Diffusion Of Sulfur Research Articles

Impact of molybdenum out diffusion and interface quality on the performance of sputter grown CZTS based solar cells

We have investigated the impact of Cu2ZnSnS4-Molybdenum (Mo) interface quality on the performance of sputter-grown Cu2ZnSnS4 (CZTS) solar cell. Thin film CZTS was deposited by sputter deposition technique using stoichiometry quaternary CZTS target. Formation of molybdenum sulphide (MoSx) interfacial layer is observed in sputter grown CZTS films after sulphurization. Thickness of MoSx layer is found ~142 nm when CZTS layer (550 nm thick) is sulphurized at 600 °C. Thickness of MoSx layer significantly increased to ~240 nm in case of thicker CZTS layer (650 nm) under similar sulphurization condition. We also observe that high temperature (600 °C) annealing suppress the elemental impurities (Cu, Zn, Sn) at interfacial layer. The amount of out-diffused Mo significantly varies with the change in sulphurization temperature. The out-diffused Mo into CZTS layer and reconstructed interfacial layer remarkably decreases series resistance and increases shunt resistance of the solar cell. The overall efficiency of the solar cell is improved by nearly five times when 600 °C sulphurized CZTS layer is applied in place of 500 °C sulphurized layer. Molybdenum and sulphur diffusion reconstruct the interface layer during heat treatment and play the major role in charge carrier dynamics of a photovoltaic device.

Operando Spectromicroscopy of Lithium-Sulfur Batteries

Lithium-sulfur (Li-S) batteries are a “beyond Li-ion” technology that provides high capacity (1675 mAh g-1) while also being low cost, earth-abundant, and lightweight. Li-S batteries have a unique chemistry that achieves high capacity via chemical transformation rather than Li intercalation as in Li-ion. Elemental sulfur S8 is reduced through a series of soluble Li polysulfides (Li2Sx, 2 ≤ x ≤ 8) to a final solid discharge product Li2S, and the process is reversed upon charging. However, Li-S suffers from unrealized theoretical capacity and rapid capacity fade due to loss processes that are not well-understood. Batteries are spatially and chemically heterogeneous. Deciphering the chemical states of sulfur and the distribution of dissolved polysulfides in the anode, cathode, and especially the electrolyte during cycling is critical for realizing the potential of Li-S. We present operando characterization using sulfur K-edge X-ray absorption spectromicroscopy performed at the Stanford Synchrotron Radiation Lightsource (SSRL, BL 14-3). Synchrotron radiation provides the high energy resolution and micron-scale beam size needed to distinguish complicated polysulfide spectral features in the tender X-ray regime. From this information, we can observe a spatially and chemically varied system to gain insight into how sulfur speciation and spatial distribution contribute to capacity fade. Typically, operando X-ray characterization is conducted perpendicular to battery electrodes, providing an average of the chemistry throughout the entire stack. The cross-sectional pouch cell geometry presented here provides a spatially resolved picture of sulfur diffusion between the cathode and anode, which cannot be achieved by typical characterization methods. Cells consisting of a sulfur/carbon cathode, Li anode, and 1 M LiClO4 + 0.5 LiNO3 in 1,3-dioxolane/1,2-dimethoxyethane (DOL/DME) were discharged, and maps were collected at energies sensitive to the sulfur and Li polysulfide species. Tuning the incident X-ray energy allows for targeted observations of species such as polysulfides, sulfates, elemental sulfur, and lithium sulfide during cycling. A novel electrochemical cell with well-defined electrode geometry, electrolyte volume, and current collection has been designed at SSRL to map the battery cross-section in fluorescence mode. This cell will mitigate the challenges of using pouch cells for X-ray experiments such as water and oxygen contamination and sample-to-sample variation. It will also provide more robust, longer-term cycling that better replicates the offline electrochemistry of a typical coin or pouch cell. Because the new cell will increase reproducibility, we can alter electrode architecture and electrolyte composition to directly compare polysulfide and sulfur distributions, illuminating the direct influence that these parameters have on battery chemistry. Using this new design, changes in sulfur and polysulfide chemistry are systematically correlated to structure and performance.

