# Molecular dynamics simulation of solar salt (NaNO3-KNO3) mixtures

A. Anagnostopoulos, Alessio Alexiadis, Yulong Ding

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A. Anagnostopoulos, Alessio Alexiadis, Yulong Ding. Molecular dynamics simulation of solar salt (NaNO3-KNO3) mixtures. Solar Energy Materials and Solar Cells, 2019, 200, pp.109897. 10.1016/j.solmat.2019.04.019. hal-05432508

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Molecular dynamics simulation of solar salt (NaNO3-KNO3)
mixtures

A. Anagnostopoulos, A. Alexiadis, Y. Ding

University of Birmingham, School of Chemical Engineering, Birmingham, United Kingdo

**Abstract**

Molten salts have extended applications in concentrated solar power (CSP) installations, both as heat transfer and energy storage materials. In this study, a set of Lennard-Jones interatomic parameters are introduced for simulating NaNO3 and KNO3, as well as their most frequently industrially used mixture the so-called solar-salt (60% NaNO3 – 40% KNO3). Local structures are studied via radial distribution functions. Furthermore, density, thermal conductivity, self-diffusivity, viscosity and surface tension are calculated, from melting to decomposition temperature, and compared with experimental data. The local structures are calculated with both existing and presented interatomic potentials and are found to be in excellent agreement. Additionally, density, viscosity and surface tension present minor differences from literature data. Thermal conductivity, in terms of absolute values is in the proximity of reported data but is questionable in terms of trend. Finally, self-diffusion coefficients declinate from measured values, but are similar in terms of trend. Results are found to be in good agreement. This work represents the first extended validated effort in modelling molten nitrate salts and their mixtures at elevated temperatures using a Lennard-Jones potential, providing new tools that can aid in the fundamental understanding of molten salt structures at the molecular scale.

**1. Introduction**

Nowadays, 22.1% of global electricity production comes from renewable sources, with 1% of that being harvested from solar photovoltaics (PV) and concentrated solar power (CSP) installations. Hydropower is still the most common renewable technology. However, the use of solar PV and CSP grows at a rate of 30% every year [1].

Due to their low cost, good thermal properties and low vapour pressure, molten salts have extended applications in CSP plants, both as a heat transfer fluid and an energy storage medium. Molten nitrates are the most frequently used salts due to their thermal stability and relatively low cost. Their mixtures, and specifically that of sodium and potassium nitrate, have a lower melting point than the independent components and thus a larger liquid phase range, leading to a larger operating range and minimal energy demand to remain in liquid form [2]. The optimal mixture is the pure molten salt eutectic (50% NaNO3 and 50% KNO3), but due to the higher cost, mixtures with 60% NaNO3 and 40% KNO3 are preferred; the properties of the latter mixture are almost identical to the pure.

Study of the behaviour of molten salts can further improve the understanding of their behaviour, as well as identify areas where technical improvements are possible. High working temperatures make measurement of the material properties difficult. Molecular dynamics (MD) simulations present an alternative prediction tool.
MD simulations of molten salts is an ongoing issue, starting in the late 1970s. The first works aimed to validate interatomic parameters of molten chlorides, due to their applications in nuclear energy. Studies were conducted on the structure of molten sodium, potassium and lithium and rubidium chloride [3–5]. Studies on chlorides are ongoing until today. Recently, Ding et al. studied the structure of NaCl and KCl and their mixtures and accurately calculated their properties using RNEMD methods [6]. In a similar work, Bengtson et al. investigated LiCl and KCl mixtures focusing on the changes in local structures and topological distributions [7]. Wang et al. computed the transport properties of LiF, BeF and ThF4 molten salt, using a polarizable force field, and observed that the electrical conductivity increases rapidly from 873 K to 1273 K, while the opposite was observed in the case of the viscosity [8,9]. Sun et al. also performed a study on four binary chloride systems (LiCl-RbCl, LiCl-CsCl, NaCl-RbCl and NaCl-CsCl). The study examined the impact of LiCl and NaCl on both the structures and the transport properties of RbCl and CsCl. It was observed that the positive ions lead to weaker interactions between the counterions and hence affect the final structure of the mixture [10]. In terms of molten carbonates, in another study by Ding et al., a series of calculations regarding local structures and transport properties were performed for binary carbonate mixtures of Na2CO3 and K2CO3, and in a subsequent publication the effect of the molar compositions on the local structures of the molten carbonate eutectics was further investigated [11,12].

