Diffusion coefficients and local structure in basic molten ... - CNRS

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Diffusion coefficients and local structure in basic molten fluorides: in situ NMR measurements and molecular dynamics simulationsw Vincent Sarou-Kanian,a Anne-Laure Rollet,*ab Mathieu Salanne,b Christian Simon,b Catherine Bessadaa and Paul A. Maddenc Received 25th June 2009, Accepted 28th September 2009 First published as an Advance Article on the web 20th October 2009 DOI: 10.1039/b912532a The local structure and the dynamics of molten LiF–KF mixtures have been studied by nuclear magnetic resonance (NMR) and molecular dynamics simulations. We have measured and calculated the self-diffusion coefficients of fluorine, lithium and potassium across the full composition range around the liquidus temperature and at 1123 K. Close to the liquidus temperature, DF, DLi and DK change with composition in a way that mimics the phase diagram shape. At 1123 K DF, DLi and DK depend linearly on the LiF molar fraction. These results show that the composition affects the self-diffusion of anions and cations more weakly than the temperature. The activation energy for diffusion was also determined and its value can be correlated with the strength of the anion–cation interaction in molten fluoride salts.

1. Introduction Molten salts are a particular class of liquids. They differ from the classical solvents like liquid water because of the ionic character of all their components. On the atomic scale, the structure is governed by the combination of coulombic and short-range repulsion forces.1 Several families of molten salts can be distinguished, depending on the chemical properties of the liquid. In the case of high melting temperature systems, these are mainly dependent on the nature of the anions, so they are commonly named molten chlorides, fluorides, oxides, etc. Among these families of molten salts, molten fluorides have a particular importance from a technological point of view because of their potential use as solvent and coolant in several generation IV nuclear reactor concepts.2,3 This explains the continuous effort devoted to the study of the physico-chemical and electrochemical properties of molten fluorides since the early 1990s despite the substantial experimental difficulties encountered when studying them: one has to deal with the problems of high temperatures ranging from 500 to 1800 K, concerning corrosiveness and volatility. It is now well known that within the family of molten fluorides important modifications in the thermodynamic and transport properties occur when the nature of the cation is changed.4,5 One can distinguish acidic cations, which tend to a

Conditions Extreˆmes : Mate´riaux a` Haute Tempe´rature et Irradiation – CNRS, 1D avenue de la Recherche Scientifique, 45071 Orle´ans cedex 2, France. E-mail: [email protected], [email protected]; Tel: 33 2 38257682 b UPMC univ. Paris 06, CNRS, ESPCI, UMR 7195 PECSA, F-75005 Paris, France. E-mail: [email protected], [email protected], [email protected] c Department of Materials, University of Oxford, Parks Road, Oxford, UK OX1 3PH. E-mail: [email protected] w Electronic supplementary information (ESI) available: Self-diffusion coefficients versus composition in LiF–BeF2 molten salt. See DOI: 10.1039/b912532a

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form long-lived ionic bonds with the fluoride anions6,7 from basic ones, which provide ‘‘free’’ fluoride anions to the melt, even though a proper scale of acidity remains to be built in these media.8 Molten lithium fluoride (LiF) and potassium fluoride (KF) are archetypal basic molten salts, and so are their mixtures. The viscosity of these mixtures is known to be of the same order of magnitude as liquid water, which means that these liquids are highly fluidic.9 Up to now no reliable information on the diffusion coefficients of the different species has been available, and the objective of this work is to provide such data for all the LiF–KF compositions, and to study their evolution with temperature. To achieve this objective, two independent techniques are employed. The first is experimental, and it employs a newly developed experimental capability.10 The diffusion coefficients are directly measured by the high temperature pulsed field gradients nuclear magnetic resonance experiments (HT PFG NMR), for temperatures ranging between 750 and 1123 K. This technique has numerous advantages: the acquisition of data is rapid, one can select an isotope, and it does not necessitate the use of any model to link the measured data to the diffusion coefficient.11 These experiments were supplemented by molecular dynamics (MD) simulations. In this method, the system is treated on the atomic scale, and Newton’s equation of motion is propagated for a given set of particles, which allows for the determination of dynamic properties. The interaction potential between the various species is of ab initio accuracy and includes dipole polarization effects. It has already been tested against various types of experimental data, and is shown to reproduce accurately quantities like electrical conductivity, heat capacity, viscosity, etc, of different molten fluoride systems.12 In this paper, both methods will be described in the first section. Then the data collected will be compared and discussed. A particular emphasis will be given to the composition and temperature dependence. Phys. Chem. Chem. Phys., 2009, 11, 11501–11506 | 11501

