Recentemente foi descoberto que diversos calcogenetos de metais de transição podem ter o estado charge density waves (CDW) suprimido a partir de pressão hidrostática e dopagens, e, por conseguinte, o estado supercondutor emerge. Nesse contexto, este trabalho apresenta um estudo sistemático de propriedades físicas de amostras poli e monocristalinas de dois compostos do sistema Nb-Te, NbTe2 e NbTe4. Com relação ao composto NbTe2, os resultados aqui apresentados demonstram que esse composto é mais um exemplo de material que exibe ambos os estados a pressão atmosférica e sem dopagens. No que tange as propriedades do NbTe4, este trabalho demonstra que amostras deficientes em telúrio tem a anomalia na curva de resistividade elétrica relacionada a formação do estado CDW amplificada e, a deficiência em telúrio é também capaz de fazer emergir supercondutividade em 5.5 K. Este trabalho também sugere algumas mudanças no diagrama de equilíbrio de fases Nb-Te publicado na base de dados da sociedade americana de metalurgia (ASM). As fases Nb5Te4 e Nb3Te4 foram identificadas como sendo fases de altas temperaturas que são formadas a partir de reações eutetóides. Além do mais, nossos resultados demonstram que a região entre as fases NbTe2 e NbTe4 consiste, na verdade, de uma região bifásica. Durante a realização deste trabalho, outro composto foi investigado, o NiTe2. Nesse composto, nossos resultados demonstram que a intercalação de Ti faz emergir um estado supercondutor em 4.5 K e cuja temperatura de transição parece insensível a pressão hidrostática. Cálculos de estrutura de bandas sugerem fortemente que o composto NiTe2 intercalado com Ti pode ser mais um exemplo de supercondutor com aspectos topológicos em sua superfície de Fermi. / Recently was demonstrated that it is possible to suppress the charge density waves (CDW) ground states while, simultaneously, a superconductor state emerges in several transition metal chalcogenides (TMC), by means of hydrostatic pressure or chemical doping. Within this context, this work presents a systematic study on physical properties of two Nb chalcogenides, NbTe2 and NbTe4. Our results demonstrate that NbTe2 is another example of a TMC which exhibit both stabilities at atmospheric pressure and without doping. Regarding the physical properties of NbTe4, we have demonstrated that Te deficiency increases significantly the anomaly in the electrical resistivity as function of temperature behavior related with the CDW formation. At the same time, Te deficiency can also cause a SC state to emerge at 5.5 K. This work also presents a review of the binary phase diagram, Nb-Te, and some changes are proposed. Nb5Te4 and Nb3Te4 were identified as high temperature phases originated from eutectoid reactions. Furthermore, our results demonstrated that the region between the phases NbTe2 and NbTe4 are, in fact, a two-phase region, differently from what is proposed in the actual version of the phase diagram. Also, during this work, another chalcogenide was investigated, NiTe2. Our results demonstrate that Ti can be intercalted between the Van der Waals gaps of the structure and consequently a superconductor state emerges at 4.5 K. The critical temperature is found to be insensitive to hydrostatic pressure. Band structure strongly suggests that NiTe2 could be another example of a superconductor with topological aspects in its Fermi surface.

The thesis entitled “Exploring Intermolecular Space by Charge Density Analysis in Molecular Crystals” consists of five chapters. A short introductory note highlights the importance of intermolecular interactions and presents the current status of charge density analysis to obtain insights into such interactions. Charge density analysis of crystalline materials by using high resolution X-ray diffraction data has become routine and enables derivation of reliable one electron properties associated with the electron density. The results obtained from single crystal X-ray diffraction data at low temperature have been compared with periodic theoretical calculations using B3LYP/6-31G** methods to unequivocally establish the nature of weak interactions. Chapter 1 describes the quantitative analysis of Cl∙∙∙Cl intermolecular interactions in compounds 2-chloro-3-quinolinyl methanol, 2-chloro-3-hydroxypyridine and 2-chloro-3-chloromethyl-8-methylquinoline, which are corresponding to type I (trans and cis) and type II (L) geometries of Cl∙∙∙Cl interactions respectively. The 3D static deformation density plots from charge density analysis unequivocally suggest that both ‘cis’ and ‘trans’ type I geometries show decreased repulsion whereas type II geometry is attractive based on the nature of “polar flattening” of the electron density around the Cl atom. The topological features derived at bond critical point (BCP) of Cl∙∙∙Cl interactions also support the observed results. Chapter 2 discusses hetero-halogen (Cl∙∙∙F) and homo-halogen (F∙∙∙F) intermolecular interactions involving “organic fluorine” in compounds 2-chloro-4-fluorobenzoic acid and 4-flurobenzamide respectively. Charge density distributions show polar flattening effects at both atoms Cl and F, however the extent of polarization is small on F in comparison with that of the Cl atom. 3D static deformation density plots depict δ+ ∙∙∙δ− interactions for Cl∙∙∙F intermolecular interactions while F∙∙∙F interactions show small decreased repulsion features. The topological properties of F∙∙∙F interactions bring out the similarity between F∙∙∙F and Cl∙∙∙Cl interactions. Chapter 3 describes the nature of C−Cl∙∙∙O=C halogen bond in 2, 5-dichloro-1, 4-benzoquinone, a molecule specifically chosen to depict this interaction dominantly. The topological values at bond critical point, three dimensional static deformation density features and electrostatic potential isosurfaces unequivocally establish the attractive nature of C−Cl∙∙∙O=C halogen bond in the crystalline lattice. Chapter 4 discusses the generation of multi-component systems (for example cocrystals and salts) of active pharmaceutical ingredients (API). Two systems associated with nicotinamide, one with salicylic acid and the other with oxalic acid as coformers resulting in 1:1 molecular complexes have been analyzed. The charge density analysis, particularly at the proton transfer region clearly bring out the differences between cocrystal and salt thus providing insights into the continuum in the proton transfer pathways in molecular crystals. Chapter 5 describes a new methodology [supramolecular synthon based fragment approach (SBFA)] concerning transferability of experimental charge density multipole parameters and building a database using well defined supramolecular synthons. The modularity and robustness of supramolecular synthons are used to transfer experimental charge density multipole parameters of synthons derived from a high resolution X-ray diffraction study to target molecules possessing these synthons as fragments in the crystalline lattice. The synthesized charge density and derived topological properties on target molecules using routine single crystal diffraction data are comparable with both experimental and theoretical charge density results. SBFA thus is expected to provide an additional database which can be applied to include intermolecular interactions space in the modeling directly unlike the available ones such as ELMAM, INVARIOM and UBDB. Further, SBFA approach can be extended to the determination and synthesis of charge density properties in macromolecules such as polypeptides, nucleic acids and proteins. APPENDIX contains reprints of the articles published which comprises of the work carried out in addition to the above five chapters.

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The thesis entitled “Intermolecular Interactions in Molecular Crystals: Quantitative Estimates from Experimental and Theoretical Charge Densities” consists of four chapters and an Appendix. Chapter 1 highlights the principles of crystal engineering from charge density point of view. Chapter 2 (Section I - III) deals with the evaluation of weak intermolecular interactions and in particular related to the features of concomitant polymorphism. Chapter 3 describes the co-operative role of weak interactions in the presence of strong hydrogen bonds in small bioactive molecules in terms of topological properties. Chapter 4 unravels the inter-ion interactions in terms of charge density features in an ionic salt. The general conclusions of the works presented in this thesis are provided at the end of the chapters. Appendix A explores the varieties of hydrogen bonds in a simple molecule. Identification of intermolecular interactions based purely on distance-angle criteria is inadequate and in the context of ‘quantitative crystal engineering’, recognition of critical points in terms of charge density distribution becomes extremely relevant to justify the occurrence of any interaction in the intermolecular space. The results from single crystal X-ray diffraction data at 90K (compound in chapter 4 at 113K) have been compared with those from periodic theoretical calculations via DFT method at high-level basis set (B3LYP/6-31G**) in order to establish a common platform between theory and experiment. Chapter 1 gives a brief review on crystal engineering to analyze intermolecular interactions along with the description of both experimental and theoretical approaches used in the analysis of charge densities in molecular crystals. The eight of Koch and Popelier’s criteria, defined using the theory of “Atoms in Molecules”, to characterize hydrogen bonds have also been discussed in detail. Chapter 2 (I) presents the charge density analysis in coumarin, 1-thiocoumarin, and 3-acetylcoumarin. Coumarin has been extensively studied as it finds applications in several areas of synthetic chemistry, medicinal