Dynamic Fluctuation of U3+ Coordination Structure in the Molten LiCl

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Dynamic Fluctuation of U Coordination Structure in Molten LiClKCl Eutectic via First-Principles Molecular Dynamics Simulations Xuejiao Li, Jia Song, Shuping Shi, Liuming Yan, Zhao-Chun Zhang, Tao Jiang, and Shuming Peng J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b10193 • Publication Date (Web): 03 Jan 2017 Downloaded from http://pubs.acs.org on January 4, 2017

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The Journal of Physical Chemistry

Dynamic Fluctuation of U3+ Coordination Structure in Molten LiCl-KCl Eutectic via First Principles Molecular Dynamics Simulations Xuejiao Li 1, Jia Song 2, Shuping Shi 2, Liuming Yan 2,*, Zhaochun Zhang 3,* Tao Jiang 4, Shuming Peng 4 1

Department of Physics, 2 Department of Chemistry, 3 School of Materials Science and Engineering, Shanghai University, 99 Shangda Road, Shanghai 200444, China;

4

Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621900, China ABSTRACT The dynamic fluctuation of U3+ coordination structure in molten LiCl-KCl mixture was

studied using first principles molecular dynamics (FPMD) simulations.

The radial distribution

functions, probability distribution of coordination numbers, fluctuation of coordination number and cage volume, self-diffusion coefficients and solvodynamic mean radius of U3+, dynamics of nearest U-Cl distances, and van Hove function were evaluated.

It was revealed that fast

exchange of Cl− occurred between the first and second coordination shells of U3+ accompanied with fast fluctuation of coordination number and rearrangement of coordination structure.

It

was concluded that 6-fold coordination structure dominated the coordination structure of U3+ in molten LiCl-KCl-UCl3 mixture and high temperature was conducive to the formation of low coordinated structure.

1.

*

Introduction

Corresponding author. Tel.: 8621-66132405, fax: 8621-66132405. E-mail: [email protected] (L.Y.),

[email protected] (Z.Z.)

1 ACS Paragon Plus Environment


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Molten salt mixtures, such as LiCl-KCl, NaCl-CsCl, NaCl-KCl, NaCl-CaCl2 and LiF-BeF2, are essential medium for the pyroprocessing of spent nuclear fuels attributing to their incombustibility, high boiling points, wide liquid temperature ranges, extremely high resistances to nuclear radiation and transmutation.

In addition, these molten salt mixtures are excellent

coolants attributing better thermal conductivity compared with water or organic solvents. Nowadays, pyroprocessing is becoming a more and more competitive option to the wet processing of spent nuclear fuels in the reduction of toxicity and volume of disposable nuclear waste, especially for fuel recycling in the closing of nuclear fuel cycle.1-3

Among the few

pyroprocessing techniques, electro-refining is the most important process to separate various fission product and remaining U from spent nuclear fuel. Nevertheless, the molten salt mixtures in the pyroprocessing also have disadvantages such as high corrosiveness and sensitivity of molten salt mixtures to trace impurities.

Besides,

one of the most important disadvantages is the relatively low separation factor for extraction of elements with similar chemical and/or physical properties.

In order to improve the element

separation efficiency, accurate structural and thermochemical properties, especially solute behavior in the molten salt mixtures, were widely studied using various experimental and simulation methods.

For example, high-temperature X-ray absorption fine spectroscopy (XAFS)

had been employed for the evaluation of local structure in molten LiCl-KCl-UCl3 mixture in terms of radial distribution functions (RDFs) and coordination numbers.4-7

However, the

adsorption of incident X-ray by quartz window limited the strength of X-ray going through molten salt and ratio of signal to noise.

Besides, classical molecular dynamics (MD)

simulations had been applied to the study of molten uranium trichloride,8 rare-earth trichlorides,9 and other trivalent metal chlorides.10

Recently, MD simulations were also employed to study


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the structural and transport characteristics of UCl3 and CeCl3 in molten LiCl-KCl mixture,11-12 self-diffusion coefficient and chemical diffusion coefficient of U3+ in molten LiCl-KCl eutectic,13 and activity coefficients of trivalent cations in molten LiCl-KCl using thermodynamic integration14 and polarizable ion interaction potentials.2 Despite the great success of classical MD simulations, such endeavors depend on the availability of force field models and their outputs depend on the accuracy of these force field models.

