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We present a comparative density functional theory study of Li, Na, and Mg storage energetics and diffusion in α-Sn, including the effects of temperature (vibrations). We study several concentrations corresponding to initial stages of insertion (number densities x= 1/64, 1/32, 1/16, and 1/8) as well as the final state of charge (Li17Sn4, Na15Sn4, and Mg2Sn). While final states of charge correspond to positive anode voltages for all three types of metal, insertion energetics is favorable for insertion for Li at all concentrations studied, for Na up to the concentration of x = 3/64, and Mg insertion is thermodynamically disfavored at all x. Diffusion barriers at dilute concentrations are computed to be 0.23, 0.51, and 0.44 eV for Li, Na, and Mg, respectively. Vibrations have a noticeable and temperature-, concentration-, and dopant-type dependent effect on voltages, of the order of 0.1 eV at room temperature.
We show in a theoretical density functional theory study that amorphous Si (a-Si) has more favorable energetics for Mg storage compared to crystalline Si (c-Si). Specifically, Mg and Li insertion is compared in a model a-Si simulation cell. Multiple sites for Mg insertion with a wide range of binding energies are identified. For many sites, Mg defect formation energies are negative, whereas they are positive in c-Si. Moreover, while clustering in c-Si destabilizes the insertion sites (by about 0.1/0.2 eV per atom for nearest-neighbor Li/Mg), it is found to stabilize some of the insertion sites for both Li (by up to 0.27 eV) and Mg (by up to 0.35 eV) in a-Si. This could have significant implications on the performance of Si anodes in Mg batteries.
We explore, via density functional theory (DFT) calculations, the effect on the barrier height for Li and Na diffusion in bulk Si of the presence of an extra Li/Na atom at the neighboring tetrahedral (T) or hexagonal (H) interstitial site. For both neighboring sites, the lowest diffusion barrier height is reduced, although the magnitude of the reduction depends on the inter-atomic distance between the 2 Li/Na atoms. We further calculate the effective interaction between the 2 atoms and show that it is a strong predictor of diffusion barrier heights for both Li-Si and Na-Si systems. Importantly, the correlation between inter-dopant interaction and barrier height may be used in future work to predict the diffusion barriers at higher concentration of inserted atoms.
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