23 resultados para resonator-coupling elements
Resumo:
A dilution refrigerator has been constructed capable of producing steady state temperatures less than .075°K. The first part of this work is concerned with the design and construction of this machine. Enough theory is presented to allow one to understand the operation and critical design factors of a dilution refrigerator. The performance of our refrigerator is compared with the operating characteristics of three other dilution refrigerators appearing in the present literature.
The dilution refrigerator constructed was used to measure the nuclear contribution to the low temperature specific heat of a pure, single-crystalline sample of rhenium metal. Measurements were made in magnetic fields from 0 to 12.5 kOe for the temperature range .13°K - .52°K. The second part of this work discusses the results of these experiments. The expected nuclear contribution is not found when the sample is in the superconducting state. This is believed to be due to the long spin-lattice relaxation times in superconductors. In the normal state, for the temperature range studied, the nuclear contribution is given by A/T2 where A = .061 ± .002 millijoules-K/mole. The value of A is found to increase to A = .077 ± .004 millijoules-K/mole when the sample is located in a magnetic field of 12.5 kOe.
From the measured value of A the splitting of the energy levels of the nuclear spin system due to the interaction of the internal crystalline electric field gradients with the nuclear quadrupole moments is calculated. A comparison is made between the predicted and measured magnetic dependence of the specific heat. Finally, predictions are made of future nuclear magnetic resonance experiments which may be performed to check the results obtained by calorimetery here and further, to investigate existing theories concerning the sources of electric field gradients in metals.
Resumo:
The Mössbauer technique has been used to study the nuclear hyperfine interactions and lifetimes in W182 (2+ state) and W183 (3/2- and 5/2- states) with the following results: g(5/2-)/g(2+) = 1.40 ± 0.04; g(3/2- = -0.07 ± 0.07; Q(5/2-)/Q(2+) = 0.94 ± 0.04; T1/2(3/2-) = 0.184 ± 0.005 nsec; T1/2(5/2-) >̰ 0.7 nsec. These quantities are discussed in terms of a rotation-particle interaction in W183 due to Coriolis coupling. From the measured quantities and additional information on γ-ray transition intensities magnetic single-particle matrix elements are derived. It is inferred from these that the two effective g-factors, resulting from the Nilsson-model calculation of the single-particle matrix elements for the spin operators ŝz and ŝ+, are not equal, consistent with a proposal of Bochnacki and Ogaza.
The internal magnetic fields at the tungsten nucleus were determined for substitutional solid solutions of tungsten in iron, cobalt, and nickel. With g(2+) = 0.24 the results are: |Heff(W-Fe)| = 715 ± 10 kG; |Heff(W-Co)| = 360 ± 10 kG; |Heff(W-Ni)| = 90 ± 25 kG. The electric field gradients at the tungsten nucleus were determined for WS2 and WO3. With Q(2+) = -1.81b the results are: for WS2, eq = -(1.86 ± 0.05) 1018 V/cm2; for WO3, eq = (1.54 ± 0.04) 1018 V/cm2 and ƞ = 0.63 ± 0.02.
The 5/2- state of Pt195 has also been studied with the Mössbauer technique, and the g-factor of this state has been determined to be -0.41 ± 0.03. The following magnetic fields at the Pt nucleus were found: in an Fe lattice, 1.19 ± 0.04 MG; in a Co lattice, 0.86 ± 0.03 MG; and in a Ni lattice, 0.36 ± 0.04 MG. Isomeric shifts have been detected in a number of compounds and alloys and have been interpreted to imply that the mean square radius of the Pt195 nucleus in the first-excited state is smaller than in the ground state.
Resumo:
Part I.
The interaction of a nuclear magnetic moment situated on an internal top with the magnetic fields produced by the internal as well as overall molecular rotation has been derived following the method of Van Vleck for the spin-rotation interaction in rigid molecules. It is shown that the Hamiltonian for this problem may be written
HSR = Ῑ · M · Ĵ + Ῑ · M” · Ĵ”
Where the first term is the ordinary spin-rotation interaction and the second term arises from the spin-internal-rotation coupling.
The F19 nuclear spin-lattice relaxation time (T1) of benzotrifluoride and several chemically substituted benzotrifluorides, have been measured both neat and in solution, at room temperature by pulsed nuclear magnetic resonance. From these experimental results it is concluded that in benzotrifluoride the internal rotation is crucial to the spin relaxation of the fluorines and that the dominant relaxation mechanism is the fluctuating spin-internal-rotation interaction.
Part II.
