Developing and characterizing bulk metallic glasses for extreme applications

Metallic glasses have typically been treated as a “one size fits all” type of material. Every alloy is considered to have high strength, high hardness, large elastic limits, corrosion resistance, etc. However, similar to traditional crystalline materials, properties are strongly dependent upon the constituent elements, how it was processed, and the conditions under which it will be used. An important distinction which can be made is between metallic glasses and their composites. Charpy impact toughness measurements are performed to determine the effect processing and microstructure have on bulk metallic glass matrix composites (BMGMCs). Samples are suction cast, machined from commercial plates, and semi-solidly forged (SSF). The SSF specimens have been found to have the highest impact toughness due to the coarsening of the dendrites, which occurs during the semi-solid processing stages. Ductile to brittle transition (DTBT) temperatures are measured for a BMGMC. While at room temperature the BMGMC is highly toughened compared to a fully glassy alloy, it undergoes a DTBT by 250 K. At this point, its impact toughness mirrors that of the constituent glassy matrix. In the following chapter, BMGMCs are shown to have the capability of being capacitively welded to form single, monolithic structures. Shear measurements are performed across welded samples, and, at sufficient weld energies, are found to retain the strength of the parent alloy. Cross-sections are inspected via SEM and no visible crystallization of the matrix occurs.

Next, metallic glasses and BMGMCs are formed into sheets and eggbox structures are tested in hypervelocity impacts. Metallic glasses are ideal candidates for protection against micrometeorite orbital debris due to their high hardness and relatively low density. A flat single layer, flat BMG is compared to a BMGMC eggbox and the latter creates a more diffuse projectile cloud after penetration. A three tiered eggbox structure is also tested by firing a 3.17 mm aluminum sphere at 2.7 km/s at it. The projectile penetrates the first two layers, but is successfully contained by the third.

A large series of metallic glass alloys are created and their wear loss is measured in a pin on disk test. Wear is found to vary dramatically among different metallic glasses, with some considerably outperforming the current state-of-the-art crystalline material (most notably Cu₄₃Zr₄₃Al₇Be₇). Others, on the other hand, suffered extensive wear loss. Commercially available Vitreloy 1 lost nearly three times as much mass in wear as alloy prepared in a laboratory setting. No conclusive correlations can be found between any set of mechanical properties (hardness, density, elastic, bulk, or shear modulus, Poisson’s ratio, frictional force, and run in time) and wear loss. Heat treatments are performed on Vitreloy 1 and Cu₄₃Zr₄₃Al₇Be₇. Anneals near the glass transition temperature are found to increase hardness slightly, but decrease wear loss significantly. Crystallization of both alloys leads to dramatic increases in wear resistance. Finally, wear tests under vacuum are performed on the two alloys above. Vitreloy 1 experiences a dramatic decrease in wear loss, while Cu₄₃Zr₄₃Al₇Be₇ has a moderate increase. Meanwhile, gears are fabricated through three techniques: electrical discharge machining of 1 cm by 3 mm cylinders, semisolid forging, and copper mold suction casting. Initial testing finds the pin on disk test to be an accurate predictor of wear performance in gears.

The final chapter explores an exciting technique in the field of additive manufacturing. Laser engineered net shaping (LENS) is a method whereby small amounts of metallic powders are melted by a laser such that shapes and designs can be built layer by layer into a final part. The technique is extended to mixing different powders during melting, so that compositional gradients can be created across a manufactured part. Two compositional gradients are fabricated and characterized. Ti 6Al¬ 4V to pure vanadium was chosen for its combination of high strength and light weight on one end, and high melting point on the other. It was inspected by cross-sectional x-ray diffraction, and only the anticipated phases were present. 304L stainless steel to Invar 36 was created in both pillar and as a radial gradient. It combines strength and weldability along with a zero coefficient of thermal expansion material. Only the austenite phase is found to be present via x-ray diffraction. Coefficient of thermal expansion is measured for four compositions, and it is found to be tunable depending on composition.

