Thermodynamic assessment of the cs–te binary system

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 48 (2015) 1–12 Contents lists available at ScienceDirect CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry journal homepage: www.elsevier.com/locate/calphad Thermodynamic assessment of the Cs–Te binary system T.-N. Pham Thi a,n, J.-C. Dumas a, V. Bouineau a, N. Dupin b, C. Guéneau c, S. Gossé c, P. Benigni d, Ph. Maugis d, J. Rogez d a DEN/DEC/SESC—CEA Cadarache, 13108 Saint-Paul Lez Durance Cedex, France Calcul Thermo, 63670 Orcet, France c DEN/DANS/DPC/SCCME—CEA Saclay, 91191 Gif-sur-Yvette Cedex, France d IM2NP—UMR CNRS 7334 & Université Aix-Marseille, Avenue Escadrille Normandie Niemen, 13397 Marseille Cedex 20, France b art ic l e i nf o a b s t r a c t Article history: Received 10 April 2014 Received in revised form 13 October 2014 Accepted 18 October 2014 Available online 25 October 2014 In this work, we present the review of phase diagram, crystallographic data and thermodynamic data of the Cs–Te binary system. The thermodynamic modeling of this system is also performed with the aid of the Thermo-Calc software. The thermodynamic descriptions derived in this work are based on the databases of Scientific Group Thermodata European (SGTE) and TBASE (ECN, Petten, Netherland) for the pure elements and the gaseous species. The compound formation and liquid mixing Gibbs energy expressions are obtained by a least square optimization procedure. Comparisons between calculated and available experiments results are presented. A satisfactory agreement is achieved. & Elsevier Ltd. All rights reserved. Keywords: Cesium Tellurium, fuel cladding gap Thermodynamics computational modeling Calphad 1. Introduction The operating conditions of mixed oxide fuels (MOX) in Sodium cooled Fast Reactor (SFR) are very severe combining high temperature, high linear rating and high temperature gradient. Due to those conditions, the volatile Fission Products (FP) like cesium and tellurium generated in the central region of the fuel pellet migrate outward through the radial cracks of the fuel matrix. At high burn up, a mixture of compounds of FP is formed in the fuel-cladding gap. This layer of FP compounds located between the external surface of the fuel pellet and the inner cladding surface is called in french the Joint Oxyde Gaine (JOG). The knowledge of phase equilibria and thermodynamic properties of the Cs–Te system is thus crucial for understanding and modeling the diffusion processes during the formation of the JOG. In addition, these two elements are also involved in the inner corrosion of fuel cladding, which occurs at high burn-up in the Fast Breeder Reactor (FBR). The magnitude of this corrosion has been assessed for three types of FBR steel cladding [1,2], namely advanced austenitic [3–7], high strength ferritic/martensitic [8], and oxide dispersion strengthened [9–12] steels. The objective of this paper is to derive a thermochemical description of the Cs–Te system using the CALPHAD method. Literature data on the crystal structures, thermodynamic properties n Corresponding author. E-mail address: phamtamngoc@yahoo.fr (T.-N. Pham Thi). http://dx.doi.org/10.1016/j.calphad.2014.10.006 0364-5916/& Elsevier Ltd. All rights reserved. and phase diagram of the Cs–Te system are reviewed and a set of consistent data is selected. A thermodynamic model is chosen for each phase of the system and the corresponding parameters are optimized. Comparisons between calculated and experimental results are presented. 2. Literature review and selected experimental data Experiments in the Cs–Te system are extremely difficult because: – Like all alkali metals, Cs is very reactive with oxygen and water. Cs–Te compounds present, although to a lesser extent, the same tendency. All the stages of the experimental process, from the synthesis of the samples to their final characterization must be performed under inert atmosphere or vacuum. All the experimenters mentioned that the handling, preparation, measurement and characterization of the material were performed in a glove-box filled with dried argon. Manipulations outside a glove box require the use of ampules sealed under vacuum or inert gas. – The reactivity between Cs and Te is very high. Prins and Cordfunke [13] mentioned that a violent reaction occurs when Cs and Te are directly mixed. Likewise, if Te powder is in contact with Cs in a sealed glass ampoule, slight heating above room temperature resulted in an explosive reaction cracking of T.-N. Pham Thi et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 48 (2015) 1–12 the ampule. Hence, the main difficulty lies in the synthesis of a first compound e.g. Cs2Te from the elements. After this keystage, all the other Cs–Te mixtures can be prepared by mixing quantities of the somewhat less reactive compound with Cs or with Te. Within a glove box, Adamson and Leighty [14] have synthesized Cs2Te samples in a controlled way by adding small Te pieces one at a time to liquid Cs in a tall containing cup box, allowing the reaction to subside before each subsequent addition. Then the content of the cup was carefully heated at 523 K to assist the reaction. An alternative method is based on the fact that, even if both elements have a significant vapor pressure above 900 K (PCs and PTe reach atm at respectively 944 K and 1261 K [15], Cs is much more volatile than Te. This characteristic has been used by Chuntonov et al. [16], Cordfunke and coworkers [13,17–21], Schewe-Miller and Böttcher [22] to synthesize Cs–Te samples by solid gas reaction. The principle of the method is to put solid quantities of Cs and Te in separate compartments of a common reaction volume. On heating, Cs is distilled into the reaction zone which contains Te. A slow attack of solid Te by Cs vapour occurs and a Cs–Te compound is formed. A third method, the so-called ammonia thermal synthesis, has been used by Böttcher and coworkers to elaborate Cs2Te2 [23], Cs2Te3 [24], Cs2Te5 [25] and CsTe4 [26] from the elements. The solvent is ammonia under supercritical conditions (e.g. 500 K, 1000 bar). Because of the difficulties mentioned above, few teams have worked on the system and in a recent inquiry, the present authors have not been able to find any commercial supplier of anyone of the Cs–Te compounds. 