decomposition) is not known with certitude [17].

Optimized thermodynamic data
The standard enthalpies of formation and standard entropies at 298.15 K optimized in this work are listed in Table 8 and shown in Fig. 5(a), where they are compared to the selected values (see Section 2).A very good agreement is obtained, within the experimental uncertainties.
The calculated enthalpy increments and heat capacities of Cs  and 4, where they are compared to the available literature data.As explained in more detail in the literature review, the estimation by Smith et al. [27] for the heat capacity of Cs 2 Mo 2 O 7 was preferred over the DSC data of Kohli [43].The heat capacity function at high temperature shows a smooth transition with the low-temperature data.
Finally, the calculated transition enthalpies associated with the invariant reactions in the Cs 2 MoO 4 -MoO 3 pseudo-binary section are listed in Table 7 and shown in Fig. 5(b), where they are compared to the experimental data available.The enthalpy of fusion of -Cs 2 MoO 4 is in very good agreement with the data of Denielou et al. [41] (selected in the review by Cordfunke and Konings [23]).The calculated transition for the congruent melting of -Cs 2 Mo 2 O 7 is 77.7 kJ⋅mol −1 , in good agreement with the experimental data within the measured uncertainties.The calculated enthalpy of congruent melting of Cs 2 Mo 3 O 10 in the present model is slightly higher than the experimental data,   The calculated (total) vapour pressure of the congruent equilibrium Cs 2 MoO 4 (cr, l) = Cs 2 MoO 4 (g) is shown in Fig. 6 and compared to the data of Johnson [45], Tangri et al. [46], Cordfunke et al. [47], Yamawaki et al. [48], Kazenas et al. [49], and Stolyarova et al. [50].Note that the thermodynamic functions of Cs 2 MoO 4 (g) were not optimized in this work, but taken from [51].Only the thermodynamic functions of Cs 2 MoO 4 (cr) and of the liquid solution were optimized so as to match as best as possible the known phase diagram data in the Cs 2 MoO 4 -MoO 3 section and thermodynamic data on Cs 2 MoO 4 (cr).The calculated vapour pressures are given by the following equations for the temperature ranges 1000-1214 K and 1232-1300 K, respectively: The agreement with the experimental data of

Table A.1
Summary of the thermodynamic data for pure elements and oxides selected in the Cs-Mo system. refers to the phase of the element stable at 298.15 K.

Fig. 3 .
Fig. 3. (a) Enthalpy increments of Cs 2 MoO 4 calculated with the present description (solid line) compared to the literature data of Osborne et al.[35], Konings and Cordfunke[40], and Kohli and Lacom[42].(b) Heat capacity of Cs 2 MoO 4 calculated with the present description (solid line) compared to the literature data of Osborne et al.[35] and Kohli and Lacom[42].

Fig. 4 .
Fig. 4. Heat capacity of Cs 2 Mo 2 O 7 calculated in the model (solid line) compared to the literature data of Kohli[43] and Smith et al.[27].

5 .
(a) Enthalpies of formation at 298.15 K calculated in the present model, and comparison with the experimental data selected in this work (see Section 2); (b) Transition enthalpies calculated in the present model at the transition temperature, and comparison with the literature data of Denielou et al. [41] and Smith et al. [17].

Table 2
Thermodynamic data reported on the cesium polymolybdates.

Table 3
Re-calculated enthalpies of formation of the cesium polymolybdates based on an uncertainty of 1% on the enthalpy of formation of MoO 3 (cr) involved in the thermochemical cycles of the solution calorimetry measurements.The values selected for the present assessment are marked in bold.

Table 5
Experimental data on the vaporization behaviour of Cs 2 MoO 4 .KEMS: Knudsen Effusion Mass Spectrometry.
a The authors report a 5% uncertainty on the vapour pressures.bTheauthorsreport a 10% uncertainty on the vapour pressures.cMolybdenum effusion cell with gold liner and alumina crucible inside the gold liner.dY 2 O 3 -stabilized zirconia condenser tube with a protective gold tube.eMolybdenum effusion cell with alumina liner.fData based on cesium analyses.g Data based on molybdenum analyses.h Dry oxygen carrier gas.

2
MoO 4 ( and ), Cs 2 Mo 2 O 7 ( and ), Cs 2 Mo 3 O 10 , Cs 2 Mo 4 O 13 , Cs 2 Mo 5 O 16 , and Cs 2 Mo 7 O 22 .They are treated as stoichiometric.Their Gibbs energies have been expressed based on the recommended enthalpies of formation, entropies and heat capacities (see literature review).The enthalpies of formation and standard entropies have been further optimized to fit the phase equilibrium data in the Cs 2 MoO 4 -MoO 3 pseudo-binary section.Moreover, only the heat capacity of Cs 2 MoO 4 has been optimized, with a single function for the  and  modifications.The heat capacity of Cs 2 Mo 2 O 7 was taken from the selection made in the literature review without further optimization.The heat capacities of Cs 2 Mo 3 O 10 , Cs 2 Mo 4 O 13 , Cs 2 Mo 5 O 16 , and Cs 2 Mo 7 O 22 were calculated using the Neumann-Kopp rule applied to Cs 2 MoO 4 and MoO 3 , and were not further optimized.
a Data measured by DSC.b Data measured by TG-DSC.

Table 8
Enthalpies of formation and standard entropies of the ternary cesium molybdates optimized in this work.MoO 4 are in very good agreement with the literature data.The  to  transition temperature of Cs 2 Mo 2 O 7 is calculated at 650 K, as reported in the work of Smith et al.

2
Mo 2 O 7 + Cs 2 Mo 3 O 10 } and 0.35 K higher than the eutectic equilibrium {Liq = -Cs 2 Mo 2 O 7 + -Cs 2 MoO 4 }, which is not possible to distinguish experimentally.A post-characterization using microscopy would be required after thermal analysis to ascertain if -Cs 2 Mo 2 O 7 shows a congruent melting or a peritectic decomposition upon heating.The congruent melting of Cs 2 Mo 3 O 10 is calculated at 812.3 K, which is again in between the data of Smith et al.
[17] K).By contrast with the other studies, Salmon and Caillet report a peritectic decomposition for Cs 2 Mo 4 O 13 at 797 K[29], while Spitsyn and Kuleshov[26]report a melting at 807 K. Finally, the calculated peritectic decompositions of Cs 2 Mo 5 O 16 and Cs 2 Mo 7 O 22 (i.e.808.7 K and 836.2 K, respectively) are in very good agreement with the data of Smith et al.[17]selected for the optimization.