Geological evolution of two crustal scale shear zones. Part I. The Rand thrust complex, northwestern Mojave Desert, California. Part II. The Magdalena metamorphic core complex, north central Sonora, Mexico

The geology and structure of two crustal scale shear zones were studied to understand the partitioning of strain within intracontinental orogenic belts. Movement histories and regional tectonic implications are deduced from observational data. The two widely separated study areas bear the imprint of intense Late Mesozoic through Middle Cenozoic tectonic activity. A regional transition from Late Cretaceous-Early Tertiary plutonism, metamorphism, and shortening strain to Middle Tertiary extension and magmatism is preserved in each area, with contrasting environments and mechanisms. Compressional phases of this tectonic history are better displayed in the Rand Mountains, whereas younger extensional structures dominate rock fabrics in the Magdalena area.

In the northwestern Mojave desert, the Rand Thrust Complex reveals a stack of four distinctive tectonic plates offset along the Garlock Fault. The lowermost plate, Rand Schist, is composed of greenschist facies metagraywacke, metachert, and metabasalt. Rand Schist is structurally overlain by Johannesburg Gneiss (= garnet-amphibolite grade orthogneisses, marbles and quartzites), which in turn is overlain by a Late Cretaceous hornblende-biotite granodiorite. Biotite granite forms the fourth and highest plate. Initial assembly of the tectonic stack involved a Late Cretaceous? south or southwest vergent overthrusting event in which Johannesburg Gneiss was imbricated and attenuated between Rand Schist and hornblende-biotite granodiorite. Thrusting postdated metamorphism and deformation of the lower two plates in separate environments. A post-kinematic stock, the Late Cretaceous Randsburg Granodiorite, intrudes deep levels of the complex and contains xenoliths of both Rand Schist and mylonitized Johannesburg? gneiss. Minimum shortening implied by the map patterns is 20 kilometers.

Some low angle faults of the Rand Thrust Complex formed or were reactivated between Late Cretaceous and Early Miocene time. South-southwest directed mylonites derived from Johannesburg Gneiss are commonly overprinted by less penetrative north-northeast vergent structures. Available kinematic information at shallower structural levels indicates that late disturbance(s) culminated in northward transport of the uppermost plate. Persistence of brittle fabrics along certain structural horizons suggests a possible association of late movement(s) with regionally known detachment faults. The four plates were juxtaposed and significant intraplate movements had ceased prior to Early Miocene emplacement of rhyolite porphyry dikes.

In the Magdalena region of north central Sonora, components of a pre-Middle Cretaceous stratigraphy are used as strain markers in tracking the evolution of a long lived orogenic belt. Important elements of the tectonic history include: (1) Compression during the Late Cretaceous and Early Tertiary, accompanied by plutonism, metamorphism, and ductile strain at depth, and thrust driven? syntectonic sedimentation at the surface. (2) Middle Tertiary transition to crustal extension, initially recorded by intrusion of leucogranites, inflation of the previously shortened middle and upper crustal section, and surface volcanism. (3) Gravity induced development of a normal sense ductile shear zone at mid crustal levels, with eventual detachment and southwestward displacement of the upper crustal stratigraphy by Early Miocene time.

Elucidation of the metamorphic core complex evolution just described was facilitated by fortuitous preservation of a unique assemblage of rocks and structures. The "type" stratigraphy utilized for regional correlation and strain analysis includes a Jurassic volcanic arc assemblage overlain by an Upper Jurassic-Lower Cretaceous quartz pebble conglomerate, in turn overlain by marine strata with fossiliferous Aptian-Albian limestones. The Jurassic strata, comprised of (a) rhyolite porphyries interstratified with quartz arenites, (b) rhyolite cobble conglomerate, and (c) intrusive granite porphyries, are known to rest on Precambrian basement north and east of the study area. The quartz pebble conglomerate is correlated with the Glance Conglomerate of southeastern Arizona and northeastern Sonora. The marine sequence represents part of an isolated arm? of the Bisbee Basin.

