Th. doct.-ing.--Méc.--Toulouse--I.N.P., 1981 : 181.

Starting from a classical mechanical model, a set of Langevin equations for the surface diffusion of adsorbed molecules is developed. In contrast to previous work, these Langevin equations take full account of the rotations and internal vibrations of the adsorbed molecule. These equations are then applied to a stiff dimer diffusing in one dimension, and the results compared with previous calculations for the same system. It is shown that the modifications in our new approach give significantly different results than this previous calculation, and therefore must be taken into account in future calculations for systems of this kind. Next a new approximation method is developed by assuming that the motion of the molecule is confined to the lowest energy path between adsorption sites. This method is applicable to an arbitrarily complex molecule, and is complimentary to the first method, in that it can account for deformation of the molecule by the surface but not the internal vibrations of the molecule (whereas the first method accounts for internal vibrations but not deformation). This approximation method is then applied to a flexible dimer in two dimensions (one dimension along the surface and one perpendicular). The results are discussed and compared with those of the stiff dimer in one dimension, explaining and clarifying the difference between our results and those of previous calculations.

Surface diffusion of group III and IV metals on Si(100) is studied. Three methods for obtaining diffusion barriers are presented and discrepancies in published results are discussed. Room temperature growth of Al on Si(100) is studied using STM, observing a monomodal scaled island size distribution function. A Kinetic Monte Carlo simulation model is employed to obtain bonding energies and diffusion barriers for Al/Si(100). The best agreement between the measured and simulated characteristics is found for strongly anisotropic diffusion with barriers 0.60 eV in the direction orthogonal to the Si dimer rows and 0.80 eV in the parallel direction. Modifications of the cooling system required for observing metal adatom diffusion on Si(100) using STM are described and the first low-temperature experiment is carried out.

At the microscopic level, many materials are made of smaller and randomly oriented grains. These grains are separated by grain boundaries which tend to decrease the electrical and thermal conductivity of the material. The motion of grain boundaries is an important phenomenon controlling the grain growth in materials processing and synthesis. Mathematical modeling and simulation is a powerful tool for studying the motion of grain boundaries. The research reported in this thesis is focused on the numerical simulation and analysis of a coupled surface and grain boundary motion which models the evolution of grain boundary and the diffusion of the free surface during the process of grain growth. The “quarter loop” geometry provides a convenient model for the study of this coupled motion. Two types of normal curve velocities are involved in this model: motion by mean curvature and motion by surface diffusion. They are coupled together at a triple junction. A front tracking method is used to simulate the migration. To describe the problem, different formulations are presented and discussed. A new formulation that comprises partial differential equations and algebraic equations is proposed. It preserves arc length parametrization up to scaling and exhibits good numerical performance. This formulation is shown to be well-posed in a reduced, linear setting. Numerical simulations are implemented and compared for all formulations. The new formulation is also applied to some other related problems. We investigate numerically the linear stability of the travelling wave solutions for the quarter loop problem and a simple grain boundary motion problem for both curves in two dimensions and surfaces in three dimensions. The numerical results give evidence that they are convectively stable. A class of high order three-phase boundary motion problems are also studied. We consider a region where three phase boundaries meet at a triple junction and evolve with specified normal velocities. A system of partial differential algebraic equations (PDAE) is proposed to describe this class of problems by extending the discussion for the coupled surface and grain boundary motion. The linear well-posedness of the system is analyzed and numerical simulations are performed.

No description available.