For the actinide elements, high quality force field models are not yet available and

only universal or generic force field models have been developed.15

On the other hand, first

principles molecular dynamics (FPMD) simulations calculate interionic forces from first principles on-the-fly and thus avoid the use of empirical force field models.

One of the

disadvantages FPMD is the calculation cost, therefore, the simulated evolution time is much shorter than classical MD.

For example, Bengtson and Morgan et al. had evaluated the density,

thermal expansion coefficient, bulk modulus, and diffusivity for molten LiCl, KCl, and LiCl-KCl eutectic at multiple temperatures based on FPMD simulations.16

FPMD simulation were also

applied to the study of electrodeposition of U from molten LiCl-KCl eutectic onto Mo(110) surface and thermo-kinetic properties of molten LiCl-KCl eutectic.17-18

Furthermore, Nam et al.

employed FPMD simulations to calculate redox potential, solute diffusion coefficients, and structural information of Li, Sr, La, Nd, Ce, Zr, U and Eu in LiCl-KCl and Li, Be, Zr, Fe and Cr in Li2BeF4.19

These simulations enriched the understanding of characteristics of molten salts,

especially solute behavior, and provided essential physicochemical data for the research and development of pyroprocess. In the work, we will elucidate U3+ behavior in molten LiCl-KCl eutectic by FPMD simulations, specifically its local structure and dynamic fluctuation, which are unobtainable from



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experimental technologies, of coordination sphere in terms of coordination numbers, U-Cl distances and volumes of coordination cages.

These studies will increase the understanding of

U3+ behavior, and provide basic information for the simulations of separation processes and for the chemical control of high-temperature molten salt reactor systems.

2.

Computational methods The MD simulations were carried out by combination of classical MD and FPMD.16, 20

The simulated molten LiCl-KCl-UCl3 system was comprised of 38 Li+, 26 K+, 2 U3+, and 70 Cl− ions in a cubic simulation cell, corresponding to a molar composition of 3% UCl3 (2 U3+/(2 U3+ + 38 Li+ + 26 K+)) in molten LiCl-KCl eutectic.

The simulation cell was firstly pre-equilibrated

using classical MD in NVT ensemble as implemented in the LAMMPS package.21

The

Born-Huggins-Mayer (BHM) potential, one of the most widely accepted force-field models for molten salts and mixtures, was employed in the classical MD simulations because of its appropriate balance between simplicity and accuracy.

During the calculation of short range

interionic interactions, the cutoff radius was set to approximately the half of simulation cell, and the long range coulombic interaction was evaluated using the Ewald summation algorithm.22 The Verlet integration scheme was employed in the classical MD simulations with an integration step time of 1 fs, and the simulations process was as follows:

First, 50,000 steps of simulations

were carried out using the NVE ensemble to bring the system to the specified temperatures. Then, another 500,000 steps of simulations were carried out in the NPT ensemble with Nosé-Hoover thermostat and barostat to optimize the cell volumes, and the cell volumes were evaluated as average between the 400 ps and 500 ps of simulations and used as input in the following NVT ensemble simulations.

Finally, the NVT ensemble classical MD simulations


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were conducted for 1,000,000 steps, and the final configurations were used as input for the FPMD simulations. After the classical MD simulation, the equilibrium cell volume was further optimized in NVE ensemble at five fixed volumes for each given temperature using FPMD as implemented in the Vienna Ab initio Simulation Package (VASP).23-25

The free energies were evaluated as the

averages over 2,000 time steps in the NVE ensemble. For each temperature, the free energies were fitted to a quadratic polynomial of cell volumes, and the equilibrium volume was evaluated as cell volume with the minimum free energy.

Finally, production FPMD simulation in NVT

ensemble was carried out for about 12,000 simulation steps at this equilibrium volume and corresponding temperature.

In order to explore the effect of temperature, this process was

repeated for five times at preset temperatures of 858, 886, 921, 960, and 1019 K because experimental densities were available at these temperatures for molten LiCl-KCl mixture.26 During all the simulations, periodic boundary conditions (PBC) were applied to eliminate boundary effects.