Crosscutting structural relationships between the pre-Middle Cretaceous supracrustal section, younger plutons, and deformational fabrics allow the tectonic sequence to be determined. Earliest phases of a Late Cretaceous-Early Tertiary orogeny are marked by emplacement of the 78 ± 3 Ma Guacomea Granodiorite (U/Pb zircon, Anderson et al., 1980) as a sill into deep levels of the layered Jurassic series. Subsequent regional metamorphism and ductile strain is recorded by a penetrative schistosity and lineation, and east-west trending folds. These fabrics are intruded by post-kinematic Early Tertiary? two mica granites. At shallower crustal levels, the orogeny is represented by north directed thrust faulting, formation of a large intermontane basin, and development of a pronounced unconformity. A second important phase of ductile strain followed Middle Tertiary? emplacement of leucogranites as sills and northwest trending dikes into intermediate levels of the deformed section (surficial volcanism was also active during this transitional period to regional extension). Gravitational instabilities resulting from crustal swelling via intrusion and thermal expansion led to development of a ductile shear zone within the stratigraphic horizon occupied by a laterally extensive leucogranite sill. With continued extension, upper crustal brittle normal faults (detachment faults) enhanced the uplift and tectonic denudation of this mylonite zone, ultimately resulting in southwestward displacement of the upper crustal stratigraphy.

Strains associated with the two ductile deformation events have been successfully partitioned through a multifaceted analysis. R_f/Ø measurements on various markers from the "type" stratigraphy allow a gradient representing cumulative strain since Middle Cretaceous time to be determined. From this gradient, noncoaxial strains accrued since emplacement of the leucogranites may be removed. Irrotational components of the postleucogranite strain are measured from quartz grain shapes in deformed granites; rotational components (shear strains) are determined from S-C fabrics and from restoration of rotated dike and vein networks. Structural observations and strain data are compatable with a deformation path of: (1) coaxial strain (pure shear?), followed by (2) injection of leucogranites as dikes (perpendicular to the minimum principle stress) and sills (parallel to the minimum principle stress), then (3) southwest directed simple shear. Modeling the late strain gradient as a simple shear zone permits a minimum displacement of 10 kilometers on the Magdalena mylonite zone/detachment fault system. Removal of the Middle Tertiary noncoaxial strains yields a residual (or pre-existing) strain gradient representative of the Late Cretaceous-Early Tertiary deformation. Several partially destrained cross sections, restored to the time of leucogranite emplacement, illustrate the idea that the upper plate of the core complex bas been detached from a region of significant topographic relief. 50% to 100% bulk extension across a 50 kilometer wide corridor is demonstrated.

Late Cenozoic tectonics of the Magdalena region are dominated by Basin and Range style faulting. Northeast and north-northwest trending high angle normal faults have interacted to extend the crust in an east-west direction. Net extension for this period is minor (10% to 15%) in comparison to the Middle Tertiary detachment related extensional episode.

Charge symmetry in ^(13)N and ^(13)C a coupled-channel model

A set of coupled-channel differential equations based on a rotationally distorted optical potential is used to calculate the wave functions required to evaluate the gamma ray transition rate from the first excited state to the ground state in ^(13)C and ^(13)N. The bremsstrahlung differential cross section of low energy protons is also calculated and compared with existing data. The marked similarity between the potentials determined at each resonance level in both nuclei supports the hypothesis of the charge symmetry of nuclear forces by explaining the deviation of the ratios of the experimental E1 transition strengths from unity.

Measurement of the neutron (^3He) spin structure function at low Q^2 : a connection between the Bjorken and Drell-Hearn-Gerasimov sum rules

The spin dependent cross sections, σT_1/2 and σT_3/2 , and asymmetries, A_∥ and A_⊥ for ³He have been measured at the Jefferson Lab's Hall A facility. The inclusive scattering process ³He(e,e)X was performed for initial beam energies ranging from 0.86 to 5.1 GeV, at a scattering angle of 15.5°. Data includes measurements from the quasielastic peak, resonance region, and the deep inelastic regime. An approximation for the extended Gerasimov-Drell-Hearn integral is presented at a 4-momentum transfer Q² of 0.2-1.0 GeV².

