Photonic crystals are artificial structures with a periodically varying refractive index. This property allows photonic crystals to control the propagation of photons, making them desirable components for novel photonic devices. Photonic crystals are also termed as "semiconductors of light", since they control the flow of electromagnetic radiation similar to the way electrons are excited in a semiconductor crystal. The scale of periodicity in the refractive index determines the frequency (or wavelength) of the electromagnetic waves that can be manipulated. This thesis presents a detailed analysis of photonic crystals at visible, x-ray, and terahertz frequencies. Self-assembly and spin-coating methods are used to fabricate colloidal photonic crystals at visible frequencies. Their dispersion characteristics are examined through theoretical as well as experimental studies. Based on their peculiar dispersion property called the superprism effect, a sensor that can detect small quantities of chemical substances is designed. A photonic crystal that can manipulate x-rays is fabricated by using crystals of a non-toxic plant virus as templates. Calculations show that these metallized three-dimensional crystals can find utility in x-ray optical systems. Terahertz photonic crystal slabs are fabricated by standard lithographic and etching techniques. In-plane superprism effect and out-of-plane guided resonances are studied by terahertz time-domain spectroscopy, and verified by numerical simulations.

The three projects within this work address the difficulties of controlling biomolecular crystal formats (i.e. size and shape), producing 3-D ordered composite materials from biomolecular crystal templates, and understanding the mechanism of a practical iron oxide synthesis. The unifying thread consistent throughout these three topics is the development of methods to manipulate nanomaterials using a bottom-up approach. Biomolecular crystals are nanometer to millimeter sized crystals that have well ordered mesoporous solvent channels. The overall physical dimensions of these crystals are highly dependent on crystallization conditions. The controlled growth of micro- and nanoprotein crystals was studied to provide new pathways for creating smaller crystalline protein materials. This method produced tetragonal hen egg-white lysozyme crystals (250--100,000 nm) with near monodisperse size distributions (<15%). With this degree of control, existing protein crystal applications such as drug delivery and analytical sensors can reach their full potential. Applications for larger crystals with inherently ubiquitous pore structures could extend to materials used for membranes or templates. In this work, the porous structure of larger cowpea mosaic virus crystals was used to template metal nanoparticle growth within the body centered cubic crystalline network. The final composite material was found to have long range ordering of palladium and platinum nonocrystal aggregates (10nm) with symmetry consistent to the virus template. Nanoparticle synthesis itself is an immense field of study with an array of diverse applications. The final piece of this work investigates the mechanism behind a previously developed iron oxide synthesis to gain more understanding and direction to future synthesis strategies. The particle growth mechanism was found to proceed by the formation of a solvated iron(III)oleate complex followed by a reduction of iron (III) to iron (II). This unstable iron(II) nucleates to form a wustite (FeO) core which serves as an epitaxial surface for the magnetite (Fe3O4) shell growth. This method produces spherical particles (6-60nm) with relative size distributions of less than 15%.

In this dissertation, the fracture toughening behavior of ferroelectric materials under different electromechanical loading conditions is predicted and compared to available experimental observations. A multi-axial, electromechanically coupled, incremental phenomenological constitutive model for ferroelectric ceramics is developed first. The constitutive model is then implemented within the finite element method to study the effects of electric field on the Mode I steady crack growth under plane stress and plane strain conditions. Toughening behaviors of electrically permeable cracks are simulated on both initially unpoled and poled materials with electric field applied in-plane or parallel to the crack front. The finite element results give detailed electromechanical fields, remanent strain and remanent polarization distributions, domain switching zone shapes and sizes, and the crack tip energy release rate. It is shown that the toughening is related to the size of the concentrated switching zone that is confined to a small region around the crack tip. The model predicts a range of phenomena that indicate that the toughening is dependent on both the level of electric filed applied and on the polarization state. In addition to the effects of electric field, the effects of the plane-stress constraint and transverse stress are also established in the out-of-plane poled cases. In a similar manner to the electrically permeable cracks, the crack growth simulations for electrically conducting crack face boundary conditions are also performed. The results predict the toughening variations under combined electromechanical loadings for poled or unpoled materials. The electromechanical fields from the finite element results are used to determine the stress and electric field intensity factors around the crack tip. The favorable comparison of the present model to the experimental observations suggest that ferroelectric switching behavior is more accurately modeled with an incremental plasticity formulation, rather than as an unstable phase transformation. The nonlinear studies of this dissertation not only explain most available experimental phenomena but also enhance the understanding of the nature of fracture in ferroelectric ceramics.

