New insights and coupled modelling of the structural and thermodynamic properties of the LiF-UF4 system

LiF-UF 4 is a key binary system for molten ﬂ uoride reactor technology, which has not been scrutinized as thor- oughly as the closely related LiF-ThF 4 system. The phase diagram equilibria in the system LiF-UF 4 are explored in this work with X-ray diffraction (XRD) and differential scanning calorimetry (DSC). The short-range ordering in the molten salt solution is moreover surveyed with Extended X-ray Absorption Fine Structure spectroscopy (EXAFS) and interpreted using a combination of standard ﬁ tting of the EXAFS data and Molecular Dynamics (MD) simulations with a Polarizable Ion Model (PIM) potential. The density, excess molar volume, thermal expansion, heat capacity, and enthalpy of mixing are extracted from the MD simulations across a range of temper- aturesandcompositions;thebehaviorisnon-ideal,withreasonablygoodagreementwiththeexperimentaldata. Also calculated is the distribution of heteropolyanions in the liquid solution, and modelled using the quasi-chemical formalism in the quadruplet approximation taking into account the existence of the single-shell complexes [UF 7 ] 3 − , [UF 8 ] 4 − , and the dimeric species [U 2 F 14 ] 6 − . Subjecting the optimization of the excess Gibbs energy parameters of the liquid solution to the constraints of the phase diagram data and local structure of the melt as derived from the EXAFS and coupled MD simulations, a CALPHAD-type assessment is proposed, linking structural and thermodynamic properties, with a rigorous physical description of the melt.

New insights and coupled modelling of the structural and thermodynamic properties of the LiF-UF 4 system

Introduction
The Molten Salt Reactor (MSR) is a type of nuclear reactor whose main characteristic is a fuel in the liquid state that also serves as the primary coolant: a stream of molten fluorides or chlorides. The reactor was originally conceived as a candidate engine to power aircraft in the Aircraft Reactor Experiment (ARE) [1], designed, built and operated by Oak Ridge National Laboratory (ORNL) in the 1950's. Later, the potential of such reactors as a civilian power source was recognized and demonstrated during the Molten Salt Reactor Experiment (MSRE), also in ORNL in the 1960's [2]. More recently, the Generation IV International Forum, a group of fourteen member countries pursuing research and development for the next generation of nuclear reactors, has selected the MSR as one of six key nuclear energy systems to replace the current fleet of Generation II Light Water Reactors [3].
The LiF-UF 4 system was a key component of the MSRE fuel ( 7 LiF-BeF 2 -ZrF 4 -UF 4 ) [4], and its phase diagram was investigated as part of the original research effort at ORNL by Barton et al. in 1958 [5]. Many years later, in 2010, a CALPHAD (Calculation of PHase Diagram) [6] thermodynamic model of the binary system was optimized based on the experimental data from ORNL using a modified quasi-chemical model in the quadruplet approximation to describe the liquid solution [7]. This system is also critically important in the proposed fuel of future reactors, such as 7 LiF -ThF 4 -233 UF 4 for the Molten Salt Fast Reactor (MSFR) [8], LiF -BeF 2 -ThF 4 -UF 4 for the liquid-fueled thorium molten salt reactor (TMSR-LF) [9], and the ThorCon reactor which aims to be a scale-up of the MSRE [10]. Despite this, there have been no more phase diagram data gathered since 1958 to compare with the original measurements, as it has been done extensively for other systems, e.g. LiF-ThF 4 [11].
This work gives new insights into the phase equilibria of this key system using Differential Scanning Calorimetry (DSC) combined with Xray Diffraction (XRD) measurements.
In a wider effort to understand the structure of molten (Li,U)F x salt and its relationship with macroscopic thermodynamic (and transport) properties which are highly relevant for reactor design and operation, in-situ high temperature Extended X-ray Absorption Fine Structure (EXAFS) spectroscopy measurements of the system are performed for the first time at high UF 4 content. They are furthermore interpreted with the help of Molecular Dynamics (MD) simulations, which have proved throughout several years already to be an invaluable tool for characterizing the thermo-physical and thermo-chemical properties of molten salts [12][13][14][15]. The structural information obtained from the EXAFS data, interpreted and extended to a wider range of temperatures and compositions using MD, is ultimately linked to the phase diagram equilibria and excess thermodynamic properties. Using both experimental and simulated data as input, a coupled structuralthermodynamic model is developed using an advanced modified quasi-chemical model in the quadruplet approximation, with a formalism similar to the recent assessment of the LiF -BeF 2 system [16].

Reagent preparation and handling
The purity of LiF (ultra-dry from Alfa Aesar, 0.9999 ± 0.0001 mass fraction purity) and UF 4 (International Bio-Analytical Industries, 0.9999 ± 0.0001 mass fraction purity) reported by the suppliers correlated well with X-ray diffraction (XRD) and Differential Scanning Calorimetry (DSC) tests. LiF has a white color while UF 4 is green, and both were handled in either powder or pressed pellet form. The experimental compositions reported hereafter were prepared by mixing either powder or pellet fragments of the pure salts in the required stoichiometric ratios. As fluoride salts are highly sensitive to water and air, handling and preparation of samples took place inside the dry atmosphere of an argon-filled glove box, where H 2 O and O 2 content were kept below 5 ppm.
The DSC heat flow signal for both LiF and UF 4 showed only one event assigned to the melting point, and no other thermal events that could be attributed to impurities. The measured onset temperatures, after correction for the effect of the heating rate, are in good agreement with the literature: (1118 ± 5 K) and (1306 ± 5 K), respectively, vs. 1121.3 K (LiF, [17]), and (1307.9 ± 3.0) K (UF 4 , [18]).

