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Multinuclear NMR of 93Nb, 45Sc, and 207Pb has been carried out to study the structure, disorder, and dynamics of a series of important solid solutions: perovskite relaxor ferroelectric materials (1-x) Pb(Mg1/3Nb 2/3)O3-x Pb(Sc1/2Nb1/2)O 3 (PMN-PSN).;93Nb NMR investigations of the local structure and cation order/disorder are presented as a function of PSN concentration, x. The superb fidelity and accuracy of 3QMAS allows us to make clear and consistent assignments of spectral intensities to the 28 possible nearest B-site neighbor (nBn) configurations, (NMg, NSc, NNb), where each number ranges from 0 to 6 and their sum is 6. For most of the 28 possible nBn configurations, isotropic chemical shifts and quadrupole product constants have been extracted from the data. The seven configurations with only larger cations, Mg 2+ and Sc3+ (and no Nb5+) are assigned to the seven observed narrow peaks, whose deconvoluted intensities facilitate quantitative evaluation of, and differentiation between, different models of B-site (chemical) disorder. The "completely random" model is ruled out and the "random site" model is shown to be in qualitative agreement with the NMR experiments. to obtain quantitative agreement with observed NMR intensities, the random site model is slightly modified by including unlike-pair interaction energies.;To date, 45Sc studies have not been as fruitful as 93Nb NMR because the resolution is lower in the 45Sc spectra. The lower resolution of 45Sc spectra is due to a smaller span of isotropic chemical shift (40 ppm for 45Sc vs. 82 ppm for 93Nb) and to the lack of a fortuitous mechanism that simplifies the 93Nb spectra; for 93Nb the overlap of the isotropic chemical shifts of 6-Sc and 6-Nb configurations results in the alignment of all the 28 configurations along only seven quadrupole distribution axes.;Finally we present variable temperature 207Pb static, MAS, and 2D-PASS NMR studies. Strong linear correlations between isotropic and anisotropic chemical shifts show that Pb-O bonds vary from more ionic to more covalent environments. Distributions of Pb-O bond lengthes are also quantitatively described. Such distributions are used to examine two competing models of Pb displacements; the shell model and the unique direction model. Only the latter model is able to reproduce the observed Pb-O distance distribution.

A planar antenna RF plasma enhanced chemical vapor deposition apparatus was built for carbon nanostructure syntheses. When operated in inductive and capacitive plasma discharging modes, two carbon nanostructures, carbon nanotube (CNT) and carbon nanosheet (CNS), were synthesized, respectively.;A nanosphere lithography method was developed and used to prepare catalyst patterns for CNT growth. Using capacitively coupled C2H2/NH 3 plasma, randomly oriented CNT were synthesized on Ni dot patterned Si substrates. Aligned CNT arrays were grown on SiO2 coated Si substrates, using both C2H2/NH3 and CH 4/H2 capacitive plasmas.;When operated in inductive coupling mode, CNS were successfully deposited on a variety of substrates without any catalyst. Carbon nanosheets are a novel two-dimensional structure, have smooth surface morphologies and atomically thin edges, and are free-standing roughly vertical to substrate surfaces. CNS have a defective graphitic crystalline structure, and contain only C and H elements. Typical CNS growth parameters are 680??C substrate temperature, 40% CH4 in H2, 900 W RF power, and 100 mTorr total gas pressure. Morphology, growth rate, and structure of CNS change with the variations in the growth parameters. Increasing substrate temperature yields a less smooth morphology, a faster growth rate, and more defects in CNS; increasing CH 4 concentration causes a faster growth rate and more defects in CNS, but only slightly changes the morphology; increasing RF power results in a more smooth morphology, a faster growth rate, and less defects in CNS; and decreasing total gas pressure induces a less smooth morphology, a faster growth rate, and more defects in CNS.;In CNS growth mechanism, a base layer forms underneath the vertical sheets; the growth of CNS is through growth species surface diffusion; the electric field near substrate surfaces promotes and keeps the vertical orientation of the CNS, and the atomic hydrogen etching keeps the CNS atomically thin.;Carbon nanosheets have large surface areas, and can stabilize metal thin films into particles 3-5 nm in diameters. For field emission testing, typical CNS have turn-on fields of 5-10 V/mum, a maximum emission current of 28 mA, an emission current density of 2 mA/mm2, and a life-time of 200 hours.

