Solid state NMR chemical shifts as an alternative to diffraction data in the determination of SIC polytypic structures

Silicon carbide, which has many polytypic modifications of a very simple and very symmetric structure, is an excellent model system for exploring, the relationship between chemical shift, long-range dipolar shielding, and crystal structure in network solids. A simple McConnell equation treatment of bond anisotropy effects in a poly type predicts chemical shifts for silicon and carbon sites which agree well with the experiment, provided that contributions from bonds up to 100 A are included in the calculation. The calculated chemical shifts depend on three factors: the layer stacking sequence, electrical centre of gravity, and the spacings between silicon and carbon layers. The assignment of peaks to lattice sites is proved possible for three polytypes (6H, 15R, and 3C). The fact that the calculated chemical shifts are very sensitive to layer spacings provides us a potential way to detennine and refine a crystal structure. In this work, the layer spacings of 6H SiC have been calculated and are within X-ray standard deviations. Under this premise, the layer spacings of 15R have been detennined. 29Si and 13C single crystal nmr studies of 6H SiC polytype indicate that all silicons and carbons are magnetically anisotropic. The relationship between a magnetic shielding tensor component and layer spacings has been derived. The comparisons between experimental and semi-empirical chemical shielding tensor components indicate that the paramagnetic shielding of silicon should be included in the single crystal chemical shift calculation.

Developing a numerical inverse-theory-based extraction of orientation-dependent relaxation rates from partially- relaxed spectra

Second-rank tensor interactions, such as quadrupolar interactions between the spin- 1 deuterium nuclei and the electric field gradients created by chemical bonds, are affected by rapid random molecular motions that modulate the orientation of the molecule with respect to the external magnetic field. In biological and model membrane systems, where a distribution of dynamically averaged anisotropies (quadrupolar splittings, chemical shift anisotropies, etc.) is present and where, in addition, various parts of the sample may undergo a partial magnetic alignment, the numerical analysis of the resulting Nuclear Magnetic Resonance (NMR) spectra is a mathematically ill-posed problem. However, numerical methods (de-Pakeing, Tikhonov regularization) exist that allow for a simultaneous determination of both the anisotropy and orientational distributions. An additional complication arises when relaxation is taken into account. This work presents a method of obtaining the orientation dependence of the relaxation rates that can be used for the analysis of the molecular motions on a broad range of time scales. An arbitrary set of exponential decay rates is described by a three-term truncated Legendre polynomial expansion in the orientation dependence, as appropriate for a second-rank tensor interaction, and a linear approximation to the individual decay rates is made. Thus a severe numerical instability caused by the presence of noise in the experimental data is avoided. At the same time, enough flexibility in the inversion algorithm is retained to achieve a meaningful mapping from raw experimental data to a set of intermediate, model-free

I must walk through the gate : an ontological necessity

This research is a self-study into my life as an athlete, elementary school teacher, leamer, and as a teacher educator/academic. Throughout the inquiry, I explore how my beliefs and values infused my lived experiences and ultimately influenced my constructivist, humanist, and ultimately my holistic teaching and learning practice which at times disrupted the status quo. I have written a collection of narratives (data generation) which embodied my identity as an unintelligent student/leamer, a teacher/learner, an experiential learner, a tenacious participant, and a change agent to name a few. As I unpack my stories and hermeneutically reconstruct their intent, I question their meaning as I explore how I can improve my teaching and learning practice and potentially effect positive change when instructing beginning teacher candidates at a Faculty of Education. At the outset I situate my story and provide the necessary political, social, and cultural background information to ground my research. I follow this with an in depth look at the elements that interconnect the theoretical framework of this self-study by presenting the notion of writing at the boundaries through auto ethnography (Ellis, 2000; Ellis & Bochner, 2004) and writing as a method of inquiry (Richardson, 2000). The emergent themes of experiential learning, identity, and embodied knowing surfaced during the data generation phase. I use the Probyn' s (1990) .. metaphor of locatedness to unpack these themes and ponder the question, Where is experience located? I deepen the exploration by layering Drake's (2007) KnowlDo/Be framework alongside locatedness and offer descriptions of learning moments grounded in pedagogical theories. In the final phase, I introduce thirdspace theory (Bhabha, 1994; Soja, 1996) as a space that allowed me to puzzle educational dilemmas and begin to reconcile the binaries that existed in my life both personally, and professionally. I end where I began by revisiting the questions that drove this study. In addition, Ireflect upon the writing process and the challenges that I encountered while immersed in this approach and contemplate the relevance of conducting a self-study. I leave the reader with what is waiting for me on the other side of the gate, for as Henry James suggested, "Experience is never limited, and it is never complete."