We study the unusual phases seen in charge transfer salts (CTS) at 1/2 and 1/4 filling. We use the Holstein-Hubbard model (HHM) and the Peierls extended Hubbard model (PEH) to study competing phases in CTS. In the 1/2illed HHM the Holstein coupling promotes a Peierls charge-density wave phase while the on-site Coulomb repulsion U gives rise to antiferromagnetic correlations and a Mott insulating state. Takada et al. have shown possibility of a third metallic phase between the Mott and the Peierls phase. We investigate the presence of an intermediate phase between the Mott and Peierls phase using Stochastic Series Expansion (SSE) method. We used charge and spin susceptibilities to determine the phase boundaries. As the coupling is increased a spin gap opens followed by the Peierls transition. The intermediate phase is metallic and has a spin gap but no charge gap. Transitions from the Mott to intermediate and intermediate to Peierls state are Kosterlitz-Thouless type (KT). As the coulomb repulsion is increaed beyond certain value the two KT transitions fuse to give a single first order transition. Similar behavior is seen at 1/4illed HHM. We also studied the temperature dependence of charge ordering (CO) in 1/4illed CTS. Most previous theoretical studies of the on CTS have concentrated on ground state or T=0 properties. Here we show the evolution of charge ordered (CO) state with temperature and directly related the experimental phase diagram with our theoretical results. Our calculations show that as temperature is lowered the Wigner crystal state gives way to spin-Peierls state with a different pattern of CO. Also we show that the critical value of nearest neighbor Coulomb repulsion is depends on the total spin and is different for different spin subspace.

No description available.

No description available.

A Kondo lattice Hamiltonian for arbitrary total angular momentum J is formulated using a pseudofermion representation and without addition of RKKY interaction terms. An Hartree-Fock treatment is applied, and both variational and Green's function methods are used to calculate physical quantities from the linearized Hamiltonian. The Kondo phase is represented by finite hybridization. Magnetic ordering is examined via ordering vectors, but coexistence with the Kondo phase is not allowed. Phase diagrams are produced in S=1/2 and J=3/2 with second-order transitions at Kondo-paramagnetic and magnetic-paramagnetic boundaries, and first order transitions between Kondo and magnetic phases. Various coupling strengths are explored. Magnetic phases found include antiferromagnetism, ferromagnetism, and spin-density wave ordering of both commensurate and incommensurate varieties. In S=1/2, the magnetic phase exhibits a spike in critical temperature at half-filling. In J=3/2, the Kondo phase is reentrant at weaker coupling but not at stronger coupling. / Physics

An investigation of electrochemical storage device materials has been undertaken in four parts. The bulk and interfacial resistance of Na+ beta-alumina tubes were separated using a galvanostatic charge-discharge method. Sodium silicide was characterized to better understand its synthesis. BiMn2O5 was produced using a sol-gel method and tested for pseudocapacity. Different lithium ion anode and cathode materials were deposited using a new electrophoretic deposition method. A novel galvanostatic charge-discharge method was developed for the determination of bulk and interface resistance in Na+ beta-alumina solid electrolytes [BASE]. Dense and duplex BASE tubes were tested by varying the exposed surface area. The results of dense BASE tube pairs were used to determine the bulk and interfacial resistance components, while duplex BASE tubes were tested to determine the reduction in interfacial resistance. It was found that duplex tubes had reduced the interfacial resistance by 75%, when compared to a uniformly dense electrolyte. Sodium silicide was characterized using various methods to better understand the phase and the Na-Si phase diagram. EMF experiments using Na+ BASE tubes was used to determine the activity in the silicon rich region of the phase diagram, which showed a sodium activity of 0.5 at 550°C. TGA/DSC was used to determine phase transformation temperatures, as well as the heat of formation for NaSi, which was recorded to be below 1 kJ mol-1. A sol-gel precipitation method was used to produce fine BiMn2O5 powders used for supercapacitors. The powders resulting from a consistent method were tested for pseudocapacitance using bulk and thin film electrodes. Bulk electrodes had a gravimetric capacitance of 10 F g-1, while thin film electrodes only reached 2.6 F g-1. Lithium ion battery anode (Li4Ti5O12) and cathode (LiFePO4, LiMn2O4, LiMn1.5Ni0.5O4) materials were electrophoretically deposited with the assistance of PAZO-Na and CMC-Na. Cathodes were successfully deposited on aluminium substrates, and were tested in the potential window 2 – 4.3 V. The LiFePO4 cathodes showed capacity of 146.7 mAh g-1 at C/10, while showing capacity retention of 103% after 50 cycles. / Thesis / Doctor of Philosophy (PhD) / The goal of this work is to examine materials used in different types of electrochemical storage devices. The modification of resistive properties of β-alumina electrolytes are examined for use in high temperature sodium batteries. Electrophoretic deposition methods are used to rapidly make thin electrodes for lithium ion batteries and supercapacitors. The stoichiometric compound NaSi, a potentially safer and greener method of producing hydrogen gas, is characterized for a better understanding of its properties, and therefore production.

