I. Rigid body penetration into brittle materials. II. Phase change effect on shock wave propagation

Part I.

We have developed a technique for measuring the depth time history of rigid body penetration into brittle materials (hard rocks and concretes) under a deceleration of ~ 10⁵ g. The technique includes bar-coded projectile, sabot-projectile separation, detection and recording systems. Because the technique can give very dense data on penetration depth time history, penetration velocity can be deduced. Error analysis shows that the technique has a small intrinsic error of ~ 3-4 % in time during penetration, and 0.3 to 0.7 mm in penetration depth. A series of 4140 steel projectile penetration into G-mixture mortar targets have been conducted using the Caltech 40 mm gas/ powder gun in the velocity range of 100 to 500 m/s.

We report, for the first time, the whole depth-time history of rigid body penetration into brittle materials (the G-mixture mortar) under 10⁵ g deceleration. Based on the experimental results, including penetration depth time history, damage of recovered target and projectile materials and theoretical analysis, we find:

1. Target materials are damaged via compacting in the region in front of a projectile and via brittle radial and lateral crack propagation in the region surrounding the penetration path. The results suggest that expected cracks in front of penetrators may be stopped by a comminuted region that is induced by wave propagation. Aggregate erosion on the projectile lateral surface is < 20% of the final penetration depth. This result suggests that the effect of lateral friction on the penetration process can be ignored.

2. Final penetration depth, P_max, is linearly scaled with initial projectile energy per unit cross-section area, e_s , when targets are intact after impact. Based on the experimental data on the mortar targets, the relation is P_max(mm) 1.15e_s (J/mm² ) + 16.39.

3. Estimation of the energy needed to create an unit penetration volume suggests that the average pressure acting on the target material during penetration is ~ 10 to 20 times higher than the unconfined strength of target materials under quasi-static loading, and 3 to 4 times higher than the possible highest pressure due to friction and material strength and its rate dependence. In addition, the experimental data show that the interaction between cracks and the target free surface significantly affects the penetration process.

4. Based on the fact that the penetration duration, t_max, increases slowly with e_s and does not depend on projectile radius approximately, the dependence of t_max on projectile length is suggested to be described by t_max(μs) = 2.08e_s (J/mm² + 349.0 x m/(πR²), in which m is the projectile mass in grams and R is the projectile radius in mm. The prediction from this relation is in reasonable agreement with the experimental data for different projectile lengths.

5. Deduced penetration velocity time histories suggest that whole penetration history is divided into three stages: (1) An initial stage in which the projectile velocity change is small due to very small contact area between the projectile and target materials; (2) A steady penetration stage in which projectile velocity continues to decrease smoothly; (3) A penetration stop stage in which projectile deceleration jumps up when velocities are close to a critical value of ~ 35 m/s.

6. Deduced averaged deceleration, a, in the steady penetration stage for projectiles with same dimensions is found to be a(g) = 192.4v + 1.89 x 10⁴, where v is initial projectile velocity in m/s. The average pressure acting on target materials during penetration is estimated to be very comparable to shock wave pressure.

7. A similarity of penetration process is found to be described by a relation between normalized penetration depth, P/P_max, and normalized penetration time, t/t_max, as P/P_max = f(t/t_max, where f is a function of t/t_max. After f(t/t_max is determined using experimental data for projectiles with 150 mm length, the penetration depth time history for projectiles with 100 mm length predicted by this relation is in good agreement with experimental data. This similarity also predicts that average deceleration increases with decreasing projectile length, that is verified by the experimental data.

8. Based on the penetration process analysis and the present data, a first principle model for rigid body penetration is suggested. The model incorporates the models for contact area between projectile and target materials, friction coefficient, penetration stop criterion, and normal stress on the projectile surface. The most important assumptions used in the model are: (1) The penetration process can be treated as a series of impact events, therefore, pressure normal to projectile surface is estimated using the Hugoniot relation of target material; (2) The necessary condition for penetration is that the pressure acting on target materials is not lower than the Hugoniot elastic limit; (3) The friction force on projectile lateral surface can be ignored due to cavitation during penetration. All the parameters involved in the model are determined based on independent experimental data. The penetration depth time histories predicted from the model are in good agreement with the experimental data.