The FPMD simulations employed the PBE functionals and the energy was

evaluated using a 1x1x1 k-point mesh.27

The wave functions of valent electrons, Li(2s1),

Cl(3s23p5), K_sv(3s23p64s1) and U_s(5f36s26p66d17s2), were expanded in plane wave basis set with a cutoff energy of 420 eV, and the core electrons were approximated by projector-augmented wave (PAW) pseudopotentials.28 Spin polarization was always applied for FPMD simulations to properly depict unpaired electrons of U3+.

The ionic coordinates were

updated at a relatively short time step of 1 fs to reduce energy drift and the energetic evolution (figure S1) was appended in the supporting information (SI).

3.

Results and discussion



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3.1

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Equilibrium densities of the molten salt mixture The equilibrium density (ρe) of the molten salt mixture at each simulation temperature

was evaluated from its equilibrium cell volume (Ve) which was optimized by fitting the free energies (F) to Ve based on quadratic polynomial (as shown in figure S2 in the SI).

In order to

make a comparison between the FPMD simulation density and experimental density, the experimental density of molten LiCl-KCl-UCl3 mixture was approximated by isometric mixing of molten LiCl-KCl and UCl3. Since the temperature dependence of experimental density for molten LiCl-KCl and pure UCl3 were,26, 29 LiCl-KCl = 2.029 − 5.274 × 10

(1)

= 13.652 − 7.943 × 10

(2)

respectively, the density of molten LiCl-KCl-UCl3 mixture was evaluated as, iso = 2.273 − 5.428 × 10

(3)

From table 1, it could be seen that the FPMD density ρe was in good agreement with the isometric mixing density of molten LiCl-KCl and UCl3 with small deviation of 1.53% (in maximum) in temperature range of 858.4 to 1019.4 K. As the temperature dependence of density was an essential property of materials representing the position of energy minimum on the energetic hypersurface in configurational space, the agreement between FPMD density and experimental density was evidence that our computational method was reliable for the simulation of molten LiCl-KCl-UCl3 mixture.

Table 1.

Equilibrium cell size a and volume Ve of the simulation cell, and various densities of the molten LiCl-KCl-UCl3 mixture

T (K)

a (Å)

Ve (Å3)

ρe (g cm−3)

ρiso (g cm−3)


deviation (%)

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3.2

858.4

15.756

3911.45

1.801

1.802

-0.02

886.0

15.804

3947.31

1.783

1.783

0.00

920.5

15.796

3941.32

1.768

1.760

0.44

969.8

15.846

3978.86

1.753

1.727

1.53

1019.4

16.020

4111.38

1.707

1.693

0.84

Radial distribution functions The radial distribution functions were the most important structural information

obtainable from the trajectory recorded during the FPMD simulations at every time steps.30

In

figure 1, it showed the RDFs g(") and integrated RDFs $(") of the molten LiCl-KCl-UCl3 mixture at an average temperature of 886.0 K which was consistent with the preset temperature. The first peak positions, at 2.319, 3.045 and 3.827 Å for %Li-Cl ("), %K-Cl (") and %Cl-Cl ("), respectively, were longer than corresponding literature values in molten LiCl-KCl mixture at 2.20, 3.00 and 3.79 Å evaluated from classical MD simulations using Fumi-Tosi force field model.31

However, these first peak positions were slightly shorter than literature values at 2.46

Å for %Li-Cl (") in pure molten LiCl and 3.10 Å for %K-Cl (") in pure molten KCl deduced from X-ray diffraction and Neutron diffraction, respectively.32

The sharp peak for %U-Cl (") at 2.710

Å was consistent with literature value at 2.77 Å in molten LiCl-KCl eutectic with 5 mol.% UCl3 evaluated from XAFS observation.5

The first shell coordination numbers (CNs) at 4.22, 7.62

and 6.26 for Li+, K+ and U3+ coordinated by Cl− evaluated from $(") also agreed well with corresponding values in molten LiCl-KCl or LiCl-KCl-UCl3 mixtures evaluated from MD simulations.5, 31



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Fig. 1

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RDFs g(r) and integrated RDFs n(r) for molten LiCl-KCl-UCl3 mixture (FPMD, NVT

ensemble, 886.0 K, color online)

In table 2, it summarized the first peak positions and CNs for all ion pairs in molten LiCl-KCl-UCl3 mixture at five temperatures.

