THERMODYNAMICS OF MOLTEN SALTS FOR NUCLEAR APPLICATIONS

Ondej Bene

JRC-ITU-TN-2008/40

INSTITUTE OF CHEMICAL TECHNOLOGY, PRAGUE

Faculty of Chemical Technology Department of Inorganic Chemistry

Dissertation

THERMODYNAMICS OF MOLTEN SALTS FOR NUCLEAR APPLICATIONS

Author: Ing. Ondej Bene

Supervisor: Prof. Dr. Ing. David Sedmidubsk, Dr. Rudy J. M. Konings

Study program: Chemistry

Field of study: Inorganic Chemistry Prague 2008

VYSOK KOLA CHEMICKO-TECHNOLOGICK V PRAZE Fakulta chemick technologie

stav Anorganick Chemie

Disertan prce

Termodynamika jadernch paliv na bzi roztavench sol

Autor: Ing. Ondej Bene

kolitel: Prof. Dr. Ing. David Sedmidubsk, Dr. Rudy J. M. Konings

Studijn program: Chemie

Studijn obor: Anorganick Chemie Praha 2008

Declaration

The thesis was worked out at the Department of Inorganic Chemistry, Institute of Chemical Technology, Prague, from August 2005 to September 2008. I hereby declare that I have worked out the thesis independently while noting all the resources employed as well as co-authors. I consent to the publication of the thesis under Act No. 111/1998, Coll., on universities, as amended by subsequent regulations. Prague, 19.9.2008 .................................................................................................. Signature

Acknowledgement

I want to thank Dr. Rudy J. M. Konings who supervised my thesis at my working place in the Institute for Transuranium Elements (ITU) in Karlsruhe, who was always very willing to help me with whatever task I wanted to discuss. I also want to thank him for very fruitful advices he gave me in the course of my 3 years stay in ITU. I acknowledge my Professor David Sedmidubsk who was always very open for discussion on any topic, not only concerning thermodynamics. Dr. Philippe Zeller is thanked for advices and guidance in the field of ab initio calculations.

Furthermore I would like to thank my PhD colleagues, namely Dr. J. P. M. van der Meer and C. Knzel from ITU for their help and for their enthusiasm to solve problems together. The technical support staff from the material research unit of ITU is thanked for their significant help, especially concerning the new designs and developments in the lab.

I acknowledge the European Commission for support given in the frame of the program 'Training and Mobility of Researchers' as well as the ACTINET for the fellowship provided in order to temporarly stay in CEA Saclay to perform the ab initio calculations.

Ing. Ondej Bene Title: Thermodynamics of the molten salts for nuclear applications Supervisor: Prof. Dr. Ing. David Sedmidubsk Study programme: Chemistry Subprogramme: Inorganic Chemistry SUMMARY

The molten salt reactor (MSR) is one of the six reactor concepts of the Generation IV initiative, an international collaboration to study the next generation nuclear power reactors. The fuel of the MSR is based on the dissolution of the fissile material (235U, 233U or 239Pu) in a matrix of a molten salt that must fulfill several requirements with respect to its physical properties. These requirements are very well satisfied by the various systems containing alkali metal and alkali earth fluorides.

In this study in total 32 binary fluoride systems have been thermodynamically assessed in order to predict the fuel properties in terms of the melting behaviour, the vapour pressure and the solubility of the actinides in the fuel matrix. Based on these properties, in total eight fuel compositions for the MSR have been proposed.

As part of the experimental study, two gas tight crucibles have been developped in order to measure the fluoride samples up to high temperatures. One is designed for a drop calorimeter used to measure the heat capacity of the (Li,Na)F liquid solution, whereas the other one is designed for a Differential Scanning Calorimeter (DSC) which was used to determine the equilibrium data points of the NaNO3-KNO3, RbF-CsF and CaF2-ThF4 binary systems. The data of the two latter systems were used to improve our thermodynamic database.

The Schottky contributions of the UPd3 sample were measured by the drop calorimeter and a very good correlation to the theoretical curve has been obtained. This measurement also confirmed that the drop calorimetry is in general a very sensitive method to determine relatively small energies.

An approach of obtaining the excess Gibbs energies of the solutions ab initio has been demonstrated in the case of (Rb,Cs)F solid solution and a very good correlation with the measured solidus and liquidus data has been observed.

Outline: Chapter 1 Introduction ................................................................................................ 1 Chapter 2 Nuclear Energy .......................................................................................... 3 2.1 Nuclear Force .................................................................................................. 3 2.2 Nuclear Fission ............................................................................................... 4 Isotopical compositions of the fuels ......................................................... 6 2.3 The Nuclear Fuel Cycle .................................................................................. 7 2.4 Nuclear Reactors ............................................................................................. 7 Current types of nuclear power reactors .................................................... 7 Generation IV reactors .............................................................................. 9 2.5 Molten Salt Reactor ......................................................................................... 11 MSR description ........................................................................................ 11 Advantages of the MSR ............................................................................. 12 Drawbacks of the MSR .............................................................................. 13 History of the MSR .................................................................................... 13 Fuel concepts in the MSR .......................................................................... 14 Other nuclear applications of the molten salts ........................................... 15 Chapter 3 Thermodynamics ....................................................................................... 18 3.1 Thermodynamic modelling ............................................................................. 19

Thermodynamic models for the excess Gibbs parameters of the binary solutions .................................................................................................... 25

Thermodynamic origin of phase diagrams ............................................... 29 Higher order systems approximation ........................................................ 30 Ternary phase diagrams ............................................................................ 33 Chapter 4 Thermodynamic Data ............................................................................... 38 4.1 Calorimetry ..................................................................................................... 39 Temperature calibration ............................................................................ 42 Schottky determination in UPd3 ................................................................ 46 High temperature heat capacity ..................................................... 46 The Schottky anomaly in UPd3 ..................................................... 48 Encapsulation technique for the drop mode .............................................. 52 Heat capacity of the (Li,Na)F liquid solution ............................................ 58 4.2 Equilibrium studies ......................................................................................... 63 Temperature calibration ............................................................................. 65 Encapsulation technique for the DSC detector .......................................... 65 Measurement of the NaNO3-KNO3 phase diagram ................................... 69 Measurement of the RbF-CsF phase diagram ............................................ 70 Measurement of the CaF2-ThF4 phase diagram ......................................... 73 4.3 First principle calculations ............................................................................... 78 (Rb,Cs)F solid solution ............................................................................... 78 ab initio calculation .................................................................................... 79 Configurational energy models .................................................................. 80 Calculation of the partition function .......................................................... 83 Bragg-Williams model ................................................................... 84 The quasi-chemical Guggenheim model .................................... 85 Thermodynamic assessment of the RbF-CsF phase diagram ..................... 85

Chapter 5 Binary Systems ............................................................................................ 91 5.1 Fluoride systems .............................................................................................. 92 LiF-NaF system ......................................................................................... 92 LiF-KF system ........................................................................................... 92 LiF-RbF system ......................................................................................... 92 LiF-CsF system .......................................................................................... 94 LiF-BeF2 system ........................................................................................ 97 LiF-LaF3 and NaF-LaF3 systems ............................................................... 97 LiF-ZrF4 system ......................................................................................... 102 LiF-PuF3 system ......................................................................................... 102 NaF-KF system .......................................................................................... 102 NaF-RbF system ......................................................................................... 102 NaF-CsF system ......................................................................................... 109 NaF-BeF2 system ....................................................................................... 111 NaF-PuF3 system ........................................................................................ 112 KF-RbF system ........................................................................................... 113 KF-CsF system ........................................................................................... 114 KF-LaF3 system ......................................................................................... 115 RbF-CsF system ......................................................................................... 117 RbF-LaF3 system ........................................................................................ 117 CsF-LaF3 system ........................................................................................ 117 UF4-ZrF4 system ......................................................................................... 119 BeF2-ZrF4 system ....................................................................................... 121 BeF2-PuF3 and LaF3-PuF3 systems ............................................................. 121 KF-PuF3, RbF-PuF3 and CsF-PuF3 systems ............................................... 123 5.2 Chloride systems .............................................................................................. 129 NaCl-UCl3 system ...................................................................................... 129 NaCl-PuCl3 system ..................................................................................... 129 UCl3-PuCl3 system ..................................................................................... 131 MgCl2-UCl3 system .................................................................................... 131 MgCl2-PuCl3 system ................................................................................... 132 Chapter 6 Ternary systems .......................................................................................... 134 LiF-NaF-KF phase diagram ........................................................................ 134 LiF-NaF-RbF phase diagram ...................................................................... 135 LiF-NaF-BeF2 phase diagram ..................................................................... 135 LiF-BeF2-PuF3 phase diagram .................................................................... 138 NaF-BeF2-PuF3 phase diagram ................................................................... 140 LiF-NaF-PuF3 phase diagram ..................................................................... 140 LiF-BeF2-ZrF4 phase diagram .................................................................... 148 Chapter 7 Nuclear Fuel Compositions ........................................................................ 152 7.1 Molten Salt thermal reactor: LiF-BeF2-ZrF4-UF4 system ................................ 153 7.2 Actinide burner non-moderated reactor: LiF-NaF-BeF2-PuF3 system ............. 157 melting behaviour ....................................................................................... 157 vapour pressure ........................................................................................... 160 7.3 Actinide burner non-moderated reactor: LiF-NaF-KF-RbF-(CsF)-PuF3

system .................................................................................................................... 162

melting behaviour ....................................................................................... 162 solubility for actinides ................................................................................ 163 vapour pressure ........................................................................................... 172 influence of the CsF fission product .......................................................... 176 7.4 Molten salt fast breeder fuel: NaCl-MgCl2-UCl3-PuCl3 system ...................... 179 melting behaviour ....................................................................................... 179 vapour pressure ........................................................................................... 180 Chapter 8 Conclusions and Summary......................................................................... 184 Appendix 1 - The thermodynamic data of all pure compounds considered in this study ........................................................................................................................ 189 Appendix 2 - The excess Gibbs energy data used in this study ........................................ 194 Bibliography ...................................................................................................................... 199

Chapter 1

Introduction

The molten salt reactor (MSR) is one of the six reactor concepts of the Gen-eration IV (GenIV) initiative, an international collaboration to study the nextgeneration nuclear power reactors. The fuel of the MSR is based on the dis-solution of the fissile material (235U, 233U or 239Pu) in a matrix of a moltensalt that must fulfill several requirements with respect to its physical proper-ties. These requirements are very well fulfilled by the various systems containingalkali metal and alkali earth fluorides.

