Impurity scattering in a Luttinger liquid with electron-phonon coupling

We study the influence of electron-phonon coupling on electron transport through a Luttinger liquid with an embedded weak scatterer or weak link. We derive the renormalization group (RG) equations, which indicate that the directions of RG flows can change upon varying either the relative strength of the electron-electron and electron-phonon coupling or the ratio of Fermi to sound velocities. This results in a rich phase diagram with up to three fixed points: an unstable one with a finite value of conductance and two stable ones, corresponding to an ideal metal or insulator.

Quantum wire hybridized with a single-level impurity

We have studied low-temperature properties of interacting electrons in a one-dimensional quantum wire (Luttinger liquid) side-hybridized with a single-level impurity. The hybridization induces a backscattering of electrons in the wire which strongly affects its low-energy properties. Using a one-loop renormalization group approach valid for a weak electron-electron interaction, we have calculated a transmission coefficient through the wire, T(epsilon), and a local density of states, nu(epsilon) at low energies epsilon. In particular, we have found that the antiresonance in T(epsilon) has a generalized Breit-Wigner shape with the effective width Gamma(epsilon) which diverges at the Fermi level.

Impurity scattering in Luttinger liquid with electron-phonon coupling

We study the influence of electron-phonon coupling on electron transport through a Luttinger liquid with an embedded weak scatterer or weak link. We derive the renormalization group (RG) equations which indicate that the directions of RG flows can change upon varying either the relative strength of the electron-electron and electron-phonon coupling or the ratio of Fermi to sound velocities. This results in the rich phase diagram with up to three fixed points: an unstable one with a finite value of conductance and two stable ones, corresponding to an ideal metal or insulator.

Seminar 1 impurity in the tomonaga-luttinger model:a functional integral approach

This chapter explains a functional integral approach about impurity in the Tomonaga–Luttinger model. The Tomonaga–Luttinger model of one-dimensional (1D) strongly correlates electrons gives a striking example of non-Fermi-liquid behavior. For simplicity, the chapter considers only a single-mode Tomonaga–Luttinger model, with one species of right- and left-moving electrons, thus, omitting spin indices and considering eventually the simplest linearized model of a single-valley parabolic electron band. The standard operator bosonization is one of the most elegant methods developed in theoretical physics. The main advantage of the bosonization, either in standard or functional form, is that including the quadric electron–electron interaction does not substantially change the free action. The chapter demonstrates the way to develop the formalism of bosonization based on the functional integral representation of observable quantities within the Keldysh formalism.

Functional integral bosonization for an impurity in a Luttinger liquid

We use a functional integral formalism developed earlier for the pure Luttinger liquid (LL) to find an exact representation for the electron Green function of the LL in the presence of a single backscattering impurity in the low-temperature limit. This allows us to reproduce results (well known from the bosonization techniques) for the suppression of the electron local density of states (LDOS) at the position of the impurity and for the Friedel oscillations at finite temperature. In addition, we have extracted from the exact representation an analytic dependence of LDOS on the distance from the impurity and shown how it crosses over to that for the pure LL.

Effect of methane concentration in hydrogen plasma on hydrogen impurity incorporation in thick large-grained polycrystalline diamond films

We investigate the impact of methane concentration in hydrogen plasma on the growth of large-grained polycrystalline diamond (PCD) films and its hydrogen impurity incorporation. The diamond samples were produced using high CH4 concentration in H2 plasma and high power up to 4350 W and high pressure (either 105 or 110 Torr) in a microwave plasma chemical vapor deposition (MPCVD) system. The thickness of the free-standing diamond films varies from 165 µm to 430 µm. Scanning electron microscopy (SEM), micro-Raman spectroscopy and Fourier-transform infrared (FTIR) spectroscopy were used to characterize the morphology, crystalline and optical quality of the diamond samples, and bonded hydrogen impurity in the diamond films, respectively. Under the conditions employed here, when methane concentration in the gas phase increases from 3.75% to 7.5%, the growth rate of the PCD films rises from around 3.0 µm/h up to 8.5 µm/h, and the optical active bonded hydrogen impurity content also increases more than one times, especially the two CVD diamond specific H related infrared absorption peaks at 2818 and 2828 cm−1 rise strongly; while the crystalline and optical quality of the MCD films decreases significantly, namely structural defects and non-diamond carbon phase content also increases a lot with increasing of methane concentration. Based on the results, the relationship between methane concentration and diamond growth rate and hydrogen impurity incorporation including the form of bonded infrared active hydrogen impurity in CVD diamonds was analyzed and discussed. The effect of substrate temperature on diamond growth was also briefly discussed. The experimental findings indicate that bonded hydrogen impurity in CVD diamond films mainly comes from methane rather than hydrogen in the gas source, and thus can provide experimental evidence for the theoretical study of the standard methyl species dominated growth mechanism of CVD diamonds grown with methane/hydrogen mixtures.