Scalable Approach To Construct Free-Standing and Flexible Carbon Networks for Lithium–Sulfur Battery

Reconstructing carbon nanomaterials (e.g., fullerene, carbon nanotubes (CNTs), and graphene) to multidimensional networks with hierarchical structure is a critical step in exploring their applications. Herein, a sacrificial template method by casting strategy is developed to prepare highly flexible and free-standing carbon film consisting of CNTs, graphene, or both. The scalable size, ultralight and binder-free characteristics, as well as the tunable process/property are promising for their large-scale applications, such as utilizing as interlayers in lithium-sulfur battery. The capability of holding polysulfides (i.e., suppressing the sulfur diffusion) for the networks made from CNTs, graphene, or their mixture is pronounced, among which CNTs are the best. The diffusion process of polysulfides can be visualized in a specially designed glass tube battery. X-ray photoelectron spectroscopy analysis of discharged electrodes was performed to characterize the species in electrodes. A detailed analysis of lithium diffusion constant, electrochemical impedance, and elementary distribution of sulfur in electrodes has been performed to further illustrate the differences of different carbon interlayers for Li-S batteries. The proposed simple and enlargeable production of carbon-based networks may facilitate their applications in battery industry even as a flexible cathode directly. The versatile and reconstructive strategy is extendable to prepare other flexible films and/or membranes for wider applications.

Model of diffusion of sulfur in soda-lime-silicate glass: An experimental and comparative study

The diffusion property of sulfur on the soda-lime-silicate float glass surface was studied by using secondary ion mass spectroscopy(SIMS). According to the Fick`s Second Law, two models of diffusion of sulfur on the glass surface were built. When the diffusion of sulfate (S6+) is considered uniquely, the concentration-depth profile of sulfur can not be fitted very well, especially on the top surfaces of the air side and tin side of float glass. So the diffusion of sulfide (S2-) on the profile of sulfur can not be ignored. The concentration-depth profile of sulfur on both sides of glass can be fitted more exactly when both S6+ and S2- are considerd. Based on the above-mentioned fitting results, it is concluded that the diffusion coefficents of S6+ and S2- of tin side are larger than those of the air side. Moreover, the diffusion coefficents are related to the contacted medium.

Polymer-Capped Sulfur Copolymers as Lithium–Sulfur Battery Cathode: Enhanced Performance by Combined Contributions of Physical and Chemical Confinements

Flexible polymers show high potential applications in rechargeable lithium–sulfur (Li–S) batteries for their capability of confining sulfur diffusion and tolerance to large volume expansion during lithiation. Herein, sulfur is copolymerized with 3-butylthiophene via radical polymerization by heating the mixture of both components at controlled temperatures. Further capping of the thus-synthesized copolymer CP(S3BT) with highly conductive PEDOT:PSS thin film substantially enhances the electrical conductivity. With the resulting polymer hybrids as the cathode material, a Li–S battery is constructed which shows an initial discharge capacity of 1362 mA h g–1 at 0.1 C and a reversible capacity of 631 mA h g–1 even at 5 C. Moreover, the polymer cathode exhibits a high capacity of 682 mA h g–1 after 500 charge–discharge cycles at 1 C with 99.947% retention per cycle. The remarkable performance is attributed to the synergetic effects of (i) high conductivity resulting from both the conducting blocks of poly(3-but...