The interfacial dynamics of a viscous droplet immersed in a viscous medium are considered. The characteristic equation is derived using a normal-mode analysis, and solved for arbitrary, finite fluid properties. The cylinder functions in the characteristic equation are solved using a continued fraction algorithm, and the complex decay factor is searched using a modified quasilinearization minimization scheme. Oscillation frequency and damping rate results are presented for various cases of practical interest (liquid-gas and liquid-liquid systems), and the effect of external medium properties are discussed. It is shown that viscosity of the host medium plays an important part in determining the dynamics of the droplet. Numerical results are also compared to exact solutions for limiting cases, and to existing experimental data for both the fundamental and higher-order modes. It is shown that frequency predictions match very well with experiment, and that damping rate predictions underestimate experimental observation in some cases, possibly due to presence of surface impurities. The application of these results to the measurement of surface tension and viscosity of liquid droplets from single-droplet levitation experiments is also discussed. A new inverse method is developed to determine surface tension and viscosity from a knowledge of the frequency of oscillations, damping rate, droplet radius, droplet mass (or density), and mode of oscillations. Results are presented for various modes of oscillations in nondimensional form. Finally, the effect of static deformation and external forces on the oscillations of a liquid droplet are considered with special reference to levitation. For an arbitrary static shape deformation, the frequency spectrum is shown to split into (2l $-$ 1) peaks for a mode l oscillation, and this frequency split is calculated to first order for mode 2, 3, and 4 oscillations. The deformation is then assumed to be a consequence of a general external force, and the frequency split and the static deformation are calculated in terms of the external force parameters. Droplets levitated by acoustic, electromagnetic, and combined acoustic-electromagnetic forces are considered in particular, and it is shown that the effects of asphericity adequately explain the splitting of frequency spectra commonly observed in experiments. The interpretation of spectra with regard to accurate surface tension measurement using the oscillations of levitated droplets is discussed, and the results are applied to some previous experimental results. It is shown that the accuracy of surface tension measurements can improve remarkably if the asphericity caused by the levitating force, and the resultant frequency-split, are taken into account.

Novel materials have been self-assembled in the plasma generated by laser vaporization of targets under various conditions. This technique along with the Fourier Transform Ion Cyclotron Resonance (FT-ICR) supersonic cluster beam apparatus and transmission electron microscope (TEM) makes it possible to study both the properties and the growth mechanisms of these new materials. Based on the experimental results and theoretical studies employed the self-consistent (SCF) Hartree-Fock (HF) method and density functional theory (DFT), the growth mechanisms of metallofullerenes referred as extended isolated pentagon rules (EIPR), of single-walled carbon nanotubes denoted as size-limited break-diffusion-formation (SLBDF) mechanism and of multi-walled tubes as lip-lip interaction, have been proposed. The laser-vaporization technique has also been found to be able to produce higher yield and less amorphous carbon covered single-walled nanotubes than does the DC arc discharge.

In recent years, the search for new mixed-metal chalcogenide compounds has become important for the development of new materials that can be used in advanced opto-electronic devices. The exploratory synthesis of quasi-low-dimensional chalcogenide compounds, particularly mixed-metal sulfides and selenides that contain a reduced early transition metal cation, has been investigated. Several interesting compounds with novel structures and physical properties have been isolated during the course of studies. Four mixed-metal sulfides containing reduced titanium (III) have been synthesized: (RE)$\sb6$InTiS$\sb{12}$ (where RE = Nd, Sm, and Gd) and Gd$\sb3$TiS$\sb6$. The structures of these reduced phases are characterized by pseudo-one-dimensional chains of fused TiS$\sb6$ octahedra sharing opposite edges. Also, a new series of quasi-two-dimensional sulfides as well as selenides which are structurally categorized as misfit-layer compounds with the general formula ((A,M)Q) $\sb6$(TQ$\sb2$)$\rm\sb{5m}$ (where A = Ca, Sr; M = Bi, Pb, La, Ce, Nd, T = Ti, Nb, and Q = S, Se and m = 1, 2) has been discovered and systematically studied. In exploring mixed-metal chalcogenide systems via the molten halide flux crystal growth method, a new family of chalcohalide phases was serendipitously synthesized. These newly discovered chalcohalide compounds, CdBiQ$\sb2$X (Q = S, X = Cl, Br; Q = Se, X = Br, I), possess an interesting layered-like structure in which the anion ordering is governed by the size difference between the chalcogen (S$\sp{2-}$ and Se$\sp{2-}$) and halogen (Cl$\sp-$, Br$\sp-$, and I$\sp-$) anions. The detailed discussion is in results part I, II, and III, respectively. Synthetically, a conventional high-temperature solid-state ceramic method has been employed for the bulk synthesis. Vapor transport and/or molten salt flux methods have been used to grow sizable single crystals for structure characterization and physical property measurements. Several analytical techniques have been utilized to characterize these new materials, such as single crystal and powder X-ray diffraction, Weissenberg X-ray photography, thermal analysis (DTA), and four-probe conductivity measurements. Other relevant techniques for characterization of inorganic solids were also used, e.g., electron microscopy, infrared (reflectance) spectroscopy. This study provides necessary understanding of phase compatibility in mixed-cation and mixed-anion systems and in turn for the future design synthesis of advanced chalcogenide materials.

