Calculated Self-diffusion Coefficients Research Articles

Molecular dynamics simulations of the local structure and physicochemical properties of CaCl2 molten salt

Abstract CaCl2 molten salt, as a common electrolyte in the process of molten salt electrolysis, has a high decomposition potential and a strong ability to bind O2−. So the study of the structure and properties of CaCl2 is significant for the molten salt electrolysis. In this paper, molecular dynamics simulations (MD) method was used to investigate the variation rule of the local structure and physicochemical properties of CaCl2 molten salt with temperature. The results show that the temperature has less effect on the heterozygous ion pairs and more effect on the homozygous ion pair. With the increase of temperature, the interaction between ion pairs is weakened, the coordination number decreases, the local structure changes a little, and the structural configuration tends to be an irregular octahedral structure with vacancies. The calculated self-diffusion coefficients, viscosities, and ionic conductivities are consistent well with the reality, but there is a significant error in densities due to the strong polarization effect of Ca2+ compared to the reality. The local structure directly determines the thermodynamic properties of the molten salts. This study promotes the basic theoretical research on alkaline earth metal-containing molten salts and is an important reference for the study of molten salt electrolysis process.

Molecular Dynamics Simulation of Diffusion Behavior in Liquid Sn and Pb

This study aimed to clarify the effect of a unique structure with a “shoulder,” which represents a hump on the high wave vector side of the first peak of static structure factor, in liquid Sn (liq-Sn) on the self-diffusion behavior through molecular dynamics (MD) simulation. The MD simulations of liq-Sn at 573 K and liquid Pb (liq-Pb) at 773 K were performed for comparison. The former and latter were selected as element with and without shoulder structure and reliable self-diffusion coefficients in liquid have been measured in both elements. The calculated self-diffusion coefficients of liq-Sn and liq-Pb were reproduced as the same order of magnitude with the referred reliable data of diffusion coefficients, which were obtained by experiments on the ground. The microscopic diffusion behavior of liq-Sn is unlike that of the hard-sphere model because the atoms become sluggish in the range that corresponds to the shoulder appearing in the pair distribution function of liq-Sn as well as in the structure factor of liq-Sn based on the local atomic configurations and time-series analyses of individual atoms. Therefore, the velocity autocorrelation function (VACF) converges to zero more rapidly than that of liq-Pb, and it is reproduced by the hard-sphere model. However, the macroscopic diffusion behavior of liq-Sn expressed by the self-diffusion coefficient is the same as that of the hard-sphere model with the non-correlation of the VACF in the long time.

Local structure and dynamics of ions in LiCl-GdCl3, KCl-GdCl3 and LiCl-GdCl3-Gd2O3 melts: Ab initio molecular dynamics simulations and Raman spectroscopy

Currently, the novel technologies of gadolinium electrochemical production from raw oxide materials using molten oxide-salt media are being developed. To understand the phenomena, data on the structure of gadolinium-containing oxide-salt melts are required. In this study, using ab initio molecular dynamics (AIMD) and in situ Raman spectroscopy, we bring insight on local structure details and ion dynamics in these systems by the examples of LiCl–GdCl3, KCl–GdCl3 chloride melt and LiCl–GdCl3–Gd2O3 oxide-chloride melt with a Gd2O3 concentration up to 2 mol %. The Raman spectroscopy reveals the octahedral species [GdCl6]. According to the AIMD, the Gd-based groupings are joined by various numbers of shared chlorine anions. Gadolinium oxide in the chloride melt dissociates to form [Gd2OLi] groups, which are incorporated into the melt structure. The calculated self-diffusion coefficients of ions and the lifetimes of ion pairs showed that the local structure of the potassium containing melt is more stable as compared to that of the lithium containing melt, which is closely concurring with the divergence in conductivities of these melts. LiGdO2 and GdOCl phases were found in the solidified oxide-chloride melt LiCl–GdCl3–Gd2O3. It has been suggested that the complex oxide LiGdO2 is formed by the reaction Gd2O3 + LiCl → GdOCl + LiGdO2. Based on the obtained data, it was concluded that lithium-containing chloride melt should be considered not only as a solvent for gadolinium oxide, but also as an active reaction medium. Here, lithium is involved in ongoing chemical reactions and participate in reaction product.