Also presented are results on the performance of the polarized ³He target. Polarization of ³He was achieved by the process of spin-exchange collisions with optically pumped rubidium vapor. The ³He polarization was monitored using the NMR technique of adiabatic fast passage (AFP). The average target polarization was approximately 35% and was determined to have a systematic uncertainty of roughly ±4% relative.

Space-charge-limited current in fast neutron irradiated silicon

DC and transient measurements of space-charge-limited currents through alloyed and symmetrical n^+ν n^+ structures made of nominally 75 kΩcm ν-type silicon are studied before and after the introduction of defects by 14 MeV neutron radiation. In the transient measurements, the current response to a large turn-on voltage step is analyzed. Right after the voltage step is applied, the current transient reaches a value which we shall call "initial current" value. At longer times, the transient current decays from the initial current value if traps are present.

Before the irradiation, the initial current density-voltage characteristics J(V) agree quantitatively with the theory of trap-free space-charge-limited current in solids. We obtain for the electron mobility a temperature dependence which indicates that scattering due to impurities is weak. This is expected for the high purity silicon used. The drift velocity-field relationships for electrons at room temperature and 77°K, derived from the initial current density-voltage characteristics, are shown to fit the relationships obtained with other methods by other workers. The transient current response for t > 0 remains practically constant at the initial value, thus indicating negligible trapping.

Measurement of the initial (trap-free) current density-voltage characteristics after the irradiation indicates that the drift velocity-field relationship of electrons in silicon is affected by the radiation only at low temperature in the low field range. The effect is not sufficiently pronounced to be readily analyzed and no formal description of it is offered. In the transient response after irradiation for t > 0, the current decays from its initial value, thus revealing the presence of traps. To study these traps, in addition to transient measurements, the DC current characteristics were measured and shown to follow the theory of trap-dominated space-charge-limited current in solids. This theory was applied to a model consisting of two discrete levels in the forbidden band gap. Calculations and experiments agreed and the capture cross-sections of the trapping levels were obtained. This is the first experimental case known to us through which the flow of space-charge-limited current is so simply representable.

These results demonstrate the sensitivity of space-charge-limited current flow as a tool to detect traps and changes in the drift velocity-field relationship of carriers caused by radiation. They also establish that devices based on the mode of space-charge-limited current flow will be affected considerably by any type of radiation capable of introducing traps. This point has generally been overlooked so far, but is obviously quite significant.

An investigation of techniques for the measurement and interpretation of cosmic ray isotopic abundances

An instrument, the Caltech High Energy Isotope Spectrometer Telescope (HEIST), has been developed to measure isotopic abundances of cosmic ray nuclei in the charge range 3 ≤ Z ≤ 28 and the energy range between 30 and 800 MeV/nuc by employing an energy loss -- residual energy technique. Measurements of particle trajectories and energy losses are made using a multiwire proportional counter hodoscope and a stack of CsI(TI) crystal scintillators, respectively. A detailed analysis has been made of the mass resolution capabilities of this instrument.

Landau fluctuations set a fundamental limit on the attainable mass resolution, which for this instrument ranges between ~.07 AMU for z~3 and ~.2 AMU for z~2b. Contributions to the mass resolution due to uncertainties in measuring the path-length and energy losses of the detected particles are shown to degrade the overall mass resolution to between ~.1 AMU (z~3) and ~.3 AMU (z~2b).

A formalism, based on the leaky box model of cosmic ray propagation, is developed for obtaining isotopic abundance ratios at the cosmic ray sources from abundances measured in local interstellar space for elements having three or more stable isotopes, one of which is believed to be absent at the cosmic ray sources. This purely secondary isotope is used as a tracer of secondary production during propagation. This technique is illustrated for the isotopes of the elements O, Ne, S, Ar and Ca.

The uncertainties in the derived source ratios due to errors in fragmentation and total inelastic cross sections, in observed spectral shapes, and in measured abundances are evaluated. It is shown that the dominant sources of uncertainty are uncorrelated errors in the fragmentation cross sections and statistical uncertainties in measuring local interstellar abundances.

These results are applied to estimate the extent to which uncertainties must be reduced in order to distinguish between cosmic ray production in a solar-like environment and in various environments with greater neutron enrichments.

