Synthesis, characterization and chemical vapor deposition of transition metal di(tert-butyl)amido compounds

Although the transition metal chemistry of many dialkylamido ligands has been well studied, the chemistry of the bulky di(tert-butyl)amido ligand has been largely overlooked. The di(tert-butyl)amido ligand is well suited for synthesizing transition metal compounds with low coordination numbers; such compounds may exhibit interesting structural, physical, and chemical properties. Di(tert-butyl)amido complexes of transition metals are expected to exhibit high volatilities and low decomposition temperatures, thus making them well suited for the chemical vapor deposition of metals and metal nitrides. Treatment of MnBr₂(THF)₂, FeI₂, CoBr₂(DME), or NiBr₂(DME) with two equivalents of LiN(t-Bu)2 in benzene affords the two-coordinate complex M[N(t-Bu)₂]₂, where M is Mn, Fe, Co, or Ni. Crystallographic studies show that the M-N distances decrease across the series: 1.9365 (Mn), 1.8790 (Fe), 1.845 (Co), 1.798 Å (Ni). The N-M- N angles are very close to linear for Mn and Fe (179.30 and 179.45°, respectively), but bent for Co and Ni (159.2 and 160.90°, respectively). As expected, the d⁵ Mn complex has a magnetic moment of 5.53 μΒ that is very close to the spin only value. The EPR spectrum is nearly axial with a low E/D ratio of 0.014. The d⁶ Fe compound has a room temperature magnetic moment of 5.55 μΒ indicative of a large orbital angular momentum contribution. It does not exhibit a Jahn-Teller distortion despite the expected doubly degenerate ground state. Applied field Mössbauer spectroscopy shows that the effective internal hyperfine field is unusually large, Hint = 105 T. The magnetic moments of Co[N(t-Bu)₂]₂ and Ni[N(t-Bu)₂]₂ are 5.24 and 3.02 μΒ respectively. Both are EPR silent at 4.2 K. Treatment of TiCl₄ with three equivalents of LiN(t-Bu)2 in pentane affords the briding imido compound Ti₂[μ-N(t-Bu)]₂Cl₂[N(t-Bu)₂]₂ via a dealkylation reaction. Rotation around the bis(tert-butyl)amido groups is hindered, with activation parameters of ΔH‡ = 12.8 ± 0.6 kcal mol-1 and ΔS‡ = -8 ± 2 cal K-1 ·mol-1, as evidenced by variable temperature 1H NMR spectroscopy. Treatment of TiCl₄ with two equivalents of HN(t-Bu)₂ affords Ti₂Cl₆[N(t-Bu)₂]₂. This complex shows a close-contact of 2.634(3) Å between Ti and the carbon atom of one of the CH₃ substituents on the tert-butyl groups. Theoretical considerations and detailed structural comparisons suggest this interaction is not agostic in nature, but rather is a consequence of interligand repulsions. Treatment of NiI₂(PPh3)₂ and PdCl₂(PPh₃)₂ with LiN(t-Bu)₂in benzene affords Ni[N(t-Bu)₂](PPh₃)I and Pd₃(μ₂-NBut₂)2(μ₂-PPh₂)Ph(PPh₃) respectively. The compound Ni[N(t-Bu)₂](PPh₃)I has distorted T-shape in geometry, whereas Pd₃(μ₂-NBut₂)₂(μ₂-PPh₂)Ph(PPh₃) contains a triangular palladium core. Manganese nitride films were grown from Mn[N(t-Bu)₂]₂ in the presence of anhydrous ammonia. The growth rate was several nanometers per minute even at the remarkably low temperature of 80⁰C. As grown, the films are carbon- and oxygen-free, and have a columnar morphology. The spacings between the columns become smaller and the films become smoother as the growth temperature is increased. The composition of the films is consistent with a stoichiometry of Mn₅N₂.