chemistry, and photochemistry. The packing of molecules in the crystal lattice is governed by weak C−HLO and C−HLπ interactions only. The variations in charge density properties and derived local energy densities have been investigated in these regions of intermolecular interactions. The lacuna of the identification of a lower limit for the hydrogen bond formation has been addressed in terms of all eight of Koch and Popelier’s criteria, to bring out the distinguishing features between a hydrogen bond (C−HLO) and a van der Waals interaction (C−HLπ) for the first time. Chapter 2 (II) highlights the nature of intermolecular interactions involving sulfur in 1-thiocoumarin, 2-thiocoumarin, and dithiocoumarin. These compounds pack in the crystal lattice mainly via weak C−HLS and SLS interactions. The analysis of experimental and theoretical charge densities clearly categorizes these interactions as pure van der Waals in nature. The distribution of charge densities in the vicinity of the S atom has been analyzed to get better insights into the nature of sulfur in different environments. Chapter 2 (III) provides a detailed investigation of the charge density distribution in concomitant polymorphs of 3-acetylcoumarin. The electron density maps in the two forms demonstrate the differences in the nature of the charge density distribution particularly in the features associated with C−HLO and C−HLπ interactions. The net charges derived based on the population analysis via multipole refinement and also the charges evaluated via integration over the atomic basins and the molecular dipole moments show significant differences. The lattice energies calculated from experimental charge density approach clearly suggest that form A is thermodynamically stable compared to form B. Mapping of electrostatic potential over the molecular surfaces also bring out the differences between the two forms. Chapter 3 describes the analysis of charge density distribution in three small bioactive molecules, 2-thiouracil, cytosine monohydrate, and salicylic acid. These molecules pack in the crystal lattice via strong hydrogen bonds, such as N−HLO, N−HLS, and O−HLO. In spite of the presence of such strong hydrogen bonds, the weak interactions like C−HLO and C−HLS also contribute in tandem to the packing features. The distribution of charge densities in intermolecular space provides a quantitative comparison on the strength of both strong and weak interactions. The variations in electronegativity associated with the S, O, and N atoms are clearly seen in the electrostatic potential maps over the molecular surfaces. Chapter 4 deals with study of intermolecular interactions in N,N,N´N´-tetramethylethlenediammonium dithiocyanate, analyzed based on experimental charge densities from X-ray diffraction data at 113 K and compared with theoretical charge densities. The packing in the crystal lattice is governed mainly by a strong N+−H…N− hydrogen bond along with several weak interactions such as C−HLS, C−HLN, and C−HLπ. The charge density distribution in the region of inter-ionic interaction is also highlighted and the electrostatic potential map clearly provides the insights in to its interacting feature. Appendix A describes the experimental and theoretical charge density studies in 1-formyl-3-thiosemicarbazide and the assessment of five varieties of hydrogen bonds.

We perform microscopic mean-field studies of topological order in a two-dimensional topological superconductor in the Bogoliubov-de Gennes (BdG) formalism. By adopting a two-dimensional s-wave topological superconductivity (TSC) model on a minimal tight-binding system, we solve the BdG equations self-consistently to obtain not only the superconducting order parameter, but also the Hartree potential. By computing the Thouless, Kohmoto, Nightingale, and den Nijs (TKNN) number and investigating the bulk-boundary correspondence, we study the nature of Abelian and non-Abelian TSC in terms of self-consistent solutions to the BdG equations. In particular, we examine the effects of temperature and a single non-magnetic impurity deposited in the centre of the system and how they vary depending on topology. We find that the non-Abelian phase exhibits signs of unconventional superconductivity, and by examining the behaviour of this phase under both low and high Zeeman field conditions, we show that the magnitude of the Zeeman field largely dictates the susceptibility of the system to temperature. Furthermore, we investigate the possible interplay of charge density waves (CDW) and TSC. By self-consistently solving for the mean fields, we show that TSC and topological CDW are degenerate ground states---with the same excitation spectrum in the presence of surfaces---and thus can coexist in the Abelian phase. The effects of a non-magnetic impurity, which tends to pin the phase of charge density modulations, are examined in the context of topological CDW.