The first MD work on nitrate mixtures, to the best of our knowledge, was conducted by Adya et al. [13]. Mixtures of NaNO3 and NaNO2, including their eutectic, were examined by means of MD simulations. This study highlights the excellent agreement between the MD calculation and X-ray diffraction measurements. A more recent study on the specific heat capacity and thermal conductivity of molten NaNO3, including the effect of SiO2 nanoparticles, was conducted by Qiao et al. [14,15]. This study attributes the enhancement of the specific heat capacity to structural changes in the liquid-particle interface, caused by the nanoparticles. Jayaraman et al. [16] calculated the liquid and crystal phases of NaNO3, LiNO3 and KNO3, as well as their viscosities, thermal conductivities and specific heat capacities at 773 K. Excellent agreement with experimental values was found for all properties investigated. In a subsequent study [17], the free energy and melting point of the mixtures of the three nitrates, in various concentrations, was also investigated. The behaviour of Solar Salt with various concentrations of Al2O3 nanoparticles was investigated by Yanwei et al. [18]. A set of ‘ad hoc’ Lennard-Jones parameters was proposed with the purpose of investigating the interaction energy of the nanoparticle on the base fluid. The study outlined the increase in Coulombic forces in the presence of nanoparticles, as well as its effect on the specific heat capacity. Ni et al. modified the potential of Jayaraman by changing the intramolecular parameters (bond, angle and improper forces). With this adjustment on the original Buckingham potential, an improved local structure prediction and property calculation was achieved. Furthermore, a mixture of NaNO3 and KNO3 was also simulated and the viscosity, thermal conductivity and density were calculated, with good agreement [19].

The accuracy of MD calculations depends on the availability of validated interatomic potentials. In the literature, several Lennard-Jones potentials are available for NaNO3 and KNO3 in aqueous solutions. These parameters, however, are not designed for molten phases. Buckingham parameters for pure molten NaNO3 and KNO3 do exist but are not suitable for mixtures, mainly because mixing rules, like the Lorentz-Berthelot rules for the Lennard-Jones potential, are not
available for the Buckingham potential. There are, therefore, no available interatomic potentials for the simulation of the solar salt.

This study proposes a set of Lennard-Jones parameters for molten NaNO3-KNO3 mixtures commonly used in industry (60% NaNO3 and 40% KNO3). To validate the proposed potential, local structural properties such as the radial distribution function (RDF) and transport properties such as viscosity, thermal conductivity and self-diffusivity, as well as other properties such as density and surface tension, are calculated and compared with experimental data available in the literature.

## 2. Theoretical background

### 2.1. Interatomic potential

The Lennard-Jones potential is used to describe pairwise interactions between atoms:

$$ (1) \quad E_{LJ}(r) = 4\epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6} \right] $$

where σ is the finite distance at which the inter-particle potential is zero, ε the depth of the potential well, and r the distance between two atoms. Coulombic interactions are computed using:

$$ (2) \quad E_{Coulomb}(r) = \frac{c q_i q_j}{e r} $$

where C is an energy-conversion constant, qᵢ the atom charge on atoms of type i, qⱼ the atom charge on atoms of type j, and e the dielectric constant.

The Lennard-Jones potential is relatively simple and computationally inexpensive (ideal for large atom systems). Moreover, for this potential, simple rules for calculating the cross-term interaction terms exist:

$$ (3) \quad \sigma_{ij} = \frac{\sigma_i + \sigma_j}{2} $$

$$ (4) \quad \epsilon_{ij} = \sqrt{\epsilon_i \epsilon_j} $$

The optimal values of ε and σ for the Lennard-Jones potential for the pairs Na–Na, O–O, N–N and K–K are derived by fitting the NaNO3 and KNO3 Buckingham potentials of Jayaraman et al. [16]. The fitting was obtained by minimising the least-squares error between the energy-distance curves of the two potentials. However, σ of the K–K pair was slightly modified from the initially obtained value in order to compensate for the underprediction of the density of KNO3 at the melting point by the Buckingham potential.