Impact of high microwave power on hydrogen impurity trapping in nanocrystalline diamond films grown with simultaneous nitrogen and oxygen addition into methane/hydrogen plasma

In this work, we study for the first time the influence of microwave power higher than 2.0 kW on bonded hydrogen impurity incorporation (form and content) in nanocrystalline diamond (NCD) films grown in a 5 kW MPCVD reactor. The NCD samples of different thickness ranging from 25 to 205 μm were obtained through a small amount of simultaneous nitrogen and oxygen addition into conventional about 4% methane in hydrogen reactants by keeping the other operating parameters in the same range as that typically used for the growth of large-grained polycrystalline diamond films. Specific hydrogen point defect in the NCD films is analyzed by using Fourier-transform infrared (FTIR) spectroscopy. When the other operating parameters are kept constant (mainly the input gases), with increasing of microwave power from 2.0 to 3.2 kW (the pressure was increased slightly in order to stabilize the plasma ball of the same size), which simultaneously resulting in the rise of substrate temperature more than 100 °C, the growth rate of the NCD films increases one order of magnitude from 0.3 to 3.0 μm/h, while the content of hydrogen impurity trapped in the NCD films during the growth process decreases with power. It has also been found that a new H related infrared absorption peak appears at 2834 cm-1 in the NCD films grown with a small amount of nitrogen and oxygen addition at power higher than 2.0 kW and increases with power higher than 3.0 kW. According to these new experimental results, the role of high microwave power on diamond growth and hydrogen impurity incorporation is discussed based on the standard growth mechanism of CVD diamonds using CH4/H2 gas mixtures. Our current experimental findings shed light into the incorporation mechanism of hydrogen impurity in NCD films grown with a small amount of nitrogen and oxygen addition into methane/hydrogen plasma.

Mechanisms for triggering high-voltage breakdown in vacuum

The electrical and optical characteristics of a cylindrical alumina insulator (94% Al203) have been measured under ultra-high vacuum (P < 10-8 mBar) conditions. A high-resolution CCD camera was used to make real-time optical recordings of DC prebreakdown luminescence from the ceramic, under conditions where DC current magnitudes were limited to less than 50μA. Two concentric metallized rings formed a pair of co-axial electrodes, on the end-face of the alumina tube; a third 'transparent' electrode was employed to study the effect of an orthogonal electric field upon the radial conduction processes within the metallized alumina specimen. The wavelength-spectra of the emitted light was quantified using a high-speed scanning monochromator and photo-multiplier tube detector. Concurrent electrical measurements were made alongside the recording of optical-emission images. An observed time-dependence of the photon-emission is correlated with a time-variation observed in the DC current-voltage characteristics of the alumina. Optical images were also recorded of pulsed-field surface-flashover events on the alumina ceramic. An intensified high-speed video technique provided 1ms frames of surface-flashover events, whilst 100ns frames were achieved using an ultra high-speed fast-framing camera. By coupling this fast-frame camera to a digital storage oscilloscope, it was possible to establish a temporal correlation between the application of a voltage-pulse to the ceramic and the evolution of photonic emissions from the subsequent surface-flashover event. The electro-optical DC prebreakdown characteristics of the alumina are discussed in terms of solid-state photon-emission processes, that are believed to arise from radiative electron-recombination at vacancy-defects and substitutional impurity centres within the surface-layers of the ceramic. The physical nature of vacancy-defects within an alumina dielectric is extensively explored, with a particular focus placed upon the trapped electron energy-levels that may be present at these defect centres. Finally, consideration is given to the practical application of alumina in the trigger-ceramic of a sealed triggered vacuum gap (TVG) switch. For this purpose, a physical model describing the initiation of electrical breakdown within the TVG regime is proposed, and is based upon the explosive destabilisation of trapped charge within the alumina ceramic, triggering the onset of surface-flashover along the insulator. In the main-gap prebreakdown phase, it is suggested that the electrical-breakdown of the TVG is initiated by the low-field 'stripping' of prebreakdown electrons from vacancy-defects in the ceramic under the influence of an orthogonal main-gap electric field.