asymptotic multipole expansion of dispersion. These functions take the form

2. Experimental and methods 2.1

NMR

The LiF and KF salts (purity 99.99%) were purchased from Alfa Aesar. They were stored and the mixtures were prepared in a glove box under argon in order to avoid H2O and O2 contamination of the samples. The salts were confined in boron nitride crucibles (without oxide binder). The amount of salt in each crucible is ca. 50 mg. The HT PFG NMR spectra were recorded using a Bruker Avance WB 400 MHz spectrometer, operating at 9.40 T. The experimental setup has been described in details in another publication.13 Nevertheless, the principle can be recalled. The BN crucible is heated by a symmetrical irradiation of CO2 laser. Thanks to its good thermal conductivity, the crucible acts as a small furnace. The laser power is progressively increased to take the temperature about 101 above the liquidus temperature. An argon stream prevents the BN from oxidizing at high temperature. The NMR probe is a 10 mm liquid probe especially designed by the Bruker company and adapted in CEMHTI to work up to 1500 K. It is equipped with a gradient coil providing 5.5/G/cm A1 that is combined with a gradient amplifier of 10 A (Great 10A). We used an NMR pulse sequence combining bipolar gradient pulses and stimulated echo.14 This sequence is repeated with 8 gradients of increasing strength. The self-diffusion coefficients are obtained by nonlinear least-squares fitting of the echo attenuation. Measurements were performed using the following NMR parameters: times of radiofrequency magnetic field application for p/2 pulses p90 = 13 ms (19F) and p90 = 9 ms (7Li), gradient strength 0 o g o 50 Gauss cm1, gradient application time 1 o d o 5 ms. For 7Li measurements, we used a pre-saturation cycle before the diffusion sequence because of the long relaxation time T1 of this nucleus (25 s in molten LiF). The 19F chemical shifts were referred to CCl3F. 2.2

Molecular dynamics

The LiF–KF liquid mixtures have been studied by MD simulations. In the case of molten fluorides, the potential is best described as the sum of four different components: charge–charge, dispersion, overlap repulsion, and polarization.15 First the charge–charge term is V qq ðrij Þ ¼

X qi qj ioj

ð1Þ

rij

where qi is the charge on ion i, and formal charges are used throughout. The dispersion component includes dipole–dipole and dipole–quadrupole terms,

V

disp

ðrij Þ ¼ 

X ioj

"

C ij f6ij ðrij Þ 66 rij

þ

Cij f8ij ðrij Þ 88 rij

# ð2Þ

where C6ij (C8ij) is the dipole–dipole (dipole–quadrupole) dispersion coefficient, and fnij are Tang–Toennies dispersion damping functions describing the short-range correction to the 11502 | Phys. Chem. Chem. Phys., 2009, 11, 11501–11506

fnij ðrij Þ ¼ 1  cijn expðbijn rij Þ

n X ðbij rij Þk n

k¼0

k!

ð3Þ

and the parameter bij represents the distance at which the correction begins to be taken into account. The third term of the interaction potential, the repulsion overlap component, is given by: V rep ðrij Þ ¼

X

Aij expðaij rij Þ

ð4Þ

ioj

The polarization part of the potential includes charge–dipole and dipole–dipole terms, V pol ðrij Þ ¼

X

ðqi mj;a f4ij ðrij Þ  qi mi;a f4ij ðrij ÞÞ Tað1Þ ðrij Þ

ioj



X

ð2Þ

mi;a mj;b Tab ðrij Þ þ

ioj

ð5Þ

X 1 jl j2 2ai i i

Here Ta(1) and Tab(2) are the charge–dipole and dipole–dipole interaction tensors while ai is the polarizability of ion i. Again, Tang–Toennies functions are included to account for the short-range effects. The set of induced dipoles li is treated as 3N additional degrees of freedom of the system. The dipoles are determined at each time step by minimization of the total polarization energy and depend on the positions of all the atoms at the corresponding time; therefore the polarization part of the potential is considered to be a many body term. All the parameters necessary to simulate LiF–KF mixtures have been determined from a recently developed first-principles procedure. The pair parameters are summarized in Table 1. The polarizabilities were, respectively, of 7.9 and 5.0 a.u. for F and K+ ions, while the Li+ were considered to be non-polarizable. The MD simulations were performed on 11 molten salt compositions ranging from pure LiF to pure KF. All the corresponding simulation cells contained 432 ionic pairs. The mixtures were first equilibrated in the NPT ensemble following the method described by Martyna et al.,16 with a pressure fixed at 0 GPa and a temperature of 1200 K. We chose a time step of 0.5 fs and after 100 ps of equilibration, production runs of 200 ps were conducted for each composition.