Synthesis
The samples whose X-ray diffraction patterns are shown in this work were prepared by grinding powder mixtures, and heating them above melting temperatures inside a closed stainless steel crucible with a nickel liner in a tubular furnace under argon flow, with slow cooling, typically 2 K⋅min −1 , to allow for a good re-crystallization. The specific conditions for each sample are given below in Table 1.

Powder X-ray diffraction
X-ray powder diffraction (XRD) data were collected at room temperature (T = 293 ± 5 K) using a PANalytical X'Pert PRO X-ray diffractometer and a Cu anode (0.4 mm × 12 mm line focus, 45 kV, 40 mA) by step scanning at a rate of 0.0104 o ⋅ s −1 in the range 10 o <2θ<120 o in a Bragg-Brentano configuration. The X-ray scattered intensities were measured with a real time multi strip (RTMS) detector (X'Celerator). The samples were measured inside a sealed sample holder, with kapton foil cover, maintaining the dry argon atmosphere of the glove box. Structural analysis was performed with the Rietveld and LeBail methods using the FullProf suite [19].

Differential scanning calorimetry
3D-heat flow DSC measurements were performed using a Setaram Multi-Detector HTC module of the 96 Line calorimeter under argon flow at a pressure of (0.10 ± 0.005 MPa). All samples were placed inside a nickel liner and encapsulated for the calorimetric measurements inside a stainless steel crucible closed with a screwed bolt as described in [20] to avoid vaporization at high temperatures. All measurement programs started with one heating cycle reaching~1398 K and held at that temperature for 300 s (i.e. around 90 K above the fusion temperature of UF 4 as measured at 10 K⋅min −1 heating rate) to ensure complete mixing of the end-members and attainment of the equilibrium state. In general, this first cycle was followed by three successive heating cycles with a heating rate ranging between 4 and 10 K⋅min −1 , and 20-15-10-5 K⋅min −1 cooling rates.
A series of interconnected S-types thermocouples were used to record the sample temperature throughout the experiments. The temperature on the heating ramp was calibrated by measuring the melting points of standard high purity metals (In, Sn, Pb, Al, Ag, Au), following the procedure described in [21,22], thereby ensuring the measured temperatures can be translated to the International Temperature Scale (ITS-90). The temperature on the cooling ramp was obtained by extrapolation to 0 K⋅min −1 cooling rate. The melting temperature of pure compounds and transition temperatures of mixtures were derived on the heating ramp as the onset temperature using tangential analysis of the recorded heat flow, while the liquidus temperature of mixtures was taken as the peak extremum of the last thermal event as recommended in [23]. The data measured on the cooling ramp were not retained for the phase diagram optimization due to the occurrence of supercooling effects, but were used to help data interpretation and identification of transition events. The uncertainty on the measured temperatures is estimated to be ± 5 K for the pure compounds and ± 10 K for mixtures.

High-temperature EXAFS measurements
EXAFS measurements were performed at the INE beamline [24] of the KARA synchrotron facility (Karlsruhe, Germany), with 2.5 GeV and 150-170 mA as operating conditions in the storage ring. The beamline uses a Ge(422) double-crystal monochromator (DCM). Rh-coated mirrors collimate and focus the beam with spot size 300 μm × 500 μm at the sample position. Samples were probed at the U L 3 edge (17.166 keV), scanning from~17.14 to~17.77 keV. Transmission and fluorescence yield detection mode (recording the U-L α fluorescence line by two silicon drift detectors) were applied simultaneously.
A dedicated experimental set-up, described in detail in [25], designed and built to operate at the INE beamline was used for the measurements. The set-up consists of a purpose-designed furnace inside a custom-made glovebox filled with nitrogen atmosphere. The samples  (8-20 mg) were prepared in the inert atmosphere of a purified-argon glovebox by mixing and grinding stoichiometric amounts of LiF and UF 4 end-members, and then pressing pellets of thickness less than 100 μm by applying a pressure of 10 tons⋅cm −2 . The prepared pellets were sealed in a pre-dried boron nitride containment cell and loaded into the furnace chamber which was evacuated down to~2⋅10 −5 mbar to avoid reaction of the salts with residual oxygen or water. The EXAFS data were collected~50 K above liquidus temperature (as calculated from the CALPHAD model of Beneš et al. [7]). Short scans were made during the heating ramp to detect the melting of the material. The temperature was ramped up to the melting point of LiF and held for about 15 min to ensure complete melting and homogenization. The temperature was subsequently adjusted to a set value~50 K above liquidus. In addition, an equilibration time of~15-30 min was employed at the set temperature before collecting the data to ensure the signal had stabilized.
Each scan took close to 30 min, and three to four scans were accumulated to be averaged. A step size of 0.8 eV was used in the XANES region.
The energy E 0 of the edge absorption threshold position was identified as the first node of the second derivative of the signal. Prior to averaging, the spectra were aligned with the XANES spectrum of a reference yttrium (K edge = 17.0384 keV) foil, located between the second and third ionization chambers and measured concurrently with the sample. EXAFS data were collected up to~12.5 Å, and were Fourier transformed using the Hanning window over the k-range 3-9 Å −1 (dk = 2). Data treatment (normalization and extraction) of the raw XAS data was done with ATHENA software [26], version 9.25.

