First-principles Study Of Mechanical And Thermodynamic Properties Of Metal Carbides

Because of the diverse crystal structures and good physical and chemical properties, the binary metal carbides have great application value in physics, chemistry, material science and geology. In this thesis, the first-principles calculations of the density functional theory were introduced to study the mechanical and thermodynamic properties of the binary rare-earth metal carbides（Yb-C system） and binary alkaline-earth metal carbides（Ca-C system）. We focus on two main problems in our study. One problem is on the influence of the Hubbard U on the mechanical and thermodynamic properties of Yb-C system,including four special ytterbium carbides, YbC in Fm-3m phase, Yb₂C₃ in I-43 d phase,YbC₂ in I4/mmm phase and YbC₆ in P63/mmc phase. The other problem is on the pressure effects on the mechanical properties of calcium carbides, Ca₂ C in C2/m and Pnma phases and Ca₂C₃ in C2/m phase.The strong correlation of the 4f electrons in rare-earth metal carbides has important roles in their electronic structure and thermodynamics. In this thesis, a generalized gradient approximation plus a Hubbard parameter（GGA + U） formalism is used to study the mechanical and thermodynamic properties of the YbC, Yb₂C₃, YbC₂, and YbC₆ with the Hubbard U among the 4f electrons included. It shows that the lattice constants of the four ytterbium carbides increase obviously when Hubbard U increases, and inversely, most of the corresponding elastic constants decrease with enhanced Hubbard U. In Voigt-Reuss-Hill（VRH） approximation, the bulk modulus B, the Young’s modulus E and the shear modulus G are evaluated, which shows the explicit dependence of B, E and G on the Hubbard U. Among the four ytterbium carbides, YbC₆ has the largest B, E, and G,which shows that YbC₆ is hard and brittle. On the contrary, YbC₂ is relatively soft and ductile. Mechanical anisotropy was estimated using several anisotropic indices and factors.The phonon spectra reveal the thermodynamic stability of YbC₂ and YbC₆, which is consistent with experimental observations.Pressure can modify the bonding of the atoms and thus leads to changes of the physical properties of the materials. In this thesis, the mechanical properties of the Ca₂C₃ in C2/m phase（C2/m-Ca₂C₃）, Ca₂ C in C2/m phase（C2/m-Ca₂C） and in Pnma phase（Pnma-Ca₂C）under different pressures were investigated systematically. The elastic constants C11, C22 and C₃3 of the three calcium carbides increase with pressure. The C2/m-Ca₂C₃ in pressure from 0 to 30 GPa, C/2m-Ca₂ C in pressure from 0 to 7.5 GPa and Pnma-Ca₂ C in pressure from 7.5 to 30 GPa satisfy the Born-Huang lattice dynamical criteria of mechanical stability. The bulk modulus B, Young’s modulus E and shear modulus G of the three calcium carbides also increase with pressure. The directional B and E, and shear anisotropic factors show that the mechanical anisotropy of C2/m-Ca₂C₃, C2/m-Ca₂ C and Pnma-Ca₂ C also enhances with pressure. In addition, the vanishing of the enhancement of B, E and AG of C2/m-Ca₂ C with pressure in 5 to 7 GPa implies the instability of the crystal lattice structure and the possible emergence of the structure phase transition.As a summary, the strong correlation of the 4f electrons in the ytterbium-carbon rare-earth metal carbides has important influence on their mechanical and thermodynamic properties, and our study of the pressure effects on the calcium-carbon alkaline-earth metal carbides improves our understanding of the mechanical properties of the newly discovered phases of the calcium carbides.