The radiofrequency spectrum corresponding to the reorientation of the F19 nuclear moment in flurobenzene has been studied by the molecular beam magnetic resonance method. A molecular beam apparatus with an electron bombardment detector was used in the experiments. The F19 resonance is a composite spectrum with contributions from many rotational states and is not resolved. A detailed analysis of the resonance line shape and width by the method of moments led to the following diagonal components of the fluorine spin-rotational tensor in the principal inertial axis system of the molecule:
F/Caa = -1.0 ± 0.5 kHz
F/Cbb = -2.7 ± 0.2 kHz
F/Ccc = -1.9 ± 0.1 kHz
From these interaction constants, the paramagnetic contribution to the F19 nuclear shielding in C6H5F was determined to be -284 ± ppm. It was further concluded that the F19 nucleus in this molecule is more shielded when the applied magnetic field is directed along the C-F bond axis. The anisotropy of the magnetic shielding tensor, σ” - σ⊥, is +160 ± 30 ppm.
Resumo:
I report the solubility and diffusivity of water in lunar basalt and an iron-free basaltic analogue at 1 atm and 1350 °C. Such parameters are critical for understanding the degassing histories of lunar pyroclastic glasses. Solubility experiments have been conducted over a range of fO2 conditions from three log units below to five log units above the iron-wüstite buffer (IW) and over a range of pH2/pH2O from 0.03 to 24. Quenched experimental glasses were analyzed by Fourier transform infrared spectroscopy (FTIR) and secondary ionization mass spectrometry (SIMS) and were found to contain up to ~420 ppm water. Results demonstrate that, under the conditions of our experiments: (1) hydroxyl is the only H-bearing species detected by FTIR; (2) the solubility of water is proportional to the square root of pH2O in the furnace atmosphere and is independent of fO2 and pH2/pH2O; (3) the solubility of water is very similar in both melt compositions; (4) the concentration of H2 in our iron-free experiments is <3 ppm, even at oxygen fugacities as low as IW-2.3 and pH2/pH2O as high as 24; and (5) SIMS analyses of water in iron-rich glasses equilibrated under variable fO2 conditions can be strongly influenced by matrix effects, even when the concentrations of water in the glasses are low. Our results can be used to constrain the entrapment pressure of the lunar melt inclusions of Hauri et al. (2011).
Diffusion experiments were conducted over a range of fO2 conditions from IW-2.2 to IW+6.7 and over a range of pH2/pH2O from nominally zero to ~10. The water concentrations measured in our quenched experimental glasses by SIMS and FTIR vary from a few ppm to ~430 ppm. Water concentration gradients are well described by models in which the diffusivity of water (D*water) is assumed to be constant. The relationship between D*water and water concentration is well described by a modified speciation model (Ni et al. 2012) in which both molecular water and hydroxyl are allowed to diffuse. The success of this modified speciation model for describing our results suggests that we have resolved the diffusivity of hydroxyl in basaltic melt for the first time. Best-fit values of D*water for our experiments on lunar basalt vary within a factor of ~2 over a range of pH2/pH2O from 0.007 to 9.7, a range of fO2 from IW-2.2 to IW+4.9, and a water concentration range from ~80 ppm to ~280 ppm. The relative insensitivity of our best-fit values of D*water to variations in pH2 suggests that H2 diffusion was not significant during degassing of the lunar glasses of Saal et al. (2008). D*water during dehydration and hydration in H2/CO2 gas mixtures are approximately the same, which supports an equilibrium boundary condition for these experiments. However, dehydration experiments into CO2 and CO/CO2 gas mixtures leave some scope for the importance of kinetics during dehydration into H-free environments. The value of D*water chosen by Saal et al. (2008) for modeling the diffusive degassing of the lunar volcanic glasses is within a factor of three of our measured value in our lunar basaltic melt at 1350 °C.
In Chapter 4 of this thesis, I document significant zonation in major, minor, trace, and volatile elements in naturally glassy olivine-hosted melt inclusions from the Siqueiros Fracture Zone and the Galapagos Islands. Components with a higher concentration in the host olivine than in the melt (MgO, FeO, Cr2O3, and MnO) are depleted at the edges of the zoned melt inclusions relative to their centers, whereas except for CaO, H2O, and F, components with a lower concentration in the host olivine than in the melt (Al2O3, SiO2, Na2O, K2O, TiO2, S, and Cl) are enriched near the melt inclusion edges. This zonation is due to formation of an olivine-depleted boundary layer in the adjacent melt in response to cooling and crystallization of olivine on the walls of the melt inclusions concurrent with diffusive propagation of the boundary layer toward the inclusion center.