Which-path problem for one and two particles with two degrees of freedom and a relation between transverse spatial structure and group velocity of light

Quantum mechanics, optics and indeed any wave theory exhibits the phenomenon of interference. In this thesis we present two problems investigating interference due to indistinguishable alternatives and a mostly unrelated investigation into the free space propagation speed of light pulses in particular spatial modes. In chapter 1 we introduce the basic properties of the electromagnetic field needed for the subsequent chapters. In chapter 2 we review the properties of interference using the beam splitter and the Mach-Zehnder interferometer. In particular we review what happens when one of the paths of the interferometer is marked in some way so that the particle having traversed it contains information as to which path it went down (to be followed up in chapter 3) and we review Hong-Ou-Mandel interference at a beam splitter (to be followed up in chapter 5). In chapter 3 we present the first of the interference problems. This consists of a nested Mach-Zehnder interferometer in which each of the free space propagation segments are weakly marked by mirrors vibrating at different frequencies [1]. The original experiment drew the conclusions that the photons followed disconnected paths. We partition the description of the light in the interferometer according to the number of paths it contains which-way information about and reinterpret the results reported in [1] in terms of the interference of paths spatially connected from source to detector. In chapter 4 we briefly review optical angular momentum, entanglement and spontaneous parametric down conversion. These concepts feed into chapter 5 in which we present the second of the interference problems namely Hong-Ou-Mandel interference with particles possessing two degrees of freedom. We analyse the problem in terms of exchange symmetry for both boson and fermion pairs and show that the particle statistics at a beam splitter can be controlled for suitably chosen states. We propose an experimental test of these ideas using orbital angular momentum entangled photons. In chapter 6 we look at the effect that the transverse spatial structure of the mode that a pulse of light is excited in has on its group velocity. We show that the resulting group velocity is slower than the speed of light in vacuum for plane waves and that this reduction in the group velocity is related to the spread in the wave vectors required to create the transverse spatial structure. We present experimental results of the measurement of this slowing down using Hong-Ou-Mandel interference.

Cassini states for black hole binaries

Cassini states correspond to the equilibria of the spin axis of a body when its orbit is perturbed. They were initially described for planetary satellites, but the spin axes of black hole binaries also present this kind of equilibria. In previous works, Cassini states were reported as spin-orbit resonances, but actually the spin of black hole binaries is in circulation and there is no resonant motion. Here we provide a general description of the spin dynamics of black hole binary systems based on a Hamiltonian formalism. In absence of dissipation, the problem is integrable and it is easy to identify all possible trajectories for the spin for a given value of the total angular momentum. As the system collapses due to radiation reaction, the Cassini states are shifted to different positions, which modifies the dynamics around them. This is why the final spin distribution may differ from the initial one. Our method provides a simple way of predicting the distribution of the spin of black hole binaries at the end of the inspiral phase.

A unified model for the long and high jump

A simple model based on, the maximum energy that an athlete can produce in a small time interval is used to describe the high and long jump. Conservation of angular momentum is used to explain why an athlete should, run horizontally to perform a vertical jump. Our results agree with world records. (c) 2005 American Association of Physics Teachers.