The hydroisomerization of n-hexadecane over Pd/SAPOs bifunctional catalysts with different opening size: Features of the diffusion properties in pore channels and the metal-acid synergistic catalysis

In this work, SAPO-11, SAPO-31 and SAPO-41 with one-dimensional channels are synthesized hydrothermally by employing a di-n-butylamine (DBA) template, industrial silicon and aluminum sources, and the corresponding Pd/SAPOs bifunctional catalysts are prepared by loading 0.5 wt% Pd via the wet impregnation method. The diffusivity of n-hexadecane and 2-methylpentadecane in the micropores of different SAPOs is determined by molecular dynamics (MD) simulation, which indicates that the opening size has strong effects on the diffusion property of reactants and intermediates in the micropore channels. The calculated self-diffusion coefficients (Ds) of both n-hexadecane and 2-methylpentadecane based on MD simulation of three SAPOs decrease as SAPO-31 > SAPO-41 > SAPO-11, which is consistent with their minor axis size of micropores. The results of n-hexadecane hydroisomerization test indicate that the Pd/SAPO-31 catalyst shows the highest activity and iso‐hexadecane yield of 85.0% due to the significantly improved diffusion and favorable metal-acid balance. Different from Pd/SAPO-11 and Pd/SAPO-41, hydroisomerization over Pd/SAPO-31 occurs via the key lock mechanism, which leads to an increased multi-branched iso‐hexadecane proportion of 66.3% at the n-hexadecane conversion of 95.3%. The Pd/SAPO-31 catalyst is proven to be a highly effective bifunctional catalyst for the industrial production of bio-diesel with excellent low-temperature fluidity.

Molecular Dynamics and Experimental Study of the Effect of CeF3 and NdF3 Additives on the Physical Properties of FLiNaK

The paper presents the results, which are consistent within 2%, obtained both in the simulation of molecular dynamics and in the experiment on the study of the kinetic properties of molten FLiNaK with addition of lanthanide fluorides. The parameters of the Born-Huggins-Meier potential for the interaction of CeF3 or NdF3 with FLiNaK components are first calculated using the ab initio approach. The enthalpy of the system with dissolved CeF3 or NdF3 calculated in the model increases by ∼4.4% over the entire temperature range studied (800 ≤ T ≤ 1020 K). The self-diffusion coefficients of the molten salt components are calculated from the Einstein relation and also estimated from the shear viscosity data. The temperature dependences of the shear viscosity of molten FLiNaK as well as FLiNaK with additions of 15 mol % CeF3 or NdF3 are determined experimentally and by calculation. In addition, the dependence of shear viscosity on the concentration of CeF3 and NdF3 in FLiNaK is measured and calculated. The linear growth of the shear viscosity with the CeF3 and NdF3 concentrations is obtained. Experimental dependence is in good agreement with the simulated results in the case of NdF3, and there is the discrepancy while CeF3 addition. An analytical approximation of the temperature and concentration dependences for the viscosity of molten FliNaK and for the calculated self-diffusion coefficients of constituent elements is proposed. Linear approximation of temperature dependence of the self-diffusion coefficients of similar components in the corresponding extended systems is presented.

Nonlinear Arrhenius behavior of self-diffusion in β−Ti and Mo

While anomalous diffusion coefficients with non-Arrhenius like temperature dependence are observed in a number of metals, a conclusive comprehensive framework of explanation has not been brought forward to date. Here, we use first-principles calculations based on density functional theory to calculate self-diffusion coefficients in the bcc metals Mo and $\beta$-Ti by coupling quasiharmonic transition state theory and large displacement phonon calculations and show that anharmonicity from thermal expansion is the major reason for the anomalous temperature dependence. We use a modified Debye approach to quantify the thermal expansion over the entire temperature range and introduce a method to relax the vacancy structure in a mechanically unstable crystal such as $\beta$-Ti. Thermal expansion is found to weakly affect the activation enthalpy but has a strong effect on the prefactor of the diffusion coefficient, reproducing the non-linear, non-Arrhenius "anomalous" self-diffusion in both bcc systems with good agreement between calculation and experiment. The proposed methodology is general and simple enough to be applicable to other mechanically unstable crystals.