Concentration profiles of some components in the melt inclusions exhibit multicomponent diffusion effects such as uphill diffusion (CaO, FeO) or slowing of the diffusion of typically rapidly diffusing components (Na2O, K2O) by coupling to slow diffusing components such as SiO2 and Al2O3. Concentrations of H2O and F decrease towards the edges of some of the Siqueiros melt inclusions, suggesting either that these components have been lost from the inclusions into the host olivine late in their cooling histories and/or that these components are exhibiting multicomponent diffusion effects.
A model has been developed of the time-dependent evolution of MgO concentration profiles in melt inclusions due to simultaneous depletion of MgO at the inclusion walls due to olivine growth and diffusion of MgO in the melt inclusions in response to this depletion. Observed concentration profiles were fit to this model to constrain their thermal histories. Cooling rates determined by a single-stage linear cooling model are 150–13,000 °C hr-1 from the liquidus down to ~1000 °C, consistent with previously determined cooling rates for basaltic glasses; compositional trends with melt inclusion size observed in the Siqueiros melt inclusions are described well by this simple single-stage linear cooling model. Despite the overall success of the modeling of MgO concentration profiles using a single-stage cooling history, MgO concentration profiles in some melt inclusions are better fit by a two-stage cooling history with a slower-cooling first stage followed by a faster-cooling second stage; the inferred total duration of cooling from the liquidus down to ~1000 °C is 40 s to just over one hour.
Based on our observations and models, compositions of zoned melt inclusions (even if measured at the centers of the inclusions) will typically have been diffusively fractionated relative to the initially trapped melt; for such inclusions, the initial composition cannot be simply reconstructed based on olivine-addition calculations, so caution should be exercised in application of such reconstructions to correct for post-entrapment crystallization of olivine on inclusion walls. Off-center analyses of a melt inclusion can also give results significantly fractionated relative to simple olivine crystallization.
All melt inclusions from the Siqueiros and Galapagos sample suites exhibit zoning profiles, and this feature may be nearly universal in glassy, olivine-hosted inclusions. If so, zoning profiles in melt inclusions could be widely useful to constrain late-stage syneruptive processes and as natural diffusion experiments.
Resumo:
Part I
Several approximate Hartree-Fock SCF wavefunctions for the ground electronic state of the water molecule have been obtained using an increasing number of multicenter s, p, and d Slater-type atomic orbitals as basis sets. The predicted charge distribution has been extensively tested at each stage by calculating the electric dipole moment, molecular quadrupole moment, diamagnetic shielding, Hellmann-Feynman forces, and electric field gradients at both the hydrogen and the oxygen nuclei. It was found that a carefully optimized minimal basis set suffices to describe the electronic charge distribution adequately except in the vicinity of the oxygen nucleus. Our calculations indicate, for example, that the correct prediction of the field gradient at this nucleus requires a more flexible linear combination of p-orbitals centered on this nucleus than that in the minimal basis set. Theoretical values for the molecular octopole moment components are also reported.
Part II
The perturbation-variational theory of R. M. Pitzer for nuclear spin-spin coupling constants is applied to the HD molecule. The zero-order molecular orbital is described in terms of a single 1s Slater-type basis function centered on each nucleus. The first-order molecular orbital is expressed in terms of these two functions plus one singular basis function each of the types e-r/r and e-r ln r centered on one of the nuclei. The new kinds of molecular integrals were evaluated to high accuracy using numerical and analytical means. The value of the HD spin-spin coupling constant calculated with this near-minimal set of basis functions is JHD = +96.6 cps. This represents an improvement over the previous calculated value of +120 cps obtained without using the logarithmic basis function but is still considerably off in magnitude compared with the experimental measurement of JHD = +43 0 ± 0.5 cps.
Resumo:
High-resolution, natural-abundance 13C spectra have been obtained from a wide variety of organic compounds; 13C chemical shifts and coupling constants have been correlated with other molecular properties.
Geminal and vicinal, carbon-proton couplings in benzene and the five- and six-membered aromatic heterocycles have been related to the corresponding proton-proton couplings in substituted ethylenes. The carbon-proton coupling constants in benzene are JCCH = + 1.0, JCCCH = +7.4 and JCCCH = -1.1 Hz. Extended Hückel wavefunctions are uniformly poor in explaining the long-range, carbon-proton couplings in aromatic systems.