Bull's eye leaky wave antenna for terrestrial and space applications

This work presents the study of Bull's eye antenna designs, a type of leaky wave antenna (LWA), operating in the 60 GHz band. This band emerged as a new standard for specific terrestrial and space applications because the radio spectrumbecomes more congested up to the millimetre-wave band, starting at 30 GHz. Built on existing Bull's eye antenna designs, novel structures were simulated, fabricated and measured, so as to provide more exibility in the implementation of wireless solutions at this frequency. Firstly, the study of a 60 GHz Bull's eye antenna for straightforward integration onto a CubeSat is presented. An investigation of the design is carried out, from the description of the radiation mechanism supported by simulation results, to the radiation pattern measurement of a prototype which provides a gain of 19.1 dBi at boresight. Another design, based on a modified feed structure, uses a microstrip to waveguide transition to provide easier and inexpensive integration of a Bull's eye antenna onto a planar circuit. Secondly, the design of Bull's eye antennas capable of creating beam deflection and multi-beam is presented. In particular, a detail study of the deflection mechanism is proposed, followed by the demonstration of a Bull's eye antenna generating two separate beams at ±16° away from the boresight. In addition, a novel mechanically steerable Bull's eye antenna, based on the division of the corrugated area in paired sectors is presented. A prototype was fabricated and measured. It generated double beams at ±8° and ±15° from the boresight, and a single boresight beam. Thirdly, a Bull's eye antenna capable of generating two simultaneous orbital angular momentum (OAM) modes l = 3 is proposed. The design is based on a circular travelling wave resonator and would allow channel capacity increase through OAM multiplexing. An improved design based on two stacked OAM Bull's eye antennas capable of producing four orthogonal OAM modes l = (±3,±13) simultaneously is presented. A novel receiving scheme based on discretely sampled partial aperture receivers (DSPAR) is then introduced. This solution could provide a lower windage and a lower cost of implementation than current whole or partial continuous aperture.

THE IMPACT OF UPPER-LEVEL PROCESSES ON THE INTENSITY AND STRUCTURAL CHANGES OF HURRICANE SANDY (2012)

The first part of this study examines the relative roles of frontogenesis and tropopause undulation in determining the intensity and structural changes of Hurricane Sandy (2012) using a high-resolution cloud-resolving model. A 138-h simulation reproduces Sandy’s four distinct development stages: (i) rapid intensification, (ii) weakening, (iii) steady maximum surface wind but with large continued sea-level pressure (SLP) falls, and (iv) re-intensification. Results show typical correlations between intensity changes, sea-surface temperature and vertical wind shear during the first two stages. The large SLP falls during the last two stages are mostly caused by Sandy’s moving northward into lower-tropopause regions associated with an eastward-propagating midlatitude trough, where the associated lower-stratospheric warm air wraps into the storm and its surrounding areas. The steady maximum surface wind occurs because of the widespread SLP falls with weak pressure gradients lacking significant inward advection of absolute angular momentum (AAM). Meanwhile, there is a continuous frontogenesis in the outer region during the last three stages. Cyclonic inward advection of AAM along each frontal rainband accounts for the continued expansion of the tropical-storm-force wind and structural changes, while deep convection in the eyewall and merging of the final two survived frontal rainbands generate a spiraling jet in Sandy’s northwestern quadrant, leading to its re-intensification prior to landfall. The physical, kinematic and dynamic aspects of an upper-level outflow layer and its possible impact on the re-intensification of Sandy are examined in the second part of this study. Above the outflow layer isentropes are tilted downward with radius as a result of the development of deep convection and an approaching upper-level trough, causing weak subsidence. Its maximum outward radial velocity is located above the cloud top, so the outflow channel experiences cloud-induced long-wave cooling. Because Sandy has two distinct convective regions (an eyewall and a frontal rainband), it has multiple outflow layers, with the eyewall’s outflow layer located above that of the frontal rainband. During the re-intensification stage, the eyewall’s outflow layer interacts with a jet stream ahead of the upper-level trough axis. Because of the presence of inertial instability on the anticyclonic side of the jet stream and symmetric instability in the inner region of the outflow layer, Sandy’s secondary circulation intensifies. Its re-intensification ceases when these instabilities disappear. The relationship between the intensity of the secondary circulation and dynamic instabilities of the outflow layer suggests that the re-intensification occurs in response to these instabilities. Additionally, it is verified that the long-wave cooling in the outflow layer helps induce symmetric instability by reducing static stability.