The Tibetan plateau is a vast, elevated region located in central Asia, which is underlain by the thickest crust known on Earth (up to 90 km). An outstanding question of importance to many fields within geology is how and why did the Tibetan plateau form? Models attribute the growth of the plateau to a consequence of the ongoing India-Asia continental collision, but differ in the details of how the crustal thickening was accommodated: was it by underplating of Indian lower crust or by homogeneous shortening? High-grade metamorphic rocks sampled from the region potentially hold the key to answering this question, as they contain a record of past tectonic events that can discriminate between the various proposed models. This record can be decoded by integrating field, thermobarometric and geochronological techniques, to elucidate a detailed thermotectonic understanding of a region. This methodology was applied to three case studies, each of which targeted rare tectonic windows into the mid-crust of the plateau. These regions comprise Danba in eastern Tibet, Basong Tso in south-eastern Tibet and the Western Nyainqentanglha in southern Tibet. Each case study documents previously unreported metamorphic events that have allowed original interpretations to be made regarding tectonic evolution: in Danba, all metamorphism is shown to be early Jurassic; in Basong Tso, two metamorphic belts are documented that reveal a late Triassic--early Jurassic orogenic event; and in the Western Nyainqengtanglha, Cretaceous--Neogene magmatism is shown to overprint late Triassic metamorphism. Integration of the results has enabled commentary on the large scale evolution of the Tibetan plateau from the Permian until the present day, and even hinted at its future. The results indicate that the closure of the Paleotethys played an important role in the construction of the Tibetan plateau, and suggest that homogeneous crustal thickening is not a viable model for the documented exposure levels.

There has been very little research into the bioanalytical application of Microemulsion High Performance Liquid Chromatography (MELC), a recently established technique for separating an active pharmaceutical ingredient from its related substances and for determining the quantity of active drug in a dose. Also, the technique is not good at separating hydrophilic drugs of very similar chemical structures. Different phase diagrams of oil (octane or ethyl acetate), co-surfactant (butanol), surfactant (sodium dodecyl sulphate (SDS) or Brij-35) and buffer (Phosphate pH 3) were developed and several nanoemulsion mobile phases identified. Nanoemulsion mobile phase that is, prepared with SDS, octane, butanol and a phosphate buffer, failed to separate hydrophilic compounds with a very close chemical structure, such as terbutaline and salbutamol. A nanoemulsion mobile phase containing a non-ionic surfactant (Brij-35) with ethyl acetate, butanol and a phosphate buffer, was, however, successful in achieving a base line separation, and the method was validated for simultaneous determination of terbutaline and salbutamol in aqueous and urine samples. An oil-in-water (O/W) NELC method was developed and validated for the determination of formoterol in an Oxis® Turbuhaler® using pre-column fluorescence derivatisation. Although the same mobile phase was extended for separation of formoterol in urine, the formoterol peak's overlap with endogenous peaks meant that fluorescence detection could not determine formoterol in urine samples. Solid phase extraction, concentrating the final analyte 40 times, enabled determination of a low concentration of formoterol in urine samples by UV detection. The method was validated and an acceptable assay precision %CV <4.89 inter-day and %CV <2.33 intra-day was achieved. Then after the application of O/W nanoemulsion mobile phase for HPLC was extended for the separation of lipophilic drugs. The nanoemulsion liquid chromatography (NELC) method was optimised for the determination of salmeterol and fluticasone propionate in good validation data was achieved. This thesis shows that, in general, the performance of O/W NELC is superior to that of conventional High Performance Liquid Chromatography (HPLC) for the analysis of both hydrophilic and lipophilic drugs in inhaled dosage formulations and urine samples. It has been shown that NELC uses cheaper solvents and that analysis time is faster for aqueous and urine samples. This considerable saving in both cost and time will potentially improve efficiency within quality control.