CdTe/CdS solar cell junction activation: Study using MgCl2 as an environment friendly substitute to traditional CdCl2

In this work, we report a comparative study of junction activation in the CdTe/CdS solar cells using MgCl2 and CdCl2 as the Cl sources. The chloride loading over the CdTe film was controlled by taking same molar solutions of both salts. Attention was given to explore the elemental profiles of S, O, Cl, Mg, and Cu across the CdTe as well as at the junction. Sulfur diffusion into the bulk of CdTe and evidence of alloying at the junction was prominent in the case of devices activated with CdCl2 as seen from SIMS and EQE data. The device parameters such as Voc, Jsc and FF were comparable or slightly higher for devices activated with MgCl2, which is explained as due to less recombination losses, lower series resistance and higher carrier concentration at the back contact region. The dispersion in efficiency values were smaller for devices activated with MgCl2 indicating that recrystallization of the CdTe film and junction activation in presence of MgCl2 results in better spatial uniformity compared to that with CdCl2. The devices used in this study were fabricated in an all-close-spaced-sublimation (CSS) process, where both CdS and CdTe were deposited by CSS.

High near infrared absorption of hyper‐doped silicon induced by co‐doping of sulfur and nitrogen

In this paper, we investigate the dependence of NIR absorption of hyper‐doped silicon on different sulfur and nitrogen doping ratio. With different molecular proportion of N2 and SF6 background gas, femtosecond laser irradiation was used to implant co‐doping of sulfur and nitrogen into silicon. The hyper‐doped silicon presents high absorption properties in NIR and visible range. The results of first‐principles calculations demonstrate the high absorption in NIR is ascribed to the induced impurity energy levels in hyper‐doped silicon. The nitrogen doping process improves the crystallinity in the doped layer because the doped nitrogen repairs defects in silicon lattices. Given the thermal stability of nitrogen, the co‐doping dopants limit the diffusion of sulfur during the annealing process. The co‐doping process proposed in this paper provides a method to fabricate high performance NIR silicon optoelectronic device.

Adsorption and diffusion of atomic oxygen and sulfur at pristine and doped Ni surfaces with implications for stress corrosion cracking

A density-functional-theory modeling study of atomic oxygen/sulfur adsorption and diffusion at pristine and doped Ni(111) and (110) surfaces is presented. We find that oxygen and sulfur feature comparable adsorption energies over the same surface sites, however, the surface diffusion of sulfur is characterized by an activation barrier about one half that of oxygen. Calculations with different alloying elements at Ni surfaces show that Cr strongly enhances surface binding of both species in comparison to Al. These results in combination with previous modeling studies help explain the observed differences in selective grain boundary oxidation mechanisms of Ni-Cr and Ni-Al alloys.

The phase segregation in CdTe/CdS heterojunction and its effect on photo current of CdTe thin films solar cell

The S-Te inter-diffusion in CdTe/CdS heterojunction has been studied by X-ray diffraction, Atomic force microscope and Spectroscopic ellipsometry. For the first time, the phase segregation of CdTeySx compound that is confirmed by X-ray measurement has been taken into account in the analysis of ellipsometry, which promotes the analytical reliability. Benefit from the dielectric constants obtained from the ellipsometric data, the external quantum efficiency of the solar cell has been fitted without any paradoxical assumption used before. Results show that high temperature process such as Close space sublimation leads to significant S-Te inter-diffusion and shallows the junction obviously, but this does not happen in magnetron sputtered device. Tellurium diffusion into CdS can reduce the blue response of solar cell, meanwhile sulfur diffusion into CdTe lowers the band gap of CdTe which increase the quantum efficiency at long wavelength. Finally, the conversion efficiency of solar cell can be improved by suppressing the current leakage near the edge of cell. The fill factor is 54.8% and the efficiency reaches 9.28%.

Numerical and Experimental Investigation of Performance Characteristics of Lithium/Sulfur Cells