The solubility of H in single crystals and polycrystalline samples of $\rm Ni\sb{3}Al$ has been measured in equilibrium with $\rm H\sb2$ gas at atmosphere. In all cases the solubility exhibits a maximum at 750 K. A structural transformation from $\rm Ll\sb2$ (cubic) to $\rm Ll\sb2$ (tetragonal) in hydrogenated $\rm Ni\sb3Al\ (Ni\sb3Al$-H) was observed. The transformation temperature was found to be between 720 K and 870 K. No enthalpy change during this transformation was detected in the DTA experiment. The diffusivity of hydrogen in $\rm Ni\sb3Al$ has been measured in the temperature range of 588 K to 1214 K using a method involving the outgassing of hydrogen charged spheres. The diffusivity of hydrogen exhibits discontinuity in the temperature range of 753 K to 793 K. Finally, the addition of Pd (0.5 wt) is shown to significantly suppress the hydrogen embrittlement of $\rm Ni\sb3Al.$ Microstructure analysis indicates no second phase is formed due to the small amount of Pd. The addition of Pd alters the fractography of $\rm Ni\sb3Al$ charged with hydrogen. It is suggested that Pd may play a role of trapping hydrogen atoms in lattice and result in reducing the hydrogen concentration around crack tips and grain boundaries, thus improving the susceptibility of $\rm Ni\sb3Al$ to hydrogen embrittlement.

The production, properties and purification of the novel carbon nanotubes have been systematically studied. A fully automatic electric arc carbon nanotube generator is designed and constructed. The state of the electric arc is monitored and adjusted by a computer to maintain a stable growth condition. The optimum conditions for the high yield and quality of carbon nanotubes were found in this apparatus. Nanotubes grown in the arc are found to be highly defective. These defects are ascribed to the tube-tube sintering due to the excessive heat in the arc. This sintering effect can be reduced through the use of a better water-cooled cathode but can't be eliminated. A method of purification of arc grown nanotubes was developed and was found to be highly effective. A growth model is also proposed based on properties of carbon nanotubes and the electric arc in which they were grown.

The finite element method has been used to study the behavior of an aluminum alloy during elastic-plastic indentation by a rigid conical indenter to determine how the indentation process is affected by residual stress. The study was motivated by recent experimental results which showed that the hardness and elastic modulus of the alloy measured using nanoindentation methods appeared to decrease as the residual stress was increased. Biaxial radial stress was applied as a boundary condition, and indentation load-displacement curves were generated and analyzed according to various accepted methods for measuring hardness and modulus. The results of the study show that the standard methods by which hardness and elastic modulus are measured can lead to inaccuracies because they do not account for pile-up in the contact area calculations. Furthermore, if the contact area is measured properly, then hardness and elastic modulus are not significantly affected by residual stress.

A renormalization group method in real space is applied to the study of transport properties of random media. In particular, the method is applied to the study of the electrical properties of disordered materials and the study of the elastic properties of random materials. The theoretical predictions for the conductivity of disordered materials are in excellent agreement with both computer simulations and experimental results. Two microscopic models of elasticity of random materials are studied, the bond-bending model and the central-force model. The critical behavior of the elastic moduli of the bond-bending model is in good agreement with experimental and computer simulation results. The rigidity threshold of the central-force model is found not to correspond to that of pure percolation, and the predicted critical behavior of this model is found to differ markedly from that of the bond-bending model. A method to probe the universality of these two models by studying renormalization group flow diagrams, and an extension of the present method to the study of electrical breakdown and mechanical failure are proposed.