Molecular dynamics simulations
MD simulations were performed for all compositions measured by EXAFS at the corresponding experimental temperatures, i.e. 50 K above the liquidus equilibrium. In addition, the entire composition range was studied in intervals of 0.10 X(UF 4 ), at temperatures in the 900-1400 K range ( Table 3). The form of the potential used for the study of this molten salt system is the Polarizable Ion Model (PIM) with the general form suggested by Salanne et al. [27]. It has been chosen because it has already shown its usefulness in the study of several molten salt systems such as as alkali fluoride mixtures [27], LiF-BeF 2 [15,28], AF-ZrF 4 (A = Li, Na, K) [29], and LiF-ThF 4 [30]. The potential has four contributions with functional forms given in Eq. 1 to 5: charge-charge (Eq. 1), dispersion (Eq. 2), overlap repulsion (Eq.4) and polarization (Eq.5).
• Charge-charge: where q denotes the ionic formal charges.
• Dispersion: where C ij 6 (r ij ) is the dipole-dipole dispersion coefficient and C ij 8 (r ij ) is the dipole-quadrupole dispersion coefficient, while f ij 6 (r ij ) and f ij 8 (r ij ) are Tang-Toennies dispersion damping functions; they are short-range corrections to the asymptotic multipole expansion of dispersions [31]: This work only consider dipoles and quadrupoles.
• Overlap repulsion Here A ij and a ij are fitting parameters.
• Polarization In the equation above, T α (1) is the charge-dipole interaction tensor, T αβ (2) is the dipole-dipole interaction tensor, α i is the polarizability of ion i, and μ i is the set of dipoles, while g ij (r ij ) is a damping function similar to Eq. (6): The parameters were derived in a semi-classical approach from ab initio calculations by Dewan [30] and validated by comparing the data from simulations with experimental data on the phase diagram, density, viscosity, electrical conductivity, thermal conductivity, and heat capacity [30]. For completeness they are listed in Table 2: The systems were equilibrated for 500 ps in the NPT ensemble at 0 GPa and the corresponding temperature 50 K above the liquidus (Table 8), from which the equilibrium volume was taken. This was followed by a 100 ps equilibration and finally a 500 ps production run in the NVT ensemble at the same temperature. Time steps in all runs were set to 0.5 fs, while the relaxation time for both the Nosé-Hoover thermostat and barostat (for the NPT run) was set to 10 ps. The cubic simulation cell contained 600-800 ions in periodic boundary conditions. Cut-offs for the real space part of the Ewald sum and shortrange potential were both set to half the length of the cell. Simulations at higher temperatures and different compositions were also performed; they are summarized in Table 3. In this case, the NPT run was 500 ps, and the NVT production run 500 ps to 2.5 ns.

Thermodynamic modelling
Optimizations of the thermodynamic model for the LiF-UF 4 system was done according to the CALPHAD (CALculation of PHase Diagram) method [6] as implemented in the Factsage software [32]. To carry out such an optimization, the identity of the phases present in the system of interest must be known, as well as their respective Gibbs energy functions.

Pure compounds
The Gibbs energy function of a pure compound is given by: where Δ f H m o (298) is the standard enthalpy of formation, S m o (298) is the standard absolute entropy, both evaluated at a reference temperature, in this case 298.15 K (throughout this work 298 will be understood to mean 298.15 K for simplicity), and C p, m is the isobaric heat capacity expressed as a polynomial: with more terms added if necessary. In this work, the Neumann-Kopp rule [33] was used to approximate heat capacities of intermediate compounds in the absence of experimental data. The thermodynamic data for all compounds in this study are listed in Table 4. The data for both solid and liquid LiF and UF 4 were taken from [17,34], respectively. The standard enthalpy of formation and standard entropy at 298.15 K of the intermediate compounds were optimized to closely match phase equilibrium data.

