Mechanics, Lattice Dynamics, And Chemical Bonding In ZrB₂ And ZrB₁₂ From First-Principles Calculations

Zirconium borides (ZrB2 and ZrB12) have dual characters of ceramic and metal and possess high melting point, high hardness and excellent electrical conductivity, thermal and chemical resistance properties. Thus, they are excellent high-temperature ceramic materials. Although these two zirconium borides have been widely used in engineer applications, their physical and chemical properties have not yet been systematically studied. Some basic questions (including electronic structure, bonding mechanism, and phonon vibration mode, etc.) have not yet been resolved. In this thesis, by using the first-principles based on the density functional theory, we have investigated the atomic structure, electronic structure, mechanical properties and chemical bonding properties of ZrB2 and ZrB12 at their corresponding equilibrium states. The physical properties of ZrB12 under high pressure have also been analyzed in detail.Firstly, by using the density functional theory, we have numerically calculated the electronic structure, mechanical and lattice dynamical properties of ZrB2 and ZrB12 at their corresponding equilibrium states. Results show that the strong covalent bonding of B layers or clusters is responsible for the good mechanical and dynamical stabilities. The electronic density of states at the Fermi level N(EF) for ZrB12 is prominently larger than that for ZrB2, especially for Zr 4dyzdxz states. The low frequency vibration of Zr atoms makes electron-phonon interaction considerable. Through analyzing electronic structures, bonding pictures and ionicity for the two borides have been indicated quantitatively.Secondly, the pressure effects on the electronic, mechanical, and thermodynamical properties of ZrB12 have been studied from a first-principles perspective. Due to the good mechanical and dynamical stabilities of this material, our results show that the pressure effects on the structure and electronic structure are limited. However, the mechanical properties of elastic constants, elastic moduli, and elastic wave velocities as well as the thermodynamical properties of the Debye temperature and melting points are promptly enhanced by increasing pressure. Under pressure the density of states at the Fermi level N(EF) decreases while the low frequency vibration of Zr atoms increases in the energy level, which indicates a negative pressure effect on the superconductivity of ZrB12. According to phonon dispersions, we have also calculated the phonon free energy, phonon entropy, and the specific heat at constant volume under different pressure and temperature conditions...