The main task of this study was to extend the thermodynamic database ofthe various systems that are of relevance to the MSR project. The results of thiswork are very important, because once the thermodynamic model is establishedit is possible to predict some of the fuel properties such as melting behaviour,vapour pressure or solubility of actinides in the fuel matrix. Moreover it is mucheasier to optimize the fuel choice by varying the composition with respect to itsproperties.

Basically the thermodynamic modelling consists of two main parts. Firstlyall available experimental data are collected and these are then used to optimizethe phase diagrams in order to obtain the best possible fit between the exper-iment and calculated model. Hence also this study consisted of experimentaland modelling part.

The whole thesis is divided into five main sections. In the first one (Chap-ter 2) the nuclear energy topic is introduced with the scope on the principles ofnuclear reactions and their applicability. Furthermore the fuels currently beingused in the commercial power plants will be mentioned as well as the presenttypes of nuclear reactors. The last part of this section will focus on the Genera-tion IV reactor concepts with the main scope on the MSR. Its history, principlesof operation and current fuel approaches will be briefly discussed.

The next section (Chapter 3) is dedicated to thermodynamics. The princi-ples of modelling and the thermodynamic models that have been used in thisstudy for the description of the excess Gibbs energies of the solutions will beexplained. The binary and ternary phase diagrams are interpreted in sense ofthe crystallization paths and phase field equilibria.

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The experimental work performed within the frame of this thesis will bereported in the Chapter 4. The calorimetric techniques used in this study andtheir principles are explained at the beginning of this chapter and the develop-ment of a novel technique to encapsulate the fluoride salts is presented. Twodifferent crucibles have been designed, one for a drop calorimeter whereas theother one is proposed for a DSC (Differential Scanning Calorimetry) measure-ments. Furthermore the first experiments made using these newly developedcrucibles are reported in this study. The heat capacity of the (Li,Na)F liquidsolution was measured as a function of composition and an ideal behaviour hasbeen observed. It is also demonstrated on the measurement of UPd3 and ThPd3samples how sensitive is the drop calorimetry in order to determine the Schottkycontributions to the heat capacity.

The DSC crucibles were first tested on the measurement of the equilibriumdata of the NaNO3-KNO3 binary which is one of the candidate for a heat transfersalt in a sodium cooled fast reactor. New data of the solidus and liquidus pointsfrom the RbF-CsF system have been measured as well as the equilibrium dataof the CaF2-ThF4 system. At the end of this chapter the excess enthalpies ofthe (Rb,Cs)F solid solution were obtained by means of Ab initio and comparedto the experimental results.

All the binary phase diagrams assessed in this study are presented in Chapter5 where a brief description about the optimization is given, whereas some of thefluoride ternary phase diagrams are shown in the next Chapter 6. Since theternary systems of the chloride systems considered are direct fuel choices, theyare discussed in Chapter 7.

Based on the developed thermodynamic database as part of this study, totalof eight fuel compositions for the molten salt reactor have been made. Sevenof them are based on the fluoride systems, while the rest one is based on thechloride system. All fuel choices are discussed in Chapter 7 in sense of its meltingbehaviour, actinide solubility and its vapour pressure. Finally all the obtainedproperties for given fuel choices are summarized in Table 8.1 and Table 8.2 inthe last chapter 8.

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Chapter 2

Nuclear Energy

2.1 Nuclear Force

The nuclear force is responsible for binding the nucleons together within thecore of an atom. It is mediated by the baryons called pions that consist of onequark and one anti-quark. The nuclear force is sometimes called residual stronginteraction as in contrast to the strong interaction which is the force betweenthe p- and u- quarks within the protons and neutrons. In the beginning of 20thcentury scientists realized that the cores of the atoms do not have to be necessarystable and can undergo splitting into smaller particles or can fuse together whilecreating larger species. The non-stable nuclei decay spontaneously in the processcalled radioactivity while emitting new particles and large quanta of energy.Another example of a process which is powered by the nuclear force is thefission of heavy nuclides which occurs in the current types of nuclear reactorsor when the atomic bomb is triggered. This fission is also known as a chainreaction. On a cosmic scale more important process than the fission is thenuclear fusion during which the light elements fuse together and form heaviernuclides. This reaction occurs in the cores of the stars and the most abundantis the fusion of two hydrogen atoms while forming helium. Similarly as in caseof radioactive decay or fission, large amount of energy is released during thefusion process. During all the exoenergetic nuclear processes the total massof the initial nuclides is higher than the one of the products. Based on theknowledge of the mass balance of the reaction it is thus possible to evaluate thetotal energy released during the nuclear processes. This relationship is shownin Equation 2.1 and is known as Einsteins equation

E = m c2 (2.1)

where E is the energy balance, m the mass difference and c is the speed oflight in the vacuum.

At short distances, typical for the atomic nuclei, the nuclear force is strongerthan the columbic repulsion of the positively charged protons. In comparison

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Figure 2.1: Scheme of the nuclear fission of the 235U nucleus into the 141Ba and92Kr fission products.

to the interactions responsible for the chemical bonding and chemical reactionsin nature, the nuclear force is about hundred million times stronger. It is thusunderstandable that the understanding and the use of this energy is very chal-lenging for the mankind.

2.2 Nuclear Fission

Fission in nuclear chemistry is a process during which the heavy nuclei splitinto two smaller fragments, called fission products, releasing free neutrons anda large amount of energy. Based on the nature of the fission we distinguishbetween spontaneous fission and nuclear fission.

Nuclear fission is induced by a free neutron or other particle which strikean atom nucleus turning it into the metastable, excited state with one highermass number than the original atom. Such a configuration is very unstable andthe atom immediately splits into two lighter nuclei as illustrated in Figure 2.1.The figure shows the nuclear fission of the 235U atom, a typical fuel used in powerreactors, which in this case fissions forming 141Ba and 92Kr fission products whileemitting three free neutrons. The situation shown in Figure 2.1 shows only oneof many possibilities that can occur during the fission of 235U. Figure 2.2 showsthe average yields of whole range of different fission products that can be formedduring an event. From the graph it is evident that there are two peaks withmaxima corresponding to the atomic mass numbers of 95 and 140 respectively,and these fission product are the most probable to be formed after the 235Ufission.

The neutrons that are created in the fission process posses of high kinetic

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0 20 40 60 80 100 120 140 1600

1

2

3

4

5

6

7

8

Ave

rag

e Y

ield

/ (

%)

Mass number of FP

Figure 2.2: Average yield of the fission products after the thermal fission of235U.

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Figure 2.3: Scheme of the nuclear capture of the 235U nucleus.

energy (Ek 1 MeV) and are generally called as the fast neutrons in contrastto thermal neutrons which undergo moderation process (they are slowed down)and characterized by lower kinetic energies. Another situation that can occurwhen an atom is hit by a neutron is demonstrated in Figure 2.3 and is knownas nuclear capture. Similarly as in case of nuclear fission, the nuclear captureis induced by a free neutron, however, the metastable state is not split into twosmaller fragments, but it transforms into its ground state while emitting highenergy photons known as gamma rays.

Spontaneous fission follows exactly the same process as nuclear fission,except that it occurs without the atom having been struck by a neutron or otherparticle. In principle it is a form of a radioactive decay and is characteristic forsome heavy elements, specially higher actinides and trans-actinides. It has beenalso observed for most abundant actinides, uranium and thorium, but in theircase the probability of occurrence is very low.

Isotopical composition of the fuels

To maintain the chain reaction in the nuclear reactor the fissile material (thefuel) must be present. Basically there are two main isotopes that are usedas fissile materials. These are 235U and 239Pu isotopes. Their exact amountsand concentrations strongly depend on the reactor design and on the neutronspectrum used (fast, thermal). Most of the current types of commercial powerreactors are based on uranium fuel which is in a form of solid oxide pellets,called UOX fuel. Although the heavy water moderated reactors (e.g. CANDUreactor as discussed in the next section) are designed in such way that they usenatural uranium containing only 0.73 weight% of fissile 235U (the rest 99.27weight% is represented by a non-fissile 238U isotope) isotope as a fuel, in case ofthe Light Water Reactors (LWRs) (most common type of current reactors) it isnecessary to increase the content of 235U in order to sustain the chain reaction.