Crystal Engineering is the design of crystalline material using non-covalent synthesis. Co-crystals are multi-component crystals which are constructed from complementary intermolecular interactions, they are also known as supramolecular complexes. Design of such materials utilises the synthon approach, this involves the understanding of common intermolecular interactions which occur in the crystal packing and is used to design new solids with desired physical properties and chemical properties. Primary amides form supramolecular heterosynthons, these synthons represent an opportunity for a design of multi-component crystals in which one molecule contains a primary amide and a second molecule which is complimentary to the primary amide, usually carboxylic acids. The progress with regards to the screening process for the determination of co-crystals is evident in the literature, In particular, high throughput solution growth methods and solvent drop grinding. The comparison of Isonicotinamide and Benzamide as a co-crystal component has been presented. This study was motivated by the observation that the CSD contains 24 Isonicotinamide and 1 Benzamide co-crystal. The interaction with carboxylic acids is the focus of the work, in particular those which form Isonicotinamide co-crystal are being screened with Benzamide. Our work utilises a ReactArray Microvate to carry out the low throughput solution growth on a matrix of carboxylic acid with Benzamide, this study has been coupled with the Kofler hot stage microscope method which visually aids to screen and view co-crystal phase formation. Crystallisation screens have resulted in the identification of known co-crystal phases of Isonicotinamide and Benzamide, additionally new co-crystal phases have also been identified with Fumaric, 3-hydroxybenzoic acid, Mandelic Acid, 4-Nitrobenzoic Acid and Tartaric Acid. Single crystal structures of the Fumaric and 4-Nitrobenzoic acid have been obtained. In order to develop an understanding of co-crystal formation in Isonicotinamide and Benzamide with our supramolecular library, packing landscape analysis is being undertaken using both the CSD and crystal structures we have obtained. This is undertaken as collaboration with Dr Andy Parkin and Professor Gilmore (University of Glasgow), we have identified that the dSNAP analysis is a way forward for the analysis of how co-crystals pack. The analysis highlighted the subtleties that were present in the packing motifs of the Isonicotinamide co-crystals. In particular the cis and trans orientation of the amide and acid carbonyl to each other and the planar and off planar layer assemblies. All of which are required to maximise the hydrogen bond usage of the components comprising the co-crystals. Further investigations have led to the collaborative project with Syngenta Ltd in the design of a co-crystal screen using a high through-put robot, Crissy® -Automation Platform by Zinsser Analytical, using an extended screen of 16 acid coformers with Isonicotinamide, Benzamide and Nicotinamide the sample have been characterised using a reflectance diffraction method, GADDS. Further analysis of this data involves the use of polySNAP, which has led to further collaboration with Professor Gilmore's group.

La2Mo2-yWyO9 (y = 1.0 to 2.0) oxides were synthesized by conventional solid state route and studied by XRD, TC-XRD and DTA. A phase diagram of the series was proposed. The thermodynamically stable phases at room temperature are: for 1.0≤ y ≤1.2 a cubic β-La2Mo2O9 type solid solution, for 1.3≤ y ≤1.575 a biphasic mixture of β-La2Mo2O9 type + α-La2W2O9 type phases, and for 1.6≤ y ≤2.0 a triclinic α-La2W2O9 type solid solution. Inhomogeneous distribution of W is suspected in the biphasic samples. It is clear that the compounds above y =1.2 are not suitable for SOFC applications.Cationic diffusion studies were performed using SIMS on La2Mo2O9 (LMO)/La0.8Sr0.2MnO3-δ (LSM) annealed couples. Rod shaped LaMnO3 grains were observed on LMO pellet and SrMoO4 type phases were seen to be growing on LSM pellet. Hypotheses for possible reaction mechanisms are presented. Bulk diffusion coefficients of Sr and Mn in LMO and of Mo in LSM are extrapolated to be around 1x10-20 cm2.s-1 and 1x10-15 cm2.s-1, respectively, at 800oC. Similar diffusion studies were performed by depositing Mn and Sr cation rich solutions on LMO pellets and Mo rich solution on LSM pellet. Mn solution was observed to be forming, upon annealing, LaMnO3 single crystals on the surface of the LMO pellet. Mo in LSM and Sr in LMO diffusion coefficients appear to be much higher than in LMO/LSM couple experiments, namely around 1-2x10-10cm2.s-1 at 1150°C. Because of the reactivity, LMO/LSM couple is not desirable for SOFC applications, unless an appropriate buffer layer separates them.The stability of LMO and W-LMO was studied under reductive atmospheres. Successive structural changes from LMO to La7Mo7O30 (7730), an amorphous reduced phase La2Mo2O7-δ, and partial decomposition to metallic Mo were observed as a function of oxygen loss. The pO2 stability domain of La2Mo2-yWyO9 did not appear to change with W content, but the reduction kinetics varied with y. At reverse, the stability limit of the 7730 phase was found to be dependent on W content. The amorphous reduced phase can accommodate a wide range of oxygen stoichiometry (7-δ from 6.69 to 6.20), but its stability vs. pO2 is questioned. Resistivity measurements performed on a low compacity crack-free amorphous La2Mo2O7-δ sample showed significant increase in the conductivity (> 1 S.cm-1 at 1000 K) relative to La2Mo2O9, with a pseudo activation energy 0.255eV. It is postulated that n-type electronic conductivity arises from partial reduction of hexavalent Mo6+ to a mixture of Mo3+ and Mo4+.