Thesis (MSc)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: Trilayered transition metal dichalcogenides such as our sample (1T-TiSe2) have been studied for many years as systems with strong electron-electron and electron-phonon correlations. The main attraction to this family of compound is its potential to exhibit ground state phenomena known as charge density waves whose detailed physical origin has been controversially determined. In this study, we have used an ultrafast femtosecond laser based on a pump-probe technique, namely ultrafast electron diffraction, to investigate these exotic features associated with the crystal. A pump laser pulse photo-excites the crystal from its ground state and the probe pulse (ultrashort electron pulse) takes the snapshot of the evolution of the lattice generating an electron diffraction pattern of the crystal. Hence the dynamical structural behaviour can be observed in time with a subpicosecond temporal resolution. As a hexagonal close-packed structure, its signature is expected to be seen in the diffraction pattern in both a steady-state and electron time-resolved femtosecond electron diffraction. In addition, simulations of electron diffractions pattern for room and low temperature structural data via a software called Simulation and Analysis of Electron diffraction (SAED) have been carried out. Clear signatures of charge density waves were seen at low temperature. / AFRIKAANSE OPSOMMING: Drie-laag oorgangsmetaal dikhalkogeniedes soos ons voorbeeld (1T-TiSe2), word reeds vir baie jare bestudeer as sisteme met sterk elektron-elektron en elektron-fonon korrelasies. Die hoof aantrekkingskrag van hierdie sisteme is die verskynsel van ladingdigtheidsgolwe in die grondtoestand. Die fisiese oorsprong van hierdie ladingdigtheidsgolwe was bepaal te midde van verskeie teenstrydighede. In hierdie studie, maak ons gebruik van die ultravinnige femtosekonde laser gebaseerde aktiveer-interogeer tegniek, genaamd ultravinnige elektron diffraksie (UED) om unicke eienskappe wat met die kristal geassosieer is te bestudeer. In UED wek ’n ultravinnige laserpuls (aktivering) die kristal op vanaf die grondtoestand waartydens n ultravinnige elektronpuls (interogering) ’n foto neem van die evolusie van die elektron diffraksiepatroon wat deur die kristalrooster gegenereer word. Hierdie wisselwerking van die interogerings elektronpuls en die sisteem kan gevolglik teen verskeie vasgetelde tye toegelaat word. Dus kan die dinamiese strukturele gedrag waargeneem word met ’n tydresolusie in die orde van die elektronpuls (sub-pikosekondes). Siende dat die kristal ’n diggepakte-heksagonale struktuur vorm, behoort die kenmerkende diffraksiepatroon daarvan waarneembaar te wees in beide die bestendige diffraksie en femtosekonde elektron diffraksie tegnieke. In hierdie konteks was duidelike tekens van ladingdigtheidsgolwe waargeneem. Benewens was daar ook simulasies uitgevoer om die elektron diffraksiepatrone asook die strukturele data by kamer en lae temperature vas te pen. Die sagteware wat hiervoor gebruik word is genaamd Simulasie en Ontleding van Elektronendiffraksie (SAED) - Simulation and Analysis of Electron Diffraction (SAED).

We have studied the charge density wave (CDW) repolarization dynamics in blue bronze (K0.3MoO3) by applying symmetric bipolar square-wave voltages of different frequencies to the sample and measuring the changes in infrared transmittance, proportional to CDW strain. The frequency dependence of the electro-transmittance was fit to a modified harmonic oscillator response and the evolution of the parameters as functions of voltage, position, and temperature are discussed. We found that resonance frequencies decrease with distance from the current contacts, indicating that the resulting delays are intrinsic to the CDW with the strain effectively flowing from the contact. For a fixed position, the average relaxation time for most samples has a voltage dependence given by τ0 ∼ V −p, with 1 < p < 2. The temperature dependence of the fitting parameters shows that the dynamics are governed by both the force on the CDW and the CDW current: for a given force and position, both the relaxation and delay times are inversely proportional to the CDW current as temperature is varied. The long delay times (∼ 100 μs) for large CDW currents suggest that the strain response involves the motion of macroscopic objects, presumably CDW phase dislocation lines. We have done frequency domain simulations to study charge-density-wave (CDW) polarization dynamics when symmetric bipolar square current pulses of different frequencies and amplitudes are applied to the sample, using parameters appropriate for NbSe3 at T = 90 K. The frequency dependence of the strain at one fixed position was fit to the same modified harmonic oscillator response and the behavior of the parameters as functions of current and position are discussed. Delay times increase nonlinearly with distance from the current contacts again, indicating that these are intrinsic to the CDWwith the strain effectively flowing from the contact. For a fixed position and high currents the relaxation time increases with decreasing current, but for low currents its behavior is strongly dependent on the distance between the current contact and the sample ends. This fact clearly shows the effect of the phase-slip process needed in the current conversion process at the contacts. The relaxation and delay times computed (∼ 1 μs) are much shorter than observed in blue bronze (> 100 μs), as expected because NbSe3 is metallic whereas K0.3MoO3 is semiconducting. While our simulated results bear a qualitative resemblance with those obtained in blue bronze, we can not make a quantitative comparison with the K0.3MoO3 results since the CDW in our simulations is current driven, whereas the electro-optic experiment was voltage driven. Different theoretical models predict that for voltages near the threshold Von, quantities such as the dynamic phase velocity correlation length and CDW velocity vary as ξ ∼ |V/Von − 1| −ν and v ∼ |V/Von − 1|ξ with ν ∼ 1/2 and ζ = 5/6. Additionally, a weakly divergent behavior for the diffusion constant D ∼ |V/Von − 1|−2ν+ζ is expected. Motivated by these premises and the fact that no convincing experimental evidence is known, we carried out measurements of the parameters that govern the CDW repolarization dynamic for voltages near threshold. We found that for most temperatures considered the relaxation time still increases for voltages as small as 1.06Von indicating that the CDW is still in the plastic and presumably in the noncritical limit. However, at one temperature we found that the relaxation time saturates with no indication of critical behavior, giving a new upper limit to the critical regime, of |V/Von − 1| < 0.06.

