Three-dimensional models of mantle convection : influence of phase transitions and temperature-dependent viscosity

Two of the most important questions in mantle dynamics are investigated in three separate studies: the influence of phase transitions (studies 1 and 2), and the influence of temperature-dependent viscosity (study 3).

(1) Numerical modeling of mantle convection in a three-dimensional spherical shell incorporating the two major mantle phase transitions reveals an inherently three-dimensional flow pattern characterized by accumulation of cold downwellings above the 670 km discontinuity, and cylindrical 'avalanches' of upper mantle material into the lower mantle. The exothermic phase transition at 400 km depth reduces the degree of layering. A region of strongly-depressed temperature occurs at the base of the mantle. The temperature field is strongly modulated by this partial layering, both locally and in globally-averaged diagnostics. Flow penetration is strongly wavelength-dependent, with easy penetration at long wavelengths but strong inhibition at short wavelengths. The amplitude of the geoid is not significantly affected.

(2) Using a simple criterion for the deflection of an upwelling or downwelling by an endothermic phase transition, the scaling of the critical phase buoyancy parameter with the important lengthscales is obtained. The derived trends match those observed in numerical simulations, i.e., deflection is enhanced by (a) shorter wavelengths, (b) narrower up/downwellings (c) internal heating and (d) narrower phase loops.

(3) A systematic investigation into the effects of temperature-dependent viscosity on mantle convection has been performed in three-dimensional Cartesian geometry, with a factor of 1000-2500 viscosity variation, and Rayleigh numbers of 10^5-10^7. Enormous differences in model behavior are found, depending on the details of rheology, heating mode, compressibility and boundary conditions. Stress-free boundaries, compressibility, and temperature-dependent viscosity all favor long-wavelength flows, even in internally heated cases. However, small cells are obtained with some parameter combinations. Downwelling plumes and upwelling sheets are possible when viscosity is dependent solely on temperature. Viscous dissipation becomes important with temperature-dependent viscosity.

The sensitivity of mantle flow and structure to these various complexities illustrates the importance of performing mantle convection calculations with rheological and thermodynamic properties matching as closely as possible those of the Earth.

A Study on iron-based amorphous alloys : alloy development, thermodynamics and soft magnetism

Metallic glass has since its debut been of great research interest due to its profound scientific significance. Magnetic metallic glasses are of special interest because of their promising technological applications. In this thesis, we introduced a novel series of Fe-based alloys and offer a holistic review of the physics and properties of these alloys. A systematic alloy development and optimization method was introduced, with experimental implementation on transition metal based alloying system. A deep understanding on the influencing factors of glass forming ability was brought up and discussed, based on classical nucleation theory. Experimental data of the new Fe-based amorphous alloys were interpreted to further analyze those influencing factors, including reduced glass transition temperature, fragility, and liquid-crystal interface free energy. Various treatments (fluxing, overheating, etc.) were discussed for their impacts on the alloying systems' thermodynamics and glass forming ability. Multiple experimental characterization methods were discussed to measure the alloys' soft magnetic properties. In addition to theoretical and experimental investigation, we also gave a detailed numerical analysis on the rapid-discharge-heating-and-forming platform. It is a novel experimental system which offers extremely fast heating rate for calorimetric characterization and alloy deformation.