Condensed matter physics is a rapidly evolving field of research enriched with the synthesis of new materials exhibiting a bewildering variety of phenomena and advances in experimental techniques. Over the years, discoveries and innovations in electronic systems have emphasized the crucial role played by correlations among electrons behind many of the observed unusual properties and have posed serious challenges to the physics community by exposing the lack of well-controlled theoretical methods to study the class of materials known as strongly correlated electronic systems. In these systems, known theoretical techniques typically fail to capture the essential features of the many-body ground state and finite temperature properties of the systems as typical electronic interaction energies are of order of or larger than the kinetic energies. The study of strongly correlated electronic systems went through a revolution in the 1980s and 1990s after the discovery of superconductivity inorganic compounds, in heavy fermion systems and ultimately in copper oxides, referred to as cuprates, by Bednorz and Muller. In particular, the pursuit of understanding the mysterious origin of superconductivity in the cuprates and other associated strange phenomena has fascinated the condensed matter community over last two and half decades leading to most of the important unsolved, and probably interconnected, problems of quantum condensed matter physics such as the metal-insulator transition in low dimensions breakdown of Fermi liquid theory, the origin and behavior of unconventional superconductivity, quantum critical points, electronic in homogeneities and localization in interacting systems. This thesis is devoted to the study of some of the aspects of high-temperature superconductivity and associated phenomena in cuprates. In what follows, I give an overview of the organization of the thesis in to different chapters and their contents. For setting up the stage, in Chapter 1, I give a brief account of some of the remarkable phenomena and properties observed in strongly correlated electronic matter and their salient features, that continue to draw much attention and excitement in current times. The peculiarity of the state of affairs in these systems is emphasized and motivated in the background of the paradigmatic Landau Fermi liquid theory and Hubbard model, the minimal model that is expected to capture the quintessence of electronic strong correlation. In Chapter 2, starting with a brief historical account of the discovery of superconductivity in cuprates, the crystal structure of these materials, their chemical realities and basic electronic details are reviewed. This is followed by a survey of the phase diagram of cuprates, doped with, say, x number of holes per copper site, and a plethora of experimental findings that constitute the high-c puzzle. Characteristics of various observed phases, such as the superconducting, pseudo gap and strange metal phases, are discussed on the basis off acts accumulated through various experimental probes, e.g. nuclear magnetic resonance(NMR), neutron scattering, specific heat, transport and optical conductivity measurements as well as photo emission, tunnelling and Raman spectroscopies. As elucidated, these experiments point toward the need for an unconventional mechanism of superconductivity in cuprates and, more so, for the description of the rather abnormal high-temperature normal state that is realized above the superconducting transition temperature c. Keeping in mind the fact that there is no consensus even about the minimal microscopic electronic model, I review two models, namely the three band model and the t - J model; various approximate treatments of these models have dominated the theoretical developments in this field. A large number of theoretical pictures have been proposed based on different microscopic, semi-microscopic and phenomenological approaches in the past two decades for explaining the genesis of the observed strange phenomena in high-c cuprates. I include brief discussions on only a few of them while citing relevant references. As mentioned above, a variety of approximate microscopic theories, based on both strong and weak coupling approaches, as well as numerical techniques have been