We examine the energy cascades and quantum vortex structures in two-dimensional quantum turbulence through a special unitary time evolution algorithm. An early attempt at using the Lattice Boltzmann Method proved successful in correctly representing some features of the Nonlinear Schrodinger System (NLS), such as the phase shift following the one-dimensional soliton-soliton collision, as well as the two-dimentional modulation instability. However, to accurately evaluate NLS, the implicit Euler method is required to resolve the time evolution, which is computationally expensive. A more accurate and efficient method, the Quantum Lattice Gas model is employed to simulate the quantum turbulence governed by the Gross-Pitaevskii equation, an equaiton that describes the evolution of the ground state wave function for a Bose-Einstein condensate (BEC). It is discovered that when the ratio of the internal energy to the kinetic energy is below 0.05, an unexpected short Poincare recurrence occurs independent of the initial profile of the wave function. It is demonstrated that this short recurrence is destroyed as the internal energy is strengthened. to compare the two-dimensional quantum turbulence with its classical counterpart, the incompressible energy spectra of quantum turbulence is analyzed. However, the result reveals no sign of dual cascades which is a hallmark of the classical incompressible two-dimensional fluid (inverse energy cascade to large scales with a direct cascade of enstrophy to small scales). It is the spectra of the compressible energy that can exhibits multiple cascades, but this is strongly dependent on the initial condition.

Various experimental and theoretical work indicate that the local structure and chemical ordering play a crucial role in the different physical behaviors of lead-based complex ferroelectrics with the ABO 3 perovskite structure. First-principles linearized augmented plane wave (LAPW) with the local orbital extension method within local density approximation (LDA) are performed on structural models of Pb(Zr1/2Ti1/2 )O3 (PZT), Pb(Sc1/2Ta1/2)O3 (PST), Pb(Sc2/3W1/3)O3 (PSW), and Pb(Mg 1/3Nb2/3)O3 (PMN) to calculate electric field gradients (EFGs). In order to simulate these disordered alloys, various structural models were constructed with different imposed chemical orderings and symmetries. Calculations were carried out as a function of B-site chemical ordering, applied strain, and imposed symmetry. Large changes in the EFGs are seen in PZT as the electric polarization rotates between the tetragonal and rhombohedral directions. The onset of polarization rotation in monoclinic Cm symmetry strongly correlates with the shearing of the TiO6 octahedron, and there is a sharp change in slope in plots of Ti EFGs versus octahedral distortion index. The same changes in EFGs and the BO6 shearing corresponding to the change of off-centering direction are also seen in PST. In PSW and PMN, the calculated B cation EFGs showed more sensitivity to the surrounding nearest B neighboring environments. Calculated B atom EFGs in all alloys are considerably larger than those inferred from the NMR measurements. Based on comparisons with experiments, the calculated results are interpreted in terms of static and dynamic structural models of these materials.

Recent experimental and theoretical work indicates that polarization rotation via a monoclinic phase at the morphotropic phase boundary in PZT is responsible for its large piezoelectric response. We performed Linearized augmented plane wave with the local orbital extension (LAPW+LO) method within local density approximation (LDA) on B-site [001]1:1 ordered Pb(Zr 0.5Ti0.5)O3 (PZT 50/50). We use a tetragonal super-cell and constrain it with monoclinic Cm space group. Atomic forces following the formulation of Yu et al. are calculated, and the conjugate gradient method is implemented to optimize the internal coordinates. Both the tetragonal (P4mm) and monoclinic (Cm) phases are reproduced, when we strain the system while keeping the volume fixed at experimental value. Bulk spontaneous polarization, Born effective charges (Z*) and piezoelectric coefficients are computed from the Berry's phase approach. The polarization rotates between the pseudo-cubic [001] and [nunu1] directions, where nu = 1.27 in the (110) mirror plane. The piezoelectric coefficients are enhanced when polarization rotation is permitted, namely e33 = 12.6 C/m2, e15 = 10.9 C/m 2, and giant absolute values of e13 = -33 C/m 2 and e'11 = 36 C/m2, where e'11, is defined as 0.5 (e11 + e12). It gives an explanation to the big piezoelectric response measured in ceramic PZT 50/50. Furthermore, the calculated internal coordinates of monoclinic phase of PZT 50/50 at experimental value of c/a are in good agreement with the experimental data of Pb(Zr0.52Ti 0.48)O3.