Table 1 Parameters of the interaction potential (in atomic units). For all the ion pairs, b6ij = b8ij = 1.9 and c6ij = c8ij = 1.0 Ion pair ij

Aij

aij

C6ij

C8ij

b4ij

c4ij

c4ji

F–F F–Li+ F–K+ Li+–Li+ Li+–K+ K+–K+

282.3 18.8 138.8 1.0 1.0 1.0

2.444 1.974 2.04 5.0 5.0 5.0

15.0 1.2 3.9 0.1 0.3 1.0

150.0 12.2 38.7 1.0 3.2 10.0

— 1.834 1.745 — — —

— 1.335 2.500 — — —

— — 0.31 — — —

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3. Results 3.1

Local structure

The chemical shift of 19F, 19Fd has been measured as a function of the composition and the values are plotted in Fig. 1. The chemical shift is sensitive to the local environment of the observed nucleus, i.e. the first shells of neighbours.17 For solid compounds, the NMR spectrum yields as many peaks as there are different environments for the observed nucleus, if the resolution is sufficient. On the contrary, for molten salts, the nucleus experiences all the different environments during the measurement and NMR spectrum is made of only one sharp peak. However, this peak is the weighted average of all the individual peak positions that would be sampled if the measurement was infinitely fast. Therefore the observed values can be expressed as follows: d=

P nixidi

(6)

where ni is the number of fluorine involved in the ith complex, xi the molar fraction and di its chemical shift. In most molten fluoride mixtures 19Fd presents complicated variations with composition. For example, in NaF–AlF3 there are several linear variations versus AlF3 concentration.18 In rare earth fluorides AF–LnF319,20 (Ln = La, Y, Ce, Lu and A = Li, Na, K, Rb) and actinide fluorides21 AF–ThF4 the variation is a parabola. In these two cases, it has been demonstrated that fluoride ions are in rapid exchange between at least three environments: free fluorine, fluorine embedded in long-lived LnFx3x unit22 and fluorine bridging two LnFx3x units.23 Hence, the linear variation observed in Fig. 1 is different. According to eqn (6) it indicates that there is no long-lived LixFy complex or KxFy complex: a fluoride anion surrounded by a Li+ and b K+ gives a contribution to d equal to (a/a + b) 19F dLiF + (b/a + b) 19FdKF. This result confirms the free character of fluoride ions in molten alkali mixtures. The F–Li+ and F–K+ radial distribution functions extracted from MD simulations at various compositions and a temperature of 1123 K are plotted on Fig. 2. The first peak of these functions gives the structure of the solvation shell of

Fig. 1 Chemical shift of fluorine 19Fd as a function of the LiF molar fraction in molten LiF–KF.

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Fig. 2 F–Li and F–K radial distribution functions g(r) in molten LiF–KF at various xLiF.

fluoride ions. It appears clearly that the position of the maximum is nearly conserved: for all the mixtures the average first neighbours distance shifts from 1.80 A˚ (xLiF = 0.1) to 1.83 A˚ (xLiF = 1) for F–Li and from 2.46 A˚ (xLiF = 0.0) to 2.53 A˚ (xLiF = 0.9) for F–K pairs. These distances are in very good agreement with those experimentally obtained by X-ray diffraction for the eutectic mixture24 (1.85 A˚ for F–Li) and are very close to the similar molten fluoride system FLiNaK25 (1.83 A˚ for F–Li and 2.59 A˚ for F–K). The gradual shift of the maximum with composition confirms the picture of a rapid exchange between two limit environments corresponding to the structure in the pure salts. These results are consistent with the existence of LiFxK configuration (t = 0.3 ps) deduced from Raman spectra26 but cannot be compared to the complexes like those observed in YF3–AF mixtures for examples.27,28 The maximum intensity of the first peak decreases when xLiF increases for both Li–F and K–F pairs (Fig. 2). This evolution is the signature of a decrease of the association between the cations and the anions. Such a phenomenon has already been evidenced in MD simulations of the LiCl–KCl mixtures.29 Previous numerical simulations of this system have shown the existence of local heterogeneities in ionic distribution, i.e. clustering of Li+ and of part of the F ions in the KF matrix.30,31 These effects do not affect the first solvation shell because they correspond to the formation of medium range order. Ribeiro has estimated a lifetime of a few picoseconds for these clusters. It is therefore important to underline that NMR of 19F nucleus is not able here to obtain direct evidence Phys. Chem. Chem. Phys., 2009, 11, 11501–11506 | 11503