tried to understand the cuprate phase diagram and capture the aspects of strong correlations in-built in Hubbard and t -J models. On the other hand, in conventional superconductors and, in general, for the study of phase transitions, phenomenological Ginzburg-Landau(GL) functionals written down from very general symmetry grounds have provided useful description for a variety of systems. Specially, Ginzburg-Landau theory has been proven to be complementary to the BCS theory for attacking a plethora of situations in superconductors, e.g., in homogeneities, structures of an isolated vortex and the vortex lattice etc. The GL functional has found wide applicability for the study of vortex matter in high-c superconductors as well. Inspired by the success of this type of phenomenological route, we propose and develop in Chapter 3 an approach, analogous in spirit to that of Ginzburg and Landau, for the superconducting and pseudogap phases of cuprates. We encompass a large number of well known phenomenologies of cuprate superconductivity in the form of a low-energy effective lattice functional of complex spin-singlet pair amplitudes with magnitude Δm and phase m, i.e. m =Δm exp(i m), that resides on the Cu-Cubonds(indexed by m)of the CuO2 planes of cuprates. The functional respects general symmetry requirements, e.g. the -wave symmetry of the superconducting order parameter as found in experiments. The assumptions and the specific physical picture behind such an approach as well as the key empirical inputs that go into it are discussed in this chapter. We calculate the superconducting transition temperature c and the average magnitude of the local pair amplitude, Δ= (Δm), using single-site mean-field theory for the model. We show that this approximation leads to general features of the doping-temperature(x - T )phase diagram in agreement with experiment. In particular, we find a phase coherent superconducting state with d-wave symmetry below a parabolic Tc (x) dome and a phase incoherent state with a perceptible local gap that persists up to a temperature around which can be thought of as a measure of the pseudogap temperature scale T* . Further, effects of thermal fluctuations beyond the mean-field level are captured via Monte Carlo(MC) simulations of the model for a finite two-dimensional (2D) lattice. We exhibit results for Tc obtained from MC simulations as well as that estimated in a cluster mean field approximation. Based on our picture we remark on contrasting scenarios proposed for the doping dependence of the pseudogap temperature. Chapter 4 describes fluctuation phenomena related to pairing degrees of freedom and manifestations of these effects in various quantities of interest, e.g. superfluid density, specific heat etc., at finite temperature. Fluctuation effects have been studied in detail in superconductors over the years and pursued mainly using either the conventional GL functional or the BCS-framework at a microscopic level. However, the picture, in which the pseudogap phase is viewed as one consisting of bond-pairs with a d-wave symmetry correlation length growing as T approaches Tc, implies fluctuation phenomena of quite a different kind, as we discuss here. The contribution of the bond-pair degrees of freedom to thermal properties is obtained here from the lattice free-energy functional using MC simulation, as mentioned in the preceding paragraph. The results for the superfluid density or superfluid stiffness ps, a quantity measured e.g. via the penetration depth, are discussed. As shown, its doping and temperature dependence compare well with experimental results. In this chapter, I also report the calculation of the fluctuation specific heat Cv(T) and find that there are two peaks in its temperature dependence, a sharp one connected with Tc (ordering of the phase of m)and a relatively broad one(hump)connected to T* (rapid growth of the magnitude of Δm). The former is specially sensitive to the presence of a magnetic field, as we find in agreement with experiment. Vortices are relevant excitations in a superconductor and, in particular, in 2D orquasi-2D systems vortices influence the finite temperature properties in a major way. The results for the temperature dependence of vortex density obtained in the MC simulation of the GL-like model are also mentioned in Chapter 4. I report an estimate of the correlation length as well. These results might have relevance for the large Nernst signal observed over a broad temperature range above c in cuprates, as pointed out there. Properties of an isolated vortex and collective effects arising due to interaction between vortices are of much significance for understanding mixed state of type-II superconductors and thus of cuprates. The superconducting order is destroyed in the core region around the centre of a vortex and the vortex core carries signatures of the normal state in a temperature regime where it is generally unattainable due to occurrence of superconductivity. As mentioned in Chapter 5, vortex properties(e.g. electronic