The polymerization of lactic acid anhydrosulphite by anionic initiators

This thesis is primarily concerned with the synthesis and polymerization of 5-methyl-1;3, 2-dioxathiolan-4-one-2-oxide (lactic acid anhydrosulphite (LAAS)) using anionic initiators under various conditions. Poly(lactic acid) is a biodegradable polymer which finds many uses in biomedical applications such as drug-delivery and wound-support systems. For such applications it is desirable to produce polymers having predictable molecular weight distributions and crystallinity, The use of anionic initiators offers a potential route to the creation of living polymers. The synthesis of LAAS was achieved by means of an established route though the procedure was modified to some extent and a new method of purification of the monomer using copper oxides was introduced, Chromatographic purification methods were also examined but found to be ineffective. An unusual impurity was discovered in some syntheses and this was identified by means of 1H and 13C NMR, elemental analysis and GC-MS. Since poly-α-esters having hydroxyl-bearing substituents might be expected to have high equilibrium water contents and hence low surface tension characteristics which might aid bio-compatibility, synthesis of gluconic acid anhydrosulphite was also attempted and the product characterised by 1H and 13C NMR. The kinetics of the decomposition of lactic acid anhydrosulphite by lithium tert-butoxide in nitrobenzene has been examined by means of gas evolution measurements. The kinetics of the reaction with potassium tert-butoxide (and also sec-butyl lithium) in tetrahydrofuran has been studied using calorimetric techniques. LAAS was block co-polymerized with styrene and also with 1,3-butadiene in tetrahydrofuran (in the latter case a statistical co-polymer was also produced).

Chemical modification of smectite clays

Today, speciality use organoclays are being developed for an increasingly large number of specific applications. Many of these, including use in cosmetics, polishes, greases and paints, require that the material be free from abrasive impurities so that the product retains a smooth `feel'. The traditional `wet' method preparation of organoclays inherently removes abrasives naturally present in the parent mineral clay, but it is time-consuming and expensive. The primary objective of this thesis was to explore the alternative `dry' method (which is both quicker and cheaper but which provides no refining of the parent clay) as a process, and to examine the nature of the organoclays produced, for the production of a wide range of commercially usable organophilic clays in a facile way. Natural Wyoming bentonite contains two quite different types of silicate surface (that of the clay mineral montmorillonite and that of a quartz impurity) that may interact with the cationic surfactant added in the `dry' process production of organoclays. However, it is oil shale, and not the quartz, that is chiefly responsible for the abrasive nature of the material, although air refinement in combination with the controlled milling of the bentonite as a pretreatment may offer a route to its removal. Ion exchange of Wyoming bentonite with a long chain quaternary ammonium salt using the `dry' process affords a partially exchanged, 69-78%, organoclay, with a monolayer formation of ammonium ions in the interlayer. Excess ion pairs are sorbed on the silicate surfaces of both the clay mineral and the quartz impurity phases. Such surface sorption is enhanced by the presence of very finely divided, super paramagnetic, Fe2O3 or Fe(O)(OH) contaminating the surfaces of the major mineral components. The sorbed material is labile to washing, and induces a measurable shielding of the 29Si nuclei in both clay and quartz phases in the MAS NMR experiment, due to an anisotropic magnetic susceptibility effect. XRD data for humidified samples reveal the interlamellar regions to be strongly hydrophobic, with the by-product sodium chloride being expelled to the external surfaces. Many organic cations will exchange onto a clay. The tetracationic cyclophane, and multipurpose receptor, cyclobis(paraquat-p-phenylene) undergoes ion exchange onto Wyoming bentonite to form a pillared clay with a very regular gallery height. The major plane of the cyclophane is normal to the silicate surfaces, thus allowing the cavity to remain available for complexation. A series of group VI substituted o-dimethoxybenzenes were introduced, and shown to participate in host/guest interactions with the cyclophane. Evidence is given which suggests that the binding of the host structure to a clay substrate offers advantages, not only of transportability and usability but of stability, to the charge-transfer complex which may prove useful in a variety of commercial applications. The fundamental relationship between particle size, cation exchange capacity and chemical composition of clays was also examined. For Wyoming bentonite the extent of isomorphous substitution increases with decreasing particle size, causing the CEC to similarly increase, although the isomorphous substitution site: edge site ratio remains invarient throughout the particle size range studied.