Couplings between carbon and elements other than hydrogen have been observed in proton decoupled 13C spectra. All of the carbons in fluorobenzene and 1-fluoronaphthalene, but only six of the carbons in 2-fluoronaphthalene are coupled to the fluorine. One-bond, carbon-phosphorus coupling in trialkylphosphines is negative, while one-bond, carbon-phosphorus coupling in tetra-alkylphosphonium ions is positive. Atoms which do not use hybrid orbitals to form bonds to carbon (F, P(III), Se, Te) may have negative, one-bond coupling constants because of the failure of the average energy approximation. One-bond couplings between carbon and carbon, silicon, tin, lead and mercury appear to be explainable in terms of an effective nuclear charge and the s-bond order of the metal. Couplings between carbon and nitrogen and phosphorus (IV) have significant negative contributions to the Fermi contact coupling expression, though, within one series, correlations with s-bond order may be valid. Carbon-carbon coupling in cyclopropane derivatives (10-15 Hz) is consistent with a high degree of p character in the interior orbitals. Some two- and three-bond carbon-carbon coupling constants have also been observed.
Substituent effects of hydroxyl groups on the 13C chemical shifts of continuous-chain alkanes depend both on steric and electronic factors. The hydroxyl substituent effects in the long-chain, primary alcohols are α = -48.3, β = -10.2, and γ = +6.0 ppm. The upfield γ effect is attributed to steric crowding in the gauche conformations. Additivity of the hydroxyl and carbonyl and alkyl substituent effects in alkyl-substituted cyclohexanols and cyclohexanones has been demonstrated.
Resumo:
The optomechanical interaction is an extremely powerful tool with which to measure mechanical motion. The displacement resolution of chip-scale optomechanical systems has been measured on the order of 1⁄10th of a proton radius. So strong is this optomechanical interaction that it has recently been used to remove almost all thermal noise from a mechanical resonator and observe its quantum ground-state of motion starting from cryogenic temperatures.
In this work, chapter 1 describes the basic physics of the canonical optomechanical system, optical measurement techniques, and how the optomechanical interaction affects the coupled mechanical resonator. In chapter 2, we describe our techniques for realizing this canonical optomechanical system in a chip-scale form factor.
In chapter 3, we describe an experiment where we used radiation pressure feedback to cool a mesoscopic mechanical resonator near its quantum ground-state from room-temperature. We cooled the resonator from a room temperature phonon occupation of <n> = 6.5 million to an occupation of <n> = 66, which means the resonator is in its ground state approximately 2% of the time, while being coupled to a room-temperature thermal environment. At the time of this work, this is the closest a mesoscopic mechanical resonator has been to its ground-state of motion at room temperature, and this work begins to open the door to room-temperature quantum control of mechanical objects.
Chapter 4 begins with the realization that the displacement resolutions achieved by optomechanical systems can surpass those of conventional MEMS sensors by an order of magnitude or more. This provides the motivation to develop and calibrate an optomechanical accelerometer with a resolution of approximately 10 micro-g/rt-Hz over a bandwidth of approximately 30 kHz. In chapter 5, we improve upon the performance and practicality of this sensor by greatly increasing the test mass size, investigating and reducing low-frequency noise, and incorporating more robust optical coupling techniques and capacitive wavelength tuning. Finally, in chapter 6 we present our progress towards developing another optomechanical inertial sensor - a gyroscope.
Resumo:
The thesis is divided into two parts. Part I generalizes a self-consistent calculation of residue shifts from SU3 symmetry, originally performed by Dashen, Dothan, Frautschi, and Sharp, to include the effects of non-linear terms. Residue factorizability is used to transform an overdetermined set of equations into a variational problem, which is designed to take advantage of the redundancy of the mathematical system. The solution of this problem automatically satisfies the requirement of factorizability and comes close to satisfying all the original equations.
Part II investigates some consequences of direct channel Regge poles and treats the problem of relating Reggeized partial wave expansions made in different reaction channels. An analytic method is introduced which can be used to determine the crossed-channel discontinuity for a large class of direct-channel Regge representations, and this method is applied to some specific representations.
It is demonstrated that the multi-sheeted analytic structure of the Regge trajectory function can be used to resolve apparent difficulties arising from infinitely rising Regge trajectories. Also discussed are the implications of large collections of "daughter trajectories."
Two things are of particular interest: first, the threshold behavior in direct and crossed channels; second, the potentialities of Reggeized representations for us in self-consistent calculations. A new representation is introduced which surpasses previous formulations in these two areas, automatically satisfying direct-channel threshold constraints while being capable of reproducing a reasonable crossed channel discontinuity. A scalar model is investigated for low energies, and a relation is obtained between the mass of the lowest bound state and the slope of the Regge trajectory.