9. Based on planar impact and previous quasi-static experimental data, the strain rate dependence of the mortar compressive strength is described by σ_f/σ⁰_f = exp(0.0905(log(έ/έ_0) ^1.14, in the strain rate range of 10^-7/s to 10³/s (σ⁰_f and έ are reference compressive strength and strain rate, respectively). The non-dispersive Hugoniot elastic wave in the G-mixture has an amplitude of ~ 0.14 GPa and a velocity of ~ 4.3 km/s.

Part II.

Stress wave profiles in vitreous GeO₂ were measured using piezoresistance gauges in the pressure range of 5 to 18 GPa under planar plate and spherical projectile impact. Experimental data show that the response of vitreous GeO₂ to planar shock loading can be divided into three stages: (1) A ramp elastic precursor has peak amplitude of 4 GPa and peak particle velocity of 333 m/s. Wave velocity decreases from initial longitudinal elastic wave velocity of 3.5 km/s to 2.9 km/s at 4 GPa; (2) A ramp wave with amplitude of 2.11 GPa follows the precursor when peak loading pressure is 8.4 GPa. Wave velocity drops to the value below bulk wave velocity in this stage; (3) A shock wave achieving final shock state forms when peak pressure is > 6 GPa. The Hugoniot relation is D = 0.917 + 1.711u (km/s) using present data and the data of Jackson and Ahrens [1979] when shock wave pressure is between 6 and 40 GPa for ρ₀ = 3.655 gj cm³ . Based on the present data, the phase change from 4-fold to 6-fold coordination of Ge⁺⁴ with O^-2 in vitreous GeO₂ occurs in the pressure range of 4 to 15 ± 1 GPa under planar shock loading. Comparison of the shock loading data for fused SiO₂ to that on vitreous GeO₂ demonstrates that transformation to the rutile structure in both media are similar. The Hugoniots of vitreous GeO₂ and fused SiO₂ are found to coincide approximately if pressure in fused SiO₂ is scaled by the ratio of fused SiO₂to vitreous GeO₂ density. This result, as well as the same structure, provides the basis for considering vitreous Ge0₂ as an analogous material to fused SiO₂ under shock loading. Experimental results from the spherical projectile impact demonstrate: (1) The supported elastic shock in fused SiO₂ decays less rapidly than a linear elastic wave when elastic wave stress amplitude is higher than 4 GPa. The supported elastic shock in vitreous GeO₂ decays faster than a linear elastic wave; (2) In vitreous GeO₂ , unsupported shock waves decays with peak pressure in the phase transition range (4-15 GPa) with propagation distance, x, as α 1/x^-3.35 , close to the prediction of Chen et al. [1998]. Based on a simple analysis on spherical wave propagation, we find that the different decay rates of a spherical elastic wave in fused SiO₂ and vitreous GeO₂ is predictable on the base of the compressibility variation with stress under one-dimensional strain condition in the two materials.

One-dimensional models for organic magnetic materials

In the preparation of small organic paramagnets, these structures may conceptually be divided into spin-containing units (SCs) and ferromagnetic coupling units (FCs). The synthesis and direct observation of a series of hydrocarbon tetraradicals designed to test the ferromagnetic coupling ability of m-phenylene, 1,3-cyclobutane, 1,3- cyclopentane, and 2,4-adamantane (a chair 1,3-cyclohexane) using Berson TMMs and cyclobutanediyls as SCs are described. While 1,3-cyclobutane and m-phenylene are good ferromagnetic coupling units under these conditions, the ferromagnetic coupling ability of 1,3-cyclopentane is poor, and 1,3-cyclohexane is apparently an antiferromagnetic coupling unit. In addition, this is the first report of ferromagnetic coupling between the spins of localized biradical SCs.

The poor coupling of 1,3-cyclopentane has enabled a study of the variable temperature behavior of a 1,3-cyclopentane FC-based tetraradical in its triplet state. Through fitting the observed data to the usual Boltzman statistics, we have been able to determine the separation of the ground quintet and excited triplet states. From this data, we have inferred the singlet-triplet gap in 1,3-cyclopentanediyl to be 900 cal/mol, in remarkable agreement with theoretical predictions of this number.

The ability to simulate EPR spectra has been crucial to the assignments made here. A powder EPR simulation package is described that uses the Zeeman and dipolar terms to calculate powder EPR spectra for triplet and quintet states.