of such features since the residence time of ions in these clusters is short compared to NMR characteristic time. Concerning the other nuclei, the chemical shift range of 7Li is too small to give evidence of a change in local structure and the tuning range of our NMR probe does not cover the 39K frequency. 3.2

Diffusion

3.2.1 Dependence on composition. The self-diffusion coefficients of fluorine DF, lithium DLi and potassium DK in molten LiF–KF are plotted in Fig. 3 as a function of LiF molar fraction xLiF at 10 K above the liquidus temperature and at 1123 K. They are also reported in Table 2. The whole set of values obtained by HT PFG NMR and MD simulations are in good agreement.

Fig. 3 Self-diffusion coefficient of fluorine DF, lithium DLi and potassium DK as a function of LiF molar fraction xLiF: simulation (full symbol) and experiment (open symbol) at 10 K above the liquidus temperature (circle) and at 1123 K (square).

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Table 2 Self-diffusion coefficients of fluorine DF, lithium DLi and potassium DK in molten LiF–KF for various compositions and temperatures NMR D  109

MD

NMR

MD

MD

xLiF T/K DF/m2 s1 DF/m2 s1 DLi/m2 s1 DLi/m2 s1 DK/m2 s1 0 0 0.1 0.1 0.2 0.2 0.3 0.3 0.3 0.4 0.4 0.4 0.45 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.8 0.8 0.9 0.9 1 1

1123 1173 1096 1123 1043 1123 973 1023 1123 887 1023 1123 833 775 817 858 906 954 1002 1037 1085 1123 773 873 1023 1123 1173 1200 877 1023 1123 961 1023 1123 1173 1033 1123 1083 1123 1123 1173

9.5 — — 9.5 6.8 8.7 4.4 — 8.8 3.5 — 9.7 3.1 1.9 2.4 2.6 3.4 4.25 4.65 5.5 6.5 7.4 — — — — — — 3.4 — 7.7 4.55 — 7.7 — 6.0 8.55 7.3 7.8 7.2 —

7.10 8.31 6.22 6.92 5.29 6.67 3.99 4.84 6.68 2.75 4.74 6.75 — — — — — — — — — — 1.47 2.57 4.81 6.55 7.44 7.84 2.71 4.83 6.61 4.06 5.04 6.69 7.77 5.16 6.80 6.02 6.77 6.74 7.34

— — — — 5.5 6.7 5 — 8.8 3.1 — 8.4 — 1.7 — 3.4 — 5.0 — 7.4 — 9.3 — — — — — — 3.8 — 8.9 5 — 7.7 — 6.7 9 8.6 9.4 8.9 —

— — 5.13 5.45 4.26 5.62 3.42 4.18 5.78 2.44 4.27 6.02 — — — — — — — — — — 1.33 2.41 4.48 6.07 6.87 7.46 2.59 4.63 6.35 4.16 5.17 6.86 7.73 5.68 7.33 7.18 7.87 8.83 9.75

6.42 7.46 5.81 6.32 5.01 6.40 3.91 4.70 6.45 2.73 4.64 6.55 — — — — — — — — — — 1.44 2.62 4.85 6.40 7.13 7.65 2.66 4.84 6.45 4.16 5.13 6.44 7.53 5.26 7.10 6.02 6.82 — —

The striking point of this figure is that the dependence of DF, DLi and DK on composition close to the liquidus temperature mimics the LiF–KF phase diagram shape32 and has been discussed in detail in a previous publication.10 Indeed, the self-diffusion coefficient strongly decreases from pure KF to a minimum at the eutectic composition (xLiF = 0.5) and increases again up to pure LiF. The amplitude of this variation is considerable, as the values range from 2  109 to 9  109 m2 s1, spanning almost one order of magnitude. In many liquids, the composition strongly affects the dynamic properties in general and the self-diffusion coefficient in particular. This is for example the case for molten LiF–BeF2 mixtures for which all diffusion coefficients strongly decrease with increasing BeF2 concentration33 (data supplied in the ESI).w In contrast, the self-diffusion coefficients of anions and cations are here only weakly affected by the Li/K ratio, the temperature effect is much stronger. This is confirmed by the values of DF, DLi and DK determined This journal is

