Exploring thermal and mechanical properties of selected transition elements under extreme conditions: Experiments at high pressures and high temperatures

Transition metals (Ti, Zr, Hf, Mo, W, V, Nb, Ta, Pd, Pt, Cu, Ag, and Au) are essential building units of many materials and have important industrial applications. Therefore, it is important to understand their thermal and physical behavior when they are subjected to extreme conditions of pressure and temperature. This dissertation presents: • An improved experimental technique to use lasers for the measurement of thermal conductivity of materials under conditions of very high pressure (P, up to 50 GPa) and temperature (T up to 2500 K). • An experimental study of the phase relationship and physical properties of selected transition metals, which revealed new and unexpected physical effects of thermal conductivity in Zr, and Hf under high P-T. • New phase diagrams created for Hf, Ti and Zr from experimental data. • P-T dependence of the lattice parameters in α-hafnium. Contrary to prior reports, the α-ω phase transition in hafnium has a negative dT/dP slope. • New data on thermodynamic and physical properties of several transition metals and their respective high P-T phase diagrams. • First complete thermodynamic database for solid phases of 13 common transition metals was created. This database has: All the thermochemical data on these elements in their standard state (mostly available and compiled); All the equations of state (EoS) formulated from pressure-volume-temperature data (measured as a part of this study and from literature); Complete thermodynamic data for selected elements from standard to extreme conditions. The thermodynamic database provided by this study can be used with available thermodynamic software to calculate all thermophysical properties and phase diagrams at high P-T conditions. For readers who do not have access to this software, tabulated values of all thermodynamic and volume data for the 13 metals at high P-T are included in the APPENDIX. In the APPENDIX, a description of several other high-pressure studies of selected oxide systems is also included. Thermophysical properties (Cp, H, S, G) of the high P-T ω-phase of Ti, Zr and Hf were determined during the optimization of the EoS parameters and are presented in this study for the first time. These results should have important implications in understanding hexagonal-close-packed to simple-hexagonal phase transitions in transition metals and other materials.

Lattice Boltzmann modeling of fluid flow and solute transport in karst aquifers

A novel modeling approach is applied to karst hydrology. Long-standing problems in karst hydrology and solute transport are addressed using Lattice Boltzmann methods (LBMs). These methods contrast with other modeling approaches that have been applied to karst hydrology. The motivation of this dissertation is to develop new computational models for solving ground water hydraulics and transport problems in karst aquifers, which are widespread around the globe. This research tests the viability of the LBM as a robust alternative numerical technique for solving large-scale hydrological problems. The LB models applied in this research are briefly reviewed and there is a discussion of implementation issues. The dissertation focuses on testing the LB models. The LBM is tested for two different types of inlet boundary conditions for solute transport in finite and effectively semi-infinite domains. The LBM solutions are verified against analytical solutions. Zero-diffusion transport and Taylor dispersion in slits are also simulated and compared against analytical solutions. These results demonstrate the LBM’s flexibility as a solute transport solver. The LBM is applied to simulate solute transport and fluid flow in porous media traversed by larger conduits. A LBM-based macroscopic flow solver (Darcy’s law-based) is linked with an anisotropic dispersion solver. Spatial breakthrough curves in one and two dimensions are fitted against the available analytical solutions. This provides a steady flow model with capabilities routinely found in ground water flow and transport models (e.g., the combination of MODFLOW and MT3D). However the new LBM-based model retains the ability to solve inertial flows that are characteristic of karst aquifer conduits. Transient flows in a confined aquifer are solved using two different LBM approaches. The analogy between Fick’s second law (diffusion equation) and the transient ground water flow equation is used to solve the transient head distribution. An altered-velocity flow solver with source/sink term is applied to simulate a drawdown curve. Hydraulic parameters like transmissivity and storage coefficient are linked with LB parameters. These capabilities complete the LBM’s effective treatment of the types of processes that are simulated by standard ground water models. The LB model is verified against field data for drawdown in a confined aquifer.

Lattice Boltzmann Modeling of Fluid Flow and Solute Transport in Karst Aquifers

A novel modeling approach is applied to karst hydrology. Long-standing problems in karst hydrology and solute transport are addressed using Lattice Boltzmann methods (LBMs). These methods contrast with other modeling approaches that have been applied to karst hydrology. The motivation of this dissertation is to develop new computational models for solving ground water hydraulics and transport problems in karst aquifers, which are widespread around the globe. This research tests the viability of the LBM as a robust alternative numerical technique for solving large-scale hydrological problems. The LB models applied in this research are briefly reviewed and there is a discussion of implementation issues. The dissertation focuses on testing the LB models. The LBM is tested for two different types of inlet boundary conditions for solute transport in finite and effectively semi-infinite domains. The LBM solutions are verified against analytical solutions. Zero-diffusion transport and Taylor dispersion in slits are also simulated and compared against analytical solutions. These results demonstrate the LBM’s flexibility as a solute transport solver. The LBM is applied to simulate solute transport and fluid flow in porous media traversed by larger conduits. A LBM-based macroscopic flow solver (Darcy’s law-based) is linked with an anisotropic dispersion solver. Spatial breakthrough curves in one and two dimensions are fitted against the available analytical solutions. This provides a steady flow model with capabilities routinely found in ground water flow and transport models (e.g., the combination of MODFLOW and MT3D). However the new LBM-based model retains the ability to solve inertial flows that are characteristic of karst aquifer conduits. Transient flows in a confined aquifer are solved using two different LBM approaches. The analogy between Fick’s second law (diffusion equation) and the transient ground water flow equation is used to solve the transient head distribution. An altered-velocity flow solver with source/sink term is applied to simulate a drawdown curve. Hydraulic parameters like transmissivity and storage coefficient are linked with LB parameters. These capabilities complete the LBM’s effective treatment of the types of processes that are simulated by standard ground water models. The LB model is verified against field data for drawdown in a confined aquifer.