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This is achieved by uranium enrichment and the typical concentration of 235Uin the reactor grade uranium is 3-4 weight%.

Another widely used nuclear fuel is a mixed oxide of uranium and plutonium,called MOX fuel. In principle it is an alternative to the UOX fuels with similartotal concentrations ( 3-4 weight%) of the fissile isotopes (235U and 239Pu).The advantage of using the MOX fuel is mainly the possibility of using separatedfissile 239Pu which is daily produced in the nuclear reactors by neutron capturingof the non-fissile 238U nuclide.

2.3 The Nuclear Fuel Cycle

The nuclear fuel cycle consists of several stages. The primary stage, also calledfront end includes the preparation processes like mining, enrichment and fuelfabrication. It continues through the service period, during which the fuel isinstalled in the nuclear reactor and is used for energy production. The lastperiod of the fuel life time is called back end and consists of the fuel managementafter its operation in the reactor. At this stage the fuel can be either reprocessedor disposed as a nuclear waste. If the fuel is directly disposed as a nuclear wastethe fuel cycle is referred to as an open fuel cycle, also known as once-through fuelcycle. In case that the fuel is reprocessed the fuel cycle is referred to as a closedfuel cycle. During the reprocessing the fission products, minor actinides, andreprocessed uranium are separated from plutonium, which is then fabricatedinto the MOX fuel. The fission products together with the minor actinidesare disposed as a nuclear waste, but due to the very long half-life of someminor actinides (in order of 106 years) no one can guarantee that the storageassembly would resist the environmental conditions over such period of timeand the disposal is not definite. Nevertheless, this problem will be solved withthe introduction of the advanced fast reactor concepts where it is planned tore-use these minor actinides as part of the fuel.

2.4 Nuclear Reactors

Current types of nuclear power reactors

A nuclear reactor is a device in which the nuclear chain reaction is initiated,controlled and sustained at constant rate. In order to keep the chain reaction,there must be such an amount of fuel in such space configuration that the wholeassembly is in supercritical state. It is a state at which more neutrons areproduced during the nuclear fission of the fissile material than consumed by thecapturing of the atom nuclei. A numerical measure of the supercritical state isdependent on the neutron multiplication factor, k, where:

k = f l (2.2)

where f is the average amount of neutrons released during the fission and l is theaverage amount of neutrons being escaped from the system or being consumed

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during non-fissile processes. When k > 1 the mass is supercritical and the rateof fission increases. When k = 1 the mass is critical and corresponds to theequilibrium fission reaction where there is no increase or decrease of neutronpopulation. When k < 1 the mass is subcritical. At this state the populationof neutrons introduced to the system will exponentially decrease.

Based on the neutron spectrum the nuclear reactors can be divided into twomain groups. First group are the fast reactors in which the fission chain reactionis sustained by the fast neutrons, neutrons that posses of high kinetic energy.At the moment there are only few reactors of this kind used for electricity pro-duction (e.g. russian BN-600). Most of the fast reactors currently being underoperation are either prototypes (e.g. french Phenix reactor) or test reactors.The second group consists of thermal reactors characterized by a thermal neu-tron spectrum. In these reactors the neutrons are first slowed down before theystrike a fissile atom. This is done by introducing a moderator, a medium whichreduces the velocity of fast neutrons by absorbing part of their kinetic energy.Mostly used moderators in current power reactors are light water, graphite orheavy water. It is the thermal reactors that are widely used all over the worldto produce the electric power.

The most common type of the power producing reactor is the PressurizedWater Reactor (PWR) (the Russian types of PWRs are known as VVER(Water-Water Energetic Reactor)). It uses slightly enriched uranium as afuel (some concepts use MOX fuel). It is in the form of oxide pellets that areencapsulated in fuel pins and these are assembled into fuel bundles as shownin Figure 2.4. Each of the PWR cores consist of matrix of these fuel bundleswhich are continuously flushed by a light water serving as coolant and neutronmoderator. Despite the fact that the operating temperature of a PWR is wellabove the boiling point of water (Taverage 315

C), the water stays in theliquid form due to the high pressure (paverage 20 MPa) that is kept in theprimary circuit. The heat from the reactor core is delivered via the primarycircuit to the steam generators which are part of the secondary circuit. Herethe high pressure and high temperature steam is generated and is used to propelthe turbine in order to produce electricity. The water in the primary circuit iscooled and flows back to the reactor vessel.

Another concept of the power reactor is the Boiling Water Reactor(BWR). It is a similar concept as previously described PWR, only the pri-mary circuit is characterized by two-phase fluid flow (water and steam) in theupper part of the reactor core, where the temperature reaches highest values.Since the steam is produced directly in the reactor vessel the primary circuit isdirectly connected to the electricity producing turbine. Both PWRs and BWRsreactors belong to the group of Light Water Reactors (LWRs).

Third example of widely used commercial reactor is CANDU reactor(CANada Deuterium Uranium). It is very similar to PWR, although it dif-fers in some details. The first difference is that it is designed in such way thatit is feasible to use natural uranium as a fuel. In order to sustain the chainreaction in the natural uranium (only 0.73 % of fissile 235U) the moderatingratio must be very high. This is achieved by using heavy water instead of light

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Figure 2.4: Fuel bundle used in current PWRs

water (PWR and BWR case) as a primary coolant. The heat transfer and theelectricity production is designed on the same principle as described in the caseof PWR.

Generation IV reactors

All the reactor types described in the previous section belong to the group ofGeneration II reactors. These are currently commercially used power reactorsthat have been developed from the early Generation I reactors. As seen in thegeneral roadmap in Figure 2.5 the Generation III reactors are being deployedin near future, for example the Evolutionary Power Reactor (EPR) (improvedPWR) which is under construction in Finland. Compared to todays reactorsthe Generation III reactors should incorporate some improvements that havebeen developed during the lifetime of the Generation II designs. Especiallyimproved fuel technology and better passive safety (such an assembly in whichthe chain reaction automatically slows down when overheated) is incorporated.

Generation IV (GenIV) reactors will follow Generation III reactors. Theprimary goal of the GenIV reactors is to improve the nuclear safety, to minimizewaste (transmutation of long lived higher actinides will be heavily introduced)and to keep low fuel inventory while sustaining high efficiency. Furthermorethe reactor designs must be reliable and the cost to build and to run such apower plant must be minimized. In total there are six reactor concepts selectedfor the GenIV initiative, but most of them are not expected to be deployed forcommercial purposes before 2030. The six GenIV concepts are:

Very High Temperature Reactor (VHTR)

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Figure 2.5: Time evolution of the nuclear reactors

Supercritical Water Cooled Reactor (SCWR)

Gas Cooled Fast Reactor (GFR)

Sodium Cooled Fast Reactor (SFR)

Lead Cooled Fast Reactor (LFR)

Molten Salt Reactor (MSR)

The VHTR is a thermal reactor that is graphite-moderated and uses heliumgas as a primary coolant. It uses a once-through uranium fuel cycle (open fuelcycle), meaning that the spent fuel is not reprocessed. The strength of VHTRdesign is in the high outlet temperature of the reactor core which can reach1000 C. Thus its heat can be directly used to produce the hydrogen via theiodine-sulfur cycle [1] or for desalination of water. Due to the high operationaltemperature, this reactor posses of high efficiency.

The SCWR is another thermal reactor concept that is based on the once-through uranium fuel cycle, as similar as the VHTR. The coolant is a light waterin supercritical state (T > 374 C) and the primary loop is directly connectedto the turbine for electricity production, similarly as in case of BWR. The maindifference to the BWR is the state of the working fluid, which in this case iscomposed of only one phase. Basically SCWR operates at much higher temper-atures than PWRs or BWRs, and therefore its thermal efficiency is higher.

The reference GFR design is a helium cooled system based on the fast neu-tron spectrum with an outlet reactor temperature of 850 C. The primary circuit

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is directly connected to the gas turbine for electricity production. The exactfuel form is not clearly defined yet, but it will be most likely designed in suchway that the core will have high fissile material content with addition of a fer-tile material, which will breed more fuel by neutron capturing. It is importantto note that the temperatures exceeding 850 C are high enough for the ther-mochemical production of hydrogen, thus this reactor concept is possible to beused for this purpose as well as VHTR, however, different medium than heliumgas should be used for heat transfer between the reactor core and the hydrogenplant. For this purpose the molten salts are serious candidates. Higher heatcapacity, density and thermal conductivity are required for such heat trans-fer salts. As good candidates flinak (eutectic composition of the LiF-NaF-KFsystem) or the eutectic composition of the NaNO3-KNO3 system are considered.

The SFR is another fast reactor design. Concerning the fuel there are twomain options: One is based on the uranium-plutonium-minor actinide zirconiumalloy, the second one considers mixed uranium-plutonium oxide fuel. Both con-cepts employ full actinide recycle (closed fuel cycle) and the reference coolant ismolten sodium. In order to avoid the contact between sodium and water, therewill be an intermediate loop between the primary circuit and the steam gen-erator which could be operated with a molten fluoride salt or molten nitrate salt.

The LFR is a reactor concept based on a fast neutron spectrum. It usesmolten lead or lead-bismuth eutectic melt as a coolant, and a closed fuel cy-cle. The fuel is metallic, oxide or nitride-based and contains fertile uranium (tobreed more fuel) and actinides as fissile material. The reactor outlet tempera-ture is 550 C, but with the use of advanced materials it can be increased totemperatures over 850 C. In that case it would be possible to use the LFR fordirect hydrogen production.

