Study On The Ionic And Electronic Structures And Equation Of States Of Hot And Dense Matters

In the framework of density functional theory (DFT), electronic structures are described using the different energy density functions in the different temperature regions. The Thomas-Fermi model (TF), the average atom model (AA), the local density approximation (LDA) and the generalized gradient approaximation (GGA) are used in the hot dense matter, warm dense matter and low temperature region, respectively. The ion-ion pair potentials are calculated based on the electronic structures. And the classical molecular dynamics simulations are performed for the ion motion on the basis of the calculated pair potentials. In the middle region, microcosmic characters of melting and nucleation are discussed by using classical molecular dynamics.Firstly, the electronic structures and phase transitions of Aluminium and Gold have been calculated at the structure of the face-certered cubic (fcc), body-centered cubic (bcc), and hexagonal close-packed (hcp), by using the augmented plane wave plus local orbital method with two distinct exchange-correlation energy functions: the generalized gradient approaximation (GGA) and the local density approximation (LDA). The phase transitions and the equation of state (EOS) at zero temperature are obtained, and possible reasons are disscused by analyzing the electronic density of state at the different phases and different volumes. The contributions from the vibration of crystal lattice are treated by using mean field theory.With the increase of density and temperature, the matter state will be changed from solid to plasma due to the thermo-ionizaiton and pressure-ionization. In these cases, the periodical boundary condition for the electronic state does not exist any longer and the broadening of the valence electron states does not have the itinerant characteristic either. Furthemore, the electronic energy levels of the atoms and ions will be split into many sublevels due to the interactions among the particles in the hot dense plasmas. However, the splittings are generally so small that the distribution of the sublevels can be treated by broadening the corresponding energy level into energy band with a Gaussian profile, which is normalized to ensure that the integration of the density of state over one hand is equal to the statistical weight of the corresponding atomic level. The distribution of the bound electrons among the energy bands is determined by the continuum Fermi-Dirac distribution. Within a self-consistent field average atom approach, it has been shown that explicit considerations for the electronic energy level broadening have significant effects on the ionization of the atoms and the EOS in hot and dense plasmas. The instability of the pressure induced electronic ionization with density increasing, which occurs often in a normal average atom model and is avoided usually by introducing pseudo-shape resonance states, disappears naturally. As examples, the density dependence of the average ionization and the EOS of Al and Au at 1, 10, 100, and 1000 eV are presented. In the average atom (AA) model, when the energy of an electron is greater than the potential of the atomic boundary, this electron is considered to be a bound electron, and its radial distribution can be obtained from the radial Dirac equation. If one electron is smaller than the potential of the atomic boundary, it is taken to be a free electron, and the radial distribution can be obtained from Thomas-Fermi statistics. In fact, when electron energy is greater than zero, the electron is localized due to the interaction between electron and nucles in plasmas. In particular, when plasma temperature is very low, the Thomas-Fermi statistics will have big difference. So the description of free electron is modified by solving the radial Dirac equation.With the temperature decreasing, the ion-ion correlation effects become important in hot dense plasmas. In order to study the ion-ion correlation effects, we develop a model to calculate the ion-ion potentials based on temperature-dependent density functional theory (TDDFT). The electronic structures, including the energy levels and space distributions, are calculated using a modified average-atom model. The calculated electron space number density is divided into two parts: one is a uniformly distributed electronic sea with a density equaling to the total electronic density at the ionic sphere boundary, which is redistributed when space overlap occurs between the interacted ions; the left part of the electronic density represents the dramatic space variations of the electrons due to the nuclear attraction and the shell structure of the bound states, which maintains unchanged during the interactions between the ions. The ion-ion potential is obtained through space integrations for the energy density functions of electron density. Molecular dynamics simulations are performed for the ionic motions on the basis of the calculated potentials in a wide regime of density and temperature. As an example, hot and dense Al and Fe plasmas are simulated to give the EOS and ion-ion pair distribution function.When plasma temperature continues to reducing, the ionic average kinetic energy will decrease. And while the ionic average potential energy is larger than its kinetic energy, the ions will be close to each other and clusters will be formed. On the other hand, with the temperature increasing, the ionic average kinetic energy in the solid state will also increase. And solid state will become liquid state or plasma when the ionic average kinetic energy is larger than its potential energy. In the case, the molecular dynamics are performed to simulate the phase transitions among the matter state of solid, liquid, plasma and cluster with the change of temperature.