Atomic-level structure and deformation in metallic glasses

Metallic glasses (MGs) are a relatively new class of materials discovered in 1960 and lauded for its high strengths and superior elastic properties. Three major obstacles prevent their widespread use as engineering materials for nanotechnology and industry: 1) their lack of plasticity mechanisms for deformation beyond the elastic limit, 2) their disordered atomic structure, which prevents effective study of their structure-to-property relationships, and 3) their poor glass forming ability, which limits bulk metallic glasses to sizes on the order of centimeters. We focused on understanding the first two major challenges by observing the mechanical properties of nanoscale metallic glasses in order to gain insight into its atomic-level structure and deformation mechanisms. We found that anomalous stable plastic flow emerges in room-temperature MGs at the nanoscale in wires as little as ~100 nanometers wide regardless of fabrication route (ion-irradiated or not). To circumvent experimental challenges in characterizing the atomic-level structure, extensive molecular dynamics simulations were conducted using approximated (embedded atom method) potentials to probe the underlying processes that give rise to plasticity in nanowires. Simulated results showed that mechanisms of relaxation via the sample free surfaces contribute to tensile ductility in these nanowires. Continuing with characterizing nanoscale properties, we studied the fracture properties of nano-notched MGnanowires and the compressive response of MG nanolattices at cryogenic (~130 K) temperatures. We learned from these experiments that nanowires are sensitive to flaws when the (amorphous) microstructure does not contribute stress concentrations, and that nano-architected structures with MG nanoribbons are brittle at low temperatures except when elastic shell buckling mechanisms dominate at low ribbon thicknesses (~20 nm), which instead gives rise to fully recoverable nanostructures regardless of temperature. Finally, motivated by understanding structure-to-property relationships in MGs, we studied the disordered atomic structure using a combination of in-situ X-ray tomography and X-ray diffraction in a diamond anvil cell and molecular dynamics simulations. Synchrotron X-ray experiments showed the progression of the atomic-level structure (in momentum space) and macroscale volume under increasing hydrostatic pressures. Corresponding simulations provided information on the real space structure, and we found that the samples displayed fractal scaling (r^d ∝ V, d < 3) at short length scales (< ~8 Å), and exhibited a crossover to a homogeneous scaling (d = 3) at long length scales. We examined this underlying fractal structure of MGs with parallels to percolation clusters and discuss the implications of this structural analogy to MG properties and the glass transition phenomenon.

Cooperative properties of lipid bilayers : collective director fluctuations and the effects of hydrophobic mismatch in protein/lipid membrane systems

Cooperative director fluctuations in lipid bilayers have been postulated for many years. ^2H-NMR T_1^(-1), T_(1P)^(-1) , and T_2^(-1); measurements have been used identify these motions and to determine the origin of increased slow bilayer motion upon addition of unlike lipids or proteins to a pure lipid bilayer.

The contribution of cooperative director fluctuations to NMR relaxation in lipid bilayers has been expressed mathematically using the approach of Doane et al.^1 and Pace and Chan.^2 The T_2^(-1)’s of pure dimyristoyllecithin (DML) bilayers deuterated at the 2, 9 and 10, and all positions on both lipid hydrocarbon chains have been measured. Several characteristics of these measurements indicate the presence of cooperative director fluctuations. First of all, T_2^(-1) exhibits a linear dependence on S2/CD. Secondly, T_2^(-1) varies across the ^2H-NMR powder pattern as sin^2 (2, β), where , β is the angle between the average bilayer director and the external magnetic field. Furthermore, these fluctuations are restricted near the lecithin head group suggesting that the head group does not participate in these motions but, rather, anchors the hydrocarbon chains in the bilayer.

T_2^(-1)has been measured for selectively deuterated liquid crystalline DML hilayers to which a host of other lipids and proteins have been added. The T_2^(-1) of the DML bilayer is found to increase drastically when chlorophyll a (chl a) and Gramicidin A' (GA') are added to the bilayer. Both these molecules interfere with the lecithin head group spacing in the bilayer. Molecules such as myristic acid, distearoyllecithin (DSL), phytol, and cholesterol, whose hydrocarbon regions are quite different from DML but which have small,neutral polar head groups, leave cooperative fluctuations in the DML bilayer unchanged.

The effect of chl a on cooperative fluctuations in the DML bilayer has been examined in detail using ^2H-NMR T_1^(-1), T_(1P)^(-1) , and T_2^(-1); measurements. Cooperative fluctuations have been modelled using the continuum theory of the nematic state of liquid crystals. Chl a is found to decrease both the correlation length and the elastic constants in the DML bilayer.

A mismatch between the hydrophobic length of a lipid bilayer and that of an added protein has also been found to change the cooperative properties of the lecithin bilayer. Hydrophobic mismatch has been studied in a series GA' / lecithin bilayers. The dependence of 2H-NMR order parameters and relaxation rates on GA' concentration has been measured in selectively deuterated DML, dipalmitoyllecithin (DPL), and DSL systems. Order parameters, cooperative lengths, and elastic constants of the DML bilayer are most disrupted by GA', while the DSL bilayer is the least perturbed by GA'. Thus, it is concluded that the hydrophobic length of GA' best matches that of the DSL bilayer. Preliminary Raman spectroscopy and Differential Scanning Calorimetry experiments of GA' /lecithin systems support this conclusion. Accommodation of hydrophobic mismatch is used to rationalize the absence of H_(II) phase formation in GA' /DML systems and the observation of H_(II) phase in GA' /DPL and GA' /DSL systems.