Liquid solution
All excess Gibbs energy terms of the liquid solution presented here have been modelled using an advanced modified quasi-chemical model akin to the one recently reported for the LiF-BeF 2 system [16]. The modified quasi-chemical model proposed by Pelton et al. [35] is particularly well adapted to describe ionic liquids such as in the present system, as it allows to select the composition of maximum short-range ordering (SRO) by varying the ratio between the cation-cation coordination numbers Z A AB/FF and Z B AB/FF (fluorine is in this case the only anion present). The quadruplet approximation assumes a quadruplet, composed of two anions and two cations, to be the basic unit in liquid solution, and the excess parameters to be optimized are those related to the following second-nearest neighbor (SNN) exchange reaction: where the fluoride anions are represented by F, and A and B denote the cations. Δg AB/F is the Gibbs energy change associated with the SNN exchange reaction, and has the following form: where Δg AB/F o and g AB/F ij are coefficients which may or may not be temperature-dependent, but which are independent of composition.
The dependence on composition is given by the χ AB/F terms defined as: where X AA , X BB and X AB represent cation-cation pair mole fractions. The anion coordination number is finally fixed by conservation of charge in the quadruplet: where q i are the charges of the different ions, and Z F AB/FF is the anionanion coordination number, in this case fluorine-fluorine.
Despite its usefulness, the thermodynamic model just outlined does not account for the formation of molecular species or heteropolyanions in the melt. As will be discussed at length in the following sections, (Li, U)F x is not a solution in which cations and anions are completely dissociated. UF 4 is a Lewis acid and accepts fluorine anions from LiF, a Lewis Table 2 Parameter values for LiF-UF 4 PIM potential, with values in atomic units [30].
The polarizabilities of F − and U 4+ were set to 7.8935 au and 5.8537 au, respectively. Li + is considered to be non-polarizable.
b Not defined in [30], set arbitrarily. Table 3 Simulation conditions.  Compound  base. The solution, as UF 4 is added to LiF, is formed by discrete coordination complexes which link to each other as soon as their number density is high enough, forming dimers, trimers, and 'polymers' (see Fig. 10a, b). In order to capture this structural evolution and provide a more accurate description of the chemical speciation in the melt, a coupled structuralthermodynamic model comparable to the one recently reported for the LiF-BeF 2 system [16] was adopted. The key distinction made by Smith et al. [16], was to introduce quadruplets which not only include Be 2+ , but also Be 2 4+ , Be 3 6+ , assigning them coordination environments 4, 7, and 10, respectively. That is, the authors effectively included monomers, dimers, and trimers, choosing suitable compositions of maximum shortrange ordering for each one. In this work, two distinct cations were taken into account, with coordination numbers 7  . The cation-cation coordination numbers, shown in Table 5, were chosen to reflect the compositions of maximum SRO in the neighbordhood of X(UF 4 ) = 0.20 (Li 4 UF 8 ), and X(UF 4 ) = 0.25 (Li 3 UF 7 , "Li 6 U 2 F 14 ").
The choice of assigning every species with two or more bridged U 4+ centers to the dimer distribution was motivated by the need to keep fitting parameters from being too numerous to have a practical model, while still retaining a rigorous structural description. In this regard, the need to reflect more than one coordination number in the first shell surrounding U 4+ , which is such a salient feature of the (Li,U)F x melt, motivated the inclusion of two distinct monomers. Ultimately, pure UF 4 (l) is modelled as a solution of dimers. To do so, the reactions were constrained by the following Gibbs energy expressions (respectively, Eq. 13, 14): The value of 150,000 J ⋅ mol −1 is an arbitrary term to destabilize the monomers, insofar as it allows to reproduce the melting point (1307.8 K vs. (1307.9 ± 3.0) K [18]) and the enthalpy of fusion of UF 4 (45 kJ⋅mol −1 vs. 46.986 kJ⋅mol −1 [36]).
In the modified quasi-chemical model, interpolation to higher order systems is either symmetric or asymmetric, the choice depending on the similarity of the components between each other in a sublattice [37]. In the (Li,U)F x solution, the uranium cations are taken to be symmetric with respect to each other, while the smaller, monovalent, non-polarizable Li + is taken to be the asymmetric component.
Note that the denominator ∑ A ∑ B X AB/F2 adds to 1 in the {LiF + "UF 4 "} system.
Having established the composition dependence, the optimized excess Gibbs energy parameters of the binary liquid solution in the LiF-UF 4 system are shown in Eq. 16-18. The parameters were optimized based on the complex anion distribution as calculated with MD (see Fig. 15a, b) and phase diagram equilibria points of the liquidus (see Fig. 14). Δg

Brief review of literature data on the LiF-UF 4 system
Barton et al. [5] was the first to produce a sketch of the LiF-UF 4 phase diagram in 1958, shown in Fig. 1. The authors used a combination of i) thermal analysis, namely examination of cooling curves, ii) quenching of samples after equilibration, iii) differential thermal analysis, and iv) visual observation methods coupled with XRD. The authors identified three incongruently melting compounds: Li 4 UF 8 (T peritectic = 773 K), Li 7 U 6 F 31 (T peritectic = 883 K), LiU 4 F 17 (T peritectic = 1048 K) and a single eutectic at T = 763 K, X(UF 4 ) = 0.27. The features of the diagram are summarized in Table 6. Besides the stable phases, a meta-stable, so-called "X-phase" was detected by them and hypothesized to be Li 3 UF 7 .
A few years later Weaver et al. [38] studied the LiF-ThF 4 -UF 4 system and reported no ternary compounds but four solid solutions, amongst which was Li 3 (Th,U)F 7 . In 2010, the binary system was optimized by Beneš et al. [7] based on the experimental data from Barton et al. [5] using a modified quasi-chemical model in the quadruplet Barton et al. [5] reported quite a narrow range of stability for Li 4 UF 8 , i.e. from 743 K to 773 K (Fig. 1). Our attempts to quench a pure sample of composition Li 4 UF 8 were unsuccessful. Nevertheless, it was found in combination with LiUF 5 and UF 3 impurity in an attempt to isolate Li 3 UF 7 ; Li 4 UF 8 has orthorhombic symmetry and belongs to space group Pnma as identified by Brunton [39]. The diffractogram of this three-phase mixture with its LeBail refinement is shown in Fig. 2.
In another synthesis attempt, at composition X(UF 4 ) = 0.123 (diffractogram shown in Fig. 3), Li 4 UF 8 was not observed anymore, in agreement with the phase equilibria reported by Barton et al. [5].

Li 3 UF 7
Upon quenching samples with compositions ranging from X (UF 4 ) = 0.2 to 0.32 from above the solidus temperature, Barton et al. [5] observed a crystalline phase with a diffraction pattern they could not match with the established phases in the system. The authors simply designated it as X-phase and concluded that it was metastable, since it formed only during certain cooling conditions. In particular, it formed when the mass of the samples was large, but not when optimal quenching conditions (small masses) were used. They suggested 3LiF⋅UF 4 to be the stoichiometry of the X-phase. As mentioned above, an attempt to synthesize the Li 3 UF 7 phase in this work resulted in the quenching of the high temperature phase Li 4 UF 8 along with LiUF 5 , as well as a UF 3 impurity, probably due to reduction from the nickel liner. Yet in an attempt to ascertain whether or not Li 4 UF 8 is stable down to room temperature, LiUF 5 could be identified as expected, but interestingly, the other crystalline phase belonged to the same space group as one of the known phases of Li 3 ThF 7 [40], P4/ncc (Fig. 3). Thus the hypothesis that Li 3 UF 7 was the identity of the X-phase appears to be correct, as well as its metastability given the absence of the line compound at the composition where it should have formed, X(UF 4 ) = 0.25 (Fig. 2).