Observations of hydrogen and helium isotopes in solar cosmic rays

The isotopic composition of hydrogen and helium in solar cosmic rays provides a means of studying solar flare particle acceleration mechanisms since the enhanced relative abundance of rare isotopes, such as ²H, ³H and ³He, is due to their production by inelastic nuclear collisions in the solar atmosphere during the flare. In this work the Caltech Electron/Isotope Spectrometer on the IMP-7 spacecraft has been used to measure this isotopic composition. The response of the dE/dx-E particle telescope is discussed and alpha particle channeling in thin detectors is identified as an important background source affecting measurement of low values of (³He/⁴He).

The following flare-averaged results are obtained for the period, October, 1972 - November, 1973: (²H/¹H) = 7⁺¹⁰_-6 X 10^-6 (1.6 - 8.6 MeV/nuc), (³H/¹H) less than 3.4 x 10^-6 (1.2 - 6.8 MeV/nuc), (³He/⁴He) = (9 ± 4) x 10^-3, (³He/¹H) = (1.7 ± 0.7) x 10^-4 (3.1 - 15.0 MeV/nuc). The deuterium and tritium ratios are significantly lower than the same ratios at higher energies, suggesting that the deuterium and tritium spectra are harder than that of the protons. They are, however, consistent with the same thin target model relativistic path length of ~ 1 g/cm² (or equivalently ~ 0.3 g/cm² at 30 MeV/nuc) which is implied by the higher energy results. The ³He results, consistent with previous observations, would imply a path length at least 3 times as long, but the observations may be contaminated by small ³He rich solar events.

During 1973 three "³He rich events," containing much more ³He than ²H or ³H were observed on 14 February, 29 June and 5 September. Although the total production cross sections for ²H,³H and ³He are comparable, an upper limit to (²H/³He) and (³H/³He) was 0.053 (2.9-6.8 MeV/nuc), summing over the three events. This upper limit is marginally consistent with Ramaty and Kozlovsky's thick target model which accounts for such events by the nuclear reaction kinematics and directional properties of the flare acceleration process. The 5 September event was particularly significant in that much more ³He was observed than ⁴He and the fluxes of ³He and ¹H were about equal. The range of (³He/⁴He) for such events reported to date is 0.2 to ~ 6 while (³He/¹H) extends from 10^-3 to ~ 1. The role of backscattered and mirroring protons and alphas in accounting for such variations is discussed.

The abundances of ultraheavy elements in the cosmic radiation

Analysis of the data from the Heavy Nuclei Experiment on the HEAO-3 spacecraft has yielded the cosmic ray abundances of odd-even element pairs with atomic number, Z, in the range 33 ≤ Z ≤60, and the abundances of broad element groups in the range 62 ≤ Z ≤83, relative to iron. These data show that the cosmic ray source composition in this charge range is quite similar to that of the solar system provided an allowance is made for a source fractionation based on first ionization potential. The observations are inconsistent with a source composition which is dominated by either r-process or s-process material, whether or not an allowance is made for first ionization potential. Although the observations do not exclude a source containing the same mixture of r- and s-process material as in the solar system. the data are best fit by a source having an r- to s-process ratio of 1.22^(+0.25)_(0.21), relative to the solar system The abundances of secondary elements are consistent with the leaky box model of galactic propagation, implying a pathlength distribution similar to that which explains the abundances of nuclei with Z<29.

The energy spectra of the even elements in the range 38 ≤ Z ≤ 60 are found to have a deficiency of particles in the range ~1.5 to 3 GeV/amu, compared to iron. This deficiency may result from ionization energy loss in the interstellar medium, and is not predicted by propagation models which ignore such losses. ln addition, the energy spectra of secondary elements are found to be different to those of the primary elements. Such effects are consistent with observations of lighter nuclei, and are in qualitative agreement with galactic propagation models using a rigidity dependent escape length. The energy spectra of secondaries arising from the platinum group are found to be much steeper than those of lower Z. This effect may result from energy dependent fragmentation cross sections.

