Alkali (lithium and sodium) ion batteries have been attracting considerable attention as a promising power source of electronic devices due to their high energy density and long cycle life. When compared with lithium, sodium has a merit of resource abundance on the Earth's crust, leading to apparent cost lowering of battery production and thus enabling sodium ion batteries (SIBs) to be commercially viable. However, no optimal electrode materials have yet been developed as some scientific challenges are unresolved. In particular, since graphite, the intercalation-type anode material for lithium ion batteries (LIBs), exhibits extremely low specific capacity when reacting with sodium, numerous works have been devoted to finding suitable anode materials for SIBs. Recently, in order to mitigate the volume change maintaining the high specific capacity, intermetallic compounds such as FeSn2 and CoSn2 with inactive transition metals such as Fe or Co that do not directly react with Li and Na, has been proposed as the anode active material of SIBs. However, the anode activity mechanism of these intermetallic compounds has not yet been elucidated fundamentally.
We have investigated the physical properties and the anode activity mechanism FeSn2 and CoSn2, which can be used as anode active materials of sodium-ion batteries (SIBs), using first principles calculations within the density functional theory (DFT) framework.
All the DFT calculations have been carried out by applying the pseudopotential plane wave method as implemented in the QUANTUM ESPRESSO (QE, version 6.2) package. For a description of the coulombic interaction between the ionic cores and the valence electrons, we have constructed the ultrasoft pseudopotentials of the atoms by executing the LD1 code included in the QE package, using the input files provided in the PS library(1.0). Also, the Perdew–Burke–Ernzerhof (PBE) formulation within generalized gradient approximation (GGA) was adopted to describe the exchange–correlation interaction among the valence electrons. Structural optimizations were carried out with the kinetic cutoﬀ energies of 60 Ry for wave function and 600 Ry for electron density, and the special k-points with a 8×8×10 mesh.
Firstly we determined the favorable spin configurations for transition metal atoms in MSn2 and MASn2 with crystalline lattice optimization. It was found that for the case of FeSn2 the anti-ferromagnetic (AFM) configuration was energetically favorable with the best agreement of lattice constants to the experiment. For the case of CoSn2, however, the non-magnetic (NM) state was always observed though the three diﬀerent spin configurations of anti-ferromagnetic (AFM), ferromagnetic (FM) and non-magnetic (NM) were initially imposed. When replacing the M (Fe, and Co) atom by an A (Li, and Na) atom, although we initially imposed the AFM configurations on the resultant unit cell of MASn2, the FM state was observed for FeASn2 while also the NM state was realized for CoASn2.
Next, in order to determine the optimized lattice parameters of the unit cells and the density, we plotted the energy–volume curves by calculating the total energies as the unit cell volume gradually increased. It was found that replacing one Fe or Co atom in the MSn2 unit cell with an Li or Na atom induces an increase of lattice constants, tetragonal ratio and thus unit cell volume and decrease of density. To gain insight into the structural stability, we evaluated the cohesive energy and the formation energy. The formation energy of FeSn2 (-0.221 eV per atom) is lower than that of CoSn2 (-0.183 eV per atom), demonstrating that the Fe-related intermetallics is more stable than the Co-related ones. It was also observed that substituting Li or Na for an Fe or Co atom makes the compounds less stable, and this eﬀect is more pronounced for Na substitution compared to Li substitution.
Then, six independent elastic stiﬀness constants for MSn2 and MASn2 in the tetragonal phase, namely C11, C12, C13, C33, C44 and C66 were calculated. The calculated elastic constants were found to satisfy the well-known Born stability criteria for tetragonal crystals, thereby implying their mechanical stability at zero pressure. According to the Pugh criteria for ductility of solid, FeSn2 and CoSn2 are ductile materials due to their B/G values of 1.796 and 1.815 being larger than 1.75 and ν values of 0.265 and 0.267 being larger than 0.26. Interestingly, Li or Na substitution for Fe in FeSn2 induces decreases of B/G and ν values, thereby indicating a transition from ductile to brittle properties. However, Li or Na substitution for Co in CoSn2 induces increases the B/G and ν values, suggesting that Li or Na substitution increases the ductility.
Then, the average sound velocities and Debye temperatures were calculated by using the obtained elastic modulus and density. Our calculation results show that FeSn2 has higher Debye temperature than CoSn2, and moreover, Li or Na substitution reduces the θD values. Such a tendency indicates that FeSn2 is harder than CoSn2 and Li or Na substitution lowers the hardness.
We wrote the paper entitled "Influence of M/A substitution on material properties of intermetallic compounds MSn2 (M = Fe, and Co; A = Li, and Na): a first principles study" (https://doi.org/10.1039/d0nj04537c) with these results and in 2020, it was reporteded on New Journal of Chemistry (Vol.44, 2020, pp.21218-21227) published by ROYAL SOCIETY OF CHEMISTRY.