Multi-mode communications in near field exploiting OAM properties

This dissertation analyzes the exploitation of the orbital angular momentum (OAM) of the electromagnetic waves with large intelligent surfaces in the near-field region and line-of-sight conditions, in light of the holographic MIMO communication concept. Firstly, a characterization of the OAM-based communication problem is presented, and the relationship between OAM-carrying waves and communication modes is discussed. Then, practicable strategies for OAM detection using large intelligent surfaces and optimization methods based on beam focusing are proposed. Numerical results characterize the effectiveness of OAM with respect to other strategies, also including the proposed detection and optimization methods. It is shown that OAM waves constitute a particular choice of communication modes, i.e., an alternative basis set, which is sub-optimum with respect to optimal basis functions that can be derived by solving eigenfunction problems. Moreover, even the joint utilization of OAM waves with focusing strategies led to the conclusion that no channel capacity achievements can be obtained with these transmission techniques.

Schwinger and Pegg-Barnett approaches and a relationship between angular and Cartesian quantum descriptions: II. Phase spaces

Following the discussion-in state-space language-presented in a preceding paper, we work on the passage from the phase-space description of a degree of freedom described by a finite number of states (without classical counterpart) to one described by an infinite (and continuously labelled) number of states. With this it is possible to relate an original Schwinger idea to the Pegg-Barnett approach to the phase problem. In phase-space language, this discussion shows that one can obtain the Weyl-Wigner formalism, for both Cartesian and angular coordinates, as limiting elements of the discrete phase-space formalism.

The Dirac-Hestenes equation for spherical symmetric potentials in the spherical and Cartesian gauges

In this paper, using the apparatus of the Clifford bundle formalism, we show how straightforwardly solve in Minkowski space-time the Dirac-Hestenes equation - which is an appropriate representative in the Clifford bundle of differential forms of the usual Dirac equation - by separation of variables for the case of a potential having spherical symmetry in the Cartesian and spherical gauges. We show that, contrary to what is expected at a first sight, the solution of the Dirac-Hestenes equation in both gauges has exactly the same mathematical difficulty. © World Scientific Publishing Company.

Measurement of angular correlations of jets at s=1.96 TeV and determination of the strong coupling at high momentum transfers

We present a measurement of the average value of a new observable at hadron colliders that is sensitive to QCD dynamics and to the strong coupling constant, while being only weakly sensitive to parton distribution functions. The observable measures the angular correlations of jets and is defined as the number of neighboring jets above a given transverse momentum threshold which accompany a given jet within a given distance δR in the plane of rapidity and azimuthal angle. The ensemble average over all jets in an inclusive jet sample is measured and the results are presented as a function of transverse momentum of the inclusive jets, in different regions of δR and for different transverse momentum requirements for the neighboring jets. The measurement is based on a data set corresponding to an integrated luminosity of 0.7 fb -1 collected with the D0 detector at the Fermilab Tevatron Collider in pp- collisions at s=1.96 TeV. The results are well described by a perturbative QCD calculation in next-to-leading order in the strong coupling constant, corrected for non-perturbative effects. From these results, we extract the strong coupling and test the QCD predictions for its running over a range of momentum transfers of 50-400 GeV. © 2012 Elsevier B.V.

Measurement of angular correlations in Drell-Yan lepton pairs to probe Z/gamma* boson transverse momentum at sqrt(s)=7 TeV with the ATLAS detector

A measurement of angular correlations in Drell-Yan lepton pairs via the phi(eta)* observable is presented. This variable probes the same physics as the Z/gamma* boson transverse momentum with a better experimental resolution. The Z/gamma* -> e(+)e(-) and Z/gamma* -> mu(+)mu(-) decays produced in proton-proton collisions at a centre-of-mass energy of root s = 7 TeV are used. The data were collected with the ATLAS detector at the LHC and correspond to an integrated luminosity of 4.6 fb(-1). Normalised differential cross sections as a function of phi(eta)* are measured separately for electron and muon decay channels. These channels are then combined for improved accuracy. The cross section is also measured double differentially as a function of phi(eta)* for three independent bins of the Z boson rapidity. The results are compared to QCD calculations and to predictions from different Monte Carlo event generators. The data are reasonably well described, in all measured Z boson rapidity regions, by resummed QCD predictions combined with fixed-order perturbative QCD calculations or by some Monte Carlo event generators. The measurement precision is typically better by one order of magnitude than present theoretical uncertainties.

