We have qualitatively explained the experiments of McCloud and Maher (McCloud and Maher (95)) for the viscous fingering problem in which an anisotropy in the surface tension parameter was imposed by engraving a grid in one of the plates of the Hele-Shaw cell. We saw the need to approach the problem in an analytical form. Therefore we decided to extend solvability theory to incorporate the effect of anisotropy. We have introduced the anisotropy through a moving boundary condition by considering an effective anisotropic surface tension with an anisotropy entering as the simplest cosine term having the right symmetry for a square lattice. We carried out the singular perturbation appropriate for the surface tension parameter assuming the length scale introduced by the anisotropy is small in comparison with the length scale introduced by the surface tension. In this sense, the perturbation can be said to be microscopic. For the case in which the surface tension has a maximum at the finger tip, our theory provides two possible solutions: one corresponding to the solution of the isotropic case and a new solution which, below a threshold of the surface tension parameter, predicts a wider finger than the isotropic solution. Intuitively, we expect the "old" solution, namely the one that does not differ from the isotropic case, to be the selected solution for large values of the surface tension parameter and we expect the new solution to be selected for small values of the surface tension parameter. This was confirmed by dynamical simulations of the interface done by David Jasnow. His simulation predicts that for the case in which the surface tension has a maximum at the finger tip, anisotropy is irrelevant for large values of the surface tension parameter. Furthermore below a threshold in this surface tension parameter, the selected finger width is systematically wider than the corresponding isotropic case. We conclude that our solvability theory together with the dynamic

In this thesis, we develop a novel ab-initio technique to study transport in atomic scale devices based on a self-consistent solution of the Kohn-Sham equations for open systems in and out of equilibrium. Starting from the central motivating theorems of density functional theory, we introduce the basis of the ab-initio technique as currently practiced in condensed matter physics. The Kohn-Sham Hamiltonian is solved numerically by employing a Fireball atomic orbital basis set to transform the problem into matrix form. In order to study open systems, a natural screening approximation is introduced and it is demonstrated that, for the systems studied in this work, the Kohn-Sham potential is effectively screened and the screening approximation is appropriate for the study of atomic scale devices. The method developed in this thesis is contrasted with previous studies of transport in atomic scale devices and it is argued that it presents a significant advance and makes it possible to solve problems which could not previously be studied. / A few representative studies were undertaken in order to illustrate the advantage of using a self-consistent ab-initio method to study quantum transport in open systems. Several short carbon chains were coupled to Al electrodes and it was found that charge transfer plays a role in aligning the Fermi level with standing wave resonance peaks inside the atomic chain. Our study of a C60 molecular junction predicts a substantial equilibrium conductance due to charge transfer doping of three extra electrons inside the C60. Furthermore, these extra electrons may be depleted by an external gate voltage, reducing the conductance and thus producing a field-effect molecular switch. Transport and charge transfer were studied in a number of nanotube devices. Preliminary results are in agreement with recent experimental and theoretical results.

Conventional transmission Mossbauer, selective excitation double Mossbauer (SEDM), and zero-field muon spin relaxation (ZF-muSR) spectroscopy were used to identify static and dynamic magnetic disorder. With the construction of an efficient SEDM spectrometer, a consistent description of static magnetic disorder in an amorphous alloy (a-Fe80B 20) was developed using transmission Mossbauer and SEDM spectroscopy. Both methods measure the effects of the random static distribution of local magnetic environments around the Mossbauer nuclei. Magnetic fine particle systems (Fe3O4 ferrofluids, polysaccharide iron complex) were examined using transmission Mossbauer spectroscopy, and a model was developed that describes the entire range of dynamic magnetic behavior, from blocked moments on towards collective excitations and superparamagnetic moments. SEDM has measured 180° moment flips in the ferrofluids, determining a model independent relaxation rate of superparamagnetic moments. With the spectral signatures of static and dynamic magnetic phenomena identified, SEDM spectroscopy has been used to unambiguously verify the existence (a-Fe 92Zr8) and absence (Fe65Ni35) of magnetic relaxation in chemically disordered alloys. Additionally, the static and dynamic disorder in a magnetic fine particle system (a polysaccharide iron complex) and a frustrated magnet system (a-FexZr100- x), have been measured with ZF-muSR spectroscopy. The effects of collective excitations have been independently verified with ZF-muSR and moment fluctuation rates are in agreement with transmission Mossbauer spectra fit results. Two magnetic transitions have been identified with ZF-muSR in the a-FexZr100- x system, one at TC and another at Txy corresponding to transverse spin freezing, in both static and fluctuating magnetic components of muSR spectra. SEDM has been used to verify the existence of a fluctuation peak at T xy, and the time-dependent hyperfine interactions due to transverse spin freezin