In this study, we propose a modified mathematical model for Lithium/Sulfur (Li/S) cells and present a detailed numerical analysis showing the effects of (1) the presence of solid sulfur species (S8(s), Li2S2(s), Li2S(s)), (2) the solubility and diffusivity of polysulfides in the electrolyte, and (3) reaction rate constants of polysulfide reduction reactions at Li electrode on the electrochemical performance characteristics of Li/S cells including the cycling performance. The cell potential profiles predicted from numerical analysis were compared with experimental discharge and charge curves with emphasis on the possibility of the presence of the intermediate solid phase Li2S2(s). Numerical results suggest that the cell potential obtained without the consideration of the intermediate solid phase Li2S2(s) is in the best agreement with experimental results. Also, the polysulfide shuttling phenomenon has been numerically analyzed with electrolytes of different polysulfide solubility and compared with experimental cell discharge and charge curves. Our model clearly shows that the electrolyte of high polysulfide solubility and unprotected negative (anode) electrode can lead to unwanted reduction reactions of high-order polysulfides on the Li electrode, resulting in a significant overcharge problem. This agrees well with our experimental results for identical experimental conditions. Furthermore, the cycling performance of a Li/S cell was predicted, including the effect of the polysulfide shuttle on the subsequent discharge/charge curves. In the simulation, it was found that the high voltage plateau is reduced markedly in the discharge process after incomplete charge because sulfur (S8) could not be recovered when the polysulfide shuttle problem is significant. Also, it is suggested that cycling performance of Li/S cells would be improved by limiting both the polysulfide diffusivity and the reduction reaction rate of high-order polysulfides at Li electrode during charge.

Oxidation and Hot Corrosion Behavior of Plasma-Sprayed MCrAlY–Cr2O3 Coatings

The oxidation and hot corrosion behavior of two atmospheric plasma-sprayed NiCoCrAlY–Cr2O3 and CoNiCrAlY–Cr2O3 coatings, which are primarily designed for wear applications at high temperature, were investigated in this study. The two coatings were exposed to air and molten salt (75%Na2SO4–25%NaCl) environment at 800 °C under cyclic conditions. Oxidation and hot corrosion kinetic curves were obtained by thermogravimetric technique. X-ray diffraction analysis and scanning electron microscopy with energy-dispersive x-ray spectrometry were employed to characterize the coatings’ microstructure, surface oxides, and composition. The results showed that both coatings provided the necessary oxidation resistance with oxidation rates of about 1.03 × 10−2 and 1.36 × 10−2 mg/cm2 h, respectively. The excellent oxidation behavior of these two coatings is attributed to formation of protective (Ni,Co)Cr2O4 spinel on the surface, while as-deposited Cr2O3 in the coatings also acted as a barrier to diffusion of oxidative and corrosive substances. The greater presence of Co in the CoNiCrAlY–Cr2O3 coating restrained internal diffusion of sulfur and slowed down the coating’s degradation. Thus, the CoNiCrAlY–Cr2O3 coating was found to be more protective than the NiCoCrAlY–Cr2O3 coating under hot corrosion condition.

Iron pyrite thin films grown through a one-step annealing of iron oxide using sulfur sources, tert-butyl disulfide and H2S

In this work, we report synthesis of pyrite thin films using tert-butyl disulfide (TBDS) and hydrogen sulfide (H2S) in one-step atmospheric pressure sulfurization of iron oxide films at 400°C on a soda-lime glass, molybdenum coated soda-lime glass and sodium-free glass substrates. The iron pyrite thin films grown using TBDS did not require the presence of sodium to form the pyrite phase, whereas H2S grown pyrite thin films did. It was observed that the pyrite formation and thus the sulfur diffusion into the oxide film was slower in TBDS compared to H2S. The synthesized films were characterized for their surface morphology and phase identification using scanning electron microscopy, transmission electron microscopy (TEM), X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS) techniques. The S:Fe atomic ratio as well as their chemical bonding states were monitored to obtain and maintain a stoichiometric 2:1 ratio through the entire film thickness as a function of the sulfurization time by performing an XPS depth profile. Transmittance measurements confirmed the pyrite phase with an optical bandgap of 1.15eV. The TEM electron-beam diffraction spots were used to verify the impurity phases observed in XRD patterns. Hall Effect measurements showed p-type carriers for the pyrite films.