Combined Deep Learning and Classical Potential Approach for Modeling Diffusion in UiO-66.

Modeling of diffusion of adsorbates through porous materials with atomistic molecular dynamics (MD) can be a challenging task if the flexibility of the adsorbent needs to be included. This is because potentials need to be developed that accurately account for the motion of the adsorbent in response to the presence of adsorbate molecules. In this work, we show that it is possible to use accurate machine learning atomistic potentials for metal-organic frameworks in concert with classical potentials for adsorbates to accurately compute diffusivities though a hybrid potential approach. As a proof-of-concept, we have developed an accurate deep learning potential (DP) for UiO-66, a metal-organic framework, and used this DP to perform hybrid potential simulations, modeling diffusion of neon and xenon through the crystal. The adsorbate-adsorbate interactions were modeled with Lennard-Jones (LJ) potentials, the adsorbent-adsorbent interactions were described by the DP, and the adsorbent-adsorbate interactions used LJ cross-interactions. Thus, our hybrid potential allows for adsorbent-adsorbate interactions with classical potentials but models the response of the adsorbent to the presence of the adsorbate through near-DFT accuracy DPs. This hybrid approach does not require refitting the DP for new adsorbates. We calculated self-diffusion coefficients for Ne in UiO-66 from DFT-MD, our hybrid DP/LJ approach, and from two different classical potentials for UiO-66. Our DP/LJ results are in excellent agreement with DFT-MD. We modeled diffusion of Xe in UiO-66 with DP/LJ and a classical potential. Diffusion of Xe in UiO-66 is about a factor of 30 slower than that of Ne, so it is not computationally feasible to compute Xe diffusion with DFT-MD. Our hybrid DP-classical potential approach can be applied to other MOFs and other adsorbates, making it possible to use an accurate DP generated from DFT simulations of an empty adsorbent in concert with existing classical potentials for adsorbates to model adsorption and diffusion within the porous material, including adsorbate-induced changes to the framework.

Cooperative excitations in superionic PbF2.

Links between dynamical Frenkel defects and collective diffusion of fluorides in β-PbF2 are explored using Born-Oppenheimer molecular dynamics. The calculated self-diffusion coefficient and ionic conductivity are 3.2 × 10-5 cm2 s-1 and 2.4 Ω-1 cm-1 at 1000 K in excellent agreement with pulsed field gradient and conductivity measurements. The calculated ratio of the tracer-diffusion coefficient and the conductivity-diffusion coefficient (the Haven ratio) is slightly less than unity (about 0.85), which in previous work has been interpreted as providing evidence against collective 'multi-ion' diffusion. By contrast, our molecular dynamics simulations show that fluoride diffusion is highly collective. Analysis of different mechanisms shows a preference for direct collinear 'kick-out' chains where a fluoride enters an occupied tetrahedral hole/cavity and pushes the resident fluoride out of its cavity. Jumps into an occupied cavity leave behind a vacancy, thereby forming dynamic Frenkel defects which trigger a chain of migrating fluorides assisted by local relaxations of the lead ions to accommodate these chains. The calculated lifetime of the Frenkel defects and the collective chains is approximately 1 ps in good agreement with that found from neutron diffraction. This article is part of the Theo Murphy meeting issue 'Understanding fast-ion conduction in solid electrolytes'.

Calculation of self-diffusion coefficients in supercritical carbon dioxide using mean force kinetic theory.

This paper presents an application of mean force kinetic theory (MFT) to the calculation of the self-diffusivity of CO2 in the supercritical fluid regime. Two modifications to the typical application of MFT are employed to allow its application to a system of molecular species. The first is the assumption that the inter-particle potential of mean force can be obtained from the molecule center-of-mass pair correlation function, which in the case of CO2 is the C-C pair correlation function. The second is a new definition of the Enskog factor that describes the effect of correlations at the surface of the collision volume. The new definition retains the physical picture that this quantity represents a local density increase, resulting from particle correlations, relative to that in the zero density homogeneous fluid limit. These calculations are facilitated by the calculation of pair correlation functions from molecular dynamics (MD) simulations using the FEPM2 molecular CO2 model. The self-diffusivity calculated from theory is in good agreement with that from MD simulations up to and slightly beyond the density at the location of the Frenkel line. The calculation is compared with and is found to perform similarly well to other commonly used models but has a greater potential for application to systems of mixed species and to systems of particles with long range interatomic potentials due to electrostatic interactions.