A Cerenkov-ΔΕ-Cerenkov detector for high energy cosmic ray isotopes and an accelerator study of ^(40)Ar & ^(56)Fe fragmentation

This thesis has two major parts. The first part of the thesis will describe a high energy cosmic ray detector -- the High Energy Isotope Spectrometer Telescope (HEIST). HEIST is a large area (0.25 m²sr) balloon-borne isotope spectrometer designed to make high-resolution measurements of isotopes in the element range from neon to nickel (10 ≤ Z ≤ 28) at energies of about 2 GeV/nucleon. The instrument consists of a stack of 12 NaI(Tl) scintilla tors, two Cerenkov counters, and two plastic scintillators. Each of the 2-cm thick NaI disks is viewed by six 1.5-inch photomultipliers whose combined outputs measure the energy deposition in that layer. In addition, the six outputs from each disk are compared to determine the position at which incident nuclei traverse each layer to an accuracy of ~2 mm. The Cerenkov counters, which measure particle velocity, are each viewed by twelve 5-inch photomultipliers using light integration boxes.

HEIST-2 determines the mass of individual nuclei by measuring both the change in the Lorentz factor (Δγ) that results from traversing the NaI stack, and the energy loss (ΔΕ) in the stack. Since the total energy of an isotope is given by Ε = γM, the mass M can be determined by M = ΔΕ/Δγ. The instrument is designed to achieve a typical mass resolution of 0.2 amu.

The second part of this thesis presents an experimental measurement of the isotopic composition of the fragments from the breakup of high energy ⁴⁰Ar and ⁵⁶Fe nuclei. Cosmic ray composition studies rely heavily on semi-empirical estimates of the cross-sections for the nuclear fragmentation reactions which alter the composition during propagation through the interstellar medium. Experimentally measured yields of isotopes from the fragmentation of ⁴⁰Ar and ⁵⁶Fe are compared with calculated yields based on semi-empirical cross-section formulae. There are two sets of measurements. The first set of measurements, made at the Lawrence Berkeley Laboratory Bevalac using a beam of 287 MeV/nucleon ⁴⁰Ar incident on a CH₂ target, achieves excellent mass resolution (σ_m ≤ 0.2 amu) for isotopes of Mg through K using a Si(Li) detector telescope. The second set of measurements, also made at the Lawrence Berkeley Laboratory Bevalac, using a beam of 583 MeV/nucleon ⁵⁶FeFe incident on a CH₂ target, resolved Cr, Mn, and Fe fragments with a typical mass resolution of ~ 0.25 amu, through the use of the Heavy Isotope Spectrometer Telescope (HIST) which was later carried into space on ISEE-3 in 1978. The general agreement between calculation and experiment is good, but some significant differences are reported here.

Stopping power of gases for heavy ions

Pulse-height and time-of-flight methods have been used to measure the electronic stopping cross sections for projectiles of ¹²C, ¹⁶O, ¹⁹F, ²³Na, ²⁴Mg, and ²⁷Al, slowing in helium, neon, argon, krypton, and xenon. The ion energies were in the range 185 keV ≤ E ≤ 2560 keV.

A semiempirical calculation of the electronic stopping cross section for projectiles with atomic numbers between 6 and 13 passing through the inert gases has been performed using a modification of the Firsov model. Using Hartree-Slater-Fock orbitals, and summing over the losses for the individual charge states of the projectiles, good agreement has been obtained with the experimental data. The main features of the stopping cross section seen in the data, such as the Z₁ oscillation and the variation of the velocity dependence on Z₁ and Z₂, are present in the calculation. The inclusion of a modified form of the Bethe-Bloch formula as an additional term allows the increase of the velocity dependence for projectile velocities above v_o to be reproduced in the calculation.

Imperfection Insensitive Thin Shells

The buckling of axially compressed cylindrical shells and externally pressurized spherical shells is extremely sensitive to even very small geometric imperfections. In practice this issue is addressed by either using overly conservative knockdown factors, while keeping perfect axial or spherical symmetry, or adding closely and equally spaced stiffeners on shell surface. The influence of imperfection-sensitivity is mitigated, but the shells designed from these approaches are either too heavy or very expensive and are still sensitive to imperfections. Despite their drawbacks, these approaches have been used for more than half a century.

