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One quasi-direct gap phase (Amm2) and three indirect gap phases (C2/m-16, C2/m-20, and I-4) of silicon allotropes are proposed. The detailed theoretical study on the structure, density of states, elastic properties, sound velocities, and Debye temperature of these four phases is carried out by using first principles calculations. The elastic constants of these four phases are calculated by strain-stress method. The elastic constants and the phonon calculations manifest all novel silicon allotropes in this paper are mechanically and dynamically stable at ambient condition. The B/G values indicate that these four phases of silicon are brittle materials at ambient pressure. The anisotropy properties show that C2/m-20 phase exhibits a larger anisotropy in its elastic modulus, shear elastic anisotropic factors, and several anisotropic indices than others. We have found that the Debye temperature of the four novel silicon allotropes gradually reduces in the order of C2/m-20 > Amm2 > C2/m-16 > I-4 at ambient pressure. V

A general strategy of understanding the catalytic mechanism for a high-performance bio-based porous carbon supported ZnNb2O6 hybrid catalyst is illustrated.

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