<p dir="ltr">Knowledge of transport processes plays a critical role in the development and application of materials in many technologies. As manufacturing technologies continue to push the geometries of materials to smaller scales, traditional means of predicting and measuring transport properties begin to fail. Micro and nanoscopic effects tend to alter transport phenomena in materials, leading to new physics and different properties from the bulk state. In particular, the dynamics of thermal transport of a material varies greatly in both spatial and temporal senses. Different energy carriers have intrinsically different mechanisms of thermal transport; depending on the time and lengths scales in question, the contribution to the overall thermal transport by one carrier may be vastly different than others. To characterize and understand the dynamics of thermal transport at these small scales, novel ultrafast experimental techniques and theories are crucially needed. This work will discuss the efforts made to develop a framework to measure and differentiate the dynamics of transport processes of a material due to different energy carriers using ultrafast optical techniques. This dissertation is organized as follows.</p><p dir="ltr">Chapter 1 gives a background in the theory of thermal transport. This will serve as the foundation for the physical models that are used to extract thermal properties from experimental works. A brief review of the advances in ultrafast experimental and theoretical works will also be given. This will assist in placing this work in the context of ongoing work in the thermal transport community. Chapter 2 illustrates the experimental setups and physical models used to measure the effective thermal transport properties of thin film materials. Steady-state optical measurements are used to quantify the effective, in-plane, anisotropic, thermal conductivity of a 2D material. Time resolved, ultrafast optical measurements are used to quantify the effective, out-of-plane, thermal conductivity of a material. Chapters 3 and 4 demonstrate the capabilities of an ultrafast spatiotemporal scanning pump-probe system, where the high temporal and nanometric resolution measurements directly probe the electron contribution to thermal transport in metals as well as the ambipolar diffusion of carriers in semiconductors. Lastly, Chapter 5 summarizes this dissertation and provides a discussion on the use of the developed experimental capabilities to probe transport of emerging materials.</p>

<p>Crystal growth has been recognized as a paradigm for non-equilibrium pattern formation for decades. Scientific interest in this field has focused on the growth rates and curvature of branches in snow flake-like structures patterned after a solid's crystallographic orientations. Similar patterns have been extensively identified in solidification of metals and organic metal analogues and are known as dendrites, which is originated from a Greek word "dendron" meaning tree.</p> <p>Dendritic spacing and morphology established during casting often sets the final microstructure and second phase formation that develops during manufacturing of alloys. This is particularly true in emerging technologies such as twin belt casting of aluminum alloys, where a reduced amount of thermomechanical processing reduced the possibility of modifying microstructure from that determined at the time of solidification. Predicting and controlling these microstructure of cast alloys has thus been a driving force behind various studies on solidification of materials.</p> <p>Mg-based alloys are another class of materials gaining importance due to the high demand for weight reduction in the transportation industry which accordingly reduces the gas consumption. While the solidified microstructure and its effect on the material properties have been the subject of intensive studies, little is known about the fundamental mechanisms that determine dendritic microstructure in Mg alloys and its evolution under directional growth conditions.</p> <p>This thesis investigates the relationship between the microstructure and cooling conditions in unsteady state upward directional solidification of Al-Cu and Mg-Al alloys. The four-fold symmetry of Al-Cu alloys are used to study the dynamical spacing selection between dendrites, as the growth conditions vary dynamically, whereas, the Mg-Al system with a six-fold symmetry is used to study a competition between neighbouring, misoriented grains and the effect of this as the resulting microstructure. Mg-Al also presents a situation wherein the cooling conditions dynamically vary from the preferred crystallographic growth direction. Analysis of phase field simulations is used to shed some light on the morphological development of dendrite arms during solidification under transient conditions. Our numerical results are compared to new casting experiments.</p> <p>Chapter three studies spacing selection in directional solidification of Al-Cu alloys under transient growth conditions. New experimental results are presented which reveal that the mean dendritic spacing versus solidification front speed exhibits plateau-like regions separated by regions of rapid change, consistent with previous experiments of Losert and co-workers. In fact, The primary spacing of a dendritic array grown under transient growth conditions displays a distribution of wavelengths. As the rate of change in solidification front velocity is decreased, the evolution of the spacing follows the prediction of the geometrical models within a band of spacing fluctuations. The width of the band is shown to highly depend on the rate of the solidification front velocity acceleration, such that the higher the rate, the wider the band of available spacings. Quantitative phase field simulations of directional solidification with dynamical growth conditions approximating those in the experiments confirm this behavior. The mechanism of this type of change in mean dendrite arm spacing is consistent with the notion that a driven periodically modulated interface must overcome an energy barrier before becoming unstable, in accord with a previous analytical stability analysis of Langer and co-workers.</p> <p>In chapter four, it is demonstrated both computationally and experimentally that a material's surface tension anisotropy can compete with anisotropies present in processing conditions during solidification to produce a continuous transition from dendritic microstructure morphology to so-called seaweed and fractal-like solidification microstructures. The phase space of such morphologies is characterized and the selection principles of the various morphologies explored are explained. These results have direct relevance to the microstructure and second phase formation in commercial lightweight metal casting.</p> / Doctor of Philosophy (PhD)