This thesis proposes a novel method to design imperfection-insensitive cylindrical shells subject to axial compression. Instead of following the classical paths, focused on axially symmetric or high-order rotationally symmetric cross-sections, the method in this thesis adopts optimal symmetry-breaking wavy cross-sections (wavy shells). The avoidance of imperfection sensitivity is achieved by searching with an evolutionary algorithm for smooth cross-sectional shapes that maximize the minimum among the buckling loads of geometrically perfect and imperfect wavy shells. It is found that the shells designed through this approach can achieve higher critical stresses and knockdown factors than any previously known monocoque cylindrical shells. It is also found that these shells have superior mass efficiency to almost all previously reported stiffened shells.

Experimental studies on a design of composite wavy shell obtained through the proposed method are presented in this thesis. A method of making composite wavy shells and a photogrametry technique of measuring full-field geometric imperfections have been developed. Numerical predictions based on the measured geometric imperfections match remarkably well with the experiments. Experimental results confirm that the wavy shells are not sensitive to imperfections and can carry axial compression with superior mass efficiency.

An efficient computational method for the buckling analysis of corrugated and stiffened cylindrical shells subject to axial compression has been developed in this thesis. This method modifies the traditional Bloch wave method based on the stiffness matrix method of rotationally periodic structures. A highly efficient algorithm has been developed to implement the modified Bloch wave method. This method is applied in buckling analyses of a series of corrugated composite cylindrical shells and a large-scale orthogonally stiffened aluminum cylindrical shell. Numerical examples show that the modified Bloch wave method can achieve very high accuracy and require much less computational time than linear and nonlinear analyses of detailed full finite element models.

This thesis presents parametric studies on a series of externally pressurized pseudo-spherical shells, i.e., polyhedral shells, including icosahedron, geodesic shells, and triambic icosahedra. Several optimization methods have been developed to further improve the performance of pseudo-spherical shells under external pressure. It has been shown that the buckling pressures of the shell designs obtained from the optimizations are much higher than the spherical shells and not sensitive to imperfections.

Two topics in elementary particle physics. I. Crossing as a group and elimination of exotic channels. II. Real parts of meson-nucleon forward scattering amplitudes.

I. Crossing transformations constitute a group of permutations under which the scattering amplitude is invariant. Using Mandelstem's analyticity, we decompose the amplitude into irreducible representations of this group. The usual quantum numbers, such as isospin or SU(3), are "crossing-invariant". Thus no higher symmetry is generated by crossing itself. However, elimination of certain quantum numbers in intermediate states is not crossing-invariant, and higher symmetries have to be introduced to make it possible. The current literature on exchange degeneracy is a manifestation of this statement. To exemplify application of our analysis, we show how, starting with SU(3) invariance, one can use crossing and the absence of exotic channels to derive the quark-model picture of the tensor nonet. No detailed dynamical input is used.

II. A dispersion relation calculation of the real parts of forward π^±p and K^±p scattering amplitudes is carried out under the assumption of constant total cross sections in the Serpukhov energy range. Comparison with existing experimental results as well as predictions for future high energy experiments are presented and discussed. Electromagnetic effects are found to be too small to account for the expected difference between the π^-p and π⁺p total cross sections at higher energies.

Effects of density differences on lateral mixing in open-channel flows

This study investigates lateral mixing of tracer fluids in turbulent open-channel flows when the tracer and ambient fluids have different densities. Longitudinal dispersion in flows with longitudinal density gradients is investigated also.

Lateral mixing was studied in a laboratory flume by introducing fluid tracers at the ambient flow velocity continuously and uniformly across a fraction of the flume width and over the entire depth of the ambient flow. Fluid samples were taken to obtain concentration distributions in cross-sections at various distances, x, downstream from the tracer source. The data were used to calculate variances of the lateral distributions of the depth-averaged concentration. When there was a difference in density between the tracer and the ambient fluids, lateral mixing close to the source was enhanced by density-induced secondary flows; however, far downstream where the density gradients were small, lateral mixing rates were independent of the initial density difference. A dimensional analysis of the problem and the data show that the normalized variance is a function of only three dimensionless numbers, which represent: (1) the x-coordinate, (2) the source width, and (3) the buoyancy flux from the source.