2.1. Phase diagram data In 1937, Bergmann [27] reported a congruent melting point of Cs2Te at 953 K which is nowadays judged as a too low value. According to Adamson and Leighty [14], it could be explained by the sensitivity of Cs2Te to the presence of oxygen impurity during their measurement. A specimen of Cs2Te which have been purposely contaminated by Adamson and Leighty [14] started melting at approximately 973 K. In 1980, Böttcher [24] synthesized the Cs2Te3 compound and determined its crystal structure. Adamson and Leighty [14] and Chuntonov et al. [16] are the first authors to investigate the Cs–Te phase diagram in a large composition range by thermal analysis. Adamson and Leighty [14] have combined a thermal arrest method with direct visual observation to measure the melting and freezing temperatures over the 9:1 4Cs:Te41:9 composition range. By comparison with the transition temperatures of known materials, the accuracy of the thermal arrest method is estimated by the authors to be 72 K at 573 K and 75 K at 923 K. The accuracy of visual observation was about 710 K. On the basis of their thermal analysis results and the knowledge of the existence of Cs2Te and Cs2Te3 from literature [24,27], they proposed a phase diagram which should be regarded as extremely tentative. Their diagram features two additional cesium tellurides, Cs3Te2 and CsTe, which melt by peritectic reaction, and an extremely low temperature eutectic reaction between 67 at% and 90 at% Te. However, the authors suggested that polytellurides richer in Te than Cs2Te3 may exist. Independently, Chuntonov et al. [16] have studied the Cs–Te system in the entire range of concentration using a large number of alloys, by differential thermal analysis (DTA) on both heating and cooling in the Te rich side of Cs2Te, and by magnetic susceptibility measurements on cooling for the Cs rich side of Cs2Te. They reported seven solid compounds: Cs2Te, Cs3Te2, Cs5Te4, CsTe, Cs2Te3, Cs2Te5 and CsTe5. The isothermal transformation temperatures are determined by DTA on heating with an accuracy of 73 K. Chuntonov et al. have encountered difficulties in determining the liquidus temperatures because of pronounced supercoolings reaching 70–90 K. They have arbitrarily adopted the average values between the values obtained under heating and cooling conditions as the liquidus temperatures. This method of calculation is hard to justify. The values obtained on heating and cooling are not given by Chuntonov et al. and detailed information is lacking to accurately correct their experimental points. However, in the range 33–50 at% Te, their liquidus values are in good agreement with those measured on heating by de Boer and Cordfunke [17]. Consequently, the numerical values of the experimental data points of Chuntonov et al. used in the present assessment have been obtained by digitizing their original figure without any correction. Several inconsistencies between the phase diagrams presented by Adamson and Leighty [14] and Chuntonov et al. [16] should be noted: – The melting of Cs2Te3 was found at 668 K in [16] instead of 707 K in [14]. But, both studies agree on the 40 K temperature difference between the eutectic temperature CsTe þCs2Te32L and the melting temperature of Cs2Te3. – The liquidus values measured by Adamson and Leighty are however often significantly lower than the corresponding Chuntonov et al. values (10, 40, and 67 at% Te). – On the Te rich side, Chuntonov et al. [16] report an eutectic reaction L-CsTe5 þCs2Te5 at 488 K and a peritectic reaction CsTe52L þTe at 536 K. Adamson and Leighty [14] mention only one invariant temperature at 498 K between 60 at% and 99 at% Te. – The liquidus value of the 90 at% Te alloy measured at 723 K by Adamson and Leighty is considered highly unlikely as it is the same value as the melting temperature of pure tellurium. The numerous experimental points of Chuntonov et al. for Te480 at% establish that the liquidus is considerably lower than indicated by Adamson and Leighty. Adamson and Leighty have used open alumina crucibles during their thermal arrest measurements and the complete apparatus was operated inside an inert atmosphere glove box. They mentioned Cs vaporization occurring, particularly for Cs rich alloys. Chuntonov et al. have used 0.5 g samples in sealed ampules that avoid this problem. Hence, the results of Chuntonov et al. are considered more reliable than those of Adamson and Leighty. In 1984, Prins and Cordfunke [13] have investigated the Cs–Te system by X-ray powder diffraction experiments. They found that the compounds Cs2Te, Cs3Te2, Cs2Te3 and Cs2Te5 are stable at room temperature. The existence of CsTe4 is confirmed and structural transitions in this compound are identified at 393 K and 498 K. However, their samples with ratios: – Te:Cs ¼5:4 and Te:Cs ¼ 1:1 were mixtures of Cs3Te2 and Cs2Te3, and – Te:Cs ¼5:1 were mixtures of CsTe4 and pure tellurium. It is concluded that the existence of the Cs5Te4, CsTe and CsTe5 assumed without any structural investigation by Chuntonov et al. [16], is not confirmed by the X-ray powder patterns obtained by Prins and Cordfunke. The crystal structure of CsTe4 has been independently determined by Böttcher and Kretschmann [26]. The phase diagram of Cordfunke and Konings [28] is a compilation of former results. In the more critical assessment of Sangster and Pelton [29], the CsTe5 compound is discarded. It is worth noting that the phase T.