excitation spectrum at the vortex core) in BCS superconductors have been explored theoretically, at a microscopic level through the Bogoliubov-deGennes(BdG) theory as well as using the Ginzburg-Landau functional. However, properties of vortices in cuprate superconductors have been found to be much more unusual than could possibly be captured by straightforward extensions of BCS theory to a -wave symmetry case. Chapter 5 briefly reviews the experimental findings on vortices in the superconducting state of cuprates, mainly as probed by Scanning Tunnelling Microscopy(STM) as well as from other probes such as NMR, neutron scattering, SR etc. I discuss some of the consequences of our GL-like functional regarding vortex properties, namely that of the vortex core and the region around it. We use our model to find Δm and m at different sites m for a 2π vortex whose core is at the midpoint of a square plaquette of Cu lattice sites. The vortex is found to change character from being primarily a phase or Josephson vortex for small x to a more BCS-like or Abrikosov vortex with a large diminution in the magnitude Δm as one approaches the vortex core, for large . Here I do not make any direct comparison with experimental data but discuss implications of our results in the background of existing experimental facts. Unravelling the mysteries of high-Tc cuprates should necessarily involve the understanding of electronic excitations over a broad regime of doping and temperature encompassing the pseudo gap, superconducting and strange metal states. A phenomenological theory which aims to describe the pseudo gap phase as one consisting of preformed bond-pairs, is required to include both unpaired electrons and Cooper pairs of the same electrons coexisting and necessarily coupled with each other. In our Ginzburg Landau approach only the latter are explicit, while the former are integrated out. However, effects connected with the pair degrees of freedom are often investigated via their coupling to electrons, one very prominent examples being Angle Resolved Photoemmision Spectroscopy(ARPES),in which the momentum and energy spectrum of electrons ejected from the metal impinged by photons is investigated. In Chapter 6, we develop a unified theory of electronic excitations in the superconducting and pseudo gap phases using a model of electrons quantum mechanically coupled to spatially and temporally fluctuating Cooper pairs(the nearest neighbour singlet bond pairs). We discuss the theory and a number of its predictions which seem to be in good agreement with high resolution ARPES measurements, which have uncovered a number of unusual spectral properties of electrons near the Fermi energy with definite in-plane momenta. We show here that the spectral function of electrons with momentum ranging over the putative Fermi surface(recovered at high temperatures above the pseudogap temperature scale) is strongly affected by their coupling to Cooper pairs. On approaching Tc i.e. the temperature at which the Cooper pair phase stiffness becomes nonzero, the inevitable coupling of electrons with long-wavelength(d-wave symmetry) phase fluctuations leads to the observed characteristic low-energy behavior as reported in Chapter 6. Collective d-wave symmetry superconducting correlations develop among the pairs with a characteristic correlation length ξ which diverges on approaching the continuous transition temperature Tc from above. These correlations have a generic form for distances much larger than the lattice spacing. As we show here, the effect of these correlations on the electrons leads, for example, to a pseudogap in electronic density of states for T > T c persisting till T* , temperature-dependent Fermi arcs i.e. regions on the Fermi surface where the quasiparticle spectral density is non zero for a zero energy excitation and to the filling of the antinodal pseudogap in the manner observed. Further, the observed long-range order(LRO) below c leads to a sharp antinodal spectral feature related to the non zero superfluid density, and thermal pair fluctuations cause a deviation(‘bending’) of the inferred ‘gap’ as a function of k from the expected d-wave form (cos kxa - cos kya). The bending, being of thermal origin, decreases with decreasing temperature, in agreement with recent ARPES measurements. I conclude in Chapter 7 by mentioning some natural directions in which the functional and the approach used here could be taken forward. The phenomenological theory proposed and developed in this thesis reconciles and ties together a range of cuprate superconductivity phenomena qualitatively and confronts them quantitatively with experiment. The results, and their agreement with a large body of experimental findings, strongly support the mechanism based on nearest neighbor Cooper pairs, and emergence of long-range -wave symmetry order as a collective effect arising from short range interaction between these pairs. This probably points to the way in which high-c superconductivity will be understood.