LiUF 5
Barton et al. [5] reported the line compound Li 7 U 6 F 31 to be stable, guessing the stoichiometry based on the existence of Na 7 U 6 F 31 and K 7 U 6 F 31 . Discrepancies between the density obtained from the mass of two formula units and the proposed cell parameters [41], and that obtained from measurements raised doubts about the validity of the 7:6 stoichiometry, however. The mismatch between the crystal sytem and space group of the putative phase Li 7 U 6 F 31 (tetragonal, I4 1 /a) and Standard uncertainties u are u(X(UF 4 ))) = 0.05. b Global average of the experimental runs appearing in Table 6. A 7 U 6 F 31 (A = Na, K) (trigonal, R3) raised further concerns. Addressing these doubts, Brunton [42] later showed that the correct formula is LiUF 5 . More recently Yeon et al. also grew LiUF 5 crystals in a hydrothermal environment [43]. In this work, a sample of high purity LiUF 5 (space group I4 1 /a) could be crystallized from a melt with composition X (UF 4 ) = 0.5 (Fig. 4). LiUF 5 was thus included in the thermodynamic model and it is recommended that molten salt databases use this compound rather than Li 7 U 6 F 31 .

LiU 4 F 17
No crystal structure determination could be found in the literature for either LiU 4 F 17 or LiTh 4 F 17 , and there were no thermal-analysis data collected by Barton et al. [5] in the vicinity of X(UF 4 ) = 0.8. However, the calorimetric measurements reported in the LiF-ThF 4 system [11] support the existence of such a phase, as do the DSC data collected in this work, listed in Table 6. Furthermore, Cousson and Pages [44] were able to prepare crystals of LiAn 4 F 17 (An = Th, U), of tetragonal  symmetry, and narrowed down the possible space groups of the compounds to three: I4/m, I4, or I4. Unfortunately LiU 4 F 17 could not be isolated as a pure phase material in the present work, but a sample with composition X(UF 4 ) = 0.80 yielded a phase which could not be attributed to either LiUF 5 (which also precipitated in the sample), or UF 4 , as would be the case if LiU 4 F 17 did not exist. With the aid of a LeBail refinement, it could be established that amongst the space groups suggested by Cousson and Pages, I4 is the most likely one, as it resulted in the best fit to the data, shown in Fig. 5. Note that there is a third phase in the refinement, again identified as UF 3 .

DSC measurements
The equilibria data in LiF-UF 4 were investigated in this work with DSC, with good agreement with the equilibria reported by Barton et al. [5]. The invariant equilibria as reported by the authors is compared to those calculated and measured in the present work, Table 6. The calorimetric measurements are presented in Table 7, and overlayed with the calculated phase diagram in Fig. 14 (▲, red). The local structure characteristics of molten (Li,U)F x salt were studied as a function of composition with three samples with increasing UF 4 content: X(UF 4 ) = 0.25, 0.50, 0.67. Their k 2 χ(k) spectra are shown in Figs. 6a-8a, accompanied by the corresponding Fourier transform moduli in Figs. 6b-8b. In all figures the experimental data are compared with the results obtained from our MD simulations (red). These were computed by using the Cartesian coordinates of the ions in the NVT production runs as input for the FEFF8.40 code [45] and averaging over2 5,000 configurations. The resulting EXAFS signal could then be directly compared to the experimental one. Additionally, fits were calculated using the standard EXAFS Eq. [46] without cumulants (blue). Four parameters were refined during the fitting process with the standard EXAFS equation: the energy shift from the L 3 edge (ΔE 0 ), Debye-Waller factor (σ 2 ), the expected U\ \F distance E[R U−F ], and the coordination number (CN). They are listed in Table 8. Even though fitting of the EXAFS equation is routinely applied to liquid systems, it assumes a Gaussian distribution of interionic distances between equivalent neighbors and the absorbing central atom which does not reflect distributions in actual liquids, especially at high temperatures, where thermal disorder and anharmonicity start to play a major role [47]. The actual radial distribution functions (denoted as g(r) or RDF) can, for instance, be obtained from neutron diffraction data or tallied from a large number of observations so as to capture thermal disorder and anharmonicity, as in MD. An example, at the composition X (UF 4 ) = 0.25, is shown in Fig. 9, where two peaks corresponding to the first two U\ \F coordination shells are shown. A fluoride ion can be   defined to belong to the first coordination shell of U 4+ when the U\ \F distance is less than R cutoff , i.e. the first minimum of the U\ \F RDF (marked by the red line). The peak is skewed to the right, such that the most probable distance (maximum of the first peak) and expected bond length within the first shell, given by: although close, do not coincide, a feature which cannot possibly be captured by a Gaussian distribution. Notwithstanding, it can be seen that the tail on the right is thin and comes close to zero, such that the peak can be reasonably approximated by a bell curve. In contrast, the same is not true for the second peak visible in the RDF, which has a fat tail on the right, and a bell curve would surely make a poor fit of it. For that reason, the fits included here are only for the first coordination shell, and are intended as an approximation to gauge the MD results.