Cross-term interactions are calculated using the Lorentz-Berthelot mixing rules (Eq. (3) and Eq. (4)). Table 1 shows all parameters used in the simulations.

### 2.2. Intramolecular potential
The bond, angle and improper dihedral potentials of the nitrate (NO3) structure are also accounted for. The N–O bond is simulated as a harmonic bond, with a harmonic bond constant of 525.0 (kcal mol–1 Å–1) and an equilibrium bond length of 1.2676 Å. The O–N–O angle is simulated as a harmonic angle with an angular constant of 105.0 (kcal mol–1 rad–2) and an equilibrium angle of 120°. The improper O–N–O–O is simulated by a harmonic improper dihedral potential with constant 60.0 (kcal mol–1 rad–2) and equilibrium angle of 0.0. The values for the intramolecular parameters are taken from Qiao et al. [14]. For all three cases the equation has the following format:

$$ (5) E = K(r - r_0)^2 $$

where E is the harmonic potential, K a constant and $r_0$ the equilibrium bond length in the case of the bond, or the equilibrium angle in the case of the angle, or improper dihedral potential.

## 2.3. Simulation details

All simulations were performed using the LAMMPS software package [20]. Pure molten NaNO3, KNO3 and three mixtures (Table 2) were investigated. The 59.66%–40.44% mixture was selected because it is the most commonly used mixture in the CSP industry. The 50%–50% molar mixture is close to the eutectic mixture of the two salts, while the third mixture (40.44%–59.66%) was chosen to test the accuracy of the proposed potential when KNO3 is the major component of the mixture.

For the pure salts, the crystalline structures of NaNO3 and KNO3 are taken from Gonschorek et al. and Adiwidjaja et al., respectively, and replicated in all dimensions, so that the resulting system consists of 4900 atoms [21,22].

Quenching is applied to the initial cell for equilibration. After a Polak-Ribiere structural minimisation [23], the system is rapidly heated from 293 K to 1300 K in 0.3 ns, in the NVT ensemble with a Nosé-Hoover thermostat and barostat [24]. Subsequently, it is equilibrated at 1300 K for 0.5 ns in the NVT ensemble, followed by a slow cool down to the melting point in the NPT ensemble for 1 ns [25]. The final structure is obtained by further relaxing the system in the NVT ensemble for 0.5 ns.

The cut-off of the interatomic potential is set at 15 Å, with long-range and Coulombic interactions computed using Hockney’s Particle-Particle Particle-Mesh (PPPM) method [26]. The equations of motion are solved using the Verlet leap-frog algorithm [27]. In all simulations, the timestep is 0.001 ps.

For the solar salt, the NaNO3 and KNO3 unit cells are replicated to achieve the desired atomic molar ratio. To avoid atomic overlap, a variable random displacement of all atoms is applied in all three dimensions, using a LAMMPS routine called fix move. A minimisation and quenching process, as described above, is then applied to obtain the final structure.

## 2.4. Calculated properties
In this work, local structure (RDF), transport properties (viscosity and thermal conductivity) and surface tension are calculated for the pure molten salts, as well as their mixtures. The computational methodology for each property is described below.

### 2.4.1. Radial distribution function

The radial distribution function $g_{AB}(r)$, or pair correlation function, is the probability of encountering an atom B at a distance r from atom A. It is described by:

$$ (6) g_{AB}(r) = \frac{V n_B(r)}{N_B 4\pi r^2 dr} $$

where V is the volume of the system, $n_B(r)$ is the number of B particles in a spherical shell of radius r and thickness $dr$ centred on atom A, and $N_B$ is the total number of B particles.