These values were similar to the classical MD

simulations with first peak positions at 2.22, 3.03 and 2.66 Å for %Li-Cl ("), %K-Cl (") and %U-Cl ("), and corresponding CNs at 3.97 ~ 4.05, 6.61 ~ 6.88, and 7.08 ~ 7.19, respectively.12

In

addition, the CN for U-Cl ion pair (CNU-Cl) was also in good agreement with experimental value of 6.6 in LiCl-KCl eutectic with 5% UCl3 at 823 K.5

The ups and downs of interatomic

distances were attributed to statistical error of the limited sampling space.

However, these

values only changed slightly with temperature (also shown in figure S3 of SI), reflecting the conservation of local structures above melting point in the molten salt mixture.

Therefore, it

could be concluded that the FPMD reproduced satisfactory local structures for the molten LiCl-KCl-UCl3 mixture.

Table 2

The first peak positions R (Å) and coordination numbers CN in the molten 8 ACS Paragon Plus Environment

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LiCl-KCl-UCl3 mixture evaluated from FPMD simulations at multiple temperatures T (K) T

RLi-Cl

RK-Cl

RU-Cl

673

2.22 a

3.03 a

2.66 a

RCl-Cl

CNLi-Cl

CNK-Cl

CNU-Cl

4.02 a

6.76 a

7.13 a

2.77 b

823

CNCl-Cl

6.6 b

858.4

2.312

3.092

2.702

3.816

4.35

7.15

6.35

10.18

886.0

2.319

3.045

2.710

3.827

4.22

7.62

6.26

10.61

920.5

2.276

3.024

2.726

3.731

4.18

6.80

6.17

10.66

969.8

2.326

3.054

2.718

3.783

4.15

7.73

6.22

12.01

1019.4

2.230

3.019

2.202

3.752

3.94

6.66

6.13

10.47

1096

2.20 c

3.00 c

3.79 c

3.86 c

5.98 c

11.62 c

1200

2.85 d

8.0 d

1200

2.84 e

6.0 e

1200

2.82 f

7.05 f

(a) 3 mol.% UCl3 in LiCl-KCl eutectic at 673 K;12 (b) 5 mol.% UCl3 in LiCl-KCl eutectic at 823 K;5 (c) molten LiCl-KCl eutectic at 1096 K;31 (d) pure molten UCl3 at 1200 K;8 (e) pure molten UCl3 at 1200 K;33 (f) pure molten UCl334

3.3

Dynamic coordination structure of U3+ In order to study the dynamic coordination structure of U3+, the time series of

coordination numbers of U3+ (time series of CNs) were evaluated for each time step (12,000 steps in total) by counting the number of Cl− anions within a cutoff distance of 3.500 Å with application of PBC.

This cutoff distance gave an average coordination number of 6.16 at 886.0

K, consistent with the corresponding value of 6.26 evaluated from the integrated RDF as shown



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in table 2, and was also reasonable compared with peak position of %U-Cl (") as shown in figure 1. From this time series of CNs, the probability distribution of coordination numbers for U3+ was evaluated as shown in figure 2.

In overall, a U3+ was involved in 4- to 8-coordinated

structures in its first coordination shell, and the 6-fold coordination structure (CN = 6) accounted for the largest portion, and 7-fold came the second followed by 5-fold.

At 858.4 K, the 6-fold

coordination structure claimed 78.04% portion of all the simulation time and decreasing slightly fluctuated with increasing temperature.

On the other hand, the 5-fold coordination structure

increased approximately with increasing temperature ranging from 1.78% at 858.4 K to 13.6% at 1019.4 K.

The 7-fold coordination structure increased with temperature at low temperature,

maximized at 920.5 K, and decreased at high temperatures.

The 8-fold and 4-fold coordination

structures were negligible claiming only 2.06% portion in maximum.

Therefore, it was

concluded that the coordination structure of U3+ fluctuated dynamically, low temperature was conducive to the formation of high coordinated structure, and high temperature causes low coordinated structure.

The phenomenon was also supported by the RDFs and integrated RDFs

of U-Cl pair at different temperatures shown in figure S3, where the plateau of $U-Cl (") for 858.4 K was higher than that for 1019.4 K and the first peak position of g(") slightly shifted left with increasing temperature. Our simulations were consistent with experimental observations and classical MD simulations reported in literatures (table 2).