Computer Experiments on Self-diffusion Coefficients of Some Liquid Metals

The available experimental self-diffusion coefficients of twenty-two liquid elements near their melting temperatures are compared with the calculated data by the first-principal dynamics simulation. The holistic evaluation shows that the calculated self-diffusion coefficients are in reasonable agreement with the experimental data. For liquid metals with loose-packed structure, the self-diffusion coefficient decreases in general with the increase of packing fraction. For liquid metals with close-packed structure in which the coordination number is larger than 11.5, the self-diffusion coefficient fluctuates around 2.0×10-9 m2s-1, except for liquid Al, Ti and Li of which the self-diffusion coefficients are anomalously large. The packing fraction can only partially account for the self-diffusion coefficient of liquid metals.

First principles investigation on selective hydrogen sensing properties of α-phase TeO2

α-phase TeO2 is a promising sensing material because of its unique ability to detect hydrogen gas. To investigate atomic-level mechanism on gas sensing of TeO2, the interaction between H2, NH3, SO2, CO2, H2S, CH4 gases and TeO2 are studied via first principles simulations. By the calculated adsorption energy, radial distribution function, band gap and charge transfer, TeO2 shows a superior selective detection performance to hydrogen and it is consistent with experimental conclusion. The H–H bond of H2 break after adsorption and a new H–O bond with length of 0.98 Å forms between TeO2 and H2. Moreover, the adsorption of H2 causes an obvious increasing of DOS near the Fermi level, indicating a clear change in the electric conductivity. The calculated self-diffusion coefficients show that the diffusion of hydrogen molecule in TeO2 is much easier than the other gases, suggesting a fast response of H2 by TeO2. This work provides a theoretical foundation for analysis and design of TeO2-based hydrogen sensor.

Unveiling the role of atomic defects on the electronic, mechanical and elemental diffusion properties in CuS

Effects of atomic defects on electronic properties, mechanical stability, and elemental diffusivity in CuS (or covellite) were investigated by first-principles calculations. The metallic CuS shows higher structural and mechanical stabilities compared to CuxS phases. Strong covalent bonds in pristine CuS restrict the self-diffusion of Cu and S atoms; however, different band orientations in presence of atomic vacancies result in a high degree of self-diffusion. Specially, sulfur vacancies play a prominent role in increasing the diffusion of both Cu and S. Calculated self-diffusion coefficients between 100 °C and 150 °C are of the order of 10−6 cm2/s, comparable to experiments.

Ab initio molecular dynamics simulations of molten lead oxyhalides Pb3O2X2 (X = Cl, Br, I)

ABSTRACT An examination of the molecular dynamics of molten lead oxyhalides Pb3O2X2 (X = Cl, Br, I) in terms of melt densities and subsequent constant volume runs was carried out at 973 K on the basis of density functional theory. In view of the determined local structure data, as well as the calculated self-diffusion coefficients, it is proposed that the melt comprises PbO-based associates. Due to the rather complicated spatial motif of these structures, these can be very tentatively considered as oxocentric tetrahedrons. The distance between lead ions ≈4 Å in oxide-halide melts, which is significantly shorter than in pure halide (≈5Å), is comparable with the distance between halogen anions. The pair distribution functions concerning halogens are easily explained in terms of charge ordering.

Study of local structure and ion dynamics in GdCl3 - Gd2O3 and KCl - GdCl3 - Gd2O3 melts: In situ Raman spectroscopy and ab initio molecular dynamics

The local structure and dynamics of ions in homogeneous GdCl3–Gd2O3 and KCl–GdCl3–Gd2O3 oxide-chloride melts with a gadolinium oxide concentration up to 6 mol% were studied using in situ Raman spectroscopy and ab initio molecular dynamics. Quantitative and qualitative changes in the spectral characteristics of homogeneous oxide-chloride melts compared with GdCl3 and GdCl3–KCl melts were observed. These comprised additional low-intensity vibrational bands appearing at 208, 371 and 202, 368 cm−1, respectively. No gadolinium oxide bands were detected, indicating dissociation in the chloride melt. Molecular dynamics simulations showed that oxygen in melts is adjacent to three gadolinium ions, with an inter-ionic OGd distance of 2.2 Å. The [Gd3O] associate, in turn, is incorporated into the network-like structure of the original chloride melt. As a result of this association, ion transport through the melt is hampered, as substantiated by the calculated self-diffusion coefficients.