### 2.4.2. Density

Density is calculated as:

$$ (7) \rho = \frac{\sum_i N_i M_i}{N_A V_{NPT}} $$

where $N_i$ is the number of particles of type i, $M_i$ is the molar mass of species i, $N_A$ is Avogadro's constant, and $V_{NPT}$ is the volume in the NPT ensemble.

### 2.4.3. Thermal conductivity

Thermal conductivity is calculated as the time integral of the heat flux autocorrelation function:

$$ (8) k = \frac{1}{3V k_B T^2} \int_0^\infty \langle \mathbf{J}(0) \cdot \mathbf{J}(t) \rangle dt $$

where V is the volume, $k_B$ the Boltzmann constant, T the temperature, and $\langle \cdot \rangle$ denotes ensemble averaging. The heat flux vector $\mathbf{J}$ is defined as:

$$ (9) \mathbf{J} = \sum_i e_i \mathbf{v}_i + \frac{1}{2} \sum_i \sum_{j \neq i} (\mathbf{F}_{ij} \cdot \mathbf{v}_i) \mathbf{r}_{ij} $$

where $e_i$ is the total energy, $\mathbf{v}_i$ the velocity of particle i, and $\mathbf{F}_{ij}$ the force on atom i exerted by atom j.

For the calculation of thermal conductivity, the system is first equilibrated for 1 ns in the NVT ensemble using a Nosé-Hoover thermostat at the desired temperature. After equilibration, heat flux values are averaged for 20 ns in the NVE ensemble to calculate the thermal conductivity.

### 2.4.4. Viscosity

Shear viscosity is calculated similarly:

$$ (10) \eta = \frac{V}{k_B T} \int_0^\infty \langle P_{xy}(0) P_{xy}(t) \rangle dt $$
where V is the volume, $k_B$ the Boltzmann constant, T the temperature, and $P_{xy}$ is an off-diagonal component of the stress tensor.

For the calculation of viscosity, the system is first equilibrated for 10 ns in the NVE ensemble in the presence of a Langevin barostat. After equilibration, the barostat is turned off and stress tensor values are averaged for 1 ns to calculate the shear viscosity.

### 2.4.5. Surface tension

Surface tension is calculated using the centre-of-mass definition. The z dimension of the equilibrated simulation box is doubled to avoid periodicity issues. The system is then equilibrated in NVT for 2 ns, followed by sampling for 10 ns in the NVE ensemble, during which pressure tensor data are averaged. Surface tension is obtained by:

$$ (11) \gamma = \frac{1}{2} L_z \langle P_{zz} - \frac{1}{2} (P_{xx} + P_{yy}) \rangle $$

where $L_z$ is the box length in the z direction, and $P_{xx}$, $P_{yy}$, $P_{zz}$ are the diagonal elements of the pressure tensor.

### 2.4.6. Diffusion coefficient

The diffusion coefficient is calculated using the Einstein relation via the mean-squared displacement (MSD):

$$ (12) D = \frac{1}{6} \lim_{t \to \infty} \frac{d}{dt} \left\langle \frac{1}{N} \sum_{i=1}^{N} \left| \mathbf{r}_i(t) - \mathbf{r}_i(0) \right|^2 \right\rangle $$

where $|\mathbf{r}_i(t) - \mathbf{r}_i(0)|^2$ is the squared displacement of particle i, and $\langle \cdot \rangle$ indicates averaging over the simulation time.

The system is equilibrated in the NVE ensemble, in the presence of a Langevin barostat, for 1 ns. After equilibration, the barostat is removed and MSD values are averaged for 40 ns in the NVE ensemble. The MSD is plotted versus time and the slope is used to obtain the diffusion coefficient.

## 3. Results and discussion

### 3.1. Radial distribution function

To validate the Lennard-Jones parameters proposed in this study, pure NaNO3 and KNO3 salts were simulated using both the Buckingham parameters from Jayaraman et al. [16] and the proposed Lennard-Jones potential.