Methods for characterizing paramagnetic samples by SQUID magnetometry have been developed, including robust routines for data fitting and analysis. A precursor to a potentially magnetic polymer was prepared by ring-opening metathesis polymerization (ROMP), and doped samples of this polymer were studied by magnetometry. While the present results are not positive, calculations have suggested modifications in this structure which should lead to the desired behavior.

Source listings for all computer programs are given in the appendix.

Few-cycle spatiotemporal soliton wave excited by filamentation of a femtosecond laser pulse in materials with anomalous dispersion

The nonlinear dynamics of 1.6-mu m fs laser pulses propagating in fused silica is investigated by employing a full-order dispersion model. Different from the x-wave generation in normally dispersive media, a few-cycle spatiotemporally compressed soliton wave is generated with the contrary contributions of anomalous group velocity dispersion (GVD) and self-phase-modulation. However, at the tailing edge of the pulse forms a shock wave which generates separate and strong supercontinuum peaked at 670 nm. It is also the origin of conical emission formed both in time and frequency domain with the contribution of normal GVD at visible light.

Scanning tunneling spectroscopic studies on high-temperature superconductors and Dirac materials

This thesis details the investigations of the unconventional low-energy quasiparticle excitations in electron-type cuprate superconductors and electron-type ferrous superconductors as well as the electronic properties of Dirac fermions in graphene and three-dimensional strong topological insulators through experimental studies using spatially resolved scanning tunneling spectroscopy (STS) experiments.

Magnetic-field- and temperature-dependent evolution of the spatially resolved quasiparticle spectra in the electron-type cuprate La_0.1Sr_0.9CuO₂ (La-112) T_C = 43 K, are investigated experimentally. For temperature (T) less than the superconducting transition temperature (TC), and in zero field, the quasiparticle spectra of La-112 exhibits gapped behavior with two coherence peaks and no satellite features. For magnetic field measurements at T < TC, first ever observation of vortices in La-112 are reported. Moreover, pseudogap-like spectra are revealed inside the core of vortices, where superconductivity is suppressed. The intra-vortex pseudogap-like spectra are characterized by an energy gap of V_PG = 8.5 ± 0.6 meV, while the inter-vortex quasiparticle spectra shows larger peak-to-peak gap values characterized by Δ_pk-pk(H) >V_PG, and Δ_pk-pk (0)=12.2 ± 0.8 meV > Δ_pk-pk (H > 0). The quasiparticle spectra are found to be gapped at all locations up to the highest magnetic field examined (H = 6T) and reveal an apparent low-energy cutoff at the V_PG energy scale.

Magnetic-field- and temperature-dependent evolution of the spatially resolved quasiparticle spectra in the electron-type "122" iron-based Ba(Fe_1-xCo_x)₂A_s2 are investigated for multiple doping levels (x = 0.06, 0.08, 0.12 with T_C= 14 K, 24 K, and 20 K). For all doping levels and the T < T_C, two-gap superconductivity is observed. Both superconducting gaps decrease monotonically in size with increasing temperature and disappear for temperatures above the superconducting transition temperature, T_C. Magnetic resonant modes that follow the temperature dependence of the superconducting gaps have been identified in the tunneling quasiparticle spectra. Together with quasiparticle interference (QPI) analysis and magnetic field studies, this provides strong evidence for two-gap sign-changing s-wave superconductivity.

Additionally spatial scanning tunneling spectroscopic studies are performed on mechanically exfoliated graphene and chemical vapor deposition grown graphene. In all cases lattice strain exerts a strong influence on the electronic properties of the sample. In particular topological defects give rise to pseudomagnetic fields (B ~ 50 Tesla) and charging effects resulting in quantized conductance peaks associated with the integer and fractional Quantum Hall States.

Finally, spectroscopic studies on the 3D-STI, Bi₂Se₃ found evidence of impurity resonance in the surface state. The impurities are in the unitary limit and the spectral resonances are localized spatially to within ~ 0.2 nm of the impurity. The spectral weight of the impurity resonance diverges as the Fermi energy approaches the Dirac point and the rapid recovery of the surface state suggests robust topological protection against perturbations that preserve time reversal symmetry.