-N. Pham Thi et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 48 (2015) 1–12 diagram they propose does not account for some experimental points of Chuntonov et al. (e.g. invariant reaction at 738 K) and does not mention the liquidus points reported by Drowart and Smoes [30] determined using mass spectrometric Knudsen cell method. Moreover, the phase equilibria between 33 and 55 at% Te needed further clarification. The subsequent experimental work by DSC and high temperature X-ray diffraction of De Boer and Cordfunke [17] is focused in this composition range. In the DSC measurements, the transition temperatures are measured on heating with a reported accuracy ranging between 72 and 75 K for the invariant transitions. They found that the previously reported compound Cs3Te2 was a mixture of Cs5Te3 and CsTe. They also demonstrated the existence of a slightly substoichiometric (48.3–49 at% Te) CsTe compound. These results are in agreement with the earlier X-ray diffraction investigations: – of Schewe-Miller and Böttcher [22] who identified Cs5Te3 in a sample containing 40 at% Te. – of Hobbs and Pulham [31] who also identified a slightly substoichiometric CsTe compound. In summary, the consistent results of [17,22,31] show that Cs5Te3 and CsTe are the only stable compounds in the range 33– 55 at% Te and that the Cs3Te2 and Cs5Te4 not exist. The high temperature X-ray data of De Boer and Cordfunke [17] also showed that CsTe and Cs2Te exhibit structural transitions at 673 75 K and 895 72 K respectively. A second order transition in Cs5Te3 is observed around 515 K. The later assessment by Okamoto [32] modifies the Sangster and Pelton diagram according to De Boer and Cordfunke findings. The compounds Cs2Te13, Cs4Te28 and Cs3Te22 have been synthesized by Sheldrick and Wachhold [33,34] in superheated methanol. Their crystal structures were also identified. However, Prins and Cordfunke [13] employing a different synthesis method have found that CsTe4 was in equilibrium with pure Te instead of such compounds. In the following, these polytellurides will not be taken into account due to the lack of data but it is possible that the phase equilibria in the composition range between CsTe4 and pure Te are much more complex than indicated in the critical assessments of Sangster and Pelton and Okamoto. In conclusion, the transition temperatures determined by De Boer and Cordfunke are in good overall agreement with the results of Chuntonov et al. In the CALPHAD optimization process, we have selected the more exhaustive liquidus dataset of Chuntonov et al. [16] combined with the results of Drowart and Smoes [30] which fill the lack of liquidus data on the Te rich side of Cs2Te. The six Cs2Te, Cs5Te3, CsTe, Cs2Te3, Cs2Te5 and CsTe4 solid compounds are considered. The chosen invariant reaction temperatures for these compounds are detailed as follows. Cs2Te presents a structural transition at 895 72 K [17] and congruent melting at 1093 K measured by Chuntonov et al. [16]. This value agrees with the determinations of Adamson and Leighty (1083 710 K) but is lower than the value of De Boer and Cordfunke (1104 72 K). Cs5Te3 has an incongruent melting at 934 75 K [17] according to the peritectic invariant reaction: Cs5Te32L þ β-Cs2Te. This is in excellent agreement with the invariant temperature measured by Chuntonov et al. at 933 K, but wrongly attributed to the melting of Cs3Te2. The α/β CsTe transition temperature (673 75 K) is taken from De Boer and Cordfunke, it is K below the invariant temperature of 681 K measured by Chuntonov et al. and wrongly attributed to the incongruent melting of CsTe. For the incongruent melting of CsTe, the temperature 7237 K determined by De Boer and Cordfunke is selected. This value is Table Invariant reactions and transitions of Cs–Te system. Reaction at% Te T (K) Reaction type Reference α-Cs2Te2β-Cs2Te β-Cs2Te2L Cs5Te32β-Cs2Teþ L α-CsTe2β-CsTe β-CsTe2Cs5Te3 þL CsTeþ Cs2Te32L Cs2Te32L Cs2Te52Lþ Cs2Te3 CsTe4 þCs2Te52L CsTe42Teþ L 33.2 33.3 33.2–37 49 37–49 55 60 60–71 71–80 80–100 895 1093 934 6737 723 74 6187 668 508 488 536 Structural transition Congruent melting Peritectic Structural transition Peritectic Eutectic Congruent melting Peritectic Eutectic Peritectic [17] [16] [17] [17] [17] [17] [16] [16] [16] [16] close to 15 K but below the temperature of 738 K measured by Chuntonov et al. and wrongly attributed to the incongruent melting of the hypothetic compound Cs5Te4. For the eutectic reaction between CsTe and Cs2Te3, again the selected De Boer and Cordfunke value 618 75 K is 13 K below the 631 K measured by Chuntonov et al. The melting temperature 668 K of Cs2Te3 is taken from Chuntonov et al. [16]. As already mentioned for the high Te alloy, this value is judged more reliable than the measurement of Adamson and Leighty (707 K). Cs2Te5 melts incongruently at 508 K. In the composition range of this peritectic reaction, Adamson and Leighty have reported an experimental temperature of 498 K. The eutectic temperature 488 K between Cs2Te5 and CsTe4 is from Chuntonov et al. but wrongly attributed by these authors to a reaction between Cs2Te5 and CsTe5. For the same reason, the invariant temperature 536 K measured by Chuntonov et al. [16] is attributed to the peritectic decomposition of CsTe4. The selected data are summarized in Table 1. 