Magnetic structure and magnetization reversal of lithographically patterned submicron and nanometer scaled magnets with elliptical, disk, ring shapes, and pseudo spin valve structures, were studied by magnetic force microscopy. / Magnetic measurements were performed with a custom built vacuum magnetic force microscopy with in-situ in plane magnetic fields. The MFM has been optimized with a force gradient sensitivity as high as 1 x 10-6 N/m. / By using various magnetic tips, operating in different modes, and studying different samples, the effect of the magnetic tip stray field induced distortion of the magnetic state of a submicron sized magnet is presented. Through the systematic study, a method of how to detect and to avoid these irreversible distortions is also presented. A local 'hysteresis loop' technique has been invented to study the abrupt switching behavior of individual elements. / In arrays of elongated magnetic particle array, the aspect ratio dependence of the switching indicates that the vortex state can be trapped inside the elements and form an energetic stable state, leading to a broad switching field distribution. In an array of 70 nm wide pseudo spin valve elements, parallel and antiparallel single domain configurations are found. Major and minor hysteresis loops as well as inter-layer coupling are investigated. We found that interlayer coupling leads to switching field variations. In a Permalloy disk array, the vortex state with vortex core singularity is found. The switching mechanism through the nucleation and annihilation processes is demonstrated by the local hysteresis loop. An interdot coupling-induced anisotropic switching is observed. In Permalloy ring structures, a vortex state and an 'onion' state are found. The onion state in permalloy rings with diameters of 5mum is found to be a flux closure state with a head to head domain wall. The switching behavior of these ring elements is found to be domain wall propagation.

Systems modelling nanoscale structures have been studied in the context of the theory of energy level statistics in the ballistic and mesoscopic as well as the insulating regimes. Statistics were obtained using a new unfolding scheme based on the existence of a local stationary property for fluctuations of the energy spectra. Two different models were used in the study with particular emphasis on the relevance to the physics of nanoscale devices. Thus, a quantum billiard model composed of a quasi-two-dimensional tight-binding atomic lattice was introduced. The results of the statistical analysis of the spectra of the models were compared throughout the thesis with Random Matrix Theory (RMT). The applicability of RMT and the universality predicted by RMT were verified. / The statistical behavior of energy levels for systems in the crossover region between regular and chaotic behavior was studied in all three regimes. Gradual transitions were observed for both ballistic and mesoscopic systems, and found to be similar in the cases. For systems in the insulating regime, the statistical behavior of levels was found to be of Poisson type. The transition from GOE to Poisson behavior when the system is changed from the mesoscopic to the insulating regime was also studied, a spectral dependence of the local fluctuations of energy levels was found, indicating the break-down of translation invariance of the local fluctuations. / The transition due to time reversal invariant symmetry breaking was studied by applying a uniform magnetic field to systems constructed by using a tight-binding model with non-zero off-diagonal interactions. By rescaling the transition control parameter, it was found that for both ballistic and mesoscopic systems the transition behavior can be well described by RMT. For closed systems the transition is complete when the effective area of the system encloses a flux greater than one flux quantum.

This thesis presents a structural study of Ni-Zr metallic glasses. It is the first time that a careful complete and systematic investigation into the structure of a glassy metallic system has been carried out. The results have improved our understanding of the structure of metallic glasses and clarified confusion in previous studies. The total structure factors of melt-spun and sputtered amorphous Ni$ sb{x}$Zr$ sb{1-x}$, 0.25 $ le$ x $ le$ 0.86, were obtained with an accuracy of 1-4%. Accurate partial structure factors of Ni$ sb{0.33}$Zr$ sb{0.67}$ and Ni$ sb{0.67}$Zr$ sb{0.33}$ were obtained using x-ray and neutron diffraction while those of Ni$ sb{0.33}$Zr$ sb{0.67}$ were also obtained independently using isomorphous substitution. The results confirmed the reliability of the isomorphous substitution method for Ni-Zr glasses. We have found a strong correlation between the local atomic structure and the electron transport properties of Ni-Zr glasses. No structural difference between melt-spun and sputtered Ni-Zr glasses was found. Our results show that the Faber-Ziman partial structure factors of Ni-Zr glasses is strongly composition dependent. The local topological order in amorphous Ni$ sb{0.33}$Zr$ sb{0.67}$ is found to be quite similar to that in the BCT NiZr$ sb2$ compound whereas a discrepancy in the structure is found between amorphous Ni$ sb{0.67}$Zr$ sb{0.33}$ and the FCC Ni$ sb2$Zr compound. Our results have also shown that the Ni-Zr glasses are an almost random mixture of Ni and Zr atoms and that there is no correlation between the pre-peak in the neutron structure factor and the chemical short-range order in the metallic glass.