<p>In this thesis we discuss in detail the density-matrix renormalization group (DMRG) for simulating low-energy properties of quantum spin models. We implement an original DMRG routine on the S=1/2 antiferromagnetic Heisenberg chain and benchmark its efficiency against exact results (energies, correlation functions, etc.) as well as conformal field-theoretical calculations due to finite-size scaling (ground-state energy and spin gap logarithmic corrections). Moreover, we apply the DMRG to a two-leg square ladder system, where in addition to bilinear exchange terms, we also consider an additional cyclic four-spin ring-exchange. The transposition of four spins gives rise to biquadratic exchange terms which are non-trivial to implement in the DMRG. Intermediate results of the ring-exchange are presented along with the difficulties presently encountered.</p> / Master of Science (MSc)

<p>This thesis is the result of several experiments designed to probe the low temperature physics underlying the 1D-Ising-like behaviour of chains of spins in the structure of Cobalt Niobate, CoNb2O6. A collection of prior work has been done by several groups prior to this, focusing on mapping the phase diagram above 0.5K. Interest in this material was renewed recently based upon theoretical work and experimental confirmation of the unique structure of the spins in the system. The bulk of this work was done at temperatures below the previously investigated range to probe the unique properties of this system.</p> <p>The material was grown at McMaster University using the optical floating zone technique from oxide powders. The crystal was examined and oriented using single crystal and Laue diffraction and was cut for use in further experiments. Squid magnetometry was used to confirm the material properties and phase transition temperatures, and was compared to literature values.</p> <p>Heat capacity measurements were performed locally down to 2K, and by collaborators at Waterloo in the range from 330mK to 1K. The heat capacity measurement confirmed the 2.9K transition and explored the relaxation time of the material. Cobalt niobate was found to have an exceptionally long relaxation time at low temperatures indicating strong spin-spin interactions. A sharp transition with zero applied field was found to become a broad, smooth feature at 2.9K when a small field was applied.</p> <p>We performed muSR measurements in zero, longitudinal and transverse field. The muSR results confirmed the long relaxation time found by the heat capacity measurements, which may reflect the coupling of the spin system to the lattice. Additionally, the material was never seen to statically order in zero or longitudinal field down to 700mK and up to 1T. The material was found to behave dynamically throughout all the field ranges.</p> / Master of Science (MSc)

<p>Thermoelectric (TE) materials are able to convert heat directly into electricity and vice versa. This special property makes them valuable for a variety of applications involving power generation and refrigeration. In the search for potential high-performance TE materials, a number of rare-earth (<em>RE</em>) antimonide suboxide phases have been investigated.This presentation will focus on two classes of rare-earth antimonide suboxides: the <em>RE</em>₃Sb₃O₃ and <em>RE</em>₈Sb_3-<em>_d</em>O₈ phases (<em>C</em>2/<em>m</em> space group) based on the <em>RE</em>–O frameworks and the <em>anti</em>-ThCr₂Si₂ type <em>RE</em>₂SbO₂ compounds (<em>I</em>4/<em>mmm</em> space group). The physical property measurements on the high-purity bulk samples revealed unexpected semiconducting properties in the non-charge-balanced systems, i.e.<em> RE</em>₈Sb_3-<em>_d</em>O₈ and <em>RE</em>₂SbO₂. Since the electronic structure calculations suggest that the anionic Sb states dominate the valence band at the vicinity of the Fermi level, the local structure of the Sb atomic site is believed to dictate the observed physical properties. The charge transport properties are explained within the framework of Anderson/Mott-type localizations. Ultimately, systematic investigation of the <em>RE</em>₂SbO₂ and Ho₂Sb_1-<em>x</em>Bi<em>_x</em>O₂ series reveal the large variability of the electrical properties caused by the local structural perturbations.</p> / Doctor of Philosophy (PhD)

