Theoretical Study Of Titanium Carbon Two-dimensional Structure

The discovery of graphene raises broad interest about low-dimensional structures, such as nanotubes, nanowires, nanobelts and nanosheets etc. Based on density functional theory, we research two new types of two-dimensional monolayer sheets built by us using the VASP software package. To compare with the two-dimensional sheets constructed by us, we use the CALYPSO packages to predict Ti C2 and Ti C3 two-dimensional sheets, and the most stable structure obtained is discussed in detail. The second part of our essay calculate mainly three kinds of nanoribbons gained from Ti C2 sheet. The calculation results are as follows:(1) To observe the Ti C2 sheet along vector b carefully, Ti atoms are arranged into zigzag curve and C atoms are aligned into armchair curve, named Ti C2α. Using ab initio molecular dynamics simulations, when the temperature reaches 1500 K,it maintains the stability of the structure, while when the temperature increases by 500 K, the structure is no longer stable. Phonon spectrum calculation also shows high kinetic stability. Bader charge analysis shows that magnetic moment of the Ti C2α sheet is 0.004 μB/atom. We calculate band structure using the hybrid density functional theory, and the results show that there is a band across the Fermi surface, reflecting the characteristics of the conductor. By calculating density of states, below the Fermi level, the C 2p orbital has strong hybridization with the Ti 3d orbital, while near and above the Fermi level, the contributions come mainly from the Ti 3d state.(2) To compare with the Ti C2α sheet, we used CALYPSO software package to predict new structures. We predicted about 115 kinds of structures, and picked out six structures which have different structures and the lowest enthalpy. Though geometry optimization, the Ti C2α sheet has the lowest free energy, and average freedom of each atom is-8.376 e V/atom, while the second lowest is the sheet which is predicted by CALYPSO package(Ti C2β), we carried out a detailed calculation. When the temperature reaches 1500 K, it can maintain the stability of the Ti C2β sheet, but the calculation of phonon spectra shows that there are imaginary frequencies, dynamic stability is not high. The Ti C2?? sheet is a conductor with the magnetic moment of 0.332 μB/atom. The major contributions near and above the Fermi level come from the Ti 3d states, and below the Fermi level mainly come from C 2p and Ti 3d hybrid contributions.(3) We constructed six Ti C3 monolayer sheets, and geometrical optimization showed the most stable monolayer sheet(Ti C3α), and we carried out a detailed calculation. To the Ti C3α sheet, six carbon atoms form hexagonal structure and above per two carbon atoms have a Ti atom, which form a kind of plicate two-dimensional structure. It is non-magnetic semiconductor with 0.301 e V indirect band gap, the stable temperature reaches 1500 K, while when the temperature reaches 2000 K, the structure begin to distort. By calculating density of states, Ti 3d states make main contributions for the electronic density of states near and above the Fermi level, while the electronic density of states below the Fermi level is mainly by the contribution of C 2p and Ti 3d hybrid formation.(4) By using CALYPSO software package, we gained 50 kinds of Ti C3 sheets, and picked out four structures which have different structures and the lower enthalpy. Though geometry optimization, the Ti C3α sheet have the lowest free energy, and average freedom of each atom is-8.367 e V. While the second lowest is the sheet which is predicted by CALYPSO package(Ti C3β), we carry out a detailed calculation. The Ti C3β sheet can maintain thermodynamic stability at a temperature of 800 K, and the phonon spectrum show that the maximum frequency is 1720 cm-1, indicating strong titanium-carbon bond.(5) Zigzag Ti C2 nanoribbons are nonmagnetic, which also show three different kinds of properties: metallic, semi-metallic and semiconductor with different ribbon widths. On the contrary, armchair Ti C2 nanoribbons are ferromagnetic conductor ignoring of ribbon widths. Armchair-zigzag Ti C2 nanoribbons possess ferromagnetic and show metallic and semiconductor properties with different widths. Zigzag Ti C2 nanoribbons are more stable than armchair-zigzag Ti C2 nanoribbons, while they are both more stable than armchair Ti C2 nanoribbons. Bond energies of the three kinds of nanoribbons are all increasing with increasing ribbon widths.