Electrospinning is a method of producing nano structured material from a polymer solution or melt using high strength electric fields. It is a process that has yet to find extensive industrial application yet shows promise if obstacles such as low rate of production overcome perhaps by more complete theoretical modelling. This work examines the effects of adding an ionic salt to a solution of poly(vinyl alcohol) in water. The direct effect was an increase the charge density and electric current. It was found that an increase in charge density decreases the mass deposition rate and forms a thinner initial jet. When the sign of the charge on the polymer solution was changed from positive to negative the charge density increased and the initial jet diameter and mass deposition rate also decreased. It was proposed that a smaller radius of curvature is formed by the Taylor cone at higher charge densities resulting in a smaller “virtual orifice”. The extent of the bending instability was explored and it was found that adding ionic salt results in a decrease in the bending instability resulting in thicker fibres. Changing the sign of the charge on the polymer solution from positive to negative resulted in an increase in the bending instability and resulted in thinner fibres. The charge transfer mechanisms used in different electrospinning models are explored and some assumptions not explicitly stated are discussed. From this discussion a generalized equation describing the charge transport mechanisms is proposed.

Graphene, the world's first truly two-dimensional material, is unique for having an electronic structure described by an effective Lorentz invariant theory. One important consequence is that the ratio or Coulomb energy to kinetic energy is a constant, depending only on conditions within the lattice rather than on the average charge density as in a typical Galilean invariant material. Given this unusual property, a natural question would be how do phenomena, such as screening of a Coulomb impurity, happen in graphene? Moreover, how does the addition of uniaxial strain enhance or diminish this behavior? Here I discuss our work to calculate the charge density distribution in a lattice of strained graphene under the effect of an external Coulomb impurity. Graphene can have its band structure significantly altered by the application of uniaxial strain. Two cases are here explored: relatively weak strain at some finite chemical potential, and extreme strain with zero chemical potential. In the first system, the strain induces elliptic Dirac cones, engendering some inherent directionality to graphene's electronic properties that did not exist before. This anisotropy manifests itself in the polarization function, and so too in the screening charge density. A finite chemical potential in this case is necessary for any screening to take place in graphene since, without it, there are no electron states near the Fermi level to polarize. Both in the strained and unstrained case, decaying oscillations known as Friedel oscillations are observed. The result of strain is a multifaceted anisotropy of the charge distribution: the amplitude, frequency, and the position of the first peak in the oscillations are each varied depending on the direction one observes. In the second system, extreme strain in graphene leads to a merging of Dirac cones, yielding a transition to a new energy spectrum. This band structure is unusual in that it becomes quadratic along the direction of strain while remaining linear along the perpendicular. We evaluate the screening response to a Coulomb impurity in this case at zero chemical potential, and yet long-range distribution tails are still observed. The result is a very exotic charge distribution, in which the radial distribution of charge and the angular distribution are highly coupled, and at various distances, both screening and anti-screening regions are observed around the impurity. The anti-screening regions are local, and the net induced charge density still satisfies the accepted model of screening.

Gossypol and gossypol derivatives are natural byproducts of a variety of cotton plant species that poses interesting chemical, biological, and medicinal properties that are currently heavily researched. Supporting evidence suggest that gossypol and gossypol derivatives act on the Bcl-2 proteins that have been linked to certain cancers. Gossypol amine derivatives, specifically, are actively researched and a variety of amine derivatives have already been synthesized. However, gossypol and its derivatives are challenging compounds to work with because many of its derivatives tend to exist in various tautomeric forms. When analyzing gossypol and its derivatives it is the complex electron configuration that dictates the chemical mechanism and biological activity. The following research provides a charge density study that describes in detail the electronic configuration via Bader's topological analysis of di(methoxy)gossypol and di(propylamino) gossypol. In addition, a series of crystallographic studies of gossypol amine derivatives and di(methoxy)gossypol are also analyzed.