This research is focused on the synthesis and characterization (BET, transmission electron microscopy and optical spectroscopy) of aluminum oxide condensates via a static sintering process and dynamic process of pulse laser ablation (PLA) and pulse laser ablation in liquid (PLAL). For a start, the static route of an onset coarsening-coalescence event based on the incubation time of cylindrical mesopore formation and a significant decrease of specific surface area by 50% and 70% relative to the dry pressed samples was determined by N2 adsorption-desorption hysteresis isotherm for two Al2O3 powders having 50 and 10 nm in diameter respectively on an average and with £^-type related structures, i.e. £^- and its distortion derivatives £_- and/or £c-types with {100}/{111} facets and twinning according to transmission electron microscopy. In the temperature range of 1100 to 1400oC, both powders underwent onset coarsening-coalescence before reconstructive transformation to form the stable £\-type. The apparent activation energy for such a rapid coarsening-coalescence event was estimated as 241 ¡Ó 18 and 119 ¡Ó 19 kJ/mol, for 50 and 10 nm-sized particles, respectively indicating easier surface diffusion and particle movement for the latter. The size dependence of surface relaxation and onset coarsening-coalescence of the £^−type related Al2O3 nanoparticles agrees with their recrystallization-repacking upon electron irradiation and accounts for their assembly into nano chain aggregates or a close packed manner under the radiant heating effect in a dynamic laser ablation process. In addition, ultrafine (5 nm) Al2O3 nanoparticles having a predominant £\-type structure and with an internal compressive stress up to ca. 15 GPa were synthesized by pulsed laser ablation on Al target under a very high peak power density (1.8x1011 W/cm2) with oxygen flow in vacuum. The ultrafine £\-Al2O3 was alternatively formed from the minor £^-Al2O3 nanocondensates upon electron irradiation. In such a case, the polymorphs follow a special crystallographic relationship [110]£^//[2110]£\; (111) £^//(0114)£\ with a mixed mismatch strain yet nonparallel close packed planes indicating a reconstructive type transformation. The formation of metastable £\-Al2O3 in the dynamic processes can be rationalized by the kinetic phase change from the amorphous lamellar and/or £^-Al2O3 depending on their free energy versus cell volume curves. The dense and ultrafine sized Al2O3 polymorphs with a rather low minimum band gap of 3.7 eV shed light on their natural occurrence in dynamic settings and abrasive as well as catalytic/optoelectronic applications. Furthmore, pulsed laser ablation in water under a high peak power density of 1.8 ¡Ñ 1011 W/cm2 using Q-switch mode and 1064 nm excitation was used to fabricate (H+,Al2+)-codoped Al2O3 nanocondensates having £^- and its derivative £c-type structure as characterized by electron microscopy and spectroscopy. The as-formed £^- and £c-Al2O3 nanocondensates are mainly 10 to 100 nm in size and have a significant internal compressive stress (> 10 GPa) according to cell parameters and vibrational spectroscopy, due to a significant shock loading effect in water. The £^-Al2O3 nanocondensates are nearly spherical in shape but became cubo-octahedra when grew up to ca. 100 nm to exhibit more facets as a result of martensitic £^¡÷£c transformation following the crystallographic relationship (3 11 )£c //(02 2)£^; (0 2 4 )£c//(3 11)£^. The formation of dense and (H+,Al2+)-codoped £^/£c-Al2O3 rather than aluminum hydrates sheds light on the favored phases of the Al2O3-H2O binary at high temperature and pressure conditions in natural dynamic settings. The nanocondensates thus formed have a much lower minimum band gap (5.2 eV) than bulk £\-Al2O3 for potential optocatalytic applications. Moreover, the Al2O3 nanocondensates of spinel-type related structures, i.e. £^- and £c- type with a significant internal compressive stress via pulsed laser ablation in water were subjected to prolonged dwelling in water to form columnar bayerite plates for further transformation as platy £^-Al2O3. Transmission electron microscopic observations indicated the £^-Al2O3 follows the crystallographic relationship (100)b//(011)£^; [001]b//[111]£^ with relic bayerite (denoted as b). The £^-Al2O3 also shows {111} twin/faults and rock salt-type domains due to dehydroxylation of bayerite which involves {111} shuffling and disordering of the Al ions in the octahedral and tetrahedral sites. The combined evidences of X-ray photoelectron spectroscopy, vibrational spectroscopy and UV-visible absorbance indicated that the H+, Al+ and Al2+ co-doped bayerite and £^-Al2O3 composite plates have a minimum band gap as low as ~ 5 eV for potential catalytic and electro-optical applications in water environment. Finally, pulsed laser ablation in aqueous solution of NaOH up to 1 M was employed to fabricate epitaxial NaAlO2 and £^-Al2O3 nanopartricles for electron microscopic and spectroscopic characterizations. The NaAlO2 phase (denoted as N), presumably derived from NaAlO2 .5/4H2O, was found to form intimate intergrowth with the £^-Al2O3 following a specific crystallographic relationship [211]£^//[110]N; ( 2 22) £^//(002)N and (0 2 2) £^//(110)N for a parallel close packed planes in terms of corner linked AlO4 tetrahedra and a beneficial lower interfacial energy and/or strain energy. The composite phases have significant internal compressive stress up to 7 and 40 GPa according to cell volume and IR shift results and a low minimum band gap of 5.9 eV for potential applications in UV region.