Diffusion in Binary Aqueous Solutions of Alcohols by Molecular Simulation

Based on the molecular dynamics method, the calculations for diffusion coefficients were carried out in binary aqueous solutions of three alcohols: ethanol, isopropanol, and tert-butanol. The intermolecular potential TIP4P/2005 was used for water; and five force fields were analyzed for the alcohols. The force fields providing the best accuracy of calculation were identified based on a comparison of the calculated self-diffusion coefficients of pure alcohols with the experimental data for internal (Einstein) diffusion coefficients of alcohols in solutions. The temperature and concentration dependences of the interdiffusion coefficients were determined using Darken’s Equation. Transport (Fickian) diffusion coefficients were calculated using a thermodynamic factor determined by the non-random two-liquid (NRTL) and Willson models. It was demonstrated that for adequate reproduction of the experimental data when calculating the transport diffusion coefficients, the thermodynamic factor has to be 0.64. Simple approximations were obtained, providing satisfactory accuracy in calculating the concentration and temperature dependences of the transport diffusion coefficients in the studied mixtures.

Molecular Analysis of Transport Characteristics of Li Ion in Solid State Electrolyte

These days, the demands for a new technology for producing energy without consuming fossil fuels are increasing. One reason is, for example, strict regulations of emitting CO2 and NO on cars like Euro 6 in European countries. It is predicted these regulations will be much stricter in many countries in the future. Also, the demands for a new battery that is smaller and has higher energy outputs for smartphones and computers are increasing in the 21 century. So, one of the solutions for the problems in the 21 century is inventing new battery without emitting CO2 and NO. Above all, lithium ion battery is given attention as the one of the new batteries because it has high energy density and can be stored for a long time. Lithium ion battery has some merits such as rechargeable battery, high energy density and large range of operating temperatures. With these benefits, lithium ion battery is used for electronic vehicles (EV), cellphones and computers. However, lithium ion battery has some demerits. Because its electrolyte is liquid, liquid leak and automatic firing occurs and it has low degree of design freedom. One of the solutions for these problems is all solid-state lithium ion battery whose electrolyte is solid. In our study, as the material for the electrolyte Li7La3Zr2O12 (LLZ) is chosen. LLZ can treat easily due to high chemical stability of Li ions and high ion conductivity at high temperatures. In previous research, it was revealed that LLZ has phase transition from tetragonal phase to cubic phase at about 900 K. It was also found that there are no sites in tetragonal LLZ but some sites in cubic LLZ. That is, it means LLZ has no sites below 900K and some sites above 900K. Above all, the transport mechanism of Li ion in both tetragonal LLZ and cubic LLZ at 300K was revealed by Ab-initio MD simulation. However, how the structure property of LLZ influences the transport property of Li ion at various temperatures was not revealed. The objective of this research is to reveal how the structure property of LLZ influences the transport property of Li ion in LLZ at various temperatures by molecular dynamics (MD) simulation. In this research, we simulated the self-diffusivity of Li ion from 300K to 1100K with 100K decrements. As the analysis of transport property, we calculated self-diffusion coefficients and root-mean square deviation (RMSD) of each Li ion. As the analysis of structure property, we calculated the lattice parameters and Li-Li’s radius distribution function (RDF). As the simulation system, we constructed the initial structure at first, performed NVT or NPT simulation for 225 ps to reach equilibrium state and after that started sampling for 1ns. Firstly we found a peak at 2.5Å from the results of RDF. The result is consistent with the fact that the distance between Li site and the nearest other Li site is about 2.5Å from other research. From the result of self diffusion coefficient of Li ion against temperature, we found the slope from 500K to 900K is different from the slope from 900K to 1100K. It can be considered that the difference is due to the difference of the transport mechanisms of Li ion in each LLZ phases. From the results of RMSD, we found that the temperature dependence on RMSD is large. From 600K to 800K we found some Li ions jumped to the neighboring sites and change the places. It is called “a synchronous collective motion”. From 900K to 1100K the synchronous collective motion was not seen in the graphs. From these results and the fact that there is some sites in LLZ from 900K but no sites below 900K, it can be said that Li ions move as synchronous collective motion below 900 while they do not move as synchronous collective motion but as the motion through the vacant sites from 900K to 1100K.

