Recently, lithium(Li)-based batteries have attracted significant attention due to their applications in electric vehicles and many new kinds of portable electronic devices such as cell phones. However, such batteries still need more research and improvement in order to meet the market demands for low cost and high-rate performance. Lithium-sulfur (Li-S) batteries with their high theoretical energy density, and all-solid-state Li-ion batteries (ASSLB) with their increased safety and design flexibility are among the most promising energy-storage systems. The focus of current dissertation is set on the important materials in these two kinds of batteries. The common cathode materials for Li-S batteries are S8 or Li2S. Intermediate Li-polysulfides are also formed at the cathode during the charge/discharge process. Moreover, carbon-based materials are added to sulfur cathodes in order to increase their electronic conductivity. In Li-S batteries, the Li-polysulfides migrate through the electrolyte, and their reductions and oxidations on both electrodes result in excessive utilization of the active material and self discharging. To inhibit this process, traping of Li-polysulfides in the cathode has been proposed. Here, we have investigated the ability of graphene (pristine and defective) as part of sulfur cathode to trap the Li-polysulfides. To this end, binding energies and Gibbs free energies for adsorption process of Li2Sx onto the graphene are calculated using Density Functional Theory (DFT) with PBE-D2 method. To calculate the Gibbs free energies, vibrational and configurational entropies are evaluated. It is found that the interaction of the Li-polysulfides and graphene is mostly dominated by the dispersion interactions, and pristine as well as defective graphene cannot immobilize the Li-polysulfides. Although during the adsorption of Li2Sx on monovacant graphene, one S atom is chemically attached to the defect site, the resulting S-doped graphene cannot hinder the Li-polysulfide migration either. In the next step, Li2S, which is one of the promising cathode materials in Li-S batteries, has been investigated. Similar to S8 , Li2S has a low electronic conductivity. Moreover, Li-ion conductivity of Li2S at room temperature is low, but this crystal possesses a high ionic conductivity at high temperatures. Although many experiments have been performed to study the ionic conductivity of Li2S, it has not been studied theoretically so far. In this thesis, we have studied ionic conductivity of Li2S as well as the origin of its superionic phase transition which has been reported by experimentalists. To achieve this aim, we have applied DFT and ab initio molecular dynamics (AIMD). Through AIMD simulations at different temperatures, diffusion coefficients are evaluated. Additionally, concentration of the Li ions is calculated from thermodynamics of defects as well as using the detailed balance condition. Finally, the Li-ion conductivity is obtained for various temperatures which shows the superionic phase transition for temperatures above T = 900K, in good agreement with the experimental reports. In the case of ASSLBs, although the solid electrolyte has a high ionic conductivity and a high stability, such systems do not possess a high energy density compared to the conventional cells, which is due to a large interfacial resistance at electrolyte/electrode interface. Therefore, it is of crucial importance to know the atomic and electronic structures of these interfaces. In this work, an important electrolyte/cathode interface for ASSLBs, namely Li7La3Zr2O12 /LiCoO2, has been investigated. Although several experimental researches have synthesized and studied this interface, its complex structure makes it difficult to investigate theoretically. Here, for the first time, we have modeled and studied this interface using DFT (PBE+U method) by focusing on Li7La3Zr2O12(001)/LiCoO2(10-14). To consider the effect of lattice mismatch between the two surfaces, three models with different lattice parameters for the interface have been applied. Therefore, different magnitudes of biaxial compressive and tensile strains are applied on the interface. It is shown that during the interface optimization, a Li ion moves from the surface of LiCoO2 to Li7La3Zr2O12. This ion migration is accompanied by electron transfer in the same direction attempting to neutralize the system. The electron transfer also results in the formation of certain gap states at the interface. In the next step, the possibility of cation interchange (Co↔Zr or Co↔La) has been studied at the Li7La3Zr2O12(001)/LiCoO2(10-14) interface. By calculating the energy difference between interface with interchanged cations and pristine interface, it is found that this process is possible only under a large stress along the interface normal direction. In addition, to minimize the strain on such systems during the cation interchange, the bulk models of Li7La3Zr2O12 and LiCoO2 have been considered, and the full optimization has been carried out for these bulk structures. Moreover, to increase the accuracy, HSE06 hybrid functional has been applied. Comparing with pristine Li7La3Zr2O12 and LiCoO2 bulks, the structures with Co↔Zr or Co↔La cation interchange are unfavorable. As a result, these structures can only form under a large stress which is consistent with experimental observations, showing the cation interchange during the cathode annealing at high temperatures. In the case of Li-S batteries, our findings show that pristine and even vacant graphene in sulfur cathode do not have the ability to catch the Li-polysulfides. Therefore, another way to trap the Li-polysulfides should be proposed. According to the experimental results, doping of graphene by certain dopants such as nitrogen or phosphorus can immobilize the Li2Sx molecules, and improve the performance of sulfur cathode. This process should be studied theoretically in detail, similar to what we have done for pristine and defective graphene. In order to study the Li-ion conductivity, the approach that has been used in Li2S can be applied to model superionic phase transition in ionic crystals. In addition, at Li7La3Zr2O12(001)/LiCoO2(10-14) interface, our calculations enable us to have a better understanding of processes at such interfaces which will eventually lead to fabricate the more efficient ASSLB.