High-power extracavity pulse compression in solid materials

A novel technique for high-power extracavity pulse compression with a nonlinear solid material is demonstrated. Before spectral broadening by self-phase modulation in the solid material, a short filament generated in argon is used as a spatial filter, which works for a uniform spectrum broadening over the spatial profile. Compensated by chirped mirrors, a 15-fs pulse is generated from a 32-fs input laser pulse. A total transmission larger than 80% after the solid material is achieved.

Marketing of fishing gear materials and fishing gear making in parts of Kainji Lake basin

The importance of fishing gear in fishing cannot be over-emphasized; as without it fish cannot be obtained. The method used to catch fish affects the condition in which the product is landed. This means that a bad-catching method would produced bad fish to the consumer. To achieve the goal of self-sufficiency in fish production in Nigeria, there is need to address the lingering problems of fishing gear and craft technology, especially in terms of availability of materials and their cost. The sale and making of fishing gear materials are two areas of fisheries, which are yet to be exploited by the general public as forms of businesses for livelihood. The study is conducted in villages around the lower part of Kainji Lake, towards the dam, including New Bussa. It reveals that only the fishermen themselves are involved in making their own fishing gears while those involved in the selling of fishing gear materials like the sheet netting, ropes, twines, floats, sinkers etc are business men and women who may not have any experience of fishing. Also considered in the study is the art of making fishing crafts like the canoe and gourd. Very few entrepreneurs are involved and they are so skilled that each is specialized in the making of only one kind of craft or gear

Fracture of materials undergoing solid-solid phase transformation

A large number of technologically important materials undergo solid-solid phase transformations. Examples range from ferroelectrics (transducers and memory devices), zirconia (Thermal Barrier Coatings) to nickel superalloys and (lithium) iron phosphate (Li-ion batteries). These transformations involve a change in the crystal structure either through diffusion of species or local rearrangement of atoms. This change of crystal structure leads to a macroscopic change of shape or volume or both and results in internal stresses during the transformation. In certain situations this stress field gives rise to cracks (tin, iron phosphate etc.) which continue to propagate as the transformation front traverses the material. In other materials the transformation modifies the stress field around cracks and effects crack growth behavior (zirconia, ferroelectrics). These observations serve as our motivation to study cracks in solids undergoing phase transformations. Understanding these effects will help in improving the mechanical reliability of the devices employing these materials.

In this thesis we present work on two problems concerning the interplay between cracks and phase transformations. First, we consider the directional growth of a set of parallel edge cracks due to a solid-solid transformation. We conclude from our analysis that phase transformations can lead to formation of parallel edge cracks when the transformation strain satisfies certain conditions and the resulting cracks grow all the way till their tips cross over the phase boundary. Moreover the cracks continue to grow as the phase boundary traverses into the interior of the body at a uniform spacing without any instabilities. There exists an optimal value for the spacing between the cracks. We ascertain these conclusion by performing numerical simulations using finite elements.

Second, we model the effect of the semiconducting nature and dopants on cracks in ferroelectric perovskite materials, particularly barium titanate. Traditional approaches to model fracture in these materials have treated them as insulators. In reality, they are wide bandgap semiconductors with oxygen vacancies and trace impurities acting as dopants. We incorporate the space charge arising due the semiconducting effect and dopant ionization in a phase field model for the ferroelectric. We derive the governing equations by invoking the dissipation inequality over a ferroelectric domain containing a crack. This approach also yields the driving force acting on the crack. Our phase field simulations of polarization domain evolution around a crack show the accumulation of electronic charge on the crack surface making it more permeable than was previously believed so, as seen in recent experiments. We also discuss the effect the space charge has on domain formation and the crack driving force.

Earth-abundant materials for solar hydrogen generation

A critical challenge for the 21st century is shifting from the predominant use of fossil fuels to renewables for energy. Among many options, sunlight is the only single renewable resource with sufficient abundance to replace most or all of our current fossil energy use. However, existing photovoltaic and solar thermal technologies cannot be scaled infinitely due to the temporal and geographic intermittency of sunlight. Therefore efficient and inexpensive methods for storage of solar energy in a dense medium are needed in order to greatly increase utilization of the sun as a primary resource. For this purpose we have proposed an artificial photosynthetic system consisting of semiconductors, electrocatalysts, and polymer membranes to carry out photoelectrochemical water splitting as a method for solar fuel generation.