<p>Continuum atomistic and mesoscopic models are developed and utilized in the context of studying microstructural evolution and phase selection in materials systems. Numerous phenomena are examined, ranging from defect-solute interaction in solid state systems to microstructural evolution under external driving conditions. Emphasis is placed on the derivation and development of models capable of self consistently describing the intricate mechanisms at work in the systems undergoing these phenomena.</p> <p>Namely, grain growth dynamics are studied in nanocrystalline systems under external driving conditions using a newly developed phase-field-crystal model, which couples an additional free energy source term to the standard phase-field-crystal model. Such external driving can be attributed to incident energetic particles. The nanocrystalline system is found to be susceptible to enhanced grain growth as a function of the intensity/flux associated with the external driving and the energy of driving. Static kinetic phase diagram calculations also seem to confirm that systems under external driving conditions can be forced into long metastable states.</p> <p>Early stage solute clustering and precipitation in Al alloys is also examined with a variant of the phase-field-crystal method, so-called structural phase-field-crystal models for multi-component alloys developed as part of this thesis. We find that clustering is aided by quenched-in defects (dislocations), whereby the nucleation barrier is reduced and at times eliminated, a mechanism proposed by Cahn for a single dislocation for spinodal systems. In a three-component system, we predict a multi-step mechanism for clustering, where the nature and amount of the third species plays an important role in relieving stresses caused by the quenched-in dislocations before clustering, i.e., segregation as predicted by the equilibrium phase diagram, can occur.</p> <p>Finally, we present a new coarse-graining procedure for generating complex amplitude models, i.e., complex order-parameter phase-field models, derived from phase-field-crystal models. They retain many salient atomistic features and behaviours of the original phase-field-crystal model, however is now capable of describing mesoscopic length scales like the phase-field model. We demonstrate the scheme by generating an amplitude model of the two-dimensional structural phase-fieldcrystal model, which allows multiple crystal structures to be stable in equilibrium, a crucial aspect of proper multi-scale modelling of materials systems. The dynamics are demonstrated by examining solidification and coarsening, peritectic growth, along with grain growth and the emergence of secondary phases.</p> / Doctor of Science (PhD)

<p>Ultracold atoms in an optical lattice Bloch oscillate when subject to a constant force. In the first work presented in this thesis we have theoretically studied the scenario where the optical lattice potential is provided by the electric field inside an optical cavity. The coherent atom-light interaction in a cavity gives rise to a backaction effect on the light field which can modify the intracavity field amplitude and phase. In our first treatment of this problem we model the cavity light field and atoms by classical fields and solve the coupled atom-light equations of motion. As a result, we find that the amplitude and phase of the transmitted light field is modulated at the Bloch frequency. Remarkably, the Bloch frequency itself is not modified by the backaction. Thus the transmitted light field can be used to observe the oscillations continuously, allowing high-precision measurement with small clouds of atoms.</p> <p>In the second problem presented in this thesis, we explore the band structure of the steady state solutions of the atom-cavity system. A crucial first step towards determining the band structure is the identification of an energy functional that describes the coupled atom-light system. Although, we do not include direct atom-atom interactions in our models, the coupling of the atoms to the single mode light field of the cavity introduces an effective mutual interaction which is correctly taken into account by the energy functional we introduce. Corresponding to each point in the band there exists a steady state light field associated with an average cavity photon number. The dispersive nonlinear atom-light interaction can lead to bistable solutions for this intracavity photon number. For parameters where the atom-cavity system exhibits bistability, the atomic band structure develops loop structures akin to the ones predicted for Bose-Einstein condensates in ordinary (non-cavity) optical lattices. However, in our case the nonlinearity derives from the cavity backaction rather than from direct interatomic interactions. We find both bi- and tri-stable regimes associated with the lowest band, and show that the multistability we observe can be analysed in terms of swallowtail catastrophes. Dynamic and energetic stability of the meanfield solutions is also studied, and we show that the bistable solutions have, as expected, one unstable and two stable branches. The presence of loops in the band structure can lead to a breakdown in adiabaticity during Bloch oscillations as the entire band is sampled during the dynamics. We therefore use the insight gleaned from this work in choosing parameters for the Bloch oscillation measurement proposal presented in the rest of the thesis.</p> <p>In the third work presented in the thesis, we go beyond the mean field description and consider effects of the quantised nature of the light and atomic fields. The cavity light field is always in contact with external electromagnetic fields through the partially transmissive mirrors. This coupling to the external modes enters as quantum noise in the dynamics of the intracavity field and can also be viewed as a manifestation of quantum measurement backaction corresponding to the continuous observation of the transmitted light field. We solve the Heisenberg-Langevin equations for linearized fluctuations about the atomic and optical meanfields and examine how this influences the signal-to-noise ratio of a measurement of external forces using this system. In particular, we investigate the effects of changing the number of atoms, the intracavity lattice depth, and the atom-light coupling strength, and show how resonances between the Bloch oscillation dynamics and the quasiparticle spectrum have a strong influence on the signal-to-noise ratio as well as heating effects. One of the hurdles we overcome along the way is the proper treatment of fluctuations about time-dependent meanfields in the context of cold atom cavity-QED.</p> / Doctor of Philosophy (PhD)

