Molecular Dynamics Modeling of the Structure and Na+-Ion Transport

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B: Fluid Interfaces, Colloids, Polymers, Soft Matter, Surfactants, and Glassy Materials

Molecular Dynamics Modeling of the Structure and Na+ Ion Transport in NaS + SiS Glassy Electrolytes 2

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Aniruddha M Dive, Chris J. Benmore, Martin Wilding, Steve W Martin, Scott P Beckman, and Soumik Banerjee J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b04353 • Publication Date (Web): 20 Jun 2018 Downloaded from http://pubs.acs.org on June 24, 2018

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The Journal of Physical Chemistry

S(Q) plots for 0.50 Na2S + 0.50 SiS2 calculated from ab initio MD simulations. The overall structure factor obtained from XRS is shown for comparison 243x137mm (120 x 120 DPI)

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RDF plots for Si-S and Na-S in 0.50 Na2S + 0.50 SiS2 calculated from ab initio MD is shown. Inset shows the running average coordination number (CN) of S ions around Si ions in the glass. 243x137mm (120 x 120 DPI)


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Enlarged image of Si-S tetrahedron observed within a small portion equilibrated glass is shown. The green spheres represent the Si ions, red spheres the Na+ ions and yellow spheres are the S ions. The Si – S distances between central Si ion and surrounding S ions are ~ 2.1 Å. 243x137mm (120 x 120 DPI)



Energy profile (EP) associated with a Type I Na+ ion hop is shown. The initial state in the MEP has been used as a reference zero energy state. 243x137mm (120 x 120 DPI)


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A representative mechanism for Type I Na+ ion hop is shown. The green circles depict the center of mass of Si-S tetrahedra, the yellow circles the S atom sites, the red bold circles the current position of Na ions and light red circles the prior occupied positions of the Na ions. The arrow shows the direction of the hop. 243x137mm (120 x 120 DPI)



EP associated with Type II Na+ ion hop is shown. The reaction coordinates are represented by a series of configurations obtained from the ab initio MD simulations. 243x137mm (120 x 120 DPI)


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A representative mechanism for Type II Na+ ion hop is shown. The green circles depict the center of mass of Si-S tetrahedra, the yellow circles the S atom sites, the red bold circles the current position of Na ions and light red circles the prior occupied positions of the Na ions. The arrow shows the direction of the hop. 243x137mm (120 x 120 DPI)



EP profile associated with Type III Na+ ion hop is shown. The reaction coordinates are represented by a series of configurations obtained from the ab initio MD simulations. 243x137mm (120 x 120 DPI)


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A representative mechanism for Type III Na+ ion hop is shown. The green circles depict the center of mass of Si-S tetrahedra, the yellow circles the S atom sites, the red bold circles the current position of Na ions and light red circles the prior occupied positions of the Na ions. The arrow shows the direction of the hop. 243x137mm (120 x 120 DPI)



S(Q) plots for 0.50 Na2S + 0.50 SiS2 obtained from XRS and ab initio and classical MD simulations are shown. The RDF for Si-S and Na-S pairs are shown in the inset. 243x137mm (120 x 120 DPI)


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Ionic conductivity for 0.50 Na2S + 0.50 SiS2 in the temperature range 200 K to 350 K are shown. IC stands for ionic conductivity in the figure. The experimentally measured values are as reported by Cho and Martin [29]. 243x137mm (120 x 120 DPI)



RDF plots for Na-Na ion pairs in all three glass compositions are shown 243x137mm (120 x 120 DPI)


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(a) RDF plot for S – S and (b) running average CN for S – S within a range of 3.0 Å – 5.0 Å, are shown. 243x137mm (120 x 120 DPI)



(a) RDF plot for S – S and (b) running average CN for S – S within a range of 3.0 Å – 5.0 Å, are shown. 243x137mm (120 x 120 DPI)