Lithium- and Sodium-Sulfur Cells with High Sulfur Loading

Development of advanced energy-storage systems needs to consider a balance among cost, cycle life, safety, energy, power, and environmental benignity. With these requirements, lithium-sulfur (Li-S) and sodium-sulfur (Na-S) batteries are promising candidates as next-generation energy-storage systems because of the high charge-storage capacity, natural abundance, and environmental friendliness of sulfur. However, the practical utility of Li-S and Na-S cells is hampered by the low electrochemical utilization of sulfur and severe polysulfide diffusion from the cathode to the anode. These drawbacks result in low discharge capacity and poor cycle life. The Li-S and Na-S battery chemistries have several scientific challenges in common. The degradation of both the anode and cathode active materials, as well as the decomposition of the liquid electrolyte, causes a fast capacity fade and low electrochemical utilization of the active material. Unfortunately, the efforts to overcome the persistent problems often result in the incorporation of excessive conductive carbon into the electrode and low sulfur loading per unit area. In fact, it is often easy in the literature to obtain greatly improved performance by using either low sulfur content, low sulfur loading, or low sulfur mass in a cathode. The use of low-sulfur-loading cathodes can defeat the energy-density advantage of sulfur cathodes and the purpose of Li-S and Na-S cells replacing the current lithium-ion technology. Moreover, the traditional cathode configuration borrowed from the commercial insertion-compound cathodes may not allow the pure sulfur cathode to put its unique materials chemistry to good use due to the very different battery chemistries between the solid insertion-compound oxide cathodes and the electrochemical conversion-reaction sulfur cathodes. Recognizing the importance of operating the Li-S and Na-S cells with high-sulfur-loading cathodes for being competitive with the existing lithium-ion technology, this presentation will focus on unique approaches in engineering the sulfur cathodes with high-sulfur loadings and employing solid electrolytes. The cathode engineering presented can lead the way towards employing high-loading cathodes with promising cell performance while the easily-prepared pure sulfur powders are utilized as the active material. The first high-capacity cathode engineering involves a layer-by-layer strategy. This method confines sulfur powders between porous carbon nanofiber (PCN) multi-layers. The layer-by-layer cathode facilitates fast ion and electron transport and traps the soluble polysulfide intermediates within the multilayered electrode configuration. A single-sulfur-layer cathode coupled with two-PCN layers offers a high discharge capacity of 1265 mAh g-1 at C/5 rate with good cyclability. The cathode engineering further facilitates high areal sulfur loading by increasing the number of sulfur layers. For example, a six-sulfur-layer cathode attains a high areal sulfur loading of 11.4 mg cm-2. The high-sulfur-loading cathode delivers a high initial discharge capacity of 995 mA h g-1 at C/10 rate with a corresponding areal capacity of 11.3 mA h cm-2. The second high-capacity cathode engineering involves an edge-encapsulation method. An omurice-type cathode consists of a light-weight multiwall carbon nanotube (MWCNT) thin-film as the omelette cover and the active-material filling as the fried rice. The active-material paste is first dropped onto an aluminum-foil current collector and then covered by the MWCNT thin-film, followed by pressing the edge of the electrode for the favorable edge-encapsulation of the sulfur core. As a result, the polysulfide migration is stabilized within the structural cathode due to the strong tortuosity of MWCNT layer and the edge-encapsulated cathode configuration, benefiting the capacity retention. The omurice-type cathodes exhibit a high discharge capacity (1190 mAh g-1), a long lifespan (500 cycles), and low capacity fade (0.08 % cycle-1). In addition, the structural cathodes with a good balance among high sulfur loading (4.2 – 10.0 mg cm-2), high sulfur content (50 – 60 wt. %), and high sulfur mass (4.2 – 10.0 mg cathode-1) are able to attain a high areal capacity (5.1 – 7.8 mAh cm-2). In addition, polysulfide-trapping interlayers, multi-functional separators, and solid electrolyte membranes developed in our group are integrated with the above advanced structural cathodes for suppressing polysulfide migration and alkali-metal dendrite growth. The integrated cells with high active-material loading exhibit good cyclability.

ALD Zn(O,S) Thin Films' Interfacial Chemical and Structural Configuration Probed by XAS.

