| More and more evidences from seismic tomography, mineral physics, geochem-istry and geodynamics modeling methods support that the presence of subducted slabs in the Earth's lower mantle. It is likely that the subducted slabs could penetrate the transition zone and reach the lower mantle, even the core-mantle boundary (CMB) and eventually be evolved in the global mantle convection. The mid-ocean ridge basalts (MORB) represent the crustal part of subducted oceanic plate. Many high pres-sure experiments have been conducted on pyrolite (a representative mantle rock) and MORB composition to lower mantle conditions. In contrast with pyrolite composi-tion, in which the aluminum mainly resides in MgSiO3 perovskite, an independent aluminous phase was discovered by high-pressure and high-temperature experiments in the basaltic composition. Two polymorphs of MgAl2O4 with calcium-ferrite (CF) and calcium-titanate (CT) structures are likely major end-members of the aluminous phase. Therefore, the elasticity, equation of state (EOS) and thermodynamic proper-ties of the CF phase and CT phase are indispensable knowledge for building a mantle mineralogical model and interpreting the fate of subducted slabs in the lower mantle. In this thesis, the main study methods are first principles computational techniques based on density functional theory (DFT) in the framework of pseudo-potentials and plane waves. First, the elastic constants of CF phase and CT phase were determined using strain energy density method from 0 to 80 GPa. Special investigation was per-formed around 40 GPa, which is the possible transition pressure from CF to CT, on the change of elastic velocities and seismic anisotropy. At 40 GPa, shear velocity contrast between the two phases reached its maximum with a value of 1.6%, corresponding a 0.4% jump of velocity between MORB and surrounding mantle. However, this is about 0.6% lower than one requires from seismic estimation. Thus, the mid-mantle discon-tinuity around 1000km seems unlikely caused by this phase transition. On the other hand, the CF phase and CT phase show great seismic anisotropy, e.g. the max value of shear wave splitting was 25% at 40 GPa. If the oceanic crustal materials could be aligned in a preferred direction by mantle flow, the big shear wave splitting characteris-tic may be detected by seismic observations. Next, the thermodynamic properties of CF phase were calculated. Both of the two main exchange-correlation functional in DFT method, the local density approximation (LDA) and generalized gradient approxima-tion (GGA), produce some deviations of athermal EOS from experiment. GGA gives better performance than LDA after introducing a pressure correction for the athermal EOS. Furthermore, the lattice vibrational frequencies, i.e. phonons, were obtained us-ing density functional perturbation theory. The vibrational energy can be calculated from phonon frequencies. The athermal EOS was extended to finite temperature under quasi-harmonic approximation. It was shown that the high pressure equation of states calculated from 300 to 2400 K agree very well with experiments. The calculated den-sity profile along 2000 K from 35 to 60 GPa for the subducted slabs are 2% higher than typical seismological model (PREM), conforming the hypothesis that subducted slabs can sink in the lower mantle. One can derive all thermodynamic potentials from Leg-endre transformations if the Helmholtz free energy, volume and temperature relations F(V,T) are known. In this thesis, the following thermodynamic properties, the molar volume, isothermal and adiabatic bulk modulus, thermal expansivity, constant volume and pressure heat capacities, Gruneisen parameter, entropy and enthalpy difference, are listed as tables in a pressure range of 0 to 40 GPa and a temperature range of 0 to 2000 K. The accuracy of the thermodynamic properties are validated by comparing calculated results with experiments for a simpler system, corundum, and showed ex-cellent agreement. Finally, the calculation method used in this study is also promising for other mantle minerals and will have great impact on other geological applications.
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