Studies in nuclear reactor dynamics : I. The accuracy of point kinetics. II. The effect of delayed neutrons on the spectrum of the group-diffusion operator

This thesis is a theoretical work on the space-time dynamic behavior of a nuclear reactor without feedback. Diffusion theory with G-energy groups is used.

In the first part the accuracy of the point kinetics (lumped-parameter description) model is examined. The fundamental approximation of this model is the splitting of the neutron density into a product of a known function of space and an unknown function of time; then the properties of the system can be averaged in space through the use of appropriate weighting functions; as a result a set of ordinary differential equations is obtained for the description of time behavior. It is clear that changes of the shape of the neutron-density distribution due to space-dependent perturbations are neglected. This results to an error in the eigenvalues and it is to this error that bounds are derived. This is done by using the method of weighted residuals to reduce the original eigenvalue problem to that of a real asymmetric matrix. Then Gershgorin-type theorems .are used to find discs in the complex plane in which the eigenvalues are contained. The radii of the discs depend on the perturbation in a simple manner.

In the second part the effect of delayed neutrons on the eigenvalues of the group-diffusion operator is examined. The delayed neutrons cause a shifting of the prompt-neutron eigenvalue s and the appearance of the delayed eigenvalues. Using a simple perturbation method this shifting is calculated and the delayed eigenvalues are predicted with good accuracy.

I. The crystal structure of potassium bis(tricyanovinyl)amine. II. Nuclear magnetic resonance studies of alkali halide solutions. III. Elucidation of the intramolecular hydrogen bond in acetylacetone by the deuterium isotope effect on the chemical shift of the bridge hydrogen

Part I

Potassium bis-(tricyanovinyl) amine, K⁺N[C(CN)=C(CN)₂]₂^-, crystallizes in the monoclinic system with the space group Cc and lattice constants, a = 13.346 ± 0.003 Å, c = 8.992 ± 0.003 Å, B = 114.42 ± 0.02°, and Z = 4. Three dimensional intensity data were collected by layers perpendicular to b* and c* axes. The crystal structure was refined by the least squares method with anisotropic temperature factor to an R value of 0.064.

The average carbon-carbon and carbon-nitrogen bond distances in –C-CΞN are 1.441 ± 0.016 Å and 1.146 ± 0.014 Å respectively. The bis-(tricyanovinyl) amine anion is approximately planar. The coordination number of the potassium ion is eight with bond distances from 2.890 Å to 3.408 Å. The bond angle C-N-C of the amine nitrogen is 132.4 ± 1.9°. Among six cyano groups in the molecule, two of them are bent by what appear to be significant amounts (5.0° and 7.2°). The remaining four are linear within the experimental error. The bending can probably be explained by molecular packing forces in the crystals.

Part II

The nuclear magnetic resonance of ⁸¹Br and ¹²⁷I in aqueous solutions were studied. The cation-halide ion interactions were studied by studying the effect of the Li⁺, Na⁺, K⁺, Mg⁺⁺, Cs⁺ upon the line width of the halide ions. The solvent-halide ion interactions were studied by studying the effects of methanol, acetonitrile, and acetone upon the line width of ⁸¹Br and ¹²⁷I in the aqueous solutions. It was found that the viscosity plays a very important role upon the halide ions line width. There is no specific cation-halide ion interaction for those ions such as Mg⁺⁺, Di⁺, Na⁺, and K⁺, whereas the Cs⁺ - halide ion interaction is strong. The effect of organic solvents upon the halide ion line width in aqueous solutions is in the order acetone ˃ acetonitrile ˃ methanol. It is suggested that halide ions do form some stable complex with the solvent molecules and the reason Cs⁺ can replace one of the ligands in the solvent-halide ion complex.