2.2. Crystal structure data Table summarizes the crystal structure and lattice parameter data for the pure elements and selected Cs-Te compounds. 2.3. Thermodynamic data of condensed phases Thermodynamic data are available in the literature only for Cs2Te and Cs5Te3. The corresponding values and expressions are summarized in Table 3. Thermochemical data for Cs2Te compound were estimated by Lindemer et al. [39] and by Kohli [40]. Those estimated values are discarded here in order to consider the original experimental values from Cordfunke and coworkers [7–9]. The standard enthalpy of formation has been derived from the measurement of enthalpy of dissolution of Cs2Te in {0.46 mol dm À NaClO and 0.5 mol dm À NaOH} [18]. Lately, a reevaluation of the solution enthalpy of Te in the solvent led to small correction of 1.5 kJ/mol yields the new value of À 362.972.9 kJ/ mol [19]. The heat capacity has been measured from to 340 K by adiabatic calorimetry [20]. The high temperature enthalpy increment of this compound has been measured by drop calorimetry [20]. Low and high temperature results fit smoothly and yield the thermal function of Cs2Te(s), the corresponding expression of the Gibbs energy above 298 K is given in Table 3. The formation enthalpy value ( À 362.1 kJ/mol) which is used in the Gibbs energy expression from [37] is slightly different from both the initial value [18], and the later corrected one [19] but remains within the error range of the calorimetric measurements. A value of À 352.873.5 kJ/mol is derived by Drowart and Smoes [30] from T.-N. Pham Thi et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 48 (2015) 1–12 Table Cs–Te crystal structure data. Phase Composition at% Te Pearson symbol Space group Strukturbericht designation Prototype Lattice parameter, nm a (Cs) β-Cs2Te α-Cs2Te β-Cs5Te3 α-Cs5Te3 β-CsTe α-CsTe Cs2Te3 Cs2Te5 CsTe4 Te 33.3 33.3 37.5 37.5 48.5–49.1 48.5–49.1 60 71.4 80 100 cI2 A2 Im3¯ m oP12 P212121 oPn oC20 oC28 mP20 hP3 C2/m Pm3m Pbam Cmc21 Cmcm P21/c P3121 W C23 Cs2S B2 CsCl A8 K2S3 Cs2Te5 – γ-Se b Comment Reference c 0.6141 [35] 0.9109 1.1486 0.5867 2.111 0.52 1.11639 0.8666 0.937 0.7857 0.44566 0.6655 1.507 γ¼ 90° β¼ 134.53° 0.61309 1.2065 1.228 0.7286 0.49669 0.8680 1.012 1.4155 0.59264 β¼ 93.83° c/a¼ 1.3289 [17] [6] [17] [17] [17] [17] [24] [25] [26] [36] from [16,17,30] their vapour pressure measurements using Knudsen effusion mass spectrometry. This value is lower but close to the calorimetric one. The latter, more directly determined, is preferred. In 1995, the α/β transition enthalpy and the melting enthalpy have been measured by DSC [17]. The standard enthalpy of formation and the enthalpy increment of Cs5Te3 [19] have been obtained as for Cs2Te. However, the heat capacity of this compound was not measured at low temperature. As a consequence, the entropy at 298 K is only estimated from the corresponding value of Cs2Te. Experimental measurements of the thermodynamic properties of the Cs–Te liquid phase not exist in the literature. One nonideal liquid model has been proposed by Nawada and Sreedharan [41]. They treated the single liquid phase of Cs–Te as a sub-regular solution and considered [28] and [19] values for the Gibbs energies of formation of Cs2Te and Cs5Te3 respectively. The corresponding excess Gibbs energy of the liquid phase in the temperature range 900–1100 K has been determined fiting experimental liquidus data G EL = xCs x Te {(−298 − 0.00144T ) x Te+ (−972 + 0.482713T ) xCs } (kJ/mol) This description is not fully satisfactory. Firstly, their model predicts a symmetric liquidus around Cs2Te while the shape deduced from the liquidus measurements of Adamson and Leighty [14], Chuntonov et al. [16], Drowart and Smoes [30], De Boer and Cordfunke [17] is asymmetric. Secondly, the calculated chemical potentials of Te and Cs are significantly more negative than those computed from the vapour pressure measurements of Drowart and Smoes [30]. The authors suggest that these differences could be due to the large non-stoichiometric range around Cs2-yTe and/ or to the role of oxygen that could be present in the samples. Unfortunately, the few experimental data available on that system does not allow taking into account the non-stoichiometry of Cs2Te near the melting temperature domain into the model. Table Thermodynamic functions of Cs2Te and Cs5Te3 from literature data. Compound Thermodynamic data Value or expression Method Reference Cs2Te Enthalpy of formation Δ f H = − 361, 400 ± 3200 (J/mol) [22] (later corrected -362.97 2.9 kJ/mol [18,19] Enthalpy of α/β transition of Cs2Te 1950 230 J/mol Enthalpy of melting of β-Cs2Te 71007 1000 J/mol Solution calorimetry at 298.15 K Adiabatic calorimetry [5–340 K] Drop calorimetry [468–800 K] DSC DSC Heat capacity for T 298.15 K c p = 71.01393 + 0.02410357T (J /K mol) – [37] Gibbs energy GCs Te – [37] Solution calorimetry at 298.15 K Estimated [19] [23]) Data from database of FACTSAGE software [37] Entropy at 298.15 K S = 185.1 J /K mol (derived from heat capacity measurements) Enthalpy increment H (T ) − H (298.15) = 71.0132T + 12.0523 × 10−3T − 22, 244T (J /mol) − SER 2HCs − SER HTe = − 384, 344.127645 + 297.709143T − 71.01393T ln T − 1.2051785 × Cs5Te3 10−2T [20] [17] [17] (J /mol) Enthalpy of formation Δ f H = − 942, 200 ± 8300 (J/mol) Entropy at 298.15 K S = 480 ± (J /K mol) (estimated from entropy of Cs2Te at 298.15 K) Enthalpy increment H (T ) − H (298.15) = 206.829T + 21.9365 × 10−3T + 20.8102 × 105T −1 − 70596 (J /mol) Data from database TBASE [38] [20] [19] Drop calorimetry [19] [474–856 K] Heat capacity for T 298.15 K c p = 206.83 + 4.3874 × 10−2T − 2.08 × 106 /T (J /K mol) – [38] Gibbs energy GCs Te3 – [38] − SER 5HCs − SER 3HTe = − 1, 014, 790 + 930.044T − 206.829T ln T − 0.021937T + 1, 040, 000T −1 (J /mol) T.