Thermodynamic assessment of the cs–te binary system

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.. F

Thermodynamic assessment of the Cs –Te binary system

T.-N Pham Thia,n, J.-C Dumasa, V Bouineaua, N Dupinb, C Guéneauc, S Gosséc,

P Benignid, Ph Maugisd, J Rogezd

a

DEN/DEC/SESC—CEA Cadarache, 13108 Saint-Paul Lez Durance Cedex, France

b

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

a r t i c l e i n f o

Article history:

Received 10 April 2014

Received in revised form

13 October 2014

Accepted 18 October 2014

Available online 25 October 2014

Keywords:

Cesium

Tellurium, fuel cladding gap

Thermodynamics computational modeling

Calphad

a b s t r a c t

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 da-tabases 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 ex-pressions 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

1 Introduction

The operating conditions of mixed oxide fuels (MOX) in Sodium

cooled Fast Reactor (SFR) are very severe combining high

tem-perature, 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

thus crucial for understanding and modeling the diffusion

pro-cesses 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

Lit-erature data on the crystal structures, thermodynamic properties

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

because:

– Like all alkali metals, Cs is very reactive with oxygen and water

same tendency All the stages of the experimental process, from the synthesis of the samples to theirfinal characterization must

be performed under inert atmosphere or vacuum All the ex-perimenters mentioned that the handling, preparation, mea-surement and characterization of the material were performed

in a glove-boxfilled 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

Cs and Te are directly mixed Likewise, if Te powder is in con-tact with Cs in a sealed glass ampoule, slight heating above room temperature resulted in an explosive reaction cracking of

Contents lists available atScienceDirect

CALPHAD: Computer Coupling of Phase Diagrams and

Thermochemistry

http://dx.doi.org/10.1016/j.calphad.2014.10.006

0364-5916/& Elsevier Ltd All rights reserved.

n Corresponding author.

E-mail address: phamtamngoc@yahoo.fr (T.-N Pham Thi).

the ampule Hence, the main difficulty lies in the synthesis of a

first compound e.g Cs2Te from the elements After this

key-stage, all the other Cs–Te mixtures can be prepared by mixing

quantities of the somewhat less reactive compound with Cs or

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

addi-tion 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

pres-sure above 900 K (PCsand PTereach 1 atm at respectively 944 K

and 1261 K[15], Cs is much more volatile than Te This

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

formed A third method, the so-called ammonia thermal

synthesis, has been used by Böttcher and coworkers to

elabo-rate 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)

worked on the system and in a recent inquiry, the present authors

2.1 Phase diagram data

Cs2Te at 953 K which is nowadays judged as a too low value

Ac-cording to Adamson and Leighty[14], it could be explained by the

sensitivity of Cs2Te to the presence of oxygen impurity during their

approximately 973 K

In 1980, Böttcher [24]synthesized the Cs2Te3compound and

Chuntonov et al.[16]are thefirst authors to investigate the Cs–Te

phase diagram in a large composition range by thermal analysis

method with direct visual observation to measure the melting and

range By comparison with the transition temperatures of known

materials, the accuracy of the thermal arrest method is estimated

their thermal analysis results and the knowledge of the existence

of Cs2Te and Cs2Te3from 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 Cs2Te3may exist

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

sus-ceptibility measurements on cooling for the Cs rich side of Cs2Te

They reported seven solid compounds: Cs2Te, Cs3Te2, Cs5Te4, CsTe,

temperatures are determined by DTA on heating with an accuracy

de-termining the liquidus temperatures because of pronounced su-percoolings 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,

agreement with those measured on heating by de Boer and

ex-perimental data points of Chuntonov et al used in the present assessment have been obtained by digitizing their originalfigure without any correction

Several inconsistencies between the phase diagrams presented

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 CsTeþCs2Te32L and the melting temperature of Cs2Te3

– The liquidus values measured by Adamson and Leighty are

Chuntonov et al values (10, 40, and 67 at% Te)

reaction L-CsTe5þCs2Te5 at 488 K and a peritectic reaction

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

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 men-tioned 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, Cs2Te3and Cs2Te5are stable at room temperature The existence of CsTe4 is confirmed and structural

However, their samples with ratios:

