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We report first-principles calculations on the structural, thermodynamic, electronic, elastic and dynamic properties of transition metal carbonates, MCO3 (M= Mn, Co, Ni) at 0 K. These materials are projected to be excellent candidates as precursors for advanced cathode materials in rechargeable lithium-ion batteries which employ an NMC chemistry. We have employed the plane-wave pseudopotential method framed within the density functional theory (DFT) as embedded in the VASP code. The exchange-correlation functional of Perdew, Burke and Ernzerhof (PBE) was used. Moreover, the Hubbard U-correction in the rotationally invariant form was applied to improve the description of the strongly correlated 3d electrons of the transition metals. The structural cell parameters were calculated to 96 % agreement with the experimental data, warranting the robustness of the approach employed. All MCO3 crystal systems have negative enthalpies of formation, indicating thermodynamic stability leading to good cycling performance and safety. All the elastic constants for the considered transition metal carbonates satisfied the necessary stability conditions, indicating mechanical stability. Moreover, negative vibrations are not observed in the high symmetry directions of the Brillouin zone, suggesting dynamical stability.

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Bimetallic FexPt1-x alloys with the L10 and L12 structures have recently gained a lot of consideration in practical applications for solid-state devices, storage of ultra-high density magnetic data and biomedicine. This is due to their high magnetic and magnetocrystalline anisotropy, density, and coercivity. In order to gain knowledge on the structural, electronic and mechanical properties of the cubic and tetragonal FexPt1-x alloys, we have calculated their equilibrium lattice constants, density of states, and elastic constants at 0 K, employing first-principles calculations. The calculated equilibrium lattice constants were found to be in good agreement with the experimental data to within 3 %. All independent elastic constants satisfy the necessary stability conditions for both cubic and tetragonal systems, suggesting mechanical stability. The shear anisotropic factors predict that the tetragonal FexPt1-x crystals are highly anisotropic along the {001} plane than {100}. Moreover, the percentage of bulk (AB) and shear (AG) anisotropies revealed completely isotropic systems in the bulk and slightly anisotropic in shear modulus.