This work is devoted to the study of local order in the ferroelectric PbSc1/2Ta1/2O3 (PST) and relaxor ferroelectric solid solutions (1-x)PbSC2/3W1/3O3-(x)PbTiO 3 (PSW-PT), (1x)PbSC2/3W1/3O3-(x)PbZrO 3 (PSW-PZ). Novel Magic Angle Spinning (MAS) Solid State Nuclear Magnetic Resonance (SS-NMR) experiments, including Multiple Quantum MAS (MQMAS) and Double Quantum Filtered Satellite Transition (DQF-STMAS), have been performed on these materials. A gamma function model is proposed for the distribution of quadrupole coupling constants, based on the Poissonian nature of atomic displacements. Moments for distributions may be subsequently extracted through agreement between experimental spectra and simulations implemented in novel programs. Simple crystal compound scandium oxide provides a reasonable analogue and assists in spectral interpretation. Support is given to the Random Site (RS) model for atomic ordering in Relaxor Ferroelectrics. Based on point charge calculations, significant lead displacement takes place as well as oxygen octahedral tilting. In June 2004, Donghua Zhou proposed an experimental scheme to expedite the interpretation of experimental spectra for materials such as those studied here and a realization with analysis is given.

The internal magnetic field distributions for a type II superconductor (a single crystal YBa2Cu3O7-delta ) with large normal inclusions (YBa2Cu3O 7-delta) are studied. A model based on the London Equations has been successfully developed and applied to the interpretation of the pSR data on this system. In our model, these inclusions are assumed to be cylindrical in shape and infinite in length. Therefore, this model should be especially appropriate for the prediction of field distributions in single crystal superconductors in which columnar defects have been purposely introduced to enhance pinning.;muSR experiments on a large single-crystal sample of YBa2C u3O7-delta with non-conducting YBa2Cu3 O7-delta inclusions show some interesting characteristics, especially the magnetic field distribution in the inclusion regions. In our model, the difference between the field value in the inclusions and the value at the saddle point is sensitive to the penetration depth. Comparing the calculated to observed field differences provides a new method for determining the penetration depth.

One of the most interesting and challenging problems in physics is understanding strongly correlated many-body systems, where strong interactions can yield many remarkable phenomena such as superfluidity in 4He, high-temperature superconductivity, etc. In order to attack these problems, we often need to reduce the complexity of the systems to simple models in hopes of getting better insights into the properties of the systems. The Hubbard model, the focus of this dissertation, is one of the most famous examples of such model, which describes a tunneling of electrons between nearest neighbor sites of a lattice with on-site interactions. This simple model is an important concept in condensed matter physics and provides rich understandings of electronic and magnetic properties of materials. Despite its simplicity, there is no general analytical solution to the Hubbard model beyond 1D.;The discovery of ultracold atoms and optical lattices opens up the possibility of emulating the Hubbard model in experiments. Optical lattices provide an ideal realization of the Hubbard model where relevant parameters can be tuned systematically. It makes theoretical studies of the Hubbard model increasingly attractive since a direct comparison between theoretical calculations and experimental results becomes more and more possible.;In this dissertation, the ground-state properties of the repulsive Hubbard model for weak to intermediate interaction strengths in two, three dimensions and their dimensional crossover are studied within the mean field theory. We show that the system exhibits unidirectional spin-density wave (SDW) order with antiferromagnetic correlations and a long wavelength modulation. The modulating wave is along the [0011-direction at low interaction strength U/t and along the [1111-direction at higher U/t. The evolution of the wavelength of the SDW is determined as a function of U/t, the density, and t⊥/t. With an analysis of the pairing of spins based on nesting and deformation of the Fermi surface, we discuss how these results can be rationalized and how a simple, predictive model can be constructed for the properties of the SDW states.

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