Structural characteristics of the first coordination shell
The evolution of the average coordination around U 4+ and the U\ \F interionic distance obtained by both methods is listed in Table 8. As already mentioned, an illustration of the tabulated most probable, expected, and bond cutoff lengths of the MD simulations is shown in Fig. 9. The agreement between both sets of data is good. The coordination number distribution which can be derived from the MD simulations (listed in Table 10) is dominated by 7, 8, and 9-coordinated U 4+ , resulting in an average coordination between 7 and 8. This is consistent with the coordination environment of U(IV) fluorocomplexes in the solid state [48] as well as the 7 and 8-coordinations which have been observed by absorption spectroscopy in U(IV)-containing FLiNaK and FLiBE melts by Toth [49]. Most [50], which also result in an average CN between 7 and 8 ( Table 8).
As for bond lengths, Bessada et al. [50] studied the average U\ \F distances as a function of the coordination number using MD simulations   . From the Fourier transform moduli of the EXAFS data at compositions X(UF 4 ) = 0.25 and 0.67, it seems that the most probable bond length is slightly underestimated in the MD calculations. In general, the polarizability of species, and thus the potential itself, can change as a function of composition [52], and this underestimation could perhaps be corrected by adjusting the polarizability for every composition. Nevertheless, given the thorough validation of the potential by Dewan [30], and the good results it has also produced with the EXAFS spectra collected by Bessada et al. [50], the results are satisfactory.
It is also instructive to compare with simulations of LiF-ThF 4 melts at several compositions [14,25,50,53,54]. The results of these different authors are summarized in Table 9. Even if the most probable actinidefluoride distance is very similar in both binary systems, the actinide contraction effect is evident in the bond cutoff distances, as max[R U −F ] < max [R Th−F ] at all compositions. Similarly one can observe that, Another interesting feature is that the average U\ \F distance either shortens or remains the same in molten (Li,U)F x when compared to the distance in the known solid phases (see Section 6.1): 2.34(11) 1 Å in LiUF 5 , 2.29(6) 2 Å in Li 4 UF 8 and 2.28(2) 3 Å in UF 4 . Dai et al. [54] observed a similar Th\ \F shortening in molten ThF 4 compared to ThF 4 (cr), although the authors incorrectly interpreted it as an expansion of  Table 8 Structural information of the first fluoride coordination shell around U 4+ in the (Li,U)F x solution as calculated in this work, 50 K above the liquidus line, compared to data by Bessada et al. [50] and Ocádiz-Flores et al. [51]. CN is the coordination number, σ 2 is the Debye-Waller factor, ΔE is the energy shift from the L 3 edge, R f is the goodness of fit. Standard deviations are given in parentheses.

Coordination number
Bond length EXAFS fitting Most probable distance, b bond cut-off = maximum U\ \F distance, c expected value (Eq. 19). Fig. 9 illustrates how these distances differ. 1 Averaged from the crystallographic data in [43]. 2 Averaged from the crystallographic data in [39]. 3 Averaged from the crystallographic data in [55].
the Th 4+ coordination cage upon melting. This was because they incorrectly identified a shorter bond length of 2.087 Å as the average Th\ \F distance in ThF 4 (cr) when in fact this distance corresponds to ThF 4 (g) [56]. Liu et al. [53] identified a strenghtening of the local structure upon melting by comparing the bond length in their MD simulations with a sum of the Th 4+ and F − crystal radii as tabulated by Shannon [57]: r Th−F = 2.36 Å. Again, a better approach would be to look at the average distances in ThF 4 (cr) as measured experimentally: 2.30(1) 4 Å, 2.324(19) 5 Å, and 2.32(3) 6 Å. In the aforementioned bonding analysis per CN done by Bessada et al. [50], it is clear that this strengthening of the local structure is allowed by the reduced repulsion between fluorides in the first shell as the CN decreases, and so it does from solid to liquid. Experimental [58,59] and computational [60][61][62][63] results on alkali halides reveal the same behavior. A decreased shielding of the 2 nd shell, which expands and becomes less populated, could also contribute to these changes in interionic distances [63].

Medium-range ordering
In addition to providing information on the coordination environment of the U species, the MD simulations have the benefit of giving detailed information on the medium-range structure. Two uranium ions are considered fluoride-bridged when the distance between them is less than 2 ⋅ R U−F, cutoff and less than the first minimum in the U\ \U RDF. As the UF 4 concentration increases, the number of fluoride bridges increases as well. The bridges identified consisted of 1 F − (corner-sharing), 2 F − (edge-sharing), or 3 F − (face-sharing), with corner-sharing being the dominant bridging mechanism. Dimers and trimers start to appear until a 'polymerized network' is formed, in which all the U cations are connected by bridging fluorides. This evolution is shown in Table 11 and plotted at 1121 K and 1400 K in Fig. 10a, b. The concentration of both isolated coordination complexes and dimers decrease monotonically while the fraction of polymerized species rapidly increases; trimers reach a maximum at around X(UF 4 ) = 0.2, accounting for less than 20% of the species. The speciation is quite insensitive to temperature, with the polymer fraction increasing only slightly slower with UF 4 addition at T = 1400 K.
Network-like behavior has also been observed in MD simulations of LiF-BeF 2 [15], LiF-ZrF 4 [29], LiF-ThF 4 [53,54], LiF-BeF 2 -ThF 4 [53], and LiF-ThF 4 -UF 4 [50]. From the cage-out correlation function computed in some of those studies, it seems that the fragility of the coordination environments (as measured by their lifetimes) from lowest to highest is LiF-BeF 2 > LiF-ZrF 4 > LiF-ThF 4 . This has implications on the properties at the macroscopic scale, e.g. the viscosity can change around 7 orders of magnitude from LiF to BeF 2 at a given temperature [64], while it only varies around one order of magnitude from LiF to ThF 4 [65], as it does from LiF to UF 4 [66]. Molten LiF-UF 4 is thus expected to have a similar fragility to LiF-ThF 4 , as characterized by the cage-out correlation function.
d Other compositions were studied as well by the authors, but the maximum of the RDF. was found to be insensitive to the ThF 4 concentration.