– Te:Cs¼5:4 and Te:Cs¼1:1 were mixtures of Cs3Te2and Cs2Te3, and

– Te:Cs ¼5:1 were mixtures of CsTe4and 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

compi-lation of former results

In the more critical assessment of Sangster and Pelton[29], the

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

method Moreover, the phase equilibria between 33 and 55 at% Te

needed further clarification

The subsequent experimental work by DSC and high

tem-perature X-ray diffraction of De Boer and Cordfunke[17]is focused

in this composition range In the DSC measurements, the

transi-tion temperatures are measured on heating with a reported

transi-tions They found that the previously reported compound Cs3Te2

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 Cs5Te3in a

sample containing 40 at% Te

sub-stoichiometric CsTe compound

Cs5Te3and CsTe are the only stable compounds in the range 33–

55 at% Te and that the Cs3Te2and Cs5Te4do not exist

The high temperature X-ray data of De Boer and Cordfunke[17]

also showed that CsTe and Cs2Te exhibit structural transitions at

Cs5Te3is observed around 515 K

The compounds Cs2Te13, Cs4Te28and Cs3Te22have been

have found that CsTe4was 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 CsTe4and pure

Te are much more complex than indicated in the critical

assess-ments 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

fill the lack of liquidus data on the Te rich side of Cs2Te The six

Cs2Te, Cs5Te3, CsTe, Cs2Te3, Cs2Te5and CsTe4solid compounds are

considered The chosen invariant reaction temperatures for these

compounds are detailed as follows

Cs2Te presents a structural transition at 89572 K [17] and

This value agrees with the determinations of Adamson and Leighty

(1083710 K) but is lower than the value of De Boer and Cordfunke

(110472 K)

Cs5Te3has an incongruent melting at 93475 K[17]according

to the peritectic invariant reaction: Cs5Te32Lþβ-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

Theα/βCsTe transition temperature (67375 K) is taken from

De Boer and Cordfunke, it is 8 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 72374 K

determined by De Boer and Cordfunke is selected This value is

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

631 K measured by Chuntonov et al

The melting temperature 668 K of Cs2Te3is taken from Chun-tonov 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)

Cs2Te5melts 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 Cs2Te5and CsTe5 For the same reason, the

attributed to the peritectic decomposition of CsTe4

2.2 Crystal structure data Table 2summarizes 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

Lindemer et al.[39]and by Kohli[40] Those estimated values are discarded here in order to consider the original experimental va-lues from Cordfunke and coworkers[7–9]

The standard enthalpy of formation has been derived from the

{0.46 mol dm3NaClO and 0.5 mol dm3NaOH}[18] Lately, a re-evaluation of the solution enthalpy of Te in the solvent led to small

mol[19]

The heat capacity has been measured from 5 to 340 K by adiabatic calorimetry[20] The high temperature enthalpy incre-ment of this compound has been measured by drop calorimetry [20] Low and high temperature resultsfit smoothly and yield the thermal function of Cs2Te(s), the corresponding expression of the

expression from [37] is slightly different from both the initial

the error range of the calorimetric measurements A value of

Table 1 Invariant reactions and transitions of Cs–Te system.

Reaction at% Te T (K) Reaction type Reference

α-Cs 2 Te2β-Cs 2 Te 33.2 89572 Structural transition [17]

β-Cs 2 Te2L 33.3 1093 Congruent melting [16]

Cs 5 Te 3 2β-Cs 2 Te þL 33.2–37 93475 Peritectic [17]

α-CsTe2β-CsTe 49 67375 Structural transition [17]

β-CsTe2Cs 5 Te 3 þL 37–49 72374 Peritectic [17]

CsTe þCs 2 Te 3 2L 55 61875 Eutectic [17]

Cs 2 Te 3 2L 60 668 Congruent melting [16]

Cs 2 Te 5 2LþCs 2 Te 3 60–71 508 Peritectic [16]

CsTe 4 þCs 2 Te 5 2L 71–80 488 Eutectic [16]

CsTe 4 2TeþL 80–100 536 Peritectic [16]

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, theα/βtransition enthalpy and the melting enthalpy

The standard enthalpy of formation and the enthalpy

incre-ment of Cs5Te3[19]have been obtained as for Cs2Te However, the

heat capacity of this compound was not measured at low

tem-perature 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 do not exist in the literature One

non-ideal 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 Cs5Te3respectively The corresponding

excess Gibbs energy of the liquid phase in the temperature range

900–1100 K has been determined fiting experimental liquidus data

from[16,17,30]

G x x {( 298 0.00144 )T x ( 972 0.482713 )T x } (kJ/mol)

This description is not fully satisfactory Firstly, their model predicts a symmetric liquidus around Cs2Te while the shape de-duced from the liquidus measurements of Adamson and Leighty [14], Chuntonov et al.[16], Drowart and Smoes[30], De Boer and

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 2

Cs–Te crystal structure data.