The MSR is the sixth reactor type of the Generation IV initiatives andsince the thermodynamic description of the MSR fuel is the main subject ofthis study the whole concept is described in more details in the next section.

2.5 Molten Salt Reactor (MSR)

MSR description

In a molten salt reactor the nuclear fuel is dissolved in an inorganic liquid(most likely a mixture of fluorides) that is pumped at a low pressure throughthe reactor vessel and the primary circuit and thus also serves as the primarycoolant. The heat generated by the fission process is transferred to a secondarycoolant in a heat exchanger. This secondary coolant is generally a molten saltalso. Figure 2.6 shows the MSR concept as designed by ORNL.

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Figure 2.6: MSR concept as designed by ORNL.

Advantages of the MSR

The most important advantage of the MSR is its safety. Since the fuel is inliquid state and serves as a primary coolant (thus no water or gas coolant isin direct contact with the fuel) having low vapour pressures (boiling points >1400 C) the total pressure of the primary circuit is kept very low (p 1 Bar)compared to current LWRs etc. It thus avoids the major driving force of theradioactivity release, the high pressure, during the accidents. Another aspectthat contributes to the safety of the MSR is that the reactor posses of stronglynegative temperature coefficient. It means that the chain reaction in the reactorcore is naturally slowed down (or stopped) when the temperature increases. Incase of the MSR this is invoked by the thermal expansion of the primary coolant,which pushes the fuel out of the reactor core (the fuel density decreases) andcauses subcritical state. The third issue increasing the safety of the reactor isthe possibility of draining the fuel into the emergency dump tanks in case ofan accident. The emergency tanks are installed under the reactor, as shown infigure 2.6 and are designed in such way that the fuel stays subcritical. Sincethere is a very low amount of the fission products kept in the fuel during thereactor operation (due to the online reprocessing) the heat generation from theirradioactive decay is small and the risk of overheating the system even after thechain reaction is stopped is avoided.

A big advantage of the MSR that increases the efficiency of the fuel burn-up is the possibility of performing a continuous fuel reprocessing. This can

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be done either on-line or in batches and the concept is proposed in such waythat the reprocessing chemical plant is installed on site of the nuclear reactor(no transportation of the fuel). A position of this reprocessing chemical plantwithin the MSR unit is shown in Figure 2.6. The goal of the fuel clean-up is toseparate the fission products from the fuel and put them into the nuclear waste,while the cleaned fuel is sent back into the primary circuit. It is very importantto make this separation, because most of the fission products have a very highneutron capture cross section and thus slow down the chain reaction. Due tothis online reprocessing a low initial inventory of the fissile material is possible.Moreover, it is also possible to profit from the neutron economy and design theMSRs as breeder reactors that produce more fuel than consume.

The MSR can be designed as an actinide burner reactor. It would thus bepossible to inject the minor actinides containing nuclear waste from the currenttypes of power reactors into the MSR fuel cycle and transmute these long livedisotopes into the short lived fission products. The transmutation process is verychallenging for the nuclear scientists because it would help to solve the problemof the final nuclear waste disposal which is at the moment considered as a majordraw-back of nuclear power due to the presence of the long lived actinides thatneed millions of years before they decay into the stable isotopes.

Another characteristic of the MSR is no radiation damage of the fuel dueto its liquid state. This is of importance since in the solid fuels the radiationdamage causes swelling of the fuel pins and these must be than replaced by thenew ones.

The last, but not least issue among the big advantages of the MSR is apossibility to use it for a direct hydrogen production. This is however still asubject of investigation, because special alloys would be required for structuralmaterial in order to avoid the corrosion of the fluoride salts at high temperatures.

Drawbacks of the MSR

The main disadvantage of the MSR is the corrosion of the structural materialby the molten fluoride salt, which can occur at high temperatures. However, aprofound investigation is being carried out in this field of science in order to finda compatible alloy which would serve as a structural material and would not bedamaged during the operational lifetime of the reactor. The nickel based alloys,namely Hastelloy N alloy is very promising. The MSRE (see next subsection) hasbeen based on this alloy and operated successfully over four year period with nocorrosion damage. In that case the reactor outlet temperature was 654 C, morethan 150 C less than the temperature necessary for direct hydrogen production(above 800 C). At higher temperatures the corrosion rate increases and newalloys, compatible with the molten fluoride salt must be invented.

History of the MSR

The first proposal for a molten-salt reactor dates from the 1940s when Bettisand Briant proposed it for aircraft propulsion [2]. A substantial research pro-

13

gramme was started at Oak Ridge National Laboratory (ORNL) in the USA todevelop this idea, culminating in the Aircraft Reactor Experiment (ARE) thatwas critical during several days in 1954. For ARE a mixture of NaF-ZrF4 wasused as carrier of the fissile UF4 [3, 4].

In the second half of the 1950s the molten salt technology was transferredto the civilian nuclear programme of the US. At that time many reactor con-cepts were being studied and the interest in breeder reactors was large. It wasrecognized that the molten salt reactor would be ideal for thermal breeding ofuranium from thorium [2] and the Molten Salt Reactor Experiment (MSRE)was started at ORNL to demonstrate the operability of molten-salt reactors.Because of the breeding aspect, the neutron economy in the reactor was consid-ered of key importance and 7LiF-BeF2 (flibe), with 5 % ZrF4 as oxygen getter,was selected as fuel carrier because of the very low neutron-capture cross sec-tions of 7Li and Be. The MSRE was a graphite-moderated reactor of 8 MWththat operated from 1965-1969. Three different fissile sources were used: 235UF4,233UF4 and

239PuF3. flibe was used as coolant in the secondary circuit. Theresults of MSRE, which have been reported in great detail [5], revealed that theselected materials (fuel, structurals) all behaved well and that the equipmentbehaved reliably. In that respect it was very successful.

After the MSRE a design for a prototype Molten Salt Breeder Reactor(MSBR) was made by ORNL in early 1970s [6], in which a continuous repro-cessing of the fuel was foreseen to reduce the neutron loss by capture in fissionproducts. The program was stopped in 1976, in favor of the liquid metal cooledfast reactor [2] although the technology was considered promising, but recog-nizing the technological problems that had to be solved. The MSBR design wasa 2250 MWth reactor, optimized to breed 233U from thorium in a single fluidsystem. Online pyrochemical reprocessing was planned to clean the fuel solventfrom the neutron absorbing fission products. Nevertheless interruption of reac-tor operation was planned every four years to replace the graphite moderator, asexperiments had revealed significant swelling of graphite due to radiation dam-age. Because of the online clean up of the fuel, the zirconium addition to thefuel was not necessary and flibe could be used as carrier of the fertile (ThF4)and fissile elements (UF4). As secondary coolant, a NaF-NaBF4 mixture (0.08-0.92 molar composition) was foreseen because the tritium retention of this saltis much better than flibe.

Fuel concepts in the MSR

In the section above the MSBR concept has been mentioned as a graphite mod-erated reactor that has been based on the 7LiF-BeF2-ThF4-UF4 system [6]. Thisfuel composition based on the flibe matrix still remains as an ideal candidatewhen the MSR is designed as a thermal breeder reactor (moderated reactor).In this case the neutron economy is very critical and only the isotopes withvery low neutron capture cross section in the thermal spectrum can be consid-ered as part of the fuel matrix. Thus 7LiF and BeF2 are the compounds ofconsideration.

14

Nowadays the non-moderated (fast) (although there is no moderating mediumin the reactor core, the neutrons emitted during the fission are partially moder-ated by the fluorine atom which is part of the fuel matrix - therefore the non-moderated rather than fast term is preferred in case of the MSR) reactorsare of higher interest for its possibility of transmuting the long lived actinidesproduced mostly in the thermal reactors. The transmutation is effective onlywhen initiated by high energy neutrons (epithermal or fast spectrum), becauseat that energy all the minor actinides are fissionable. Moreover the fission tocapture ratio for these nuclides is much higher in the fast than in the thermalspectrum. Another advantage of the non-moderated reactor is the absence ofthe graphite (as a moderator in the thermal MSR) in the reactor core which isvery inclinable for radiation damage and must be periodically replaced.

In case of the MSR there are two main directions of the non-moderated(fast) reactor concepts. First is an actinide burner design based on the RussianMOSART (MOlten Salt Actinide Recycler & Transmuter) concept [7] which usesthe 7LiF-NaF-BeF2-AnF3 system as a fuel. An is mainly represented by

239Puwith some addition of minor actinides. The second one is an innovative conceptcalled TMSR-NM (Non Moderated Thorium Molten Salt Reactor) that hasbeen developed by CNRS-Grenoble in France [811]. The fuel in this concept isbased on the 7LiF-232ThF4 matrix with the addition of the actinide fluorides asa fissile material. 232ThF4 is a fertile material that is bred to fissile

233UF4 by aneutron capture and consecutive beta decay. There are two initial fissile choicesin the TMSR-NM concept, (1) the 233U-started TMSR and (2) the transuranic-started TMSR with the mix of 87.5% of Pu (238Pu 2.7%, 239Pu 45.9%, 240Pu21.5%, 241Pu 10.7% and 242Pu 6.7%), 6.3% Np, 5.3% of Am and 0.9% of Cm,corresponding to the transuranic elements composition of an UOX fuel after oneuse in a PWR and five years of storage [12].