Part III

An unusually large isotope effect on the bridge hydrogen chemical shift of the enol form of pentanedione-2, 4(acetylacetone) and 3-methylpentanedione-2, 4 has been observed. An attempt has been made to interpret this effect. It is suggested from the deuterium isotope effect studies, temperature dependence of the bridge hydrogen chemical shift studies, IR studies in the OH, OD, and C=O stretch regions, and the HMO calculations, that there may probably be two structures for the enol form of acetylacetone. The difference between these two structures arises mainly from the electronic structure of the π-system. The relative population of these two structures at various temperatures for normal acetylacetone and at room temperature for the deuterated acetylacetone were calculated.

Beyond the blur: Construction and characterization of the first autonomous AO system and An AO survey of magnetar proper motions

Adaptive optics (AO) corrects distortions created by atmospheric turbulence and delivers diffraction-limited images on ground-based telescopes. The vastly improved spatial resolution and sensitivity has been utilized for studying everything from the magnetic fields of sunspots upto the internal dynamics of high-redshift galaxies. This thesis about AO science from small and large telescopes is divided into two parts: Robo-AO and magnetar kinematics.

In the first part, I discuss the construction and performance of the world’s first fully autonomous visible light AO system, Robo-AO, at the Palomar 60-inch telescope. Robo-AO operates extremely efficiently with an overhead < 50s, typically observing about 22 targets every hour. We have performed large AO programs observing a total of over 7,500 targets since May 2012. In the visible band, the images have a Strehl ratio of about 10% and achieve a contrast of upto 6 magnitudes at a separation of 1′′. The full-width at half maximum achieved is 110–130 milli-arcsecond. I describe how Robo-AO is used to constrain the evolutionary models of low-mass pre-main-sequence stars by measuring resolved spectral energy distributions of stellar multiples in the visible band, more than doubling the current sample. I conclude this part with a discussion of possible future improvements to the Robo-AO system.

In the second part, I describe a study of magnetar kinematics using high-resolution near-infrared (NIR) AO imaging from the 10-meter Keck II telescope. Measuring the proper motions of five magnetars with a precision of upto 0.7 milli-arcsecond/yr, we have more than tripled the previously known sample of magnetar proper motions and proved that magnetar kinematics are equivalent to those of radio pulsars. We conclusively showed that SGR 1900+14 and SGR 1806-20 were ejected from the stellar clusters with which they were traditionally associated. The inferred kinematic ages of these two magnetars are 6±1.8 kyr and 650±300 yr respectively. These ages are a factor of three to four times greater than their respective characteristic ages. The calculated braking index is close to unity as compared to three for the vacuum dipole model and 2.5-2.8 as measured for young pulsars. I conclude this section by describing a search for NIR counterparts of new magnetars and a future promise of polarimetric investigation of a magnetars’ NIR emission mechanism.

Part I. Energy straggling of ^4He below 2.0 MeV in Al, Ni, Au and Pt. Part II. Studies of the Ti-W metallization system on Si

Part I.

In recent years, backscattering spectrometry has become an important tool for the analysis of thin films. An inherent limitation, though, is the loss of depth resolution due to energy straggling of the beam. To investigate this, energy straggling of ⁴He has been measured in thin films of Ni, Al, Au and Pt. Straggling is roughly proportional to square root of thickness, appears to have a slight energy dependence and generally decreases with decreasing atomic number of the adsorber. The results are compared with predictions of theory and with previous measurements. While Ni measurements are in fair agreement with Bohr's theory, Al measurements are 30% above and Au measurements are 40% below predicted values. The Au and Pt measurements give straggling values which are close to one another.

Part II.

MeV backscattering spectrometry and X-ray diffraction are used to investigate the behavior of sputter-deposited Ti-W mixed films on Si substrates. During vacuum anneals at temperatures near 700°C for several hours, the metallization layer reacts with the substrate. Backscattering analysis shows that the resulting compound layer is uniform in composition and contains Ti, Wand Si. The Ti:W ratio in the compound corresponds to that of the deposited metal film. X-ray analyses with Reed and Guinier cameras reveal the presence of the ternary Ti_xW_(1-x)Si₂ compound. Its composition is unaffected by oxygen contamination during annealing, but the reaction rate is affected. The rate measured on samples with about 15% oxygen contamination after annealing is linear, of the order of 0.5 Å per second at 725°C, and depends on the crystallographic orientation of the substrate and the dc bias during sputter-deposition of the Ti-W film.