-N. Pham Thi et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 48 (2015) 1–12 2.4. Thermodynamic data of vapour pressure data The vapour pressure of Cs–Te system has been measured by five groups of authors. Chronologically, the first measurement is made by Cordfunke et al. [21]. They used the transpiration method and assumed that Cs2Te was the major compound in the gas. They also concluded that Cs2Te vaporizes congruently. Johnson and Johnson [42] observed the presence of CsTe in the gas by mass spectrometry. Wren et al. [43] and Portman et al. [44] reported the enthalpy of vaporization of the following species in the gas: Cs, Te, Te2, Te3, CsTe and Cs2Te. In 1992, the study of Drowart and Smoes [30] has shown the presence of the following species in the vapour: Cs, Te,Te2, CsTe, Cs2Te, CsTe2, Cs2Te2, and Cs2Te3. The vaporization of stoichiometric Cs2Te has been studied by both Portman et al. [44] and Drowart and Smoes [30]. Comparing the results obtained by Portman et al. at 1146 K with the results of Drowart and Smoes at 1105 K, the maximum temperature reached in their experiments, some discrepancies are denoted: – The three major species in [44] are Cs, Cs2Te2 and Te with a ratio P(Cs)/P(Cs2Te2)E 2.5, the other minor species being CsTe2, CsTe, Te3, Cs2Te and Te2 by order of decreasing abundance, – The three major species in [30] are Cs, Cs2Te2 and CsTe with a ratio P(Cs)/P(Cs2Te2)E1, the minor species being CsTe2 and Cs2Te by order of decreasing abundance. Differences in the experimental conditions could possibly explain the observed discrepancies in the composition of the vapor: Portman et al. have used an ionization energy of 40 eV instead of 15 eV used by Drowart and Smoes. So it is possible that fragmentation of larger molecules contributes to the high intensity of Cs þ and Te þ ions measured by the former authors. Portman et al. mentioned overlap between peaks in the mass spectra and difficulties in calibrating their quadrupole spectrometer resulting in large errors in the determination of partial pressures of species of molecular weight much above 300. Drowart and Smoes have used a magnetic mass spectrometer and not mention this problem probably because of the higher resolution of their apparatus. In conclusion, Portman et al. results are discarded and the more extensive dataset of Drowart and Smoes is thought to be more reliable and is selected for quantitative comparison with our modeling. 3. Thermodynamic models The Gibbs energy function G iΦ for mol of the element i in the Φ structure relative to the so called Standard Element Reference (SER) state is written as GiΦ − HiSER = a + bT + cT ln T + ∑ dn T n where n is an integer typically taking the values of 2, 3, and À 1, HiSER is the molar enthalpy of the element i in its stable state at 298.15 K and bar, and a, b, c, dn are parameters of the model. The Gibbs energies for pure cesium in the Body Centered Cubic (bcc A2) structure and in the liquid phase are taken from the SGTE pure elements database [45]. The data for tellurium in the hexagonal (hex A8) structure is taken from the review of Davydov et al. [46] as selected in the SGTE pure elements database [45]. 3.1. Stoichiometric compounds All the compounds are described as stoichiometric: (Cs)p(Te)q. For Cs2Te and Cs5Te3 for which heat capacity data are available, the corresponding Gibbs energy functions are expressed in the general form G Φo − ∑ niϕ .HiSER = a + bT + cT ln T + ∑ dn T n i where niϕ is the stoichiometry coefficient of element i in the compound Φ. For Cs2Te, all the coefficients have been optimized to fit the experimental data on heat capacity, enthalpy increment, standard entropy and enthalpy of formation. The heat capacity and enthalpy increment of Cs5Te3 calculated from the Gibbs energy function from the TBASE [38] are in good agreement with available experimental data [19]. Hence, only the enthalpy and entropy variables (a and b) in the Gibbs energy function of Cs5Te3 need to be optimized. For the other compounds CsTe, Cs2Te3, Cs2Te5, and CsTe4 compounds, as no heat capacity data are available, the Kopp– Neumann relation is used and the Gibbs energy functions of these (Cs)p(Te)q compounds are given as bcc hex G ϕ0 = pGCs + qG Te + A + BT The starting values for the variables A and B, which represent the enthalpies of formation of the compounds, were initially estimated by linear extrapolation between Cs2Te and pure Te according to [47]. 3.2. Liquid The liquid phase is described using the so-called “partially ionic two-sublattice liquid model” developed by Hillert et al. [48]. The formula of the ionic liquid can be written as (Cs+) P (Va−, Cs2 Te, Te)1 where P ¼yVa À , the site fraction of the second sublattice. The site number of the cationic sublattice, p, changes with the constitution of the second sublattice. It equals for pure Cs and goes to zero when only neutral species occupy the second sublattice. This ionic model is used to be consistent with the liquid described in the Fuelbase database [49]. It is here mathematically equivalent to the associate model (Cs, Cs2Te, and Te). The choice of constituents in the cation and anion sublattices is based on the following considerations: – Cs þ is the only species present on the cation sublattice and it occupies all the available sites hence yCs þ ¼ 1. – To compensate the charge of Cs þ cation, a hypothetical charged vacancy Va À is introduced on the