Phase Composition at% Te Pearson symbol Space group Strukturbericht designation Prototype Lattice parameter, nm Comment Reference

Table 3

Thermodynamic functions of Cs 2 Te and Cs 5 Te 3 from literature data.

Cs 2 Te Enthalpy of formation Δ H = −361, 400±3200

f 0 (J/mol) [ 22] (later corrected -362.972.9 kJ/mol

[23] )

Solution calori-metry at 298.15 K

[18 , 19]

Entropy at 298.15 K S0=185.1 /J Kmol(derived from heat capacity measurements) Adiabatic

calori-metry [5–340 K]

[20]

Enthalpy increment H T( )−H(298.15)=71.0132T+12.0523×10 − 3 2T −22, 244 ( /mol)T J Drop calorimetry

[468–800 K]

[20]

Data from database

of FACTSAGE

soft-ware [37]

Heat capacity for T 4298.15 K c p= 71.01393 + 0.02410357 ( /T J Kmol) – [37]

Cs Te2 Cs SER Te SER

2 2

Cs 5 Te 3 Enthalpy of formation Δ H = −942, 200±8300 (J/mol)

calori-metry at 298.15 K

[19]

Entropy at 298.15 K S0=480±5 ( /J Kmol)(estimated from entropy of Cs 2 Te at 298.15 K) Estimated [19]

−

−

3 2

5 1

Drop calorimetry [474–856 K]

[19]

Data from database

TBASE [38]

Heat capacity for T 4298.15 K c p=206.83+4.3874×10 −2T−2.08×10 /6T2( /J Kmol) – [38]

−

G Cs Te 5H Cs SER 3H 1, 014, 790 930.044T 206.829 lnT T

Te SER

5 3 0

2.4 Thermodynamic data of vapour pressure data

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

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

va-pour: Cs, Te,Te2, CsTe, Cs2Te, CsTe2, Cs2Te2, and Cs2Te3

The vaporization of stoichiometric Cs2Te has been studied by

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)E2.5, the other minor species being CsTe2,

CsTe, Te3,Cs2Te and Te2by order of decreasing abundance,

– The three major species in[30]are Cs, Cs2Te2and 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

ex-plain 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

frag-mentation of larger molecules contributes to the high intensity of

Portman et al mentioned overlap between peaks in the mass

spectra and difficulties in calibrating their quadrupole

spectro-meter 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 do 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

G i for 1 mol of the element i in the

Φstructure relative to the so called Standard Element Reference

(SER) state is written as

∑

− = + + +

Φ

G i H i SER a bT cTlnT d T n n

where n is an integer typically taking the values of 2, 3, and1,

HiSERis the molar enthalpy of the element i in its stable state at

298.15 K and 1 bar, and a, b, c, dnare 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

3.1 Stoichiometric compounds

All the compounds are described as stoichiometric: (Cs)(Te)

For Cs2Te and Cs5Te3for which heat capacity data are available, the corresponding Gibbs energy functions are expressed in the general form

G o n H a bT cTlnT d T

i

wheren i ϕis the stoichiometry coefficient of element i in the

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 Cs5Te3calculated

agreement with available experimental data[19] Hence, only the enthalpy and entropy variables (a and b) in the Gibbs energy function of Cs5Te3need to be optimized

For the other compounds CsTe, Cs2Te3, Cs2Te5, and CsTe4

Neumann relation is used and the Gibbs energy functions of these (Cs)p(Te)qcompounds are given as

ϕ

G0 pG Cs bcc qG Te hex A BT

The starting values for the variables A and B, which represent the enthalpies of formation of the compounds, were initially

ac-cording 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 ) (Va , Cs Te, Te)P 2 1

where P¼yVa , 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 1 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 de-scribed 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:

– Csþ is the only species present on the cation sublattice and it occupies all the available sites hence yCs þ¼1

– To compensate the charge of Csþcation, a hypothetical charged vacancy Vais 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 li-quid to support the hypothesis of the existence of such an as-sociate However, it must be noted that the corresponding solid

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

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

– 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 inFig 1versus 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:

= + +

G liq G0 G ideal G xs

Thefirst term, G0, corresponds to the Gibbs energy of a

me-chanical 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:

G y Va G Cs liq y G y G

Te Te Cs Te Cs Te

liq

G ideal RT y( lny y lny y lny )

va va Te Te Cs Te2 Cs Te2

=

G xs y y L

Te Cs Te Te Cs Te2 liq, 2

It is worth noting that an interaction parameter which is composition dependent is needed to describe the available ex-perimental data for the liquid phase in the composition range

Cs2Te–Te The termL Te Cs Te liq

(RK) polynomial function[53]as

∑

L Te Cs Te liq L (y y )

i i

Te Cs Te

liq

Cs Te Te i

,

,

2

2 2

with i¼0, 1 and 2

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.