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for each composition at 1123 K which lie on straight lines (Fig. 3) between the limiting values for the pure fluids. Some discrepancies are observed between the results obtained in the MD simulations and HT PFG NMR on the KF rich side. This mainly occurs in the case of lithium ions where the MD simulations underestimate the diffusion coefficients of F and Li+. This may be related to the inherent uncertainties of both techniques applied to molten fluorides especially the accuracy of the interaction potential used in the MD simulations and the accuracy of setting the temperature in HT PFG NMR. Complementary work using other techniques like electrochemical experiments should help in refining the whole set of data. Such techniques have already allowed the determination of the self-diffusion coefficients of electroactive species. For example, it was shown that DZr equals 2.9  109 m2 s1 at 1020 K in molten LiF–NaF–ZrF434 and that DGd increases from 1.25  109 m2 s1 to 2.6  109 m2 s1 for temperatures of 1073 to 1173 K in molten LiF–CaF2.35 The influence of the composition has already been studied in LiCl–KCl and in LiNO3–KNO3 by MD simulations28,36 has been compared to experimental data.37,38 Going from pure lithium compound to pure potassium compound a substantial decrease of the self-diffusion coefficients was observed for all species. In LiCl–KCl at 1096 K this effect was more pronounced for DLi (about 50%) than for DK (about 40%) and DCl (about 20%). At much lower temperature (575 K) in LiNO3–KNO3 the same trend occurs: DLi (about 60%), DK (about 50%) and DNO3 (about 50%). The comparison between fluoride, chloride and nitrate systems indicates the importance of the size and polarizability of the anion on the diffusive properties of all species. The larger the anion and the greater its polarizability, the greater the composition dependence. 3.2.2 Activation energy of diffusion. The activation energies, Ea, for diffusion have been determined for the three ions at the eutectic composition (xLiF = 0.5). The temperature was scanned from 773 to 1123 K for HT PFG NMR measurements and from 773 to 1200 K for the MD simulations. The logarithm of the diffusion coefficients is plotted in Fig. 4 as function of 1/RT (R is the ideal gas constant). The activation energy obtained by linear regressions on the straight lines in Fig. 4 is reported in Table 3. These values are in very close agreement with the experimental data obtained using the capillary method on similar systems:39 in molten NaF Ea = 36.0 kJ mol1 for Na+. In contrast, the activation energies in a network-like molten fluoride salts LiBeF2 are much greater32: 76 kJ mol1 for Be2+ and F, 54 kJ mol1 for Li+.

Table 3

Fig. 4 Ln(DF), Ln(DLi) and Ln(DK) versus 1/RT in molten LiF–KF (xLiF = 0.5). Lines are the results of the linear regressions.

It is known that Ea increases with the solvation cage stability, in other words, with the strength of the interaction between cation and anion. This suggests that an activation energy around 30 kJ mol1 is the signature of free species in molten fluorides.

Activation energy of diffusion

Methods

Ea(Li+) kJ mol1

Ea(K+) kJ mol1

Ea(F) kJ mol1

MD simulations HT PFG NMR

30.1 33.0

28.5

29.7 27.9

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Phys. Chem. Chem. Phys., 2009, 11, 11501–11506 | 11505

Conclusions We have studied the diffusive properties in molten LiF–KF mixtures over a wide range of composition and temperature. An overall good agreement is obtained between experiments (HT PFG NMR) and theory (MD simulations) which confirms the reliability of our results. We showed that, unlike the analogous chloride (LiCl–KCl) and nitrate (LiNO3–KNO3) systems, the composition affects the diffusive properties only weakly. The self-diffusion coefficient varies mainly with temperature. In addition, the activation energy reveals the bonding character of a given ion in the molten salt.

Acknowledgements The authors are indebted to Frank Engelke, Ernst Naumann and Klaus Zick from Bruker Co. for the NMR probe. The authors thank NMR group members of CEMHTI for valuable discussions, in particular F. Fayon. The authors are grateful to Eric Labrude for his technical help. This work has been supported by GdR PARIS and by PCR ANSF of programme PACEN.

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