<p>The pi-striped, <em>d</em>-wave superconducting (SC) state, which is a type of pair density wave wherein the SC order is spatially modulated, has recently been shown to generate the key ingredients for quantum oscillations consistent with experimental observations (Zelli <em>et al.</em>, 2011, 2012). This was accomplished with a phenomenological approach using non-self-consistent Bogoliubov-de Gennes (BdG) theory. The objective of this thesis is to explore two aspects of this approach: the addition of a charge density wave (CDW) order to the previous non-self-consistent calculations, and an attempt at stabilizing the pi-striped state in fully self-consistent BdG theory. It was found that the CDW order had a minimal effect on the Fermi surface characteristics of the pi-striped state, but that a sufficiently strong CDW degrades the Landau levels which are essential for the formation of quantum oscillations. The self-consistent mean-field calculations were unable to stabilize the pi-striped state under a range of modifications to the Hamiltonian. Free energy calculations with the modulated SC order treated as a parameter demonstrate that the pi-striped state is always less energetically favourable than the normal state for the scenarios which were considered. The results of this study constitute a basis for future, more comprehensive studies, using the BdG approach, of the stability of possible pi-striped SC phases.</p> / Master of Science (MSc)

<p>In this dissertation, the Phase Field Crystal (PFC) Method is used to study a number of problems in which interfaces and elastic effects play important roles in alloys. In particular, the three topics covered in this work are grain boundary thermodynamics in alloys, dislocation-mediated formation of clusters in binary and ternary alloys, and solutal effects in explosive crystallization. Physical phenomena associated with grain boundaries, such as Read-Shockley-like behaviour and Gibbs adsorp- tion theorem, were shown to be accurately captured in both PFC- and XPFC-type models. In fact, a connection between the solute segregation behaviour and physical properties of the system—such as energy of mixing, mismatch, and undercooling—were shown. Also, grain boundary premelting was investigated. It was shown how solute can change the disjoining potential of a grain boundary and a mechanism for hysteresis in grain boundary premelting was discussed. Regarding the phenomenon of cluster formation, a general coexistence approach and a nucleation-like approach were used to describe the mechanism consistently with observations; the process is facilitated by lowering the energy increase associated with it. The final phenomenon studied was explosive crystallization. It was shown that the temperature oscillations due to unsteady motion of an interface could be captured with PFC-type models and that this behaviour leaves patterns, such as solute traces, in the material. The versatility of this PFC formalism was demonstrated by capturing the underlying physics and elucidating the role of misfit strain in altering interface oscillations during explosive crystallization. Finally, it was demonstrated in all projects how PFC model parameters relate to coarse-grained material properties, thereby connecting these phenomena on larger scales to atomistic-scale properties.</p> / Doctor of Philosophy (PhD)

For graphene to be a viable platform for nanoscale devices, high quality growth and structures are necessary. This means structuring the SiC surface to prevent graphene from having to be patterned using standard microelectronic processes. Presented in this thesis are new processes aimed at improving the graphene as well as devices based on high quality graphene nanoribbons. Amorphous carbon (aC) corrals deposited prior to graphene growth are demonstrated to control SiC step-flow. SiC steps are shown to be aligned by the presence of the corrals and can increase SiC terrace widths. aC contacts deposited and crystallized during graphene growth are shown as a way to contact graphene without metal lift-off. Observation of the Quantum Hall Effect demonstrates the high quality of the graphene grown alongside the nanocrystalline graphite contacts. Continuing the ballistic transport measurements on sidewall graphene nanoribbons, the invasive probe effect is observed using an atomic force microscope (AFM) based technique that spatially maps the invasive probe effect. Cleaning experiments demonstrate the role of scattering due to resist residues and environmental adsorbates on graphene nanoribbons. Finally, switches based on junctions formed in the graphene nanoribbons are shown as a route toward graphene based devices.