Cracking in the welding of cupro-nickel alloys

The problem of variation in weld crack susceptibility caused by small variations in alloy and impurity elements for the 70-30 cupro-nickel alloy has been investigated. Both wrought and cast versions of the alloy have been studied, the main techniques employed being the Varestraint test and weld thermal simulation. In the wrought alloys, cracking has been found to occur mainly in the weld metal, whilst in the cast alloys cracking is extensive in both weld metal and heat affected zone. The previously reported effects of certain impurities (P,S,Si) in increasing cracking have been confirmed, and it has also been shown that Ti and Zr may both have a crack promoting effect at levels commonly found in cupro-nickels, whilst C can interact with several of the other elements investigated to produce a beneficial effect. The testing carried out using the weld thermal simulator has shown that a relationship does exist between hot ductility and weld cracking. In particular, the absence of the peak in ductility in the range 1100°C-900°C on cooling from a temperature near to the solidus is indicative of a highly crack susceptible alloy. Principal practical implications of the investigation concern the relationship of weld metal cracking to alloy composition, especially the level of certain impurities. It would appear that the upper limits permitted by the alloy specifications are unrealistically high. The introduction of lower impurity limits would alleviate the current problems of variability in resistance to cracking during welding.

Water detection in jet fuel using a polymer optical fibre Bragg grating

Water is a common impurity of jet fuel, and can exist in three forms: dissolved in the fuel, as a suspension and as a distinct layer at the bottom of the fuel tank. Water cannot practically be eliminated from fuel but must be kept to a minimum as large quantities can cause engine problems, particularly when frozen, and the interface between water and fuel acts as a breeding ground for biological contaminants. The quantities of dissolved or suspended water are quite small, ranging from about 10 ppm to 150 ppm. This makes the measurement task difficult and there is currently a lack of a convenient, electrically passive system for water-in-fuel monitoring; instead the airlines rely on colorimetric spot tests or simply draining liquid from the bottom of fuel tanks. For all these reason, people have explored different ways to detect water in fuel, however all these approaches have problems, e.g. they may not be electrically passive or they may be sensitive to the refractive index of the fuel. In this paper, we present a simple, direct and sensitive approach involving the use of a polymer optical fibre Bragg grating to detect water in fuel. The principle is that poly(methyl methacrylate) (PMMA) can absorb moisture from its surroundings (up to 2% at 23 °C), leading to both a swelling of the material and an increase in refractive index with a consequent increase in the Bragg wavelength of a grating inscribed in the material.