Energy-entropy-momentum time integration methods for coupled smooth dissipative problems

Esta tesis aborda la formulación, análisis e implementación de métodos numéricos de integración temporal para la solución de sistemas disipativos suaves de dimensión finita o infinita de manera que su estructura continua sea conservada. Se entiende por dichos sistemas aquellos que involucran acoplamiento termo-mecánico y/o efectos disipativos internos modelados por variables internas que siguen leyes continuas, de modo que su evolución es considerada suave. La dinámica de estos sistemas está gobernada por las leyes de la termodinámica y simetrías, las cuales constituyen la estructura que se pretende conservar de forma discreta. Para ello, los sistemas disipativos se describen geométricamente mediante estructuras metriplécticas que identifican claramente las partes reversible e irreversible de la evolución del sistema. Así, usando una de estas estructuras conocida por las siglas (en inglés) de GENERIC, la estructura disipativa de los sistemas es identificada del mismo modo que lo es la Hamiltoniana para sistemas conservativos. Con esto, métodos (EEM) con precisión de segundo orden que conservan la energía, producen entropía y conservan los impulsos lineal y angular son formulados mediante el uso del operador derivada discreta introducido para asegurar la conservación de la Hamiltoniana y las simetrías de sistemas conservativos. Siguiendo estas directrices, se formulan dos tipos de métodos EEM basados en el uso de la temperatura o de la entropía como variable de estado termodinámica, lo que presenta importantes implicaciones que se discuten a lo largo de esta tesis. Entre las cuales cabe destacar que las condiciones de contorno de Dirichlet son naturalmente impuestas con la formulación basada en la temperatura. Por último, se validan dichos métodos y se comprueban sus mejores prestaciones en términos de la estabilidad y robustez en comparación con métodos estándar. This dissertation is concerned with the formulation, analysis and implementation of structure-preserving time integration methods for the solution of the initial(-boundary) value problems describing the dynamics of smooth dissipative systems, either finite- or infinite-dimensional ones. Such systems are understood as those involving thermo-mechanical coupling and/or internal dissipative effects modeled by internal state variables considered to be smooth in the sense that their evolutions follow continuos laws. The dynamics of such systems are ruled by the laws of thermodynamics and symmetries which constitutes the structure meant to be preserved in the numerical setting. For that, dissipative systems are geometrically described by metriplectic structures which clearly identify the reversible and irreversible parts of their dynamical evolution. In particular, the framework known by the acronym GENERIC is used to reveal the systems' dissipative structure in the same way as the Hamiltonian is for conserving systems. Given that, energy-preserving, entropy-producing and momentum-preserving (EEM) second-order accurate methods are formulated using the discrete derivative operator that enabled the formulation of Energy-Momentum methods ensuring the preservation of the Hamiltonian and symmetries for conservative systems. Following these guidelines, two kind of EEM methods are formulated in terms of entropy and temperature as a thermodynamical state variable, involving important implications discussed throughout the dissertation. Remarkably, the formulation in temperature becomes central to accommodate Dirichlet boundary conditions. EEM methods are finally validated and proved to exhibit enhanced numerical stability and robustness properties compared to standard ones.