For example, Okamoto’s group reported a CN

value of 6.0 in molten UCl3 based on high temperature X-ray diffraction (XRD) at 1200 K.33

In

a later work with the same system and temperature, this group reported a CN value of 8.0 using polarizable ion model (PIM) MD simulations in combination with XRD.8


If the UCl3 is

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dissolved in molten LiCl-KCl eutectic, this CN value will decrease.

At 823 K, an average CN

of 6.9 or 6.6 was obtained in molten LiCl-KCl eutectic consisting of 17% or 5% UCl3 from XAFS analysis, and 7.2 or 6.8 in the corresponding systems from MD simulations.5

From this

literature, it was also evaluated that the 7-fold coordination structure was dominant for about 65% portion and the 6-fold for about 30% portion in LiCl-KCl eutectic with 5% UCl3 at 823 K.5 The CN value of 7.05 was also obtained from rigid ion model (RIM) and PIM MD simulations in combination with neutron diffraction (ND) structural analysis.34-35

These differences were

attributed to the sensitivity of coordination structure of U3+ to composition, temperature, characterization technologies (XRD, XAFS or ND), and simulation methods including force field selection, parameter settings, and data acquisition.

Fig. 2

Probability distribution of coordination numbers for U3+ in molten LiCl-KCl-UCl3

mixture (FPMD, NVT ensemble, 886.0 K, color online)

3.4

Fluctuations of coordination numbers and cage volumes Figure 3 showed the fluctuations of two coordination cages of U1 and U2 around two

U3+ cations in molten LiCl-KCl-UCl3 mixture, including fluctuation of coordination numbers and 11 ACS Paragon Plus Environment


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cage volumes.

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The cage volume was evaluated as the volume enclosed in the polyhedron

consisting of the surrounding Cl− anions and a central U3+ ion. From figure 3a, it was clear that the fast exchange of Cl− between the first and second coordination shells of U3+ accompanied with fluctuation of coordination number.

The U1 cage

had a coordination number of 7 at beginning of the FPMD simulation, and this coordination number reduced to 6 as one of the Cl− anions (Cl60) moved out of the first coordination shell at 0.624 ps.

Shortly after that, a Cl− (Cl9) moved into the first coordination shell around 2.710 Å

from the second coordination shell around 5.839 Å (see table S1) at 3.376 ps and the coordination number returned back to 7.

From figure 3a, it could be seen that the coordination

number jumped up and down between 6 and 7 during the FPMD simulation, and even dropped further to 5 between 4.964 and 5.058 ps.

(a)


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(b) Fig. 3

Fluctuation of coordination numbers CNs and cage volumes V for cage (a) U1 and (b)

U2 in molten LiCl-KCl-UCl3 mixture (FPMD, NVT ensemble, 886.0 K, color online)

Besides of the fluctuation of coordination number, the motion of Cl− relative to U3+ also caused the fluctuation of cage volume (figure 3a).

In overall, the cage volume fluctuated

greatly between 12.91 and 39.20 Å3 for cage U1 during our FPMD at 886.0 K.

Since the

comparison of any cage volumes with different coordination number was implausible, we would compare cage volume with the same coordination number.

From figure 3a, it could be seen

that the volume of cage U1 corresponded well with the coordination number, fluctuating between 29.59 and 39.20 Å3 with an average of 34.10 Å3 for CN = 7, and between 19.18 and 30.52 Å3 with an average of 25.64 Å3 for CN = 6.

This average cage volume for CN = 6 was consistence

with experimental value at 24.68 Å3 and slightly smaller than 30.54 Å3 of pure UCl3 crystal.36 Similar complex and fluctuating coordination structure was also reported by Nam et al. in their classical MD simulations.19, 37

Finally, it was concluded that the volume of U3+ cage with the



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same CN conserved despite of the exchange of Cl− between the first and second coordination shells. Compared with coordination cage U1, cage U1 showed similarly phenomena except for higher exchange frequency of Cl− between the first and second coordination shells (figure 3b). The volume of cage U2 also fluctuated in accordance with coordination number, with value between 28.66 to 39.01 Å3 in average of 34.92 Å3 for CN = 7 and between 20.85 and 31.58 Å3 in average of 25.58 Å3 for CN = 6.