. Excess density and molar volume
Relating the excess properties of molten salts to their structural properties is one of the motivations of the present work. Fig. 11a shows the comparison between density isotherms interpolated from the fitting equations to experimental data, given by Klimenkov et al. [67], and those calculated via MD in this work, in the 1000-1400 K range (in some cases the densities are extrapolated beyond the experimentally measured range). Superposed to these data are the experimental points by Blanke et al. [68] and Porter and Meaker [69], both at 1073 K. The agreement is quite good, with a slight overestimation of the density of pure UF 4 (l). The inset in Fig. 11a shows the relative excess molar volume, i.e. (V m, real − V m, ideal )/V m, ideal , calculated from the density data shown in Fig. 11a. The volumes of the end-members to compute the ideal volume of mixtures was calculated from the equations of Klimenkov et al. for the three studies in the literature.
The MD predicts a positive excess of the molar volume, growing with increasing temperature, except in a very limited region at very high LiF content for the supercooled liquid at 1000 K. The excess deduced from Porter and Meaker [69] is also negative at high LiF content, while that from Blanke et al. [68] is positive throughout the reported compositions. In both cases the linear dependences of real molar volumes with composition (not shown) indicate that the behavior is not far from ideality [34]. Finally, the excess from Klimenkov et al. [67] is mostly positive except at high UF 4 content in the case of undercooled solution at T = 1000, 1121 K. As pointed out by the authors, positive deviations from ideality indicate interaction of the components, and they attributed the maximum in the 20 to 30 mol% region (for an isotherm they examined at 1270 K) to the formation of stable [UF 7 ] 3− complexes. As was discussed before (Section 6.2), the first coordination shell may even contract upon melting, so it does not contribute to free volume. Instead, the 2nd (and higher order) shells expand and have more voids, i.e., coordination complexes are farther apart from each other in the liquid than in the solid, and even more so in the mixtures than in the pure liquids, as the  Table 11. positive excess volume reveals. This is probably due to the solvation of Li + , which is nevertheless small enough to allow extended network formation. Indeed, in the 20 to 30 mol% region the degree of polymerization rapidly increases, reaching a fraction of about 0.9 by 30 mol% (see Fig. 10a, b).
The thermal expansion (shown in the Electronic Supporting Information, ESI), calculated from the density, showed a linear dependence in temperature, and the expansion decreases as a function of UF 4 content. Network formation is likely to account for this, since there is a greater bond strength between neighboring U 4+ ions. The fits of the linear variations with temperature are listed in the ESI.

Heat capacity
Enthalpies were extracted directly from the ensemble averages of the potential energy of 0.5 ns NPT production runs at several temperatures: 900 K, 1000 K, 1121 K, 1200 K, 1300 K, and 1400 K. For every composition studied, a linear evolution of the molar enthalpy vs. temperature was obtained (see ESI). Taking linear fits of the molar enthalpies, the heat capacity could then be calculated from: The heat capacities of the end-members are very well reproduced: 65.9 vs. 64.183 [17] J⋅mol −1 ⋅K −1 (LiF) and 173.3 vs. 174.4 [34] J⋅mol −1 ⋅K −1 (UF 4 ). The heat capacity as a function of composition as calculated via MD is compared to the ideal heat capacity. Fig. 12a and b show that the heat capacity extracted from MD simulations has small deviations from additivity: much like the density, the heat capacity of the mixtures is close to ideal. For an industrial application setting this is convenient, since a reliable estimate can easily be made for both properties.

Mixing enthalpy, entropy and Gibbs energy
Plotted in Fig. 13 are the enthalpies of mixing at different temperatures (1000-1400 K) extracted from the MD simulations. Although the magnitude is likely overestimated, the negative excess at all compositions and position of the minima near X(UF 4 ) = 0.3 are reproduced at all temperatures. The Gibbs energies of mixing display similar trends to the mixing enthalpies, as the mixing entropies also contribute to favorable mixing (see ESI). The shape of the mixing entropy curve (ESI) in (Li, U)F x as calculated with the structural-thermodynamic model is somewhat closer to ideal mixing entropy than that of (Li,Th)F x , yet with significant asymmetry and an inflection point near X(UF 4 ) = 0.2 which corresponds to the strong SRO evidenced by the rapidly rising 'polymer' fraction (see Fig. 10b).
Several calorimetric measurements reveal that the enthalpy of mixing in binary molten salt systems is usually negative (LiF-BeF 2 being a notable exception, with an S-shaped curve [71]) [11,70,[72][73][74]. This is also the case for the LiF-UF 4 system according to our MD simulations, coupled structural-thermodynamic model, and the optimization previously reported by Beneš et al. [7] (Fig. 13).
Danek [75], suggested four main reasons to account for this behavior: i) change in the Coulombic repulsion energy of cations, ii) small structural changes during mixing, iii) no change in the number of firstnearest neighbors, iv) change in the state of ion polarization. In the LiF-UF 4 system, effect i) is probably the dominant one given that the uranium cation is tetravalent, and effect iii) is also likely to play a major role, as U 4+ remains 7, 8, and 9-coordinated when dissolved in LiF (Section 6.2.2), with Li + only loosely associated in the second shell.  Table 4 also). (b) Excess heat capacity of the (Li,U)F x solution derived from MD simulations. Fig. 13. Enthalpy of mixing of the (Li,U)F x solution as calculated at T = 1400 K with the present CALPHAD model (solid green line), and with the model by Beneš et al. [7], (blue dahsed line). Mixing enthalpies for the same system at different temperatures (900-1400 K) were also calculated with MD, shown with symbols as indicated in the legend. Also shown are experimental measurements of the (Li,Th)F x solution at T = 1121 K, (⊟) and 1383 K (⊞) [11], and the (Li,Zr)F x solution at 1150 K (⊠) [70].
The speciation of the complexes, however, does vary (Table. 11). In contrast, considering the loss of the network-like structure going from pure UF 4 (l) to LiF(l), the overall structural changes are not so small and effect ii) probably contributes little to the negative enthalpy in this sytem. Effect iv) would become more evident by changing the alkali secondnearest neighbor, as the polarization ability of the alkali metals reduces down the alkali metal family. This will be studied in more detail in coming works.
Although there is no data on the mixing enthalpy of LiF-UF 4 , its magnitude, calculated from the thermodynamic models (the present structural-thermodynamic and that of Beneš), is very similar to that of LiF-ThF 4 , for which experimental measurements and thermodynamic calculations are available (Fig. 13). It is expected that the mixing enthalpy will be more negative across AF-UF 4 (A = alkali metal) with increasing radius of the alkali ion, as has been observed in many systems and in particular AF-ZrF 4 [70] and AF-ThF 4 [11,76] (although more measurements are needed, e.g. in the RbF and CsF-based systems). More interesting is the influence of the tetravalent cation. Substituting Zr [VII] 4+ (r ionic~0 .78 Å [57]) with Th [VIII] 4+ (r ionic~1 .05 Å [57]) results in a less negative excess mixing enthalpy as can be seen in Fig. 13. The more negative excess in the (Li,Zr)F x solution is related to the higher stability of [ZrF z ] 4 −z anions with respect to [ThF z ] 4−z ones, and their reduced tendency to form Zr-F-Zr bridges [50]. The tendency towards a less negative deviation from ideal behavior with increasing size of the multivalent cation has been observed in other AX-MX n systems [75]. Thus, the actinide contraction effect given by the substitution of Th 4+ by U 4+ likely results in a more negative deviation from ideality, which may be offset to some extent by the larger polarizability of Th 4+ .