Deformation microstructures and recrystallization in heavily worked copper

Deformation microstructures in two batches of commercially pure copper (A and B) of allnost similar composition have been studied after rolling reductions from 5% to 95%. X- ray diffraction, optical metallography, scanning electron microscopy in the back-scattered mode, transmission and scanning electron microscopy have been used to examine the deformation microstructure. At low strains (~10 %) the deformation is accommodated by uniform octahedral slip. Microbands that occur as sheet like features usually on the {111} slip planes are formed after 10% reduction. The misorientations between rnicrobonds ond the matrix are usually small (1 - 2° ) and the dislocations within the bands suggest that a single slip system has been operative. The number of microbands increases with strain, they start to cluster and rotate after 60% reduction and, after 90 %, they become almost perfectly aligned with the rolling direction. There were no detectable differences in deformation microstructure between the two materials up to a deformation level of 60% but subsequently, copper B started to develop shear bands which became very profuse by 90% reduction. By contrast, copper A at this stage of deformation developed a smooth laminated structure. This difference in the deformation microstructures has been attributed to traces of unknown impurity in D which inhibit recovery of work hardening. The preferred orientations of both were typical of deformed copper although the presence of shear bands was associated wth a slightly weaker texture. The effects of rolling temperature and grain size on deformation microstructure were also investigated. It was concluded that lowering the rolling temperature or increasing the initial grain size encourages the material to develop shear bands after heavy deformation. Recovery and recrystallization have been studied in both materials during annealing. During recrystallization the growth of new grains showed quite different characteristics in the two cases. Where shear bands were present these acted as nucleation sites and produced a wide spread of recrystallized grain orientations. The resulting annealing textures were very weak. In the absence of shear bands, nucleation occurs by a remarkably long range bulging process which creates the cube orientation and an intensely sharp annealing texture. Cube oriented regions occur in long bands of highly elongated and well recovered cells which contain long range cumulative micorientations. They are transition bands with structural characteristics ideally suited for nucleation of recrystallization. Shear banding inhibits the cube texture both by creating alternative nuclei and by destroying the microstructural features necessary for cube nucleation.

Bulk and surface switching in Mn-Fe-based Prussian blue analogues

Many Prussian Blue Analogues are known to show a thermally induced phase transition close to room temperature and a reversible, photo-induced phase transition at low temperatures. This work reports on magnetic measurements, X-ray photoemission and Raman spectroscopy on a particular class of these molecular heterobimetallic systems, specifically on Rb0.81Mn[Fe(CN)6]0.95_1.24H2O, Rb0.97Mn[Fe(CN)6]0.98_1.03H2O and Rb0.70Cu0.22Mn0.78[Fe(CN)6]0.86_2.05H2O, to investigate these transition phenomena both in the bulk of the material and at the sample surface. Results indicate a high degree of charge transfer in the bulk, while a substantially reduced conversion is found at the sample surface, even in case of a near perfect (Rb:Mn:Fe=1:1:1) stoichiometry. Thus, the intrinsic incompleteness of the charge transfer transition in these materials is found to be primarily due to surface reconstruction. Substitution of a large fraction of charge transfer active Mn ions by charge transfer inactive Cu ions leads to a proportional conversion reduction with respect to the maximum conversion that is still stoichiometrically possible and shows the charge transfer capability of metal centers to be quite robust upon inclusion of a neighboring impurity. Additionally, a 532 nm photo-induced metastable state, reminiscent of the high temperature Fe(III)Mn(II) ground state, is found at temperatures 50-100 K. The efficiency of photo-excitation to the metastable state is found to be maximized around 90 K. The photo-induced state is observed to relax to the low temperature Fe(II)Mn(III) ground state at a temperature of approximately 123 K.

Duality of weak and strong scatterer in a Luttinger liquid coupled to massless bosons

We study electronic transport in a Luttinger liquid with an embedded impurity, which is either a weak scatterer (WS) or a weak link (WL), when interacting electrons are coupled to one-dimensional massless bosons (e.g., acoustic phonons). We find that the duality relation, ?WS?WL=1, between scaling dimensions of the electron backscattering in the WS and WL limits, established for the standard Luttinger liquid, holds in the presence of the additional coupling for an arbitrary fixed strength of boson scattering from the impurity. This means that at low temperatures such a system remains either an ideal insulator or an ideal metal, regardless of the scattering strength. On the other hand, when fermion and boson scattering from the impurity are correlated, the system has a rich phase diagram that includes a metal-insulator transition at some intermediate values of the scattering.