For nitrogen and oxygen, the distributions are almost identical, as expected, because bond, angle and improper terms are present and keep the nitrate structure rigid (Fig. 1). For sodium and potassium, minor deviations are observed between the two potentials, especially at the first peak. This is anticipated and is related to the differences in the mathematical formulations of the
Buckingham and Lennard-Jones potentials. Furthermore, the K–K interaction potential, as explained in Section 2.1, has been slightly modified to improve the accuracy of the density.

**3.2. Transport properties and surface tension for all simulated materials**

In this work, the Lennard-Jones potential is used to calculate several properties (viscosity, thermal conductivity and surface tension) of NaNO3, KNO3 and their mixtures with different compositions. Results are compared with available experimental data and summarised in Table 3.

The calculated properties were evaluated across a temperature range covering the entire liquid phase, between the melting and decomposition points, for each mixture. The melting temperatures are taken as 310 °C and 335 °C for NaNO3 and KNO3, 250 °C for the 60%–40% and 40%–60% mixtures, and 220 °C for the 50%–50% mixture. Decomposition temperatures vary depending on heating rate and atmospheric conditions. The lowest temperatures at which no decomposition occurs under any conditions are 400 °C for NaNO3 and KNO3, with the KNO3 case representing a boiling point. For the mixtures, decomposition is assumed to start at 450 °C.

For the individual components, the density prediction is excellent.

In terms of the mixtures, slight variations in density are attributed to the empirical nature of the cross-term interactions. Viscosity is overestimated. In all cases, absolute values are within 12.32% of experimental measurements. Thermal conductivity is overpredicted in all cases and shows an increasing trend. As discussed further in Section 3.2.2, this is linked both to uncertainty in thermal conductivity measurements and to how the property is defined at the molecular level. Diffusion coefficients are strongly underpredicted in all cases. However, the results illustrate a key advantage of MD studies: values can be obtained where experimental measurements are lacking, providing, if not a perfect prediction, a reasonable estimate of the trend. Surface tension values are overpredicted in all cases, but the differences from experimental measurements do not exceed 14.56%. Overall, the properties calculated using the proposed interatomic parameters are in good agreement with literature data.

In the next sections, we focus on the eutectic mixture (60% NaNO3 and 40% KNO3), which is by far the most frequently used molten salt in the CSP industry.

**3.2.1. Density**

The density of the solar salt over its full liquid-phase temperature range is shown in Fig. 2. The average difference between computed and measured values is 6.1%. This could be attributed to the cross-term interactions between Na and K, which are based on the mixing rule and therefore include some degree of inaccuracy.

At higher temperatures, kinetic energy causes the molecular structure of the liquid to become more dispersed and hence the density decreases.

**3.2.2. Thermal conductivity**

Overall, the simulations agree with the available experimental data. However, for T > 400°C (Fig. 3), the trend differs. We do not have a clear explanation for this difference, which also occurs in
other MD studies of molten nitrate salts using the Buckingham potential [19]. It should also be noted that experimental thermal conductivity measurements are particularly difficult at these temperatures and are often not consistent with each other (Fig. 3).

### 3.2.3. Viscosity

A comparison between calculated and measured values is shown in Fig. 4, with an average difference of around 10%. The trend of molten salt density with temperature (Fig. 2) confirms that at higher temperatures the liquid becomes less dense, with larger interatomic distances, leading to lower resistance to shear stress and therefore an expected reduction in viscosity.

### 3.2.4. Surface tension

Experimental and calculated results follow the same trend (Fig. 5). No experimental data were found for values above 400°C. The average percentage difference between experimental and simulated values is 8.6%.

### 3.2.5. Self-diffusion coefficient

In Fig. 6, the self-diffusion coefficients of solar salt are compared between experimental measurements and calculated values. Although the trends are similar, the discrepancy between measured and calculated values is larger for self-diffusivity than for the other properties. In general, self-diffusivity is often not very accurate in MD simulations, and the average error (94.25%) obtained here is comparable with other simulations [37–39].

## 4. Conclusions

This study presents a set of Lennard-Jones parameters capable of representing the behaviour of pure molten NaNO3 and KNO3, and their mixtures, across the temperature range relevant to solar applications.