One of the very recent designs of the MSR is the REBUS-3700 concept whichis based on the chloride salt as a fuel. It is a fast breeder reactor which hasbeen proposed by Mourogov and Bokov [13] and it is based on a U-Pu cycle,where U and Pu are present in the form of trichlorides dissolved in a matrixof liquid NaCl. In general the chlorides have higher vapor pressures and lowerthermodynamic stability at high temperatures compared to fluorides, but onthe other hand, they are less aggressive against the structural materials andtheir melting points are lower. Therefore, more fissile material can be dissolvedin the matrix and that is necessary for fast breeder reactor designs. However,the chlorides can only be used in fast reactors and not in thermal ones, due tothe relatively high parasitic neutron-capture cross-section of the chlorine atom.

Other nuclear applications of the molten salts

Molten salts are not only used as fuels (primary circuit of a MSR), but they canbe potentially used as secondary coolants in the MSR or as primary coolants insome of the advanced reactor concepts, as well as the heat transfer salts betweenthe nuclear reactor and the hydrogen production plant.

Probably the most suitable candidate as a secondary coolant of the MSR

15

is the eutectic composition of the NaF-NaBF4 system, a coolant that has beenused in the MSBR project. As an alternative the LiF-BeF2 system or the KF-KBF4 system is considered. For advanced high temperature reactors that arebased on the thermal spectrum the 7LiF-BeF2 (flibe) system is very promisingcandidate for a secondary coolant. In this case it is demanding to have highpurity of 7Li isotope (99.995 weight%), because the other naturally occurringlithium isotope, 6Li, is a neutron poison due to its very high neutron capturecross section and must be avoided from the reactor core. For secondary coolantsthis restriction does not have to be fulfilled because this salt is not in directcontact with the reactor core and does not slow down the chain reaction. Inthat case the natural isotopical composition of lithium (7.6 weight% of 6Li and92.4 weight% of 7Li) can be used.

As a secondary coolant for a fast reactor the eutectic composition of theLiCl-NaCl-MgCl2 system is proposed. In this case the salt is based on the chlo-rides which have higher neutron capture cross section than fluorides, howeverin the fast spectrum reactors the neutron economy is not as sensitive as in thethermal ones and chlorides can be of potential use. As discussed in the previoussection for a heat transfer salts the flinak system (eutectic composition of theLiF-NaF-KF system) or the eutectic composition of the NaNO3-KNO3 systemare considered. As an alternative the eutectic composition of the LiCl-KCl-MgCl2 system is proposed.

Table 2.1 summarizes the various applications of the molten salts for the nuclearapplications.

16

Table 2.1: The various applications of molten salts in the nuclear reactor science.Reactor Neutron Application Primary choice Alternative(s)type spectrumMSR Breeder Thermal Fuel 7LiF-BeF2-AnF4

Fast Fuel 7LiF-AnF4Coolant NaF-NaBF4 LiF-BeF2, KF-KBF4

MSR Burner Fast Fuel LiF-NaF-BeF2-AnF3 LiF-NaF-KF-AnF3AHTR Thermal Coolant 7LiF-BeF2VHTR Thermal Heat transfer LiF-NaF-KF LiCl-KCl-MgCl2FR Fast Coolant LiCl-NaCl-MgCl2SFR Fast Heat transfer NaNO3-KNO3

AHTR .... Advanced High Temperature Reactor

17

Chapter 3

Thermodynamics

It has been shown in the previous chapter which salt systems are the maincandidates for the nuclear applications. Basically the choice has been made ona basis of the salt properties that must fulfill following criteria (the solubilityfor actinides and the neutronic properties do not apply to coolants and the heattransfer salts):

Low melting point.

Low vapour pressure at the operating temperature of the reactor.

Wide range of solubility for actinides.

Thermodynamic stability up to high temperatures.

Stability to radiation (no radiolytic decomposition).

Low neutron capture cross section.

Compatibility with nickel-based alloys (Ni-Mo-Cr-Fe) that can be used asstructural materials (Hastelloy).

The low melting temperature is required because the lower the melting tem-perature the lower the risk of the system to freeze at certain circumstances.Another reason to ensure a low melting temperature is related to the corrosioneffects. If the salt melts at higher temperatures the operation temperature ofthe reactor must be also raised and the rate of the corrosion of the structuralmaterial by the salt increases. It is very important that the reactor inlet tem-perature is at least 50 K higher than the melting point of the salt in order tokeep a safety margin. It avoids the risk of solid precipitation which could cause,in case of the actinide rich solid precipitates, local supercriticality and result inlocal hot spots.

The low vapor pressure of the salt is not only required to keep the wholereactor circuit at low pressure, but it also avoids the change of the molten saltcomposition which can occur due to the incongruent vaporization.

18

The main objective of this work is a thermodynamic description of the flu-oride and chloride systems that are relevant for nuclear applications (fuels,coolants or heat transfer salts), based on experiments and modelling. For areactor design it is very important to have a thermodynamic description ofthese systems, because the melting behavior, the vapour pressure, thermody-namic stability at high temperatures or the solubility for actinides in the matrixof the fuel can be obtained based on these results.

It is also impossible to measure every single composition one might be in-terested in, so the solution is to develop a model that would describe the wholesystem. Moreover it is much easier to optimize the fuel (coolant or heat transfersalt) composition based on the knowledge of the phase diagrams.

3.1 Thermodynamic modelling

The main outcome of the thermodynamic modelling is the assessment of thephase diagram. It is a graph that shows stable phase fields as a function of anyvariable (temperature, pressure, composition, electric potential etc.). The mostcommon type is a T -x phase diagram which shows the stable phase fields as afunction of temperature and composition. Basically, based on the knowledgeof a T -x phase diagram one can deduce at what temperature a certain fuelor coolant composition melts, boils or decomposes. It is very important tonote that departures from equilibrium can occur in any real system, however aknowledge of the equilibrium state is usually the starting point to understand thebehaviour of certain system at given conditions. The non-equilibrium state is theconsequence of the kinetic aspects (e.g. supercooling during the glass formation)and are usual for low temperatures. At higher temperatures, typically closeto the melting temperatures and higher the thermodynamics (the equilibriumstate) becomes dominant.

In thermodynamics a simple rule applies which states that the configurationof any system which possesses a lower Gibbs energy is more stable than theone with higher energy. Hence in order to describe a T -x phase diagram, aknowledge of the Gibbs energy equations of all phases and the Gibbs equationsof mixing, in case of the presence of solutions, are required. If these data are notknown they need to be obtained by performing a thermodynamic assessment.This is usually done (and has been done in this study as well) according to theCALPHAD method including the critical review of all available data of interest(mixing enthalpies of the solutions, solidus and liquidus points etc.) followedby the optimization of the unknown data in order to obtain the best possiblefit between the experimental values and the calculated ones. In case of thefluoride and chloride systems assessed in this study, these unknown parametersare mostly the excess properties of the solutions and the thermodynamic data ofsome intermediate compounds. All the thermodynamic calculations presentedin this study have been performed using the FactSage software [14]. Figure 3.1shows an example of a T -x binary phase diagram optimized in this study. It isa LiF-NaF system and as the figure indicates, a very good agreement between

19

Figure 3.1: Binary phase diagram of the LiF-NaF system assessed in this work experimental data points by Holm [15]Phases in equlibrium: 1 - Liquid solution; 2 - LiF rich (Li,Na)F solid solution+ Liquid solution; 3 - LiF rich (Li,Na)F solid solution; 4 - LiF rich (Li,Na)Fsolid solution + NaF rich (Li,Na)F solid solution; 5 - NaF rich (Li,Na)F solidsolution + Liquid solution; 6 - NaF rich (Li,Na)F solid solution

the experimental data for solidus and liquidus measured by Holm [15] and ourcalculation has been found.

The LiF-NaF system is a simple eutectic system with a limited solubility inthe solid state in the LiF and NaF rich corners. It is evident that the solubility ofLiF in the matrix of NaF is larger than in the contrary case. This is explained bya smaller size of the Li+ cation which dissolves easier in the crystal sublattice ofa bigger Na+ cation. This trend has been confirmed by other fluoride systemsassessed in this work, especially the NaF-KF or KF-CsF systems which arediscussed further. The LiF-NaF system is taken as an example to demonstratewhich Gibbs functions are required in order to model the binary systems andhow the thermodynamic properties (heat capacity, enthalpy and entropy) arerelated to these functions.

To model any binary phase diagram it is necessary to first identify all theexisting phases. In case of the LiF-NaF system there are two pure compounds(LiF and NaF), also called end-members and they exist in the solid and liquidforms. In addition there are two solutions - the liquid solution and the solidsolution. These are created by mixing the two LiF and NaF end-members inthe liquid and solid state respectively. Figure 3.1 shows two solid solutions,however, this is the same solution described by a single Gibbs energy equation(created by mixing the same NaF and LiF end-members) which has discontinu-ity due to the immiscible region in the middle part of the phase diagram (region

20

4 in Figure 3.1).

