Dossa, Scott2024-01-192024-01-192023-09https://hdl.handle.net/11299/260162University of Minnesota Ph.D. dissertation. September 2023. Major: Physics. Advisors: Jeffrey Derby, Jorge Vinals. 1 computer file (PDF); x, 149 pages.Far more than just pretty stones, single crystals increasingly underpin the technology we rely on every day. For the technologies of tomorrow, novel materials must be discovered and synthesis of known materials must be improved. Take diamond, for example: the favored material for the production of quantum bits owing to their unique physical, thermal, and electric properties. Only synthetic diamonds are suitable for this purpose. Synthetic diamonds are grown by transporting carbon through a solvent at high temperatures and pressures --the high-pressure, high-temperature (HPHT) method. Unfortunately, diamonds grown via HPHT contain large inclusions of the solvent used in their growth which greatly limits the resulting crystal quality. Reducing or eliminating solvent inclusions in synthetically grown diamonds is critical for the continued advancement of areas which rely on diamond. When discovering new materials, rather than improving production of traditional ones, the floating-zone system is an invaluable tool. Recently, a high-pressure gas has been added to optically heated floating-zone systems as this increases the range of phase space which can be utilized for growth. The high-pressure, optical floating-zone (HPOFZ) method has been used to achieve growth of completely new materials which could not be grown at ambient pressures and to make growth easier for existing materials. This advancement has also come with challenges. At high pressures, instability of the liquid zone as well as turbulent flow in the gas phase have been reported. Evaporation of volatile components from the liquid zone is also a concern at higher pressures due to the potential to stoichiometrically alter the crystal. To understand the challenges during growth with HPOFZ and the inclusion of solvent during HPHT diamond growth, we employ mathematical models to investigate each system. Our HPOFZ model realistically represents the shape of the liquid bridge and evaporation of volatile species arising due to the temperature and flow within the system. To fundamentally understand the role of pressure in HPOFZ growth systems, these calculations are done at pressures ranging from 1 to 300 bar. From these models we find system pressure significantly affects buoyant flows in the surrounding atmosphere. Both driving force and flow strength increase nonlinearly with pressure, with the Grashof number growing with the cube of pressure and the Reynolds number scaling with pressure to the 3/2 power. Species transport is also strongly affected by pressure with evaporation from the liquid scaling with pressure to the negative 2/5 power. The HPHT model focuses on the relationship between temperature, flow, and carbon transport and its effect on the growth characteristics of diamond. This model is the first to connect phase-change kinetics governing crystal growth to the continuum transport of carbon through the growth cell. Results show the importance of convective transport driven by buoyant flow in the solvent, which increases the growth rate by nearly an order of magnitude over that obtained under diffusion alone. Parametric studies show how crystal growth may be kinetically-limited or transport-limited, depending on the value of the macroscopic kinetic coefficient. Estimating this kinetic coefficient from growth experiments yields a phase-change Damk\"{o}hler number of unity, indicating a mixed regime where phase-change kinetics and transport are comparable and strongly coupled in this system. Mechanisms responsible for slowing growth as the crystal size increases are explained. Supersaturation inhomogeneities along the facets of larger crystals are predicted, which may be relevant to solvent inclusion formation during growth.enCrystal GrowthDiamondFloating zoneHPHTMathematical ModelingThesis or Dissertation