At the microscopic level, many materials are made of smaller and randomly oriented grains. These grains are separated by grain boundaries which tend to decrease the electrical and thermal conductivity of the material. The motion of grain boundaries is an important phenomenon controlling the grain growth in materials processing and synthesis. Mathematical modeling and simulation is a powerful tool for studying the motion of grain boundaries. The research reported in this thesis is focused on the numerical simulation and analysis of a coupled surface and grain boundary motion which models the evolution of grain boundary and the diffusion of the free surface during the process of grain growth. The “quarter loop” geometry provides a convenient model for the study of this coupled motion. Two types of normal curve velocities are involved in this model: motion by mean curvature and motion by surface diffusion. They are coupled together at a triple junction. A front tracking method is used to simulate the migration. To describe the problem, different formulations are presented and discussed. A new formulation that comprises partial differential equations and algebraic equations is proposed. It preserves arc length parametrization up to scaling and exhibits good numerical performance. This formulation is shown to be well-posed in a reduced, linear setting. Numerical simulations are implemented and compared for all formulations. The new formulation is also applied to some other related problems. We investigate numerically the linear stability of the travelling wave solutions for the quarter loop problem and a simple grain boundary motion problem for both curves in two dimensions and surfaces in three dimensions. The numerical results give evidence that they are convectively stable. A class of high order three-phase boundary motion problems are also studied. We consider a region where three phase boundaries meet at a triple junction and evolve with specified normal velocities. A system of partial differential algebraic equations (PDAE) is proposed to describe this class of problems by extending the discussion for the coupled surface and grain boundary motion. The linear well-posedness of the system is analyzed and numerical simulations are performed.

At the microscopic level, many materials are made of smaller and randomly oriented grains. These grains are separated by grain boundaries which tend to decrease the electrical and thermal conductivity of the material. The motion of grain boundaries is an important phenomenon controlling the grain growth in materials processing and synthesis. Mathematical modeling and simulation is a powerful tool for studying the motion of grain boundaries. The research reported in this thesis is focused on the numerical simulation and analysis of a coupled surface and grain boundary motion which models the evolution of grain boundary and the diffusion of the free surface during the process of grain growth. The “quarter loop” geometry provides a convenient model for the study of this coupled motion. Two types of normal curve velocities are involved in this model: motion by mean curvature and motion by surface diffusion. They are coupled together at a triple junction. A front tracking method is used to simulate the migration. To describe the problem, different formulations are presented and discussed. A new formulation that comprises partial differential equations and algebraic equations is proposed. It preserves arc length parametrization up to scaling and exhibits good numerical performance. This formulation is shown to be well-posed in a reduced, linear setting. Numerical simulations are implemented and compared for all formulations. The new formulation is also applied to some other related problems. We investigate numerically the linear stability of the travelling wave solutions for the quarter loop problem and a simple grain boundary motion problem for both curves in two dimensions and surfaces in three dimensions. The numerical results give evidence that they are convectively stable. A class of high order three-phase boundary motion problems are also studied. We consider a region where three phase boundaries meet at a triple junction and evolve with specified normal velocities. A system of partial differential algebraic equations (PDAE) is proposed to describe this class of problems by extending the discussion for the coupled surface and grain boundary motion. The linear well-posedness of the system is analyzed and numerical simulations are performed. / Science, Faculty of / Mathematics, Department of / Graduate

We explore a specific small geometry containing a single thin bounded grain on a substrate with a hole at its center. By employing a mathematical model based on surface diffusion, no flux boundary conditions, and prescribed contact angles, we study the evolution of the hole as well as the exterior surface of the grain, based on energetic considerations and dynamic simulations. Our results regarding the formation and evolution of holes in thin films in small geometries shed light on various nonlinear phenomena associated with wetting and dewetting.

<p dir="ltr">We investigate the surface diffusion flow of smooth curves with anisotropic surface energy.</p><p dir="ltr">This geometric flow is the H−1-gradient flow of an energy functional. It preserves the area</p><p dir="ltr">enclosed by the evolving curve while at the same time decreases its energy. We show the</p><p dir="ltr">existence of a unique local in time solution for the flow but also the existence of a global in</p><p dir="ltr">time solution if the initial curve is close to the Wulff shape. In addition, we prove that the</p><p dir="ltr">global solution converges to the Wulff shape as t → ∞. In the current setting, the anisotropy</p><p dir="ltr">is not too strong so that the Wulff shape is given by a smooth curve. In the last section, we</p><p dir="ltr">formulate the corresponding problem when the Wulff shape exhibits corners.</p>