3.5

Self-diffusion coefficient and solvodynamic mean radius The self-diffusion coefficient of U3+ in LiCl-KCl molten salt was evaluated from the long

time limit of mean square displacement (MSD) of the same type of ions in molten mixture based on the Einstein formula, (

' = ) lim+→-

d(MSD)

(4)

d+

In figure 4, it compared the simulated self-diffusion coefficient of U3+ with experimental self-diffusion coefficient reported in three different literatures.38-40

Though experimental

self-diffusion coefficients in literatures were measured at lower temperatures than our simulation temperatures, our FPMD self-diffusion coefficients change with the same tendency compared with literature values, except the ones by Masset evaluated from two transient electrochemical measurements.38

The experimental self-diffusion coefficient was usually sensitive to the

measurement conditions, including temperature, working electrodes, electrolyte compositions and the difficulty in precise measurement of the electrode surface area.

From figure 4, it could

also be concluded that self-diffusion coefficients evaluated from cyclic voltammetry38 converged with those from chronopotentiometry39 at the Pt electrode, however, did not converge with those


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from transient electrochemical measurements on an inert tungsten electrode.

Fig. 4

Self-diffusion coefficient of U3+ in molten LiCl-KCl-UCl3 mixture (the dashed lines are

only guide to the eyes)

The solvodynamic mean radius (Rd) of an electroactive species could be evaluated from the Stokes-Einstein equation, 23 = 45 /678'

(5)

where kB is the Boltzmann constant, T the absolute temperature, D the diffusion coefficient, and η the viscosity.41

And the viscosity of molten LiCl-KCl eutectic could be evaluated from the

temperature dependence of viscosity, 8 = 8.61 × 109 exp ( as reported in literature.42

>9(? @

)

(6)

The calculated Rd of U3+ decreased from 4.37 Å to 2.23 Å as

temperature increased from 858.4 K to 1019.4 K (table 3), significantly larger than bare U3+ at about 1.025 Å.17,

43

However, the Rd was in the same range compared with the first

coordination radius of U-Cl ranging between 2.20 and 2.73 Å.


Therefore, it could be concluded


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Page 16 of 39

that the transport of U3+ will more like to drag Cl− anion in its first coordination sphere. Furthermore, the significant decrease in Rd at high temperature was an important evidence of the fast exchange of Cl− anion between the first coordination sphere and the out layers, and the decrease in effective first coordination number resulted from vibrant thermal motion.

Table 3

Self-diffusion coefficient D (10−5 cm2 s−1), experimental viscosity η (10−3 N s m−2) and

solvodynamic mean radius Rd (Å) at multiple temperatures T (K)

a

3.6

T

D

ηa

Rd

858.4

0.89

1.62

4.372

886.0

1.27

1.47

3.465

920.5

2.19

1.32

2.322

969.8

1.81

1.15

3.401

1019.4

2.67

1.02

2.750

evaluated from the temperature dependence of viscosity equation (6).

Dynamics of U3+ coordination distances The dynamic of U3+ coordination structure was critical to the atomistic explanation of

electro-refining in molten salt mixture.

Phenomenologically, the electro-refining process could

be divided into the following steps: the transport of U3+ coordinated by Cl− to the cathode, the deprivation of Cl− from U3+, the transfer of electron from cathode to U3+ (or the reduction of U3+), and the metallization (alloying) of atomic U on (with) cathode.

Therefore, the dynamic of U3+

coordination structure was related to the first two steps of electro-refining, and the fluctuation of coordination distances or the dynamics of U-Cl were studied as shown in figure 5.


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For coordination cage U1, six anions, Cl5, Cl19, Cl23, Cl28, Cl61 and Cl69, were close to the U1 cation with coordination distances fluctuated between 2.354 and 4.918 Å, with average coordination distances at 2.854, 2.790, 2.794, 2.793 and 2.906 Å, respectively.

The other three

anions, Cl9, Cl39 and Cl60, exchanged between the first and second shells, and the coordination distances fluctuated, respectively, from 2.629 to 8.262 Å, 2.445 to 8.276 Å, and 2.682 to 9.929 Å during FPMD simulation.

This fast fluctuation of coordination distances caused the change of

first shell coordination number (figure 3).

From these observations, it could be concluded that

the U3+ cation exchanged coordinated Cl− anions with environment, but the U3+ cation (or the solute species) didn’t jump from one coordination cage to another neighboring cage.