Pure compounds - condensed phases

To describe the Gibbs energy equation of pure compounds as a function oftemperature it is necessary to know the enthalpy and entropy contributions aswritten in the equation below:

G(T ) = H(T ) T S(T ) (3.1)

It is usually difficult to obtain the enthalpy and entropy functions directly andtherefore Equation 3.1 can be written as a function of the standard enthalpyof formation fH

0(298), the standard absolute entropy S0(298), both referredto a standard state temperature at T = 298.15 K (in this text this value issimplified to 298 K) and the heat capacity function of temperature Cp(T ) asgiven in the equation below:

G(T ) = fH0(298) S0(298)T +

T

298

Cp(T )dT T

T

298

(

Cp(T )

T

)

dT (3.2)

Note that the above equation describes the Gibbs function for temperatureshigher than 298 K. However this temperature range is relevant when consider-ing the salt behaviour above the ambient temperature. If one needs to describethe Gibbs functions from absolute temperature, the fH

0(298) term in Equa-tion 3.2 must be replaced by the fH

0(0) term and since the absolute entropyat T=0 K is equal to zero, the S0(298) term is eliminated. Consequently thelower limits of the two integrals in Equation 3.2 are set to 0.

Equation 3.2 can be also written in an analytical form (in some cases theinput form to the FactSage software [14]), in which the Cp contribution is rep-resented by a polynomial function of T as it is shown in Equation 3.3. In thisequation a and b are constants.

G(T ) = fH0(298) S0(298)T +

i=n

aiTi + bT ln(T ) (3.3)

The standard enthalpy of any compound is equal to the reaction enthalpy ofthe compound formation from the pure elements in their standard states (stablephase at p = 100000 Pa). An example is shown for a case of LiF on the followingformation reaction:

T = 298 K : Li(crystal) +1

2F2(gas) LiF (crystal) (3.4)

The standard reaction enthalpy of Equation 3.4 is written as:

rH0LiF (298) = fH

0LiF (crystal)(298)H

0Li(crystal)(298)

1

2H0F2(gas)(298)

(3.5)

21

and because the H0Li(crystal)(298) and H0F2(gas)

(298) terms in Equation 3.5 are

zero by definition (this applies to all elements in their standard states), thisequation can be simplified to:

rH0LiF (298) = fH

0LiF (crystal)(298) (3.6)

The absolute entropy is derived from the low temperature heat capacityaccording to the 3rd law of thermodynamics as shown in the equation below:

S0(298) =

298

0

(

Cp(T )

T

)

dT (3.7)

If the Equation 3.2, and Equation 3.3 are known, the thermodynamic stabil-ity of the pure compound is described. However, each relation applies only to asingle phase. In other words, if one wants to study a compound that undergoesany phase transition it is necessary to know the Gibbs energy functions of bothphases. In case of pure LiF in Figure 3.1 there are two phases considered; thesolid phase and the liquid phase. The Gibbs energy equations for both phaseshave been calculated in this study and are reported in Figure 3.2. It is evidentthat at the temperatures lower than the melting point, the Gibbs function of thesolid phase is more negative than the Gibbs energy function of the liquid phaseand the LiF crystal is stable in this region. Above this temperature the situationis opposite and the liquid phase becomes stable. At the melting temperature thetwo functions cross and are equal according to Equation 3.8. At this point thethermodynamic equilibrium between the solid and the liquid phase is achieved.

T = Tfus : G(T )solid = G(T )liquid (3.8)

fH0(298), S0(298) and Cp(T ) are known for most of the end-members

considered in this study and thus the construction of the Gibbs equations ispossible according to Equation 3.2. However it very often happens that thesesets of data are not compatible and do not reproduce the transition points (e.g.melting points) exactly. In such cases it is possible to correct the fH

0(298),S0(298) data of the higher temperature phase based on the knowledge of thetransition temperature and its heat in order to make a constraint at the transi-tion point. Two following equations show the calculation of fH

0(298), S0(298)for a liquid phase using the knowledge of the thermodynamic data of the solidphase:

fH0liquid(298) = fH

0solid(298) + fusH

(

Tfus

298

Cp liquidsolid(T )dT

)

(3.9)

S0liquid = S0solid +

(

fusH

Tfus

)

(

Tfus

298

(

Cp liquidsolid(T )

T

)

dT

)

(3.10)

22

200 400 600 800 1000 1200 1400 1600

-740000

-720000

-700000

-680000

-660000

-640000

-620000

G(T)solid

G(T

) / J m

ol-1

T / K

G(T)liquid

Tfusion

= 1119 K

Figure 3.2: Calculated Gibbs energy equations for solid and liquid phases ofLiF.

where Tfus is the melting (or fusion) temperature, fusH is its heat and theCp liquidsolid(T ) term is the heat capacity difference between the liquid andsolid phases in a given temperature range.

Intermediate compounds

As mentioned in the previous paragraph, the thermodynamic data of all end-members considered in this study are known and have been taken from literature(the exact references are given Appendix 1). Unfortunately the knowledge of thethermodynamic data of the intermediate compounds is very rare and thereforethe unknown parameters had to be assessed by phase diagram optimization. Inprinciple the thermodynamic data which have been assessed are fH

0(298) andS0(298), while the heat capacity is estimated according to the Neumann-Kopprule which states that the heat capacity of any intermediate compound can beobtained as sum of proportional contributions of its end-members. As an exam-ple, the heat capacity of LiNa2Be2F7, which is one of the ternary compoundsfound in the LiF-NaF-BeF2 system, has been calculated using the relation be-low:

Cp(LiNa2Be2F7)(T ) = 1 Cp(LiF )(T ) + 2 Cp(NaF )(T ) + 2 Cp(BeF2)(T )(3.11)

23

Pure compounds - gaseous phases

Figure 3.1 shows only solid-liquid equilibria in the LiF-NaF binary system.To calculate such a diagram it is necessary to have thermodynamic data of thecondensed phases relevant to that system. However, one of the aims of thisstudy is to determine vapour pressures of the molten salt compositions whichare of interest for nuclear applications. For this reason it is required to have thethermodynamic data of the gaseous species that are formed above the solid orliquid phases. The Gibbs equations of gaseous species are calculated accordingto Equation 3.2 and the vapour pressure is calculated using the following set ofrelations (Equation 3.12- 3.16):

As an example let us assume the vaporization of the pure LiF liquid phaseinto the monomeric gaseous species as given in reaction below:

LiFliquid LiFgas (3.12)

The difference in the Gibbs energy between the reactant and the product isdefined as:

GLiF (gas)(T ) GLiF (liquid)(T ) = R T ln K (3.13)

where K is the equilibrium constant of the reaction and is defined as:

K =aLiF (gas)

aLiF (liquid)(3.14)

aLiF (gas) and aLiF (liquid) in Equation 3.14 are the activities of a given speciesin the gas phase and in the liquid phase respectively. Since the activity of theliquid phase of a pure compound in equilibrium is equal to 1 and the activity ofthe gas phase is equal to its partial pressure according to Equation 3.15, wherep0 is the standard pressure and is equal to 100000 Pa (1 bar), the final relationfor the vapour pressure calculation can be written as shown in Equation 3.16.

aLiF (gas) =pLiF (gas)

p0(3.15)

pLiF (gas) = p0 exp

(

(GLiF (gas)(T ) GLiF (liquid)(T ))

RT

)

(3.16)

The thermodynamic data of all compounds and their phases considered inthis work are listed in Appendix 1.

Binary solutions

The definition of the Gibbs Energy function for pure compounds is shown inEquation 3.2. In case of the binary solutions the Gibbs function is defined byEquation 3.17 as a weighted average of Gibbs energies of the pure componentsthat the solution consists of plus the mixing contribution of these end-members.

24

G(T ) = x1G1(T ) + x2G2(T ) + Gmixing(T ) (3.17)

The mixing contribution is basically distinguished into two parts, the ideal mix-ing contribution which is related to the configurational entropy and is definedas

Gideal mixing(T ) = x1RTlnx1 + x2RTlnx2 (3.18)

and the excess Gibbs contribution which is typical for the real systems (systemwithout any excess contributions are referred to as ideal systems). CombiningEquations 3.17 and 3.18 the total Gibbs function of a solution can be writtenas:

G(T ) = x1G1(T ) + x2G2(T ) + x1RTlnx1 + x2RTlnx2 + Gexcess (3.19)

Figure 3.3 shows the influence of the various contributions to the totalGibbs function, demonstrated for the (Li,Na)F liquid solution calculated forT = 1000 K. The graph is divided into two parts. In the upper part the smallenergy contributions, the mixing energies are showed. Since the mixing occursonly in the region between the end-members these mixing contribution (ideal orexcess) are always zero at the end-member compositions. In the lower part ofthe diagram a comparison between the the linear x1G1(T )+x2G2(T ) term fromEquation 3.17, the Gibbs function of the ideal solution (Equation 3.18) and theGibbs function of the real solution is depicted. The last curve corresponds tothe total Gibbs energy of the (Li,Na)F liquid solution and is highlighted by abold line.

It is important to note that in case the solution is not created between theend-members (e.g. the solid region in the LiF-PuF3 simple eutectic systemshown in Figure 5.13) logically there are no mixing contributions and the to-tal Gibbs energy of any composition of such two-phase system is equal to thex1G1(T ) + x2G2(T ) term.