A simplified set of equations of motion for a fluid with a horizontal density gradient was integrated to give an expression for the density-induced velocity distribution. The dispersion coefficient due to this velocity distribution was also obtained. Using this dispersion coefficient in an analysis for predicting lateral mixing rates in the experiments of this investigation gave only qualitative agreement with the data. However, predicted longitudinal salinity distributions in an idealized laboratory estuary agree well with published data.

Time-dependent monoenergetic neutron transport in two adjacent semi-infinite media

An exact solution to the monoenergetic Boltzmann equation is obtained for the case of a plane isotropic burst of neutrons introduced at the interface separating two adjacent, dissimilar, semi-infinite media. The method of solution used is to remove the time dependence by a Laplace transformation, solve the transformed equation by the normal mode expansion method, and then invert to recover the time dependence.

The general result is expressed as a sum of definite, multiple integrals, one of which contains the uncollided wave of neutrons originating at the source plane. It is possible to obtain a simplified form for the solution at the interface, and certain numerical calculations are made there.

The interface flux in two adjacent moderators is calculated and plotted as a function of time for several moderator materials. For each case it is found that the flux decay curve has an asymptotic slope given accurately by diffusion theory. Furthermore, the interface current is observed to change directions when the scattering and absorption cross sections of the two moderator materials are related in a certain manner. More specifically, the reflection process in two adjacent moderators appears to depend initially on the scattering properties and for long times on the absorption properties of the media.

This analysis contains both the single infinite and semi-infinite medium problems as special cases. The results in these two special cases provide a check on the accuracy of the general solution since they agree with solutions of these problems obtained by separate analyses.

Mass measurements of some proton-rich nuclei

The Q values and 0^o cross sections of (He³, n) reactions forming seven proton-rich nuclei have been measured with accuracies varying from 6 to 18 keV. The Q values (in keV) are: Si²⁶ (85), S³⁰ (-573), Ar³⁴ (-759), Ti⁴² (-2865), Cr⁴⁸ (5550), Ni⁵⁶ (4513) and Zn⁶⁰ (818). At least one excited state was found for all but Ti⁴². The first four nuclei complete isotopic spin triplets; the results obtained agree well with charge-symmetry predictions. The last three, all multiples of the α particle, are important in the α and e-process theories of nucleo-synthesis in stars. The energy available for β decay of these three was found by magnetic spectrometer measurements of the (He³, p) Q values of reactions leading to V⁴⁸, Co⁵⁶, and Cu⁶⁰. Many excited states were seen: V⁴⁸ (3), Co⁵⁶ (15), Cu⁶⁰ (23). The first two states of S³⁰ are probably 0⁺ and 2⁺ from (He³, n) angular distribution measurements. Two NaI γ-ray measurements are described: the decay of Ar³⁴ (measured ^Ƭ1/2 = 1.2 ± 0.3s) and the prompt γ-ray spectrum from Fe⁵⁴(He³, nγ)Ni⁵⁶. Possible collective structure in Ni⁵⁶ and Ca⁴⁰, both doubly magic, is discussed.

The (He³, n) neutron energy and yield measurements utilized neutron-induced nuclear reactions in a silicon semiconductor detector. Cross sections for the most important detection processes, Si²⁸ (n, α) Mg²⁵ and Si²⁸ (n, p) Al²⁸, are presented for reactions leading to the first four states of both residual nuclei for neutron energies from 7.3 to 16.4 MeV. Resolution and pulse-height anomalies associated with recoil Mg²⁵ and Al²⁸ ions are discussed. The 0^o cross section for Be⁹ (α, n) C¹², used to provide calibration neutrons, has been measured with a stilbene spectrometer for n_o (5.0 ≤ E_α ≤ 12 MeV), n₁ (4.3 ≤ E_α ≤ 12.0 MeV) and n₂ (6.0 ≤ E_α ≤ 10.1 MeV). Resonances seen in the n_o yield may correspond to nine new levels in C¹³.