anion sublattice. – A Cs2Te neutral species is introduced on the anion sublattice. There is no measurement of the enthalpy of mixing in the liquid to support the hypothesis of the existence of such an associate. However, it must be noted that the corresponding solid compound Cs2Te has a high stability and that the liquidus around the congruent melting point of the compound has a pointed shape. It implies that the compound at the melted state also has a high stability otherwise the shape of the liquidus would not be so sharp as shown by Selleby and Hillert [50]. Moreover, these types of pointed melting points are very common in halogen- and chalcogen-based systems, in which strong ionic bonds retain the non-dissociated molecular form of intermediate phase in the liquid state [51]. These arguments indirectly justify the use of an associate model to describe the liquid. It was checked during the optimization that it was not possible to reproduce the pointed liquidus without the Cs2Te associate. T.-N. Pham Thi et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 48 (2015) 1–12 Fig. 1. Variation of site fraction in the liquid versus composition of Te and enthalpy of mixing in the liquid at 1150 K. Fig. 2. The calculated diagram of Cs–Te system from this study compared to experiments. – Finally, the neutral species Te is needed on the anion sublattice to complete the composition range up to pure tellurium. The site fractions of the various species in the liquid phase and the enthalpy of mixing in the liquid are plotted in Fig. versus the tellurium molar fraction at 1150 K. It shows that the Cs2Te associate is the major species in the liquid at the composition 33 at% Te as expected in such chemical systems. The Gibbs energy of the liquid phase is expressed as a sum of three terms: Gliq = G + Gideal + G xs The first term, G0, corresponds to the Gibbs energy of a mechanical mixture of the phase constituents; the second term, Gideal, corresponds to the entropy of mixing, and the third term, Gxs, is the so-called excess term. The integral Gibbs energy expression for this model given by Lukas et al. [52] is written as follows: liq liq liq G = yVa− 0GCs + yTe 0G Te + yCs2 Te 0GCs Te Gideal = RT (yva− ln yva− + yTe ln yTe + yCs2 Te ln yCs2 Te ) liq G xs = yTe yCs2 Te L Te , Cs2 Te It is worth noting that an interaction parameter which is composition dependent is needed to describe the available experimental data for the liquid phase in the composition range liq Cs2Te–Te. The term L Te , Cs2 Te is expanded by using Redlich–Kister (RK) polynomial function [53] as liq L Te , Cs2 Te = ∑ iL i liq Te, Cs2 Te with i¼0, and 2. (yCs2 Te − yTe )i T.-N. Pham Thi et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 48 (2015) 1–12 Fig. 3. The calculated thermodynamic function of Cs2Te from this study compared to experiments. Fig. 4. The calculated thermodynamic functions of Cs5Te3 from this study compared to experiments. The parameters iL ijliq can be temperature-dependent: i liq L ij = aij + bij T The composition dependence of the excess enthalpy is described by aij and of the excess entropy by bij. A combination of thermodynamic functions extracted from SGTE [37] and TBASE [38] databases have been selected (see Appendix A). The thermodynamic properties of the gaseous species CsTe2 observed by two groups of authors [30,44] have not been determined in TBASE [38]. This species is taken into account in this work based on the data of Appendix A.11 in Drowart and Smoes [30]. 3.3. Gas The Gibbs energy of the gas phase is written according to G gas = ∑ yi 0Gigas + RT ∑ yi ln yi i 4. Optimization procedure + RT ln P /P0 i with yi the mole fraction of the i gas species and G igas the corresponding standard Gibbs energy. The parameters of the Gibbs energy of all the gaseous species are taken from the SGTE [37] or the TBASE [38] databases and kept constant during the optimization. Based on experimental data presented in Section 2, the optimization of the phase model parameters is performed using the PARROT module of the Thermo-Calc Software in three steps: – Firstly, the parameters of the Gibbs energy for Cs2Te compound were optimized using heat capacity, enthalpy increment, T.-N. Pham Thi et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 48 (2015) 1–12 the Gibbs energy of the gaseous species are not optimized but kept constant during this step. For all phases, the numerical values of the parameters of the Gibbs energy resulting from the optimization are reported in Appendix A. 5. Results and discussion 5.1. Phase diagram Fig. 5. Enthalpy of formation of compounds in the Cs–Te system compared to experiments. entropy and enthalpy of formation data. The heat capacity measurements of Cs2Te below 298.15 K are taken into account. – The parameters of the Gibbs energy for Cs5Te3 compound were taken using heat capacity, enthalpy increment, entropy and enthalpy of formation data from [19]. – Only enthalpy and entropy terms for all the compounds as well as interaction parameters in the liquid were allowed to vary in the assessment in order to fit the whole set of selected phase diagram and thermodynamic data except the vapour pressure data in the gas phase. – Finally, the vapour pressure data are included and the thermodynamic parameters of the Gibbs energy of all the condensed phase are re-optimized. Note that the parameters of Fig. compares the assessed diagram from this study with all experimental data. As presented in Section 2.1, the experimental dataset of Adamson et al. is considered less reliable than the measurements of Chuntonov et al. and those of De Boer and Cordfunke. Moreover, the discrepancies between