Thermodynamic models for the excess Gibbs parametersof the binary solutions

Since it is very difficult to experimentally determine the excess Gibbs propertiesof the solutions, the optimization of these data is usually the main task in orderto assess phase diagrams. There are several thermodynamic models developedfor this purpose. Probably the most common is the Redlich-Kister model whichis defined as:

Gexcess = x1 x2

i=n

(x1 x2)i1 Li (3.20)

which is a function of the mole fractions (x1 and x2) and the excess Gibbsenergy coefficients (Li) that are in a polynomial form and can be a function oftemperature as given below:

25

0.0 0.2 0.4 0.6 0.8 1.0

-680000

-660000

-10000

0

x1G

1+x

2G

2+G

ideal

Gmixing

Gideal

G / J

mo

l-1

X NaF

Gexcess

x1G1+

x2G2

Gtotal

=x1G

1+x

2G

2+G

mixing

Figure 3.3: Calculated Gibbs energy equations for the (Li,Na)F liquid solutionat T=1000 K.

Ln = An + Bn T + Cn T lnT + Dn T2 + En T

3 +FnT

(3.21)

In case that i in Equation 3.20 is equal to 1 and Li is constant , the solutionis referred to as regular. Such solution is characterized by the excess Gibbsenergy minimum or maximum at x1 = x2 = 0.5 composition. In case of aregular solution the excess Gibbs energy is equal to the enthalpy of mixing withno excess entropy contribution. If this enthalpy of mixing posses of positivevalue there is a competition between an entropy of mixing term (ideal mixingterm) that produces a minimum in the Gibbs free energy at x=0.5 and theenthalpy term that has a maximum there. Thus at low temperatures there aretwo minima on the final Gibbs curve with maximum in between which resultsinto a phase separation. At high temperatures the ideal entropy term becomesdominant and the system is fully miscible. In general there is a temperaturewhere these two regions coalesce and is known as a critical point of the solution.In case of regular solution this point can be calculated according to the equationbelow:

Tc =

2R(3.22)

where is A coefficient from Equation 3.21.Another widely used formalism is the so-called classical polynomial model,

for which the excess Gibbs function is defined as:

26

Gexcess =n

i,j=1

Xi1 Xj2 Lij (3.23)

where Lij are the excess Gibbs energy parameters to be optimized and are ina polynomial form similarly to Equation 3.21. In this study this model hasbeen used to assess the excess properties of all solid solutions and for the liquiddescription of the LiF-BeF2-ZrF4-UF4 system. The obtained coefficient for bothsolutions are listed in Appendix 2.

In case of the NaF-RbF, NaF-CsF, LiF-KF, LiF-RbF and LiF-CsF binarysystems, there is no solid solubility reported. However in order to keep thethermodynamic data of the (Li,Na,K,Rb,Cs)F solid solution complete and toextrapolate this solution into higher order field (ternary, quaternary systemsetc.), these binary solutions had to be treated as systems with totally immisci-ble solid solubility. This was done by introducing relatively big arbitrary excessGibbs terms as shown in Appendix 2.

Modified Quasi-Chemical model

The modified quasi-chemical model proposed by Pelton and coworkers [16,17] has been used to optimize the excess Gibbs energy functions of most ofthe liquid solutions presented in this study. The parameters of this model arethe Gibbs energy changes gAB/X for the second nearest neighbor (SNN) pair-exchange reaction:

(AX A) + (B X B) = 2(AX B) gAB/X (3.24)

where A and B represent cations and X an anion which is in this study eitherF or Cl anion. For better understanding of the difference between the firstnearest neighbor and the second nearest neighbor, the reaction 3.24 is graph-ically shown in Figure 3.4 in a quadruplet approximation. Basically the FNNpairs are the closest cation-anion pairs, whereas the SNN pairs are the closestcation-cation pairs as indicated by the arrows. Since all of the systems studiedin this work always consisted of one type of anion (F or Cl anion), the pa-rameters to optimize were always related to the exchange reaction on the cationsublattice.

The gAB/X parameter for reaction 3.24 can be expanded as a polynomialsuch as

gAB/X = g0AB/X +

(i+j)1

gijAB/XiAB/X

jBA/X (3.25)

where g0AB/X and gijAB/X are composition independent coefficients (although

possibly temperature dependent) obtained from the optimization of the experi-mental data for binary AX BX solutions. The AB/X term is a compositionvariable and is defined as

27

Figure 3.4: Exchange reaction of the two different cations on the cation sublat-tice in the SNN approximation.

AB/X =

(

XAAXAA + XAB + XBB

)

(3.26)

where XAA, XAB and XBB represent the cation-cation pair mole fractions.In this model the definition of cation-cation coordination numbers ZAAB/XX ,

resp. ZBAB/XX is required. It is indeed true that the cation-cation coordinationnumbers differ with composition, however the chosen values correspond to thecomposition of maximum SNN short range ordering in the (A, B) X binarysubsystem [16] and therefore are composition independent. For example thedefinition of the ZKKLa/FF = 1/2Z

LaKLa/FF (case of the KF-LaF3 binary system)

corresponds to the maximum SNN short-range ordering at the K2LaF5 com-position. It is likely that at this point the excess Gibbs energy function hasits minimum and thus the studied system has here the lowest melting point.Since the quasi-chemical expression for the entropy is only approximate [16], itis not necessary that the coordination numbers correspond to the actual ones.In fact, sometimes the choice of the nonphysical values better represents thephase diagrams, because the error caused by the entropy approximation canbe partially compensated. However what is important is that the ratios ofZA,BAB/XX correspond to the composition of the maximum SNN short range or-

dering as discussed previously. The values of the cation-cation coordinationnumbers ZAAB/XX and Z

BAB/XX that have been used in this study are reported

in Table 3.1 for fluoride liquid solutions and in Table 3.2 for chloride liquidsolutions.

In order to keep the electroneutrality of the system the definition of theanion-anion coordination numbers is required. This is done according to Equa-tion 3.27 after the selection of the cation-cation coordination numbers is made.

qAZAAB/XX

+qB

ZBAB/XX=

qFZFAB/XX

+qF

ZFAB/XX(3.27)

qA, qB and qF are the absolute charges of various ions. For example in caseof the KF-LaF3 system where Z

KKLa/FF = 3, Z

LaKLa/FF = 6 and qK = 1,qLa = 3 and qF = 1, the F-F coordination number is equal to 2.4.

All the excess Gibbs parameters optimized in this study are reported in Ap-pendix 2 keeping the same notation as proposed by Chartrand and Pelton [18].

28

Table 3.1: Cation-Cation coordination numbers of the fluoride liquidsolutions assessed in this study

A B ZAAB/XX ZBAB/XX A B Z

AAB/XX Z

BAB/XX

Li+ Li+ 6 6 Li+ La3+ 2 6Na+ Na+ 6 6 Li+ Pu3+ 2 6K+ K+ 6 6 Na+ K+ 6 6Rb+ Rb+ 6 6 Na+ Rb+ 6 6Cs+ Cs+ 6 6 Na+ Cs+ 6 6Be2+ Be2+ 4.8 4.8 Na+ La3+ 2 6La3+ La3+ 6 6 Na+ Pu3+ 2 6Th4+ Th4+ 6 6 K+ Rb+ 6 6U4+ U4+ 6 6 K+ Cs+ 6 6Pu3+ Pu3+ 6 6 K+ La3+ 3 6Li+ Na+ 6 6 K+ Pu3+ 3 6Li+ K+ 6 6 Rb+ Cs+ 6 6Li+ Rb+ 6 6 Rb+ La3+ 2 6Li+ Cs+ 6 6 Rb+ Pu3+ 2 6Li+ Be2+ 3 6 Cs+ La3+ 6 9Na+ Be2+ 3 6 Cs+ Pu3+ 6 9Be2+ Pu3+ 4 6 La3+ Pu3+ 6 6

Table 3.2: Cation-Cation coordination numbers of the chloride liquidsolutions assessed in this study

A B ZAAB/XX ZBAB/XX

Na+ Na+ 6 6Mg2+ Mg2+ 6 6Na+ Mg2+ 3 6Na+ U4+ 3 6Na2+ Pu3+ 3 6Mg2+ U4+ 4 3Mg2+ Pu3+ 4 6U4+ Pu3+ 6 6

Thermodynamic origin of phase diagrams

Once the definition of the Gibbs energy-composition-temperature functions isknown for all relevant phases, the phase diagram can be calculated. Figure 3.5shows the construction of the LiF-NaF phase diagram based on the tangentmethod. The principle is indicated at four different temperatures. First graphat T = 1300 K, well above the NaF melting temperature (higher melting end-member), shows that the calculated Gibbs function of the liquid phase is alwaysmore negative than the one calculated for the solid phase. Therefore, by theprinciple that a system always seeks the state of minimum Gibbs energy, theliquid phase is stable within the whole composition range (xNaF = 0 1). Inthe second graph at T = 1200 K the two Gibbs functions cross in the NaF richpart of the phase diagram indicating sub-liquidus region. The determination

29

of the liquidus and solidus points is made by tangent method as shown in thefigure. P1 and Q1 are two points, where the tangent line (red line) touchesthe Gibbs functions of the liquid and solid phases, and correspond respectivelyto the liquidus and solidus point from the LiF-NaF phase diagram (very bot-tom graph in Figure 3.5). Third graph shows the Gibbs functions calculated atT = 1050 K. As it is seen from the figure, there are two intersections betweenthe two Gibbs functions. Therefore two tangent lines are constructed in orderto obtain two liquidus and two solidus points indicated by Q2, P

2 and P2, Q

2

points respectively. The last graph has been calculated for T = 800 K and showsthat the Gibbs energy function of the solid phase is more negative than the onefor the liquid phase. It thus indicates the sub-solidus region, meaning that noliquid phase is in equilibrium within the whole composition range. Howeverthere is a tangential line plotted on the Gibbs function of the solid phase. Thisis because there are two inflections on the Gibbs curve (it is not very obviousfrom the figure since the curvature is very broad, but the detailed calculationconfirms the inflections) indicating a miscibility gap of the solid solution. Thecompositions of the solid solution that are in equilibrium are indicated by theP3 and Q3 points.