CALPHAD assessment of the LiF-UF 4 system
The LiF-UF 4 binary system shown in Fig. 14 was optimized using both structural (Section 6.2) and calorimetric data from the literature and measured in this work by DSC (Table 7). Regarding the structural  [5] and this study (▲, red, see also Table 7). data, the complex anion distribution of the main species [UF 7 ] 3− , [UF 8 ] 4− , and [U 2 F 14 ] 6− could be reproduced accurately, as shown in Fig. 15a, b. Recall that for modelling purposes, [U 2 F 14 ] 6− species encompass dimers, trimers, and polymers. The calculated phase diagram is also in agreement with the data gathered in the present work and with the data from Barton et al. [5]. The invariant equilibria are summarized in Table 6. The system is characterized by the formation of three ternary salts, all of which melt incongruently and at higher temperatures with increasing UF 4 content: Li 4 UF 8 , LiUF 5 , and LiU 4 F 17 , and the existence of a fourth meta-stable phase with formula Li 3 UF 7 (not visible on the calculated phase diagram). The melt is characterized by a predominance of hepta, octa, and nona-coordinated [UF x ] 4−x complexes which remain isolated or form dimers, trimers, and chains of higher nuclearity through fluoride bridging, 'polymers'. Near X(UF 4 ) = 0.4, the solution is saturated with these polymeric chains, and remains so until the endmember UF 4 . This evolution is rather insensitive to temperature, at least until 1400 K, which was the maximum temperature studied here.

Conclusions
A structural and thermodynamic study of the LiF-UF 4 binary system is reported herein, in light of its relevance for MSR technology. The study set out two main objectives: i) confirm decades-old phase equilibria reported by Barton et al. [5] on which state-of-the-art MSR thermochemistry relies, ii) understand the structure of the molten salt as a function of composition, so as to link it with thermo-chemical properties and use it as input to develop a coupled structural-thermodynamic model. With regard to the first objective, it was found that the phase diagram proposed by Barton et al. is essentially correct, except for the phase with LiF:UF 4 = 7:6 stoichiometry which was found by other authors to be LiUF 5 . It was also confirmed that Li 3 UF 7 is a meta-stable phase, and it is suggested to belong to the space group P4/ncc like the isostructural Li 3 ThF 7 compound. Following Cousson and Pages [44], who narrowed down the possible space groups of LiU 4 F 17 to three (I4/m, I4, I4), it was found from a LeBail refinement that the most probable one is I4. Further work could aim to obtain these intriguing phases with high purity and elucidate their crystal structures (the structure of LiTh 4 F 17 also remains unknown).
The second objective relied on EXAFS spectroscopy as an experimental technique. Measurements were carried out at three compositions about 50 K above the liquidus temperature: X(UF 4 ) = 0.25, 0.50, and 0.67. Fitting of the standard EXAFS equation as well as MD simulations were used to interpret the EXAS measurements, while it was possible to extend the composition and temperature space of analysis with the latter technique. The calculations, in agreement with other sources in the literature, showed that (Li,U)F x (l) is a melt dominated by three coordination complexes throughout the entire composition range: [UF 7 ] 3− , [UF 8 ] 4− , and [UF 5 ] 9− , able to form a network of face, edge, or corner-sharing polyhedra. An advanced thermodynamic assessment was able to reproduce the distribution of [UF 7 ] 3− , [UF 8 ] 4− , and species of higher nuclearity accounted for by the [U 2 F 14 ] 6− dimer as calculated with MD simulations, while maintaining sound phase equilibria. Actinide contraction is apparent when the melt is compared to its (Li, Th) F x analogue, although there do not seem to be significant changes between the excess properties of both systems. It remains to be seen if in other alkali fluoride-based systems the variability is more evident.