1. J. W. Doane and D. L. Johnson, Chem. Phy3. Lett., 6, 291-295 (1970). 2. R. J. Pace and S. I. Chan, J. Chem. Phy3., 16, 4217-4227 (1982).

On the transport properties of fluid-particle flow

The hydrodynamic forces acting on a solid particle in a viscous, incompressible fluid medium at low Reynolds number flow is investigated mathematically as a prerequisite to the understanding of transport processes in two-phase flow involving solid particles and fluid. Viscous interaction between a small number of spherical particles and continuous solid boundaries as well as fluid interface are analyzed under a “point-force” approximation. Non-spherical and elastic spherical particles in a simple shear flow area are then considered. Non-steady motion of a spherical particle is briefly touched upon to illustrate the transient effect of particle motion.

A macroscopic continuum description of particle-fluid flow is formulated in terms of spatial averages yielding a set of particle continuum and bulk fluid equations. Phenomenological formulas describing the transport processes in a fluid medium are extended to cases where the volume concentration of solid particles is sufficiently high to exert an important influence. Hydrodynamic forces acting on a spherical solid particle in such a system, e.g. drag, torque, rotational coupling force, and viscous collision force between streams of different sized particles moving relative to each other are obtained. Phenomenological constants, such as the shear viscosity coefficient, and the diffusion coefficient of the bulk fluid, are found as a function of the material properties of the constituents of the two-phase system and the volume concentration of solid. For transient heat conduction phenomena, it is found that the introduction of a complex conductivity for the bulk fluid permits a simple mathematical description of this otherwise complicated process. The rate of heat transfer between particle continuum and bulk fluid is also investigated by means of an Oseen-type approximation to the energy equation.

Using Earth Deformation Caused by Surface Mass Loading to Constrain the Elastic Structure of the Crust and Mantle

Surface mass loads come in many different varieties, including the oceans, atmosphere, rivers, lakes, glaciers, ice caps, and snow fields. The loads migrate over Earth's surface on time scales that range from less than a day to many thousand years. The weights of the shifting loads exert normal forces on Earth's surface. Since the Earth is not perfectly rigid, the applied pressure deforms the shape of the solid Earth in a manner controlled by the material properties of Earth's interior. One of the most prominent types of surface mass loading, ocean tidal loading (OTL), comes from the periodic rise and fall in sea-surface height due to the gravitational influence of celestial objects, such as the moon and sun. Depending on geographic location, the surface displacements induced by OTL typically range from millimeters to several centimeters in amplitude, which may be inferred from Global Navigation and Satellite System (GNSS) measurements with sub-millimeter precision. Spatiotemporal characteristics of observed OTL-induced surface displacements may therefore be exploited to probe Earth structure. In this thesis, I present descriptions of contemporary observational and modeling techniques used to explore Earth's deformation response to OTL and other varieties of surface mass loading. With the aim to extract information about Earth's density and elastic structure from observations of the response to OTL, I investigate the sensitivity of OTL-induced surface displacements to perturbations in the material structure. As a case study, I compute and compare the observed and predicted OTL-induced surface displacements for a network of GNSS receivers across South America. The residuals in three distinct and dominant tidal bands are sub-millimeter in amplitude, indicating that modern ocean-tide and elastic-Earth models well predict the observed displacement response in that region. Nevertheless, the sub-millimeter residuals exhibit regional spatial coherency that cannot be explained entirely by random observational uncertainties and that suggests deficiencies in the forward-model assumptions. In particular, the discrepancies may reveal sensitivities to deviations from spherically symmetric, non-rotating, elastic, and isotropic (SNREI) Earth structure due to the presence of the South American craton.

Dynamics of Granular Crystals with Elastic-Plastic Contacts

We study the behavior of granular crystals subjected to impact loading that creates plastic deformation at the contacts between constituent particles. Granular crystals are highly periodic arrangements of spherical particles, arranged into densely packed structures resembling crystals. This special class of granular materials has been shown to have unique dynamics with suggested applications in impact protection. However, previous work has focused on very low amplitude impacts where every contact point can be described using the Hertzian contact law, valid only for purely elastic deformation. In this thesis, we extend previous investigation of the dynamics of granular crystals to significantly higher impact energies more suitable for the majority of applications. Additionally, we demonstrate new properties specific to elastic-plastic granular crystals and discuss their potential applications as well. We first develop a new contact law to describe the interaction between particles for large amplitude compression of elastic-plastic spherical particles including a formulation for strain-rate dependent plasticity. We numerically and experimentally demonstrate the applicability of this contact law to a variety of materials typically used in granular crystals. We then extend our investigation to one-dimensional chains of elastic-plastic particles, including chains of alternating dissimilar materials. We show that, using the new elastic-plastic contact law, we can predict the speed at which impact waves with plastic dissipation propagate based on the material properties of the constituent particles. Finally, we experimentally and numerically investigate the dynamics of two-dimensional and three-dimensional granular crystals with elastic-plastic contacts. We first show that the predicted wave speeds for 1D granular crystals can be extended to 2D and 3D materials. We then investigate the behavior of waves propagating across oblique interfaces of dissimilar particles. We show that the character of the refracted wave can be predicted using an analog to Snell's law for elastic-plastic granular crystals and ultimately show how it can be used to design impact guiding "lenses" for mitigation applications.