For validation, the simulated local structures of pure NaNO3 and KNO3 are compared with those obtained in a previous study of the same materials using the Buckingham potential. The RDF peak positions are in good agreement in all cases, except for KNO3, where the potential has been slightly adjusted to match the density at the melting point.

The transport properties (density, thermal conductivity and viscosity), as well as surface tension, of both pure molten NaNO3 and KNO3 are also investigated. Density, viscosity and surface tension agree closely with literature data, with differences not exceeding 17.11% in any case. Self-diffusivity deviates from literature values, but follows a similar trend. Thermal conductivity agrees in absolute terms but shows a trend opposite to most reported literature data. Several factors affect both measurement and calculation of thermal conductivity, making systematic agreement difficult. Further experimental and computational work is required to investigate this behaviour.

Atomic interactions are important and govern behaviour at material interfaces. A Lennard-Jones parameter set such as the one presented here can support studies of molten salt mixtures because it allows validated cross-term parameter calculation. This is relevant for systems such as molten
salt-nanoparticle mixtures, where the nanoparticle-salt interface can be studied to understand changes in properties, and for composite material formulations where information on pores, capillary forces and wetting or corrosion phenomena is needed. MD simulations can also visualise surface alteration at the atomic scale and provide results in conditions where experiments are difficult, expensive, or problematic for microstructure analysis. A simple and computationally inexpensive tool is provided to address these problems.

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<table><caption>Table 1. Lennard-Jones parameters of NaNO3 and KNO3</caption><thead><tr><th>Element</th><th>Q [e]</th><th>ε [eV]</th><th>σ [Å]</th></tr></thead><tbody><tr><td>Na</td><td>1</td><td>0.0066373</td><td>2.407</td></tr><tr><td>K</td><td>1</td><td>0.004336</td><td>3.188</td></tr><tr><td>N</td><td>0.95</td><td>0.004017509</td><td>3.431</td></tr><tr><td>O</td><td>-0.65</td><td>0.003469129</td><td>3.285</td></tr></tbody></table>

<table><caption>Table 2. NaNO3-KNO3 simulated systems</caption><thead><tr><th>NaNO3-KNO3 (%)</th><th>Sodium ions</th><th>Potassium ions</th><th>Total atoms</th></tr></thead><tbody><tr><td>59.66%-40.44%</td><td>960</td><td>384</td><td>6720</td></tr><tr><td>50%-50%</td><td>980</td><td>576</td><td>7780</td></tr><tr><td>40.44%-59.66%</td><td>860</td><td>508</td><td>6829</td></tr></tbody></table>

<caption>Table 3. Comparison between experimental measurements and calculated values for NaNO3, KNO3 and their mixtures for various properties [28–32].</caption>

Density ρ (g cm⁻³)

<table><thead><tr><th>Material</th><th>NaNO3 Tmelt</th><th>NaNO3 Tdec</th><th>KNO3 Tmelt</th><th>KNO3 Tdec</th><th>60%-40% Tmelt</th><th>60%-40% Tdec</th><th>50%-50% Tmelt</th><th>50%-50% Tdec</th><th>40%-60% Tmelt</th><th>40%-60% Tdec</th></tr></thead><tbody><tr><td>Exp</td><td>1.93</td><td>1.85</td><td>1.86</td><td>1.79</td><td>1.98</td><td>1.79</td><td>1.93</td><td>1.80</td><td>1.93</td><td>1.81</td></tr><tr><td>Sim</td><td>1.93</td><td>1.86</td><td>1.86</td><td>1.80</td><td>2.05</td><td>1.86</td><td>2.02</td><td>1.91</td><td>2.08</td><td>1.94</td></tr></tbody></table>

Viscosity η (mP s)