This thesis presents the results of a systematic study on the structural relaxation and the glass transition of ternary metal-metal glasses Zr$ sb{67}$(Ni$ sb{1-x}$Cu$ sb{x}) sb{33}$. Differential scanning calorimetry provides macroscopic evidence of structural changes from the compositional and temperature dependence of enthalpy change. Results from high precision x-ray diffraction and Mossbauer spectroscopy, performed mainly on $ rm Zr sb{67}Ni sb{10}Cu sb{23}$ (x = 0.7), complete the picture of structural changes at the atomic level. / Irreversible structural relaxation leads to densification and enthalpy release. Shear-like atomic motion enhances local atomic order, highlighting the atomic processes during the irreversible relaxation. Reversible structural relaxation involves two partly overlapping processes initiated at different temperatures, which are characterized by the solid and liquid atomic mobilities, respectively. Interatomic positional exchanges between Cu and Ni atoms change the local structure and are active during the reversible relaxation at low temperatures, which are also partly responsible for the irreversible relaxation. Above 500 K, shear-like atomic movements characterize the reversible relaxation, involving all three atomic species in a length scale of a few near-neighbor atomic shells. The overall density is unchanged during reversible relaxation. / The strong compositional dependence of the glass transition in the ternary glasses indicates an intimate association of the glass transition with interatomic bondings among different atomic species. The atomic motion from room temperature up to above the glass transition temperature, measured by the Mossbauer spectroscopy, is macroscopically tracked by the volume expansion and the enthalpy evolution. The glass transition occurs when the length scale of the atomic motion expands so rapidly that the interatomic potential can no longer maintain the on-site atomic vibration. The rapid development of translational atomic motion upon approaching the glass transition is reflected by the dramatic enhancement of the diffusive atomic motion.

We have developed new techniques, which enable us to study the kinetics of phase transitions in situ. By resistive self heating of samples, heating rates of over 10$ sp4$ K/s have been achieved. Our methods allows us to acquire x-ray diffraction patterns as quickly as every 3 ms. / We have used these new techniques of time resolved x-ray diffraction experiments to study the crystallization kinetics of amorphous NiZr$ sb2,$ CoZr$ sb2,$ FeZr$ sb2$ and Ni$ sb{36.5}$Zr$ sb{63.5}.$ The experiments were performed at beamline X20C National Synchrotron Light Source. / We have mostly focussed on the crystallization behaviour at high temperatures and therefore faster kinetics. We have found many new results and unexpected metastable phases in these systems. Most of these phases would not be seen using conventional techniques showing the importance of in situ time resolved structural measurements to study the kinetics of phase transitions.

In this thesis, I study the nanolithography of gallium arsenide samples by local oxidation with an atomic force microscope (AFM). I examine the current theoretical descriptions of the reaction kinetics and compare the results to experimental data. The main goal is to characterize the AFM oxidation process such that high quality features can be routinely patterned. I also investigate the use of alternative oxidation environments in an attempt to improve the height and aspect ratio of the AFM local oxidation features. An alternative lithography technique involving scratching under a high contact force is also studied. Finally, I discuss the steps that are necessary in order to fabricate a quantum structure with the AFM local oxidation lithography technique.

A technique for preparing tips with a radius of a few nanometers from tungsten wire is investigated. The sharp shape is obtained by electrochemical etching; further tip processing and characterization is done in ultra-high vacuum. Tips are cleaned through a high temperature annealing process and their sharpness can be quickly estimated from their field emission behaviour. Sufficiently sharp tips are imaged with a field ion microscope; full atomic characterization of the tip apex can be obtained from an analysis of the resulting images and field evaporation can be used to atomically engineer the tip apex into a desired configuration. Starting from single crystal, (111) oriented tungsten wire, a sharp tip terminating in three atoms can be fabricated; due to its geometry and its stability, this apex configuration is well suited for applications as an atomically defined electrical contact in a single molecule conductivity experiment.