the measured values of the invariant temperatures by these last two groups of authors reach 715 K. Because of supercooling effects, the uncertainty concerning the liquidus is even larger and estimated at 725 K. The calculated diagram is in overall agreement with the selected experimental data considering these error values. Two areas of controversy are pointed out. Indeed, thermal events have been detected by Chuntonov et al. at 488 K for both 0.63o x(Te)o0.7 and 0.8 ox(Te)o 0.95 which not correspond to any transition in the present assessment. An assumption can be put forward to explain this discrepancy. If the samples have followed a non-equilibrium path during a first cooling, a fraction of eutectic mixture still remains at the end of the process. During subsequent heating, melting of this fraction, will give rise to a thermal event at the eutectic temperature. For samples in the range 0.8 ox(Te) o0.95, the solid/solid phase transition in CsTe4 reported by Prins and Cordfunke [13] at 498 K could also possibly explain the thermal events detected by Chuntonov et al. at 488 K. However, existence of this transition needs further experimental confirmation and has not been taken into account in the present optimization. Fig. 6. Comparison of the partial pressure of Cs measured by Drowart and Smoes in their experiments and with the values calculated for x(Cs)/x(Te) ¼ 1.67 and 1.63. T.-N. Pham Thi et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 48 (2015) 1–12 Fig. 7. Partial pressures of the gas species in experiments and [30]. Triangles: experimental points. Solid lines: calculation this work. Fig. 8. Partial pressures of the gaseous species above condensed Cs2Te. Triangles: experiments and from [30], solid lines: calculations from this work for x(Cs)/x(Te)¼ 1.77. 5.2. Thermodynamic data The calculated enthalpy increment H(T)-H (298.15 K) for Cs2Te versus temperature is in good agreement with the experimental data (Fig. 3a). The calculated heat capacity Cp for Cs2Te versus temperature correctly reproduces the experimental measurements in the range 50–340 K. In this work, all the experimental data, both those obtained below 298.15 K and above 298.15 K, were fitted as a whole using a single analytical expression whereas two distinct functions have been used by Cordfunke et al. [20]. This difference in the fitting procedure explains the discrepancy between our and Cordfunke et al. calculated heat capacity above 340 K. Nevertheless, the heat capacity of Cs2Te above 340 K should be experimentally determined to verify the calculations. Fig. shows that the calculated enthalpy increment H(T)-H (298.15 K) for Cs5Te3 versus temperature is in good agreement with experimental results. As noted above, the heat capacity below room temperature has not been measured for this compound. The calculated and measured enthalpy of formation data are reported in Fig. 5. The calculated data for Cs2Te and Cs5Te3 are in 10 T.-N. Pham Thi et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 48 (2015) 1–12 very good agreement with the available experimental data [18,19,30]. 5.3. Vapour pressure Using the mass spectrometric Knudsen cell method, Drowart and Smoes determined the partial pressures in various experiments involving Cs and Te which are summarized in the appended Tables A.2–A.8 of Ref. [30]. Only the four experiments 5–8, which concern the binary Cs–Te system, are selected in this study for comparison. In experiments and 8, the initial samples are equimolecular mixtures of Cs2Te(s) and Cs3Te2(s) equivalent to ratio of x(Cs)/x (Te) ¼1.67 which corresponds to the stoichiometric Cs5Te3. It is likely that this sample is monophasic Cs5Te3 according to the later study of De Boer and Cordfunke [17]. The upper and lower bounds of the temperature range during experiments and are 864– 1045 K and 780–1001 K respectively. In their overlapping temperature range, both experiments are in good agreement. Drowart and Smoes mentioned that the composition of the sample may evolve by incongruent vaporization from x(Cs)/x(Te)¼ 1.67 down to 1.63. In Fig. 6, the partial pressure of Cs gaseous species calculated for x(Cs)/x(Te)¼ 1.67 and 1.63 are compared to the measured values. A better agreement with the experimental values is obtained for x(Cs)/x(Te)¼1.67. Using this ratio, Fig. shows that the two major species in the vapour are Cs and Cs2Te2 and that the partial pressures of these two species are very close. According to the calculation, Cs2Te2 is the major species in equilibrium with the liquid at high temperature whereas Cs is the major species in equilibrium with Cs5Te3(s) at lower temperature. The calculated partial pressures are in overall good agreement with the measured ones for the Cs, CsTe, Cs2Te, Cs2Te2, CsTe2, and Cs2Te3 gaseous species. Measurable partial pressures of Te and Te2 (greater than 10 À atm) are predicted by the calculation. However, except for one experiment with a Cs–Mn–C–Te sample, Drowart and Smoes reported that the signals of the Te þ and Te2 þ ions were too spoiled for their quantitative determinations. In experiments and 6, the initial samples are stoichiometric Cs2Te(s) equivalent to ratio of x(Cs)/x(Te) ¼2.00. The upper and lower bounds of the temperature range during experiments and are 916–1105 K and 840–1041 K respectively. For both experiments, the pressures are measured on cooling from the upper temperature bounds. The experimental data are plotted in Fig. 8. It was not possible to fit the experimental data using the initial ratio x(Cs)/x(Te)¼ 2.00. As Drowart and Smoes mentioned that the composition of the samples evolve by incongruent vaporization from x(Cs)/x(Te) ¼2.00 