Molecular dynamics simulation on local structure and thermodynamic properties of molten ternary chlorides systems for thermal energy storage

Molten alkali chlorides mixtures are potential thermal energy storage materials. The structure and thermodynamic properties of LiCl-NaCl-KCl systems with different KCl concentrations were investigated by molecular dynamics simulation. The force field was verified by experimental data for the density and viscosity, and its precision was compared with the first-principle-based molecular dynamics simulation results. The densities obtained from rigid ion model were in satisfactory agreement with experimental values with a minimum error of 4.9% underestimation. The discrepancy in the structural information obtained by the two methods was no more than 1%. The local structure and thermodynamic properties were simulated across a full range of KCl concentration from 900 to 1200 K. The stability of cations coordination was analyzed by cage-out correlation function. The calculated self-diffusion coefficients, shear viscosity, heat capacity, and thermal conductivity were in good agreements with the available experimental data. The results showed that addition of KCl strengthened the correlation between unlike charged ions pairs, which was verified by the stability analysis. The stability of the first coordination shell determined the shear viscosities. Change in the structure affected the thermodynamic properties.

Molecular dynamics study on fast diffusion of hydrogen molecules in filled ice II

Molecular dynamics calculations have been performed for the hydrogen hydrate C1 that is the ice II filled by the hydrogen molecules. Fast diffusion of the hydrogen molecules in the C1 crystal was observed; the calculated self-diffusion coefficient is in good agreement with the experimental value. The hydrogen molecules were observed to migrate only inside the tube-like voids in the C1 and the resulting diffusion processes were highly anisotropic in space. To diffuse the hydrogen molecules, defect or vacancy in the tube-like voids was found to be essential; no diffusion was observed for the system without vacancies.

Local structure and vibrational properties of molten lead halides PbX2 (X = Cl, Br, I) from ab initio molecular dynamics

Ab initio molecular dynamics (AIMD) was applied to calculate the local structure and dynamics parameters of molten lead halides PbX2 (X = Cl, Br, I). The thoroughness of our approach is substantiated by the variation of both cell size and temperature. The total duration of AIMD runs amounted to 600 ps. It was found that molten lead chlorides exhibit weak binding of the local structure. The latter was analyzed by means of radial distribution functions for each pair of salt constituents. The radial distribution functions exhibit pronounced liquid-like damped oscillations and weakly depend on the cell size. In terms of vibrational properties, we highlight the frequencies of 125 cm−1 and 80 cm−1 which relate to the Pb-Br and Pb-I vibrations respectively, both of a short lifetime. These results are additionally supported by the calculated self-diffusion coefficients which concur closely with experimental values.

Calculation of self-diffusion coefficient and surface tension of liquid alkali metals using square-well fluid

The self-diffusion coefficient (D) and the surface tension (γ) of the liquid alkali metals such as cesium (Cs) and rubidium (Rb) were calculated based on the Einstein's relation in a wide range of densities and temperatures. A developed mean spherical approximation (MSA) theory was applied to compute the direct correlation function using the effective square-well potential model for pair interaction in each temperature and density. The static structure factor, S(k), of the studied liquid species was evaluated by the proposed MSA theory in a wide range of wave vectors. The linear isothermal regularity equation of state was employed to determine the radial distribution function at a contact point at any thermodynamic state. A good agreement was obtained between the numerical results for both the D and γ values for the titled species and their available experimental data over the whole liquid range. For both liquids Cs and Rb, the temperature and density dependencies of the self-diffusion coefficient were investigated. Moreover, a correlation relation between the liquid surface tension and density and the temperature was found, in which the order of magnitude and sign of the coefficients were in good agreement with those obtained by experiment.