This dissertation describes efforts over the last five years to develop critical semiconductor and catalyst components for efficient and scalable photoelectrochemical hydrogen evolution, one of the half reactions for water splitting. We identified and developed Ni–Mo alloy and Ni₂P nanoparticles as promising earth-abundant electrocatalysts for hydrogen evolution. We thoroughly characterized Ni–Mo alloys alongside Ni and Pt catalysts deposited onto planar and structured Si light absorbers for solar hydrogen generation. We sought to address several key challenges that emerged in the use of non-noble catalysts for solar fuels generation, resulting in the synthesis and characterization of Ni–Mo nanopowder for use in a new photocathode device architecture. To address the mismatch in stability between non-noble metal alloys and Si absorbers, we also synthesized and characterized p-type WSe₂ as a candidate light absorber alternative to Si that is stable under acidic and alkaline conditions.

Chain-forming zintl antimonides as novel thermoelectric materials

Zintl phases, a subset of intermetallic compounds characterized by covalently-bonded "sub-structures," surrounded by highly electropositive cations, exhibit precisely the characteristics desired for thermoelectric applications. The requirement that Zintl compounds satisfy the valence of anions through the formation of covalent substructures leads to many unique, complex crystal structures. Such complexity often leads to exceptionally low lattice thermal conductivity due to the containment of heat in low velocity optical modes in the phonon dispersion. To date, excellent thermoelectric properties have been demonstrated in several Zintl compounds. However, compared with the large number of known Zintl phases, very few have been investigated as thermoelectric materials.

From this pool of uninvestigated compounds, we selected a class of Zintl antimonides that share a common structural motif: anionic moieties resembling infinite chains of linked MSb₄ tetrahedra, where $M$ is a triel element. The compounds discussed in this thesis (A₅M₂Sb₆ and A₃MSb₃, where A = Ca or Sr and M = Al, Ga and In) crystallize as four distinct, but closely related "chain-forming" structure types. This thesis describes the thermoelectric characterization and optimization of these phases, and explores the influence of their chemistry and structure on the thermal and electronic transport properties. Due to their large unit cells, each compound exhibits exceptionally low lattice thermal conductivity (0.4 - 0.6 W/mK at 1000 K), approaching the predicted glassy minimum at high temperatures. A combination of Density Functional calculations and classical transport models were used to explain the experimentally observed electronic transport properties of each compound. Consistent with the Zintl electron counting formalism, A₅M₂Sb₆ and A₃MSb₃ phases were found to have filled valence bands and exhibit intrinsic electronic properties. Doping with divalent transition metals (Zn²⁺ and Mn²⁺) on the M³⁺ site, or Na¹⁺ on the A³⁺ site allowed for rational control of the carrier concentration and a transition towards degenerate semiconducting behavior. In optimally-doped samples, promising peak zT values between 0.4 and 0.9 were obtained, highlighting the value of continued investigations of complex Zintl phases.

Synthesis and characterization of high-spin organic materials: prototypes for the polaronic ferromagnet

The design, synthesis and magnetic characterization of thiophene-based models for the polaronic ferromagnet are described. Synthetic strategies employing Wittig and Suzuki coupling were employed to produce polymers with extended π-systems. Oxidative doping using AsF_5 or I_2 produces radical cations (polarons) that are stable at room temperature. Magnetic characterization of the doped polymers, using SQUID-based magnetometry, indicates that in several instances ferromagnetic coupling of polarons occurs along the polymer chain. An investigation of the influence of polaron stability and delocalization on the magnitude of ferromagnetic coupling is pursued. A lower limit for mild, solution phase I_2 doping is established. A comparison of the variable temperature data of various polymers reveals that deleterious antiferromagnetic interactions are relatively insensitive to spin concentration, doping protocols or spin state. Comparison of the various polymers reveals useful design principles and suggests new directions for the development of magnetic organic materials. Novel strategies for solubilizing neutral polymeric materials in polar solvents are investigated.

The incorporation of stable bipyridinium spin-containing units into a polymeric high-spin array is explored. Preliminary results suggest that substituted diquat derivatives may serve as stable spin-containing units for the polaronic ferromagnet and are amenable to electrochemical doping. Synthetic efforts to prepare high-spin polymeric materials using viologens as a spin source have been unsuccessful.