In

addition, a coordination Cl− anion could stay in the first coordination sphere either for long time or for short time depending on the existence of other ions in vicinity. The dynamics of Cl− anions involved in cage U2 were more complicated compared with the cage U1.

For the coordination cage U2, twelve Cl− involved in the first coordination shell

with only four Cl− anion, Cl3, Cl14, Cl15 and Cl57, residing in the first coordination shell during our FPMD.

The coordination distances of these four residing anions fluctuated slightly around

2.766 Å, consistent with the first peak positions at 2.77 Å deduced from XAFS experiment.5 few other anions shuttled between the coordination cage and the out shells.

A

These

characteristics were consistent with classical MD simulations by Okamoto et al. who reported that larger coordination number corresponded to larger mean interionic separation.44



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(a)

(b) Fig. 5

Dynamics of coordination distances for cages (a) U1 and (b) U2 in molten

LiCl-KCl-UCl3 mixture (FPMD, NVT ensemble, 886.0 K, color online)

3.7

Van Hove function The dynamic behavior of U3+ microstructure could be assessed rigorously via van Hove

function A(", C), which was a real-space dynamical correlation function for characterizing the spatial and temporal distributions of pairs of particles in a fluid.


This function was defined as

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the probability of finding a particle at position r after a delayed time t, given that there was a particle at the origin at the time t = 0 without delay.45-46

The A(", C) could be separated into

self-part AD (", C) and distinct part A3 (", C) as followed, (

AD (", C) = 〈∑E JK( H(" + "J (0) − "J (C))〉

(7)

E

(

AM (", C) = 〈∑E JON H(" + "N (0) − "J (C))〉

(8)

E

where AD (", C) described the average motion of the particle that was originally at origin, whereas A3 (", C) described the motion of the remaining P − 1 particles.

In figure 6, it

showed the AD (", C) for U3+-U3+ and A3 (", C) for U3+-Cl– evaluated from FPMD simulations with several delayed times (C = Q3 ).

From the self-part of van Hove function AD (", C) for

U3+-U3+, it could be seen that a U3+ moved, relative to its origin position, further and further as the delayed time increased.

Furthermore, the AD (", C) gradually approached to a

Gaussian-shape function as the time delay increased to about 1000 fs indicating that the U3+ moved in random walk around its origin location. identical to the RDF of %U-Cl (") at t = 0.

For the A3 (", C) part for U3+-Cl–, it was

And then, the A3 (", C) gradually diffused as time

delay increased indicating the shuttling of Cl− around the central U3+.



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(a)

(b) Fig. 6

(a) AD (", C) for U3+-U3+ and (b) A3 (", C) for U3+-Cl– at several delayed times Q3 in

molten LiCl-KCl-UCl3 mixture (FPMD, NVT ensemble, 886.0 K, color online)

Furthermore, we calculated the maximum displacement, at 100% and 90% probabilities, of U3+ in relative to its original position as a function of delayed time from the self-part of van Hove function AD (", C) for U3+-U3+ as shown in figure 7.

After a time delay of 10 fs, it could


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be seen that a U3+ moved, relative to its origin position, to about 0.07 or 0.09 Å in maximum with 90% or 100% probability.

As the delayed time increased, the U3+ moved further and

further, with maximum displacement of 1.70 or 2.29 Å with 90% or 100% probability after a time delay of 1000 fs.

Considering that the U3+-Cl– distance was about 2.710 Å (from RDF),

the U3+ was actually still stayed in its original coordination cage after a delayed time of 1000 fs. Therefore, it could be deduced that the U3+ did not jump out of its coordination cage.

Fig. 7

Maximum displacement of U3+ in relative to its original location as a function of delayed time t

4.

Conclusions We investigated the U3+ coordination structure in molten LiCl-KCl eutectic at different

temperatures via FPMD simulations, and revealed the dynamics of structural fluctuation.

The

coordination structure of U3+ in terms of RDFs and CNs corresponded well with X-ray/neutron diffraction observation, X-ray absorption fine spectroscopy analysis and classical MD simulations.

