Research On Analytic Equation Of State And Thermophysical Properties Of Fullerene And Diamond Solids

Researches on analytic equation of state of simple solids and cage molecular solids have been made in this dissertation. Several analytic equations of state of simple solids are presented with further intention to study simple solids, such as C₆₀ and its derivative C₆₁D₂, C₇₀, C₈₄, Diamond and c-BN based on the free volume theory (FVT) and the analytic mean field approach (AMFP) theory with appropriate potential function.In charpter 1, research background and significance of the analytic equation of state are reviewed, and the present status on research of several materials are generalized. Then main concept and theory on the subject are briefly introduced such as interaction between molecules, the free volume theory and the analytic mean field approach theory as the theoretic foundation of this dissertation has been introduced.In charpter 2, analytic expressions for the equation of state and thermo-physical quantities of poly-exponential potential solid are derived. The developed formalism is applied to the C₆₀ solid. Comparisons of the theoretical results by using the double-exponential (DE) potential and Grifalco potential are given, respectively. The numerical results calculated show that the Girifalco potential is too hard and gives compression curve prominently deviated from experiments at high pressure, whereas the DE potential can well describe the thermophysical properties of C₆₀ system within wide temperature and pressure range. Moreover, the AMFP is a useful approach to consider the anharmonic effects at high temperature for solid C₆₀.In charpter 3, analytic expressions for equation of state and internal energy for the poly-exponential solid have been derived based on the AMFP method. The formalism is applied to the fcc C₆₁D₂ solid. Two sets of potential parameters are determined through fitting the experimental compression data of C₆₁D₂ up to 1 GPa and at temperature 343 K and 307 K, respectively. The thermo-physical properties including the isothermals, thermal expansivity, isochoric heat capacity, Helmholtz free energy and internal energy have been calculated and analyzed. The theoretical results are in good agreement with the experimental data of C₆₁D₂ solid available.In charpter 4, the AMFP approach is applied to the poly-exponential model solid. The analytic expressions for the Helmholtz free energy, internal energy and equation of state are derived. The formalism for the case of the DE model is applied to fcc C₇₀ and C₈₄. Two sets of potential parameters are determined by fitting the experimental compression data of C₇₀ and C₈₄, respectively. The equilibrium distance and well depth for C₆₀, C₇₀ and C₈₄ molecules are plotted, and the following sequence T s(C₈₄) > T s(C₇₀) > T s(C₆₀) is obtained. The thermophysical properties including the isothermals, thermal expansion, isochoric heat capacity, Helmholtz free energy and internal energy are calculated and analyzed. The theoretical results agree well with the experimental data available and molecular dynamics (MD) simulation results, but superior to the correlative method of unsymmetrized self-consistent field (CUSF) of Zubov. Basing the results of our calculations, we may also predict the behaviors of C₇₀ and C₈₄ at extreme conditions.In charpter 5, the AMFP approach has been applied to diamond. The potential is divided into two parts based on the spirit of embedded atom method (EAM) and the quantum effect is included. The analytic expressions for the Helmholtz free energy, internal energy and equation of state have been derived. By fitting the compression experimental data of diamond, we determined the parameters for the Morse potential and calculated the pressure dependence of the molar volume for diamond based on the AMFP method. The results obtained are in good agreement with the available experimental data. This suggests that the AMFP method is a very useful approach to study the thermodynamic properties of diamond. Additionally, we predicted the variation tendency of compression curves at high temperatures and present the potential function of diamond from theoretical calculation. Furthermore, the variation relationship of the free energy and internal energy versus the molar volume of diamond at various temperatures have been predicted and the temperature dependence of the molar volume, bulk modulus, thermal expansion coefficient and isochoric heat capacity at zero pressure have been calculated by using the formalism developed in this paper. In charpter 6, we have presented an analytic method for the derivation of equation of state and thermodynamic properties of c-BN. By fitting the experimental P-V-T data, we determined the parameters for the Morse potential. The temperature effect is included soundly. Various physical quantities including the isothermals, thermal expansion, isochoric heat capacity, Helmholtz free energy and internal energy are calculated and analyzed. The calculation results agree well with the available experimental data and the other authors'theoretical results. Moreover, the AMFP method used in this work can take the quantum effect at low temperature and anharmonic effects at high temperature for c-BN into account soundly. Numerous reasonable predictions and the change trend of the properties for c-BN at extreme conditions have been given. These results presented in this paper confirm the validity of the model used (Morse potential) for c-BN up to high temperature and pressure.In charpter 7, the research of this dissertation is summarized and the next work is predicted.