The parametersi L ij liqcan be temperature-dependent:

= +

L ij liq a b T

i

ij ij

The composition dependence of the excess enthalpy is

de-scribed by aijand of the excess entropy by bij

3.3 Gas

The Gibbs energy of the gas phase is written according to

G gas y G RT y lny RTln /P P

i

i i

gas

i

i i

0

0

with yithe mole fraction of the i gas species andG i gas the

corre-sponding standard Gibbs energy The parameters of the Gibbs

energy of all the gaseous species are taken from the SGTE[37]or

optimization

A combination of thermodynamic functions extracted from

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]

4 Optimization procedure

opti-mization 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,

Fig 3 The calculated thermodynamic function of Cs 2 Te from this study compared to experiments.

Fig 4 The calculated thermodynamic functions of Cs 5 Te 3 from this study 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 Cs5Te3compound 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 tofit 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

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

5 Results and discussion 5.1 Phase diagram Fig 2compares the assessed diagram from this study with all experimental data

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

Because of supercooling effects, the uncertainty concerning the

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

to any transition in the present assessment An assumption can be put forward to explain this discrepancy If the samples have fol-lowed a non-equilibrium path during afirst 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

phase transition in CsTe4reported 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

into account in the present optimization

Fig 5 Enthalpy of formation of compounds in the Cs–Te system compared to

experiments.

Fig 6 Comparison of the partial pressure of Cs measured by Drowart and Smoes in their experiments 7 and 8 with the values calculated for x(Cs)/x(Te)¼1.67 and 1.63.

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, werefitted as a whole using a

single analytical expression whereas two distinct functions have

been used by Cordfunke et al.[20] This difference in thefitting

procedure explains the discrepancy between our and Cordfunke

et al calculated heat capacity above 340 K Nevertheless, the heat

de-termined to verify the calculations

Fig 4 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 inFig 5 The calculated data for Cs2Te and Cs5Te3are in

Fig 7 Partial pressures of the gas species in experiments 7 and 8 [30] Triangles: experimental points Solid lines: calculation this work.

Fig 8 Partial pressures of the gaseous species above condensed Cs 2 Te Triangles: experiments 5 and 6 from [30] , solid lines: calculations from this work for x(Cs)/x(Te)¼1.77.

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

experi-ments 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 7 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 Cs5Te3according to the later

tem-perature 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)¼1.67 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 7shows that the two major species in the

vapour are Cs and Cs2Te2and that the partial pressures of these

two species are very close According to the calculation, Cs2Te2is

the major species in equilibrium with the liquid at high

tem-perature 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 Cs2Te3gaseous species

109atm) are predicted by the calculation However, except for

spoiled for their quantitative determinations

In experiments 5 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 5 and

experi-ments, the pressures are measured on cooling from the upper

temperature bounds The experimental data are plotted inFig 8

It was not possible tofit the experimental data using the initial

ratio x(Cs)/x(Te)¼2.00 As Drowart and Smoes mentioned that the

composition of the samples evolve by incongruent vaporization

ex-periments 5 and 6, different x(Cs)/x(Te) ratios have been tried in

obtained using x(Cs)/x(Te)¼1.77 for temperatures below 1040 K as

pressures remain roughly constants or even slightly decrease

whereas the calculation predicts their constant increase The

hy-pothesis 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 tem-perature because evaporation is more thermally activated than diffusion However, even using a x(Cs)/x(Te) ratio down to 0.9, we

partial pressures are in agreement with the experimental ones at

1105 K: the x(Cs)/x(Te) ratio cannot be tuned tofit 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

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, Cs2Te5and 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

ex-perimental ones for the Cs2Te and Cs5Te3compounds The calcu-lated phase diagram and the calcucalcu-lated vapour pressure of the various gas phase species are also in good agreement with avail-able 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, CsTe4is necessary to check our optimized values for the G0(T) function of the solid compounds Second, the measurement of liquid mixing enthalpy in the com-position 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 ver-sus burn-up and temperature

Appendix A Thermodynamic parameters of the condensed phases and gas phase

SeeTable A.1