From the probability distribution of coordination numbers, it was concluded that 21 ACS Paragon Plus Environment


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the 6-fold coordination structure dominated with largest portion up to 67.91 % and it was also inferred that high temperature was beneficial for the formation of low coordinated structure. The solvodynamic mean radius of U3+ in molten LiCl-KCl was also evaluated from the Stokes-Einstein equation based on the diffusion coefficient and viscosity, its significant decrease at high temperature was an evidence of the fast exchange of Cl− anion between the first coordination sphere and out layers. In addition, the coordination structure of U3+ showed a surprisingly large variation of nearest U-Cl distances from 2.306 to 9.929 Å accompanied with rearrangement of coordination cages and fast fluctuation of coordination number between 6 and 7 for most of the time. Furthermore, the variation of coordination cage volume was consistent with the fluctuation of coordination number.

The dynamic behavior of U3+ microstructure was also assessed by van

Hove function and it was indicated that the U3+ did not jump out of its coordination cage. Finally, it was concluded that the 6-fold coordination structure was predominant in the molten LiCl-KCl-UCl3 mixture with average cage volume being conserved at about 26.86 Å3. Eventually, the predictability of FPMD simulation for structural characteristics of molten salt mixtures was confirmed, and the simulation results can be useful in the establishment of database of actinide solutes behavior, which is essential for the development of efficient pyroprocess of spent nuclear fuel.

This work is a preliminary exploration and follow-up works

of other actinide solutes in molten salt are in progress.

Acknowledgements This work is supported by NSAF (Grant No. U1630102) and the National Natural Science Foundation of China (Grant Nos. 21376147 and 21573143).


They also acknowledge

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the High Performance Computing Center and the Laboratory for Microstructures, Shanghai University for computing and structural characterization. Supporting Information Available:

Additional details on calculation results are

available free of charge via the Internet at http://pubs.acs.org.

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TOC graphic


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Fig. 1 RDFs g(r) and integrated RDFs n(r) for molten LiCl-KCl-UCl3 mixture (FPMD, NVT ensemble, 886.0 K, color online) 287x229mm (300 x 300 DPI)

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Fig. 2 Probability distribution of coordination numbers for U3+ in molten LiCl-KCl-UCl3 mixture (FPMD, NVT ensemble, 886.0 K, color online) 203x140mm (300 x 300 DPI)


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Fig. 3 Fluctuation of coordination numbers CNs and cage volumes V for cage (a) U1 and (b) U2 in molten LiCl-KCl-UCl3 mixture (FPMD, NVT ensemble, 886.0 K, color online) 200x140mm (300 x 300 DPI)



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Fig. 3 Fluctuation of coordination numbers CNs and cage volumes V for cage (a) U1 and (b) U2 in molten LiCl-KCl-UCl3 mixture (FPMD, NVT ensemble, 886.0 K) 200x140mm (300 x 300 DPI)


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Fig. 4 Self-diffusion coefficient of U3+ in molten LiCl-KCl-UCl3 mixture (the dashed lines are only guide to the eyes) 287x215mm (300 x 300 DPI)



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Fig. 5 Dynamics of coordination distances for cages (a) U1 and (b) U2 in molten LiCl-KCl-UCl3 mixture (FPMD, NVT ensemble, 886.0 K, color online) 231x140mm (300 x 300 DPI)


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Fig. 5 Dynamics of coordination distances for cages (a) U1 and (b) U2 in molten LiCl-KCl-UCl3 mixture (FPMD, NVT ensemble, 886.0 K, color online) 231x140mm (300 x 300 DPI)



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Fig. 6 (a) G_s (r,t) for U3+-U3+ and (b) G_d (r,t) for U3+-Cl– at several delayed times τ_d in molten LiClKCl-UCl3 mixture (FPMD, NVT ensemble, 886.0 K, color online) 287x200mm (300 x 300 DPI)


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Fig. 6 (a) G_s (r,t) for U3+-U3+ and (b) G_d (r,t) for U3+-Cl– at several delayed times τ_d in molten LiClKCl-UCl3 mixture (FPMD, NVT ensemble, 886.0 K, color online) 287x200mm (300 x 300 DPI)



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Fig. 7 Maximum displacement of U3+ in relative to its original location as a function of delayed time t 287x229mm (300 x 300 DPI)


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TOC graphic 520x277mm (150 x 150 DPI)


Dynamic Fluctuation of U3+ Coordination Structure in the Molten LiCl

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