Operator-induced errors in Hartmann-Shack wavefront sensing:model eye study

Purpose: To evaluate the effects of instrument realignment and angular misalignment during the clinical determination of wavefront aberrations by simulation in model eyes. Setting: Aston Academy of Life Sciences, Aston University, Birmingham, United Kingdom. Methods: Six model eyes were examined with wavefront-aberration-supported cornea ablation (WASCA) (Carl Zeiss Meditec) in 4 sessions of 10 measurements each: sessions 1 and 2, consecutive repeated measures without realignment; session 3, realignment of the instrument between readings; session 4, measurements without realignment but with the model eye shifted 6 degrees angularly. Intersession repeatability and the effects of realignment and misalignment were obtained by comparing the measurements in the various sessions for coma, spherical aberration, and higher-order aberrations (HOAs). Results: The mean differences between the 2 sessions without realignment of the instrument were 0.020 μm ± 0.076 (SD) for Z3 - 1(P = .551), 0.009 ± 0.139 μm for Z3 1(P = .877), 0.004 ± 0.037 μm for Z4 0 (P = .820), and 0.005 ± 0.01 μm for HO root mean square (RMS) (P = .301). Differences between the nonrealigned and realigned instruments were -0.017 ± 0.026 μm for Z3 - 1(P = .159), 0.009 ± 0.028 μm for Z3 1 (P = .475), 0.007 ± 0.014 μm for Z4 0(P = .296), and 0.002 ± 0.007 μm for HO RMS (P = 0.529; differences between centered and misaligned instruments were -0.355 ± 0.149 μm for Z3 - 1 (P = .002), 0.007 ± 0.034 μm for Z3 1(P = .620), -0.005 ± 0.081 μm for Z4 0(P = .885), and 0.012 ± 0.020 μm for HO RMS (P = .195). Realignment increased the standard deviation by a factor of 3 compared with the first session without realignment. Conclusions: Repeatability of the WASCA was excellent in all situations tested. Realignment substantially increased the variance of the measurements. Angular misalignment can result in significant errors, particularly in the determination of coma. These findings are important when assessing highly aberrated eyes during follow-up or before surgery. © 2007 ASCRS and ESCRS.

On the Range of the Fourier Transform Associated with the Spherical Mean Operator

We characterize the range of some spaces of functions by the Fourier transform associated with the spherical mean operator R and we give a new description of the Schwartz spaces. Next, we prove a Paley-Wiener and a Paley-Wiener-Schawrtz theorems.

Carrier momentum relaxation in highly doped polar semiconductors and semiconductor heterostructures

Highly doped polar semiconductors are essential components of today’s semiconductor industry. Most strikingly, transistors in modern electronic devices are polar semiconductor heterostructures. It is important to thoroughly understand carrier transport in such structures. In doped polar semiconductors, collective excitations of the carriers (plasmons) and the atoms (polar phonons) couple. These coupled collective excitations affect the electrical conductivity, here quantified through the carrier mobility. In scattering events, the carriers and the coupled collective modes transfer momentum between each other. Carrier momentum transferred to polar phonons can be lost to other phonons through anharmonic decay, resulting in a finite carrier mobility. The plasmons do not have a decay mechanism which transfers carrier momentum irretrievably. Hence, carrier-plasmon scattering results in infinite carrier mobility. Momentum relaxation due to either carrier–plasmon scattering or carrier–polar-phonon scattering alone are well understood. However, only this thesis manages to treat momentum relaxation due to both scattering mechanisms on an equal footing, enabling us to properly calculate the mobility limited by carrier–coupled plasmon–polar phonon scattering. We achieved this by solving the coupled Boltzmann equations for the carriers and the collective excitations, focusing on the “drag” term and on the anharmonic decay process of the collective modes. Our approach uses dielectric functions to describe both the carrier-collective mode scattering and the decay of the collective modes. We applied our method to bulk polar semiconductors and heterostructures where various polar dielectrics surround a semiconducting monolayer of MoS2, where taking plasmons into account can increase the mobility by up to a factor 15 for certain parameters. This screening effect is up to 85% higher than if calculated with previous methods. To conclude, our approach provides insight into the momentum relaxation mechanism for carrier–coupled collective mode scattering, and better tools for calculating the screened polar phonon and interface polar phonon limited mobility.