<table><thead><tr><th>Material</th><th>NaNO3 Tmelt</th><th>NaNO3 Tdec</th><th>KNO3 Tmelt</th><th>KNO3 Tdec</th><th>60%-40% Tmelt</th><th>60%-40% Tdec</th><th>50%-50% Tmelt</th><th>50%-50% Tdec</th><th>40%-60% Tmelt</th><th>40%-60% Tdec</th></tr></thead><tbody><tr><td>Exp</td><td>2.94</td><td>2.17</td><td>2.57</td><td>2.07</td><td>4.61</td><td>1.48</td><td>4.72</td><td>1.57</td><td>—</td><td>—</td></tr><tr><td>Sim</td><td>3.42</td><td>2.47</td><td>2.27</td><td>1.92</td><td>3.87</td><td>1.51</td><td>3.91</td><td>1.79</td><td>3.46</td><td>1.63</td></tr></tbody></table>

Thermal conductivity k (W m⁻¹ K⁻¹)

<table><thead><tr><th>Material</th><th>NaNO3 Tmelt</th><th>NaNO3 Tdec</th><th>KNO3 Tmelt</th><th>KNO3 Tdec</th><th>60%-40% Tmelt</th><th>60%-40% Tdec</th><th>50%-50% Tmelt</th><th>50%-50% Tdec</th><th>40%-60% Tmelt</th><th>40%-60% Tdec</th></tr></thead><tbody><tr><td>Exp</td><td>0.51</td><td>0.50</td><td>0.41</td><td>0.38</td><td>0.48</td><td>0.53</td><td>0.48</td><td>0.53</td><td>0.46</td><td>0.51</td></tr><tr><td>Sim</td><td>0.64</td><td>0.68</td><td>0.58</td><td>0.54</td><td>0.56</td><td>0.44</td><td>0.59</td><td>0.54</td><td>0.71</td><td>0.62</td></tr></tbody></table>

Self-diffusion D (cm² s⁻¹ × 10⁻⁵)

<table><thead><tr><th>Material</th><th>NaNO3 Tmelt</th><th>NaNO3 Tdec</th><th>KNO3 Tmelt</th><th>KNO3 Tdec</th><th>60%-40% Tmelt</th><th>60%-40% Tdec</th><th>50%-50% Tmelt</th><th>50%-50% Tdec</th><th>40%-60% Tmelt</th><th>40%-60% Tdec</th></tr></thead><tbody><tr><td>Exp</td><td>3.37</td><td>4.93</td><td>1.48</td><td>2.22</td><td>1.36</td><td>3.23</td><td>—</td><td>—</td><td>—</td><td>—</td></tr></tbody></table>
<table><caption>Surface tension γ (mN m⁻¹)</caption><tr><td>Sim</td><td>0.893</td><td>1.76</td><td>0.364</td><td>0.823</td><td>0.352</td><td>1.532</td><td>0.124</td><td>1.345</td><td>0.257</td><td>1.834</td></tr></table>

<table><thead><tr><th>Material</th><th>NaNO3 Tmelt</th><th>NaNO3 Tdec</th><th>KNO3 Tmelt</th><th>KNO3 Tdec</th><th>60%-40% Tmelt</th><th>60%-40% Tdec</th><th>50%-50% Tmelt</th><th>50%-50% Tdec</th><th>40%-60% Tmelt</th><th>40%-60% Tdec</th></tr></thead><tbody><tr><td>Exp</td><td>119.8</td><td>115.5</td><td>116.7</td><td>107.3</td><td>118.9</td><td>108.2</td><td>120.7</td><td>107.1</td><td>120.1</td><td>106.3</td></tr><tr><td>Sim</td><td>135.7</td><td>129.4</td><td>128.6</td><td>122.2</td><td>136.3</td><td>114.2</td><td>133.4</td><td>115.2</td><td>136.5</td><td>119.8</td></tr></tbody></table>
<figure><img src="image_2.png" /><figcaption>Fig. 1. Radial Distribution function of NaNO3 and KNO3, comparison between Buckingham and Lennard-Jones potentials</figcaption></figure>
<figure><img src="image_3.png" /><figcaption>Fig. 1. (continued)</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Fig. 2. Density of Solar Salt (60% NaNO3-40% KNO3), comparison with experimental data [28].</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 3. Thermal Conductivity of Solar Salt (60% NaNO3-40% KNO3), comparison with experimental data [2,32–36]</figcaption></figure>