The ability to precisely control interfaces of atomic layer deposited (ALD) zinc oxysulfide (Zn(O,S)) buffer layers to other layers allows precise tuning of solar cell performance. The O K- and S K-edge X-ray absorption near edge structure (XANES) of ∼2–4 nm thin Zn(O,S) films reveals the chemical and structural influences of their interface with ZnO, a common electrode material and diffusion barrier in solar cells. We observe that sulfate formation at oxide/sulfide interfaces is independent of film composition, a result of sulfur diffusion toward interfaces. Leveraging sulfur’s diffusivity, we propose an alternative ALD process in which the zinc precursor pulse is bypassed during H2S exposure. Such a process yields similar results to the nanolaminate deposition method and highlights mechanistic differences between ALD sulfides and oxides. By identifying chemical species and structural evolution at sulfide/oxide interfaces, this work provides insights into increasing thin film solar cell efficiencies.

In-situ CdS/CdTe heterojuntions deposited by pulsed laser deposition

In this paper pulsed laser deposition (PLD) methods are used to study p-n CdTe/CdS heterojunctions fabricated in-situ. In-situ film deposition allows higher quality p-n interfaces by minimizing spurious contamination from the atmosphere. Morphologic and structural analyses were carried for CdTe films deposited on various substrates and different deposition conditions. The electrical characteristics and performance of the resulting p-n heterojunctions were studied as function of substrate and post-deposition anneal temperature. In-situ growth results on diodes with a rectification factor of ~105, an ideality factor <2, and a reverse saturation current ~10−8A. The carrier concentration in the CdTe film was in the range of ~1015cm−3, as measured by C-V methods. The possible impact of sulfur diffusion from the CdS into the CdTe film is also investigated using High Resolution Rutherford Back-Scattering.

Transfer-Free Growth of Atomically Thin Transition Metal Disulfides Using a Solution Precursor by a Laser Irradiation Process and Their Application in Low-Power Photodetectors.

Although chemical vapor deposition is the most common method to synthesize transition metal dichalcogenides (TMDs), several obstacles, such as the high annealing temperature restricting the substrates used in the process and the required transfer causing the formation of wrinkles and defects, must be resolved. Here, we present a novel method to grow patternable two-dimensional (2D) transition metal disulfides (MS2) directly underneath a protective coating layer by spin-coating a liquid chalcogen precursor onto the transition metal oxide layer, followed by a laser irradiation annealing process. Two metal sulfides, molybdenum disulfide (MoS2) and tungsten disulfide (WS2), are investigated in this work. Material characterization reveals the diffusion of sulfur into the oxide layer prior to the formation of the MS2. By controlling the sulfur diffusion, we are able to synthesize continuous MS2 layers beneath the top oxide layer, creating a protective coating layer for the newly formed TMD. Air-stable and low-power photosensing devices fabricated on the synthesized 2D WS2 without the need for a further transfer process demonstrate the potential applicability of TMDs generated via a laser irradiation process.

Migration of sulphur in thermal barrier coatings during heat treatment

The sulphur effect in thermal barrier coatings (TBCs) mainly refers to a segregation of sulphur at the interface between thermally grown oxide (TGO) and the bond coat, which significantly deteriorates scale adhesion to alloys. Restricted by the extremely low concentrations of sulphur (0–10ppm) in TBCs, previous investigations using conventional analytical techniques failed to provide a complete mechanism for the migration of sulphur. In this study, high resolution secondary ion mass spectrometry (NanoSIMS) was employed to detect trace sulphur distributions in commercial TBCs. After heat treatments, sulphur segregates at three typical areas in TBCs: (1) the yttria stabilized zirconia (YSZ) top coat; (2) the TGO/bond coat interface and (3) the grit blasted surface. This indicates that during heat treatment a significant outward diffusion of sulphur occurs from the superalloy to YSZ top coat through the TGO, and a possible mechanism for the migration of sulphur in TBCs is described. The undesired “sulphur effect” on scale adhesion was suggested to be caused by the formation of residual sulphides beneath the alumina scale with weaker ionic bonding to alloy cations. Possible solutions are suggested aiming to alleviate the sulphur effect in TBCs.