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(a) RDF plot for Si – Si and (b) running average CN for Si – Si within a range of 3.5 Å to 6.5 Å, are shown. 243x137mm (120 x 120 DPI)



(a) RDF plot for Si – Si and (b) running average CN for Si – Si within a range of 3.5 Å to 6.5 Å, are shown. 243x137mm (120 x 120 DPI)


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Molecular Dynamics Modeling of the Structure and Na+ Ion Transport in Na2S + SiS2 Glassy Electrolytes A. Dive1, C. Benmore2, M. Wilding3, S. W. Martin4, S. Beckman1 and S. Banerjee

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School of Mechanical and Materials Engineering, Washington State University Pullman, Washington 99164-2920 2 Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439 3 Department of Chemistry, University College London, London, United Kingdom 4 Department of Materials Science and Engineering, Iowa State University, Ames, Iowa 50011

Abstract Solid-state sodium batteries, a relatively safe and potentially cost-effective energy storage technology, have attracted increasing scientific attention recently for application in stationary gridscale energy storage. Identifying solid electrolytes with high electrochemical stability and high Na+ ion conductivity at room temperature is critically important to enable high energy densities with enhanced rate capabilities. We evaluated sodium sulfide-silicon sulfide, x Na2S + (1-x) SiS2, glasses as potential glassy solid electrolytes (GSEs) using molecular dynamics (MD) simulations. We employed ab initio MD to determine ion conduction mechanisms, to calculate energy barriers for ion hops, and to correlate these to the local short-range structure of 0.50 Na2S + 0.50 SiS2 glass. To simulate much larger systems for accurately calculating the ionic conductivity, we parameterized empirical Buckingham-type potential and performed classical MD simulations. After validating these calculations by comparing the structure obtained from MD with that from X-ray scattering (XRS) data, we calculated the ionic conductivity of these glasses for the range of

Corresponding Author, Tel: +1 509 3350294, E-mail: [email protected]

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0.33 ” x ” 0.67 compositions. The calculated ionic conductivities at room temperature were in the range of ~10-5 S/cm for the x = 0.50 composition and increased significantly with sodium sulfide (x) content. These calculations provide theoretical insights on the role of Na2S content on the ionic conductivity of GSEs aiding in the selection of specific compositions to enhance the ionic conductivity.

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Introduction Ever increasing demands for energy coupled with the economic and environmental demerits of fossil fuels have led to significant emphasis on renewable energy sources. Renewable energy sources, however, provide intermittent energy, making the use of energy storage devices1,2 unavoidable for load leveling. Energy and power density requirements for these electrical grid storage systems are enormous. While lithium ion technology has dominated consumer and automobile markets, economic concerns3 due to limited lithium reserves have motivated research on alternative lower cost chemistries for grid-scale energy storage. The natural abundance of sodium, nearly 1,500 times more abundant than lithium, makes sodium-based batteries4-6 a promising alternative, despite their low energy density relative to lithium counterparts. Employing an electrolyte with high ionic conductivity at room temperature and high electrochemical stability is critical to achieving high energy density and improved rate capabilities. While conventional organic liquid electrolytes have relatively high ionic conductivities, their known flammability and low electrochemical stability are significant safety concerns at grid-scale. For these reasons, solid state sodium-based batteries7, 8 with solid electrolytes (SEs) that are nonflammable and possess better electrochemical stability are an attractive alternative. However, SEs typically have lower ionic conductivities at room temperature compared to their liquid counterparts. Therefore, several studies have attempted to develop solid-state electrolytes9-12 (SSEs), both crystalline and amorphous with superior ionic conductivity and electrochemical stability to improve the performance of solid-state sodium batteries13-16 (SSSBs). Amorphous solids17 such as glasses often have higher ionic conductivities than their crystalline counterparts. The combined disordered short-range order (SRO) and long-range order (LRO) structures in the 3



