Research On Elastic And Thermodynamic Properties For MgO, C-BN And Other Crystal Under High Pressure

MgB₂, anatase, MgO, SrO and super-hardness C-BN have received much attention from both physicist and geophysicist in experimental investigations and theoretical studies, due to their outstanding physical and chemical properties. This paper is to study their elastic and thermodynamic properties. By studying their electronic structures the nature of various physical properties of solids can be well understood. Solids are composed of numerous atoms and each atom has a nucleus and some electrons. Generally, it is not practical to solve the equation of a many-particle system like this directly and we must make some simplifications and approximations. We employ molecular dynamics(MD) method with empirical potential (Buckingham potential) to investigate MgB₂ and anatase, and the first principle method to study MgO, SrO and super-hardness C-BN. In order to calculate the elastic constants of MgO and SrO under high pressure, we employ a self-consistent-field(SCF) Hartree-Fock linear combination of the atomic orbital method. The basis sets used, suggested by Zupan and Causa et al. are for the study of elastic constants of these alkaline earth oxides under ambient condition. For C-BN, we employ the density-functional approximation using the Becke and Perdew-Wang nonlocal exchange and correlation functional. The basis sets used, suggested by Orlando et al. are for the study of diamond, Si, BN, BP, SiC and AlP elastic properties with CRYSTAL program under ambient condition in 1990. The exponents of the most diffuse sp and d shells for each atom have been optimized by searching for the minimum crystalline energy.This dissertation reviews briefly researches on a many-particle system and solid mechanic at first. Secondly, theory of first principle, molecular dynamics method and elasticity for crystal are introduced in detail. Thirdly, these elastic matrixes for seven crystals are shown. At last, elastic and thermodynamic properties and compressibility for MgB₂, anatase, MgO, SrO and super-hardness C-BN are studied. The calculated results agree quite well with the comparable experimental data and the values of others work and some new results are obtained that have never been fully reported before. These results are helpful to understand the physical mechanisms of the material at elevated pressure, and provide a solid theoretical foundation for material application under high pressure.Firstly, we establish Buckingham potential for MgB₂ and anatase by general utility lattice program(GULP) at ambient condition. Elastic and thermodynamic properties and compressibility for MgB₂ and anatase have been investigated in detail with Buckingham potential. The calculated results agree quite well with the comparable experimental data and the values of others work and the first time we obtain elastic constants of anatase under ambient condition. We find that the structure is more compressible in the c direction than in the a/b direction, which is consistent with the relatively weaker(Mg-B or Ti-O) bonds that determine the c axis length. In order to deal with the sensitivity of the charge transferring among Ti and O atoms to the local environment, the partial charge on each ion may be looked as a fitting parameter in the simulations. The results show that our methods are successful in resolving the difficulty for MD. The method to deal with the sensitivity of the charge to the local environment may be successfully applied for the analogous research. At the same time, we learn that the compression ratio of MgB₂ and anatase change nonlinearly, which increase rapidly as pressure varies. Lastly, we point out that the Buckingham potential used in this paper should be credible in the range of 12 GPa. However, the precision of two-body potential may be lowered with increased pressure since atomic interaction should be strengthened when pressure increases. In order to obtain more precision results at ambient condition or more credible results at high pressure, multi-body potential should be taken into account.For MgO, SrO and C-BN by CRSTAL program at ambient condition, we study firstly equilibrium lattice constants and elastic constants, which agree quite well with the comparable experimental data and the values of others work. Notice, it is we, the fast time, who obtain the elastic constants for B2-type MgO and Sro and theoretically point out that the B2-type MgO and SrO are unstable under ambient condition by the generalized elastic stability criteria. By the third-order Brich-Murnaghan's equation of state, we obtain the P-V relation and calculate elastic constants at elevated pressure for MgO, SrO and C-BN based on the pre-work. In the calculated pressure range, c₄₄ of the B1-type MgO and SrO doesn't vanish, which disagrees with the results of Tsuchiya et. al. However, it is consistent with the theory on phase transformation of Hunter et. al. We find that the noncentral contribution in the interatomic force is larger in MgO under pressure than in SrO, because the difference of the ion radius between Mg²⁺ and O^2- is larger than that of the ion radius between Sr²⁺ and O^2-, and Mg²⁺ has a larger electronegativity than Sr²⁺. By Cauchy relation, we find that the noncentral contribution in the interatomic force in C-BN becomes larger as the pressure increases, which proves that the noncentral many-body force becomes more and more important at high pressure. Thus, it is necessary to consider third-order and fourth-order elastic constants when the anharmonic properties of C-BN by means of elastic constants at high pressure are under discussion. In the range of 200 GPa, the elastic isotropic point of C-BN is not found, but to find that c₁₁ is more sensitive to pressure than c₁₂ and c₄₄. By the generalized elastic stability criteria c₁₁+2c₁₂＞0,c₄₄＞0, c₁₁-c₁₂＞0, we find that C-BN is stable in the range of 200 GPa. Systematics of elastic for C-BN under high pressure has been firstly investigated. For B1- type MgO and SrO, thermodynamic properties(Debye temperature, longitudinal and the transverse elastic wave velocity) have been initially investigated under high pressure, and we find that Debye temperature, longitudinal and the transverse elastic wave velocity increase with applied pressures. For C-BN, thermodynamic properties(Debye temperature, thermal expansion coefficient, specific heat, Poisson ration, longitudinal and the transverse elastic wave velocity) have been also the first time investigated under high pressure, and we get to know that Debye temperature, longitudinal and the transverse elastic wave velocity, and Poisson ration increase with applied pressures. However, the specific heat and thermal expansion coefficient decrease with the applied pressures, due to the effect of increasing pressure on C-BN is the same with decreasing temperature of it. These results propose abundant data for the further theoretical investigation.