Sulphur diffusion in β-NiAl and effect of Pt additive: an ab initio study

Diffusivities of detrimental impurity sulfur (S) in stoichiometric and Pt doped β-NiAl were evaluated using density functional theory calculations. The apparent activation energy and the pre-exponential factor of diffusivity via the next nearest neighbour (NNN) and interstitial jumps were evaluated to identify possible preferred diffusion mechanism(s). By calculating the electron localization function (ELF), the bonding characteristics of S with its surrounding atoms were assessed for the diffusion process. By comparison with the experimental results, the S diffusion through the NNN vacancy-mediated mechanism is found to be favoured. Addition of Pt in β-NiAl was found to significantly reduce the S diffusivity, and an associated electronic effect was explored. The elucidation of the above mechanisms may shed light on the development of new Pt-modified doped β-NiAl bond coats that can extend the life of oxidation resistant and thermal barrier coatings.

A simple, experiment-based model of the initial self-discharge of lithium-sulphur batteries

One of the main challenges in the development of lithium-sulphur batteries is the so called “shuttle mechanism”, which involves the diffusion of sulphur and polysulphides from the sulphur electrode to the lithium electrode, where they get reduced via chemical reactions with lithium. The shuttle mechanism decreases the capacity delivered by the battery, hampers its rechargeability, and promotes battery self-discharge. We have developed a simple model of the shuttle mechanism that reproduces quantitatively the rate of the initial self discharge of lithium-sulphur batteries. The rate of sulphur and polysulphide diffusion has been quantified by studying cells with varying number of separators between the electrodes. We have found that it is essential that the model incorporates the presence of carbon additive in the sulphur electrode, which slows down the decrease of the open circuit potential with time. The model also reproduces well the rate of self-discharge of lithium-sulphur cells containing sulphur dissolved in the electrolyte. In conclusion, the present model provides a basic understanding of the mechanism of self-discharge of lithium-sulphur cells, and allows quantifying the two main causes of sulphur loss at the sulphur electrode: sulphur diffusion across a concentration gradient and sulphur reaction with polysulphides formed at the lithium electrode.

Atomistic Modeling of Sulfur Vacancy Diffusion Near Iron Pyrite Surfaces

Through density functional calculations, we investigated the diffusion of isolated sulfur vacancies (VS) from the bulk of iron pyrite (cubic FeS2) to the (100) and (111) surfaces. The influence of vacancy depth on the vacancy formation energy and the activation energy for vacancy diffusion are discussed. Significantly, we find that VS defects tend to migrate toward stoichiometric and sulfur-rich surfaces through sequential “intra-dimer” and “inter-dimer” hops. We find a pre-exponential constant (D0) of 9 × 10–7 m2 s–1 and an activation energy (E) of 1.95 eV for sulfur vacancy diffusion in bulk pyrite, corresponding to a vacancy diffusion coefficient DV = D0 exp(−E/kT) = 9 × 10–40 m2 s–1 at 25 °C and 5 × 10–18 m2 s–1 at 600 °C. The activation energy is smaller near the surface (e.g., E = 1.5 eV near the stoichiometric (100) surface), resulting in faster vacancy diffusion near the surface than in the bulk. Using the formation enthalpy of VS at the (100) surface, E = 2.37 eV, we find a sulfur diffusivity in bulk pyrite DS = 7 × 10–47 m2 s–1 at 25 °C and 2 × 10–20 m2 s–1 at 600 °C. The calculated DS values are in reasonable agreement with experiment only at intermediate temperatures (∼275–625 °C). Our results show that bulk and near-surface sulfur vacancies can be healed in sulfur-rich conditions at reasonably high temperatures. The mechanism of vacancy diffusion presented here should be useful in managing VS defects during the fabrication of high-quality pyrite samples for solar energy conversion applications.