Higher order systems approximations

After the binary phase diagram are assessed, the higher order systems can beextrapolated based on the knowledge of the binary excess Gibbs energy data.The way of extrapolating the higher order systems is a very important tool,because it is very difficult and time consuming to measure every ternary (orhigher) system. Already among the 10 fluorides considered in this study 120ternary (10!/3!7!) and 210 (10!/4!6!) quaternary systems are formed. Takinginto account the fact how many measurements are necessary in order to preciselydescribe even a very simple ternary phase diagram, the way of extrapolatingthese systems is sometimes the only possible choice.

There are several formalisms proposed, among which the Muggianu, Kohlerand Kohler/Toop formalism are most widely used. The first two are symmet-ric, whereas the Kohler/Toop formalism is asymmetric where one of the end-members is singled out. The use of a symmetric model in case an asymmetricmodel is more appropriate can give rise to errors. Graphical schemes of theexcess Gibbs energy approximation for a single ternary composition using threementioned approaches is shown in Figure 3.6.

As illustrated in the figure, the excess Gibbs energy of the ternary com-position x is calculated as a contribution of the excess Gibbs energies of thep, q and r compositions from the A-B, A-C and B-C binary subsystemsrespectivelly.

In this study two groups of symmetry have been established. The first oneconsisted of LiF, NaF, KF, RbF and CsF compounds in case of the fluoridesand NaCl in case of chloride systems, whereas BeF2, LaF3, ZrF4, UF4 and PuF3compounds in case of fluorides and MgCl2, UCl3 and PuCl3 compounds from

30

solid

G

G

liquid

2

`P

QP

2

2

Q

Q`2

G

/ J

mol-

1

-658000

-665000

-672000

-679000

Gliquid

Gsolid

Q3

3P

-620000

-630000

-640000

-650000

-660000

G

/ J

mol-

1

G / J

mol-

1

G

G

solid

liquid

Q

P3

3

-679000

-700000

-693000

-685000

Gsolid

Gliquid

G

/ J

mo

l

-693000

-700000

-707000

-714000

-1

1300

1200

1100

1000

900

800

700

600

T / K

0 0.40.2 0.6 0.8 0

PQ

QP

P

P

Q

Q

1

1

2

2

22` `

33

X (NaF)

Figure 3.5: LiF-NaF phase diagram compared to the Gibbs energy-composition

curves at four temperatures, illustrating the tangent construction.

31

Figure 3.6: Some graphical model for estimating the ternary thermodynamic

properties using the data of the binary subsystems.

32

the chloride systems belong to the other group of symmetry. Such distinguishingwas based on the fact, that the alkali halides form ionic species in the liquidsolutions while the compounds from the other group rather form molecularspecies. It has been actually observed that better approximation of the higherorder systems is achieved when these two groups of symmetry are considered.All higher order systems presented in this study have been extrapolated usingthe Kohler symmetric or Kohler/Toop asymmetric formalism.

After the higher order systems are extrapolated, in case that some experi-mental description is known and in case that the extrapolated phase diagramdeviates from these results, the correction can be done by introducing ternary(or higher) excess Gibbs parameters of the multi-component solutions. In thisstudy these parameters have been implemented in some of the systems in orderto best reproduce the experimentally determined liquidus temperatures.

The optimized ternary parameters obtained in this study are listed in Ap-pendix 2.

Ternary phase diagrams

As in case of the binary systems the sum of the mole fractions of the end-members in the ternary systems is unity (xA+xB +xC = 1). Thus there are twoindependent composition variables (e.g. xA = 1xB xC). An example of theternary phase diagram is shown in Figure 3.7. It is an isothermal representationof the NaCl-MgCl2-PuCl3 system calculated at T=800 K. The compositions atthe corners of the triangle correspond to the end-members and the edges arethe binary phase diagrams of the NaCl-MgCl2, NaCl-PuCl3 and MgCl2-PuCl3systems. The lines that are parallel to the NaCl-PuCl3 edge represent constantamount of MgCl2, while the lines parallel to the NaCl-MgCl2 and MgCl2-PuCl3edges represent constant amounts of PuCl3 and NaCl respectively. For examplethe point a corresponds to the composition of xNaCl = 0.2, xMgCl2 = 0.4 andxPuCl3 = 0.4. There are five equilibrium phase fields in the phase diagram.One contains single phase, labeled as B region, and is characterized by the(Na,Mg,Pu)Clx liquid solution. Three regions are characterized with two-phasefields, A, C and D, where the equilibrium between NaCl and liquid solution,MgCl2 and liquid solution and PuCl3 and liquid solution respectively is achieved.In these regions the dashed lines represent tie-lines which are the lines showingfor every point within the phase region the equlibria between the correspondingend-members and the definite composition of the liquid solution. For examplea sample with an overall composition b consists of pure PuCl3 and the liquidsolution of the c composition (xNaCl = 0.51, xMgCl2 = 0.27 and xPuCl3 =0.22). The relative proportion of these two phases is determined by the leverrule as shown below:

moles of liquid

moles of PuCl3=

bd

bc(3.28)

The last region (E) of the phase diagram from Figure 3.7 contains three phases

33

Figure 3.7: Isothermal NaCl-MgCl2-PuCl3 ternary phase diagram calculated at

T=800 K.

which are in the d, e and f corners of the E subtriangle. The phases inequlibriium are pure MgCl2 (f point), pure PuCl3 (d point) and the liquidsolution with the composition corresponding to the e point. To determinethe relative proportions of these three phases the same rule applies for thisE subtriangle as was discussed for the whole ternary system. Thus the pointa contains 17 mol% of MgCl2, 34 mol% of PuCl3 and 49 mol% of the liquidsolution with the xNaCl = 0.41, xMgCl2 = 0.47 and xPuCl3 = 0.12 composition.

Another widely used representation among the ternary phase diagrams isthe polythermal projection of the liquidus surfaces. An example of such a phasediagram is given in Figure 3.8 showing the assessed NaCl-MgCl2-UCl3 system.The color lines represent the liquidus isotherms and the field that is surroundedby these lines is the region of homogeneous liquid solution. Based on this plot aternary composition with the lowest melting point can be determined. Accord-ing to the Figure 3.8 this point corresponds to the lowest ternary eutectic E1at T=719 K.

The black lines with the arrows are the univariant lines (also known as Alke-

34

Figure 3.8: Liquidus projection of the NaCl-MgCl2-PuCl3 ternary phase dia-

gram.

Primary phase fields: A NaCl; B Na2MgCl4; C NaMgCl3; D MgCl2; E UCl3

made lines) and they meet at invariant equilibria which are in general of threekinds; ternary eutectic (E) (three arrows coming together), ternary peritectic(P) (one arrow entering, two arrows leaving) and ternary quasi-peritectic (U)(two arrows entering and one arrow leaving). In case of Figure 3.8 there are twoternary eutectics (E1 at T=719 K and E2 at T=720 K) and one quasi-peritectic(U at T=731 K). The univariant lines divide the phase diagram into several re-gions of different primary phase fields during crystallization. Figure 3.8 consistsof five phase fields with primary phases: NaCl (region (A)), Na2MgCl4 (B),NaMgCl3 (C), MgCl2 (D) and UCl3 (E).

Figure 3.8 contains one saddle point s (solid dot between E1 and E2 on theunivariant line) which is characterized by the maximum temperature along theE1E2 univariant line, but at the same time represents the minimum temperatureon the liquidus surface along the section between two solids (Na2MgCl4 (B) andUCl3 (E)) that are primary crystallization phases in the neighboring regions.

Another important feature that can be derived based on the knowledge ofthe liquidus projection of the ternary system is the crystallization path of anycomposition within the phase diagram. An example of the crystallization path

35

determination is shown in Figure 3.8. Let us consider the initial compositionof the liquid solution represented by point a (xNaCl = 0.21, xMgCl2 = 0.72and xUCl3 = 0.07). Since this point belongs to the primary phase field ofMgCl2, this compound will also be the first solid to precipitate upon the coolingand according to the phase diagram the first crystal will appear at T=916 K(between the 900 K and 925 K isotherm). During further cooling the liquid phasebecomes depleted in MgCl2, but the ratio NaCl/UCl3 in the liquid remainsconstant. Therefore the crystallization path in this temperature range is astraight line (red line with arrows in Figure 3.8) passing through the MgCl2end-member and the initial composition a. It must be noted that in case thata solid solution rather than the pure compound is formed, the crystallizationpath would not be a straight line in this region.

When the composition of the liquid reaches the univariant line in point bat T=867 K the UCl3 compound starts to precipitate. At this point the relativeproportions of solid MgCl2 and the liquid solution is defined by the lever ruleon the Dab tie-line according to:

moles of liquid

moles of MgCl2=

Da

ab(3.29)