GSEs results in a larger and more available free-volume for ion conduction often considered as important reasons for improved ionic conductivity18-20. The local SRO structure of a GSE is dependent on the specific composition and chemistry of the glass. Sulfide glasses21-26, have relatively high ionic conductivities (~ 10-2 S/cm27) at room temperature compared to their oxide analogues as predicted by the Anderson-Stuart model28 and the weak electrolyte theory29. Substituting sulfur for oxygen greatly reduces the bond energy between the sodium cation and sulfur anion. Moreover, the greater polarizability of sulfur reduces the activation energy for Na+ ion hops. One of the first measurements of the ionic conductivity of a 0.50 Na2S + 0.50 SiS2 glass (~ 10-5 S/cm) was reported by Barrau et al.30. This work was followed by a more detailed study by Cho and Martin31, where they investigated a range of sodium sulfide -silicon sulfide, x Na2S + (1-x) SiS2, glasses for 0.45 ” x ” 0.65. Their results indicated that the ionic conductivity of these GSEs increased with increasing concentration of Na2S, with the maximum ionic conductivity of ~ 10-4 S/cm measured for the 0.65 Na2S + 0.35 SiS2 GSE. This increase in ionic conductivity was qualitatively explained using the combination of the Christensen et al.32 and McElfresh and Howitt (MH) model33, which estimates the activation energy for ion hops as a function of ion jump distance, the dielectric permittivity, shear modulus, and the size of the interstitial doorways connecting the cation sites. However, the change in local structure of these sodium sulfide GSEs with composition and its related implications on ionic conductivity, which is essential for design of new electrolytes, are still not well understood. The ion jumps, which ultimately determine the ionic conductivity of glasses, happen at the atomistic scale. Ab initio molecular dynamics (MD), which performs quantum calculations to determine the forces on atoms and solves classical equations of motion at specific temperatures, is 4


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therefore well suited to analyze ion migration within these glasses and relate them to the local structure. Furthermore, ab initio MD can capture complex chemical reactions during the formation of glasses by melt-quench processes and can generate representative structures, as evidenced from previous work of Islam et al.34-36 and Ceder et al.37-39 on lithium oxide and lithium sulfide based glasses. Shah et al. have summarized different multiscale modeling techniques addressing the complex issues for developing high performance lithium ion batteries40. In the present study, ab initio MD simulations have been performed to calculate the migration barriers for Na+ ions in 0.50 Na2S + 0.50 SiS2 GSE to provide insights into the local structures that are important for Na+ ion diffusion. The distribution of stable Na+ ion sites is strongly correlated to the local SRO structure of these glasses. The concentration of stable Na+ ion sites and the migration barriers for long-range diffusion can therefore be tuned to achieve enhanced ionic conductivity at room temperature. Despite the high accuracy of ab initio MD simulations to replicate the local SRO structure, the system size that can be simulated is quite small, just a few hundred atoms due to the intensive computational requirements. In amorphous or glassy materials, there is a complete lack of LRO. Thus, the results obtained from ab initio MD simulations on these relatively small systems cannot be directly linked to long range transport properties such as diffusivity and ionic conductivity of bulk materials. Therefore, classical MD simulations, which rely on empirical force fields to define the interactions between various ions, Na+, Si+4 and O2-, was used to simulate larger systems (of the order of 20,000 atoms). While classical MD has been utilized extensively to study oxide glasses41-47 based on empirical force fields, force fields are not available for sodium silicon sulfide glasses. Therefore, an empirical force field was parameterized for the 0.50 Na2S + 0.50 SiS2 glass 5



and validated by comparing the local SRO structure with that obtained by analyzing X-ray scattering data (XRS). Motivated by an opportunity to tailor the Na+ ion conductivity, a range of sodium silicon sulfide glasses were simulated using the validated classical force field. Prior work by Cho and Martin31 reported that the glass formation range for x Na2S + (1-x) SiS2 is 0.40

Molecular Dynamics Modeling of the Structure and Na+-Ion Transport

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