down to x(Cs)/x(Te) ¼1.77 during the experiments and 6, different x(Cs)/x(Te) ratios have been tried in the calculation. An acceptable fit of the experimental values is obtained using x(Cs)/x(Te) ¼1.77 for temperatures below 1040 K as seen in Fig. 8. Between 1040 K and 1105 K, the experimental pressures remain roughly constants or even slightly decrease whereas the calculation predicts their constant increase. The hypothesis of a vaporization under non-equilibrium conditions is ruled out by Drowart and Smoes, who found no evidence of small evaporation coefficient for one or several species or of too small vaporizing surface in comparison with the area of the effusion orifice. They concluded that their effusion system was operating very close to equilibrium. As the evaporation is not congruent, the composition of the evaporating surface is different from the composition of the bulk. This phenomenon tends to be more pronounced at high temperature because evaporation is more thermally activated than diffusion. However, even using a x(Cs)/x(Te) ratio down to 0.9, we were not able to find a composition for which all the calculated partial pressures are in agreement with the experimental ones at 1105 K: the x(Cs)/x(Te) ratio cannot be tuned to fit simultaneously the partial pressure of the Cs rich species (Cs and Cs2Te) on one side, and the partial pressures of equimolar or Te rich species (CsTe, Cs2Te2, Cs2Te3, and CsTe2) on the other side. The reason for this discrepancy is not clearly understood. 6. Conclusion This work presents the first thermodynamic assessment of the binary system Cs–Te, system of primary importance in the nuclear fuel considered for the SFR. Six stoichiometric solid compounds Cs2Te and Cs5Te3, CsTe, Cs2Te3, Cs2Te5 and CsTe4, the liquid and gas phases are taken into account. We have chosen to describe the liquid phase by a partially ionic two-sublattice model equivalent to an associated model with an interaction between Cs2Te and Te in the liquid phase. The fitted thermodynamic properties agree well with the experimental ones for the Cs2Te and Cs5Te3 compounds. The calculated phase diagram and the calculated vapour pressure of the various gas phase species are also in good agreement with available experimental data. Experimental work is needed to improve the thermodynamic description of the system. First, the determination of the formation enthalpies of CsTe, Cs2Te3, Cs2Te5, CsTe4 is necessary to check our optimized values for the G0(T) function of the solid compounds. Second, the measurement of liquid mixing enthalpy in the composition range between Cs2Te and Te would be interesting because the actual description of the liquid phase only relies on the knowledge of solid/liquid equilibria. This description of the binary Cs–Te system will be introduced in our general (U-Pu-FP-O) thermodynamic database in order to perform thermochemical calculations of irradiated MOX fuel versus burn-up and temperature. Appendix A. Thermodynamic parameters of the condensed phases and gas phase See Table A.1. T.-N. Pham Thi et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 48 (2015) 1–12 11 Table A.1 Gibbs energy parameters of condensed phases and gas phase in the Cs–Te system. Phase Function energy of Gibbs References Cs2Te SER SER GCs Te − 2HCs − HTe = − 375621 + 306.615T − 73.043T ln T This work β-Cs2Te 0 G β− Cs2 Te = GCs2 Te + 1950 − 2.17877T Cs5Te3 SER SER GCs Te3 − 5HCs − 3HTe = − 967568.6 + 892.108T − 206.829T ln T − 0.021937T CsTe bcc hex GCsTe = + GCs + 0.96GTe − 188, 138 + 3.258T β-CsTe G β− CsTe Cs2Te3 bcc hex GCs Te3 = 2GCs + 3GTe − 4, 085, 336 + 10.864T This work Cs2Te5 bcc hex GCs Te5 = 2GCs + 5GTe − 409, 659 − 4.83T This work CsTe4 GCsTe This work Liquid (Cs+) − 9.1 × 10−3T + 7.3 × 10−7T + 17688T −1 This work + 1, 040, 000T −1 = GCsTe bcc GCs = p (Te, + VA−, This work − 1300 + 1.93T hex 4GTe − 20, 175.9 − 17.786T This work Cs2 Te)1 LIQ SER G Te − HTe = GLIQTE LIQ SER G Te − HTe = GLIQTE LIQ = G o GCs β − Cs2 Te + 23, Te 430 − 21.888T LCs2 Te, Te = − 62, 848 − 41.615T LCs2 Te, Te = 50, 917 LCs2 Te, Te = − 11, 938 Gas CsTe GAS G CsTe SER SER − HCs − HTe = 50, 214.1 + 27.5031T − 46.534T ln T − 3.33415 × 10−3T TBASE [38] + 2.28 × 10−6T + 147, 835T −1 − 1.72 × 10−9T + 3.78 × 10−13T + RT ln P [298.15 − 900 K] = 53, 805.9 − 3.84238T − 42.363T ln T − 4.7583 × 10−3T − 1.28 × 10−6T − 307825T −1 − × 10−10T − 1.32 × 10−14 T + RT ln P [900 − 2700 K] Cs2Te2 GAS SER SER GCs Te2 − 2HCs − 2HTe = − 1.42735 × 10 + 1.04633 × 10 T TBASE [38] − 83.1410T ln T − 9.10−7T + 3.5 × 10−11 T + 3.667 × 104T −1 + RT ln P [298.15 − 3000 K] Cs2Te GAS SER SER GCs Te − 2HCs − HTe = − 84, 295.4 + 33.7086T − 58.196T ln T − 3.2 × 10−6T + 4.65 × TBASE [38] 10−10T + 21465T −1 − 4.26667 × 10−14T + 1.67 × 10−18T + RT ln P [298.15 − 3000 K] Cs2Te3 GAS SER SER GCs Te3 − 2HCs − 3HTe = − 169, 753 + 202.289T − 108.066T ln T − 1.37 × 10−5T + 2.02334 × 10−9 T3 + 64, TBASE [38] 435T −1 − 1.88083 × 10−13T + 7.44 × 10−18T + RT ln P [298.15 − 3000 K] CsTe2 GAS SER SER GCsTe − HCs − 2HTe = − 1041.8548 + 34.0274T − 58.13682T ln T −6× 10−5T + 1.543 × 10−8T + 40, This work 665.83012T −1 − 2.5384 × 10−12T + 1.8386 × 10−16T + RT ln P [298.15 − 3000 K] Appendix B. 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The thermodynamic. modeling of this system is also performed with the aid of the Thermo-Calc software. The thermodynamic descriptions derived in this work are based on the da- tabases of Scientific Group Thermodata. derive a thermochemical de- scription of the Cs–Te system using the CALPHAD method. Lit- erature data on the crystal structures, thermodynamic properties and phase diagram of the Cs–Te system are