Au layers of about 1000 Å thickness were deposited onto unreacted Ti-W films on Si. When annealed at 400°C these samples underwent a color change,and SEM micrographs of the samples showed that an intricate pattern of fissures which were typically 3µm wide had evolved. Analysis by electron microprobe revealed that Au had segregated preferentially into the fissures. This result suggests that Ti-W is not a barrier to Au-Si intermixing at 400°C.

High pressure states in condensed matter: I. High pressure behavior of the iron-sulphur system with applications to the earth's core. II. Empirical equation of state for organic compounds at high pressures

Part I:

The earth's core is generally accepted to be composed primarily of iron, with an admixture of other elements. Because the outer core is observed not to transmit shear waves at seismic frequencies, it is known to be liquid or primarily liquid. A new equation of state is presented for liquid iron, in the form of parameters for the 4th order Birch-Murnaghan and Mie-Grüneisen equations of state. The parameters were constrained by a set of values for numerous properties compiled from the literature. A detailed theoretical model is used to constrain the P-T behavior of the heat capacity, based on recent advances in the understanding of the interatomic potentials for transition metals. At the reference pressure of 10⁵ Pa and temperature of 1811 K (the normal melting point of Fe), the parameters are: ρ = 7037 kg/m³, K_S0 = 110 GPa, K_S' = 4.53, K_S" = -.0337 GPa-1, and γ = 2.8, with γ α ρ^-1.17. Comparison of the properties predicted by this model with the earth model PREM indicates that the outer core is 8 to 10 % less dense than pure liquid Fe at the same conditions. The inner core is also found to be 3 to 5% less dense than pure liquid Fe, supporting the idea of a partially molten inner core. The density deficit of the outer core implies that the elements dissolved in the liquid Fe are predominantly of lower atomic weight than Fe. Of the candidate light elements favored by researchers, only sulfur readily dissolves into Fe at low pressure, which means that this element was almost certainly concentrated in the core at early times. New melting data are presented for FeS and FeS₂ which indicate that the FeS₂ is the S-hearing liquidus solid phase at inner core pressures. Consideration of the requirement that the inner core boundary be observable by seismological means and the freezing behavior of solutions leads to the possibility that the outer core may contain a significant fraction of solid material. It is found that convection in the outer core is not hindered if the solid particles are entrained in the fluid flow. This model for a core of Fe and S admits temperatures in the range 3450K to 4200K at the top of the core. An all liquid Fe-S outer core would require a temperature of about 4900 K at the top of the core.

Part II.

The abundance of uses for organic compounds in the modern world results in many applications in which these materials are subjected to high pressures. This leads to the desire to be able to describe the behavior of these materials under such conditions. Unfortunately, the number of compounds is much greater than the number of experimental data available for many of the important properties. In the past, one approach that has worked well is the calculation of appropriate properties by summing the contributions from the organic functional groups making up molecules of the compounds in question. A new set of group contributions for the molar volume, volume thermal expansivity, heat capacity, and the Rao function is presented for functional groups containing C, H, and O. This set is, in most cases, limited in application to low molecular liquids. A new technique for the calculation of the pressure derivative of the bulk modulus is also presented. Comparison with data indicates that the presented technique works very well for most low molecular hydrocarbon liquids and somewhat less well for oxygen-bearing compounds. A similar comparison of previous results for polymers indicates that the existing tabulations of group contributions for this class of materials is in need of revision. There is also evidence that the Rao function contributions for polymers and low molecular compounds are somewhat different.

Nature of the radical intermediates in a substituted cyclopropylcarbiny-allylcarbinyl system

We have sought to determine the nature of the free-radical precursors to ring-opened hydrocarbon 5 and ring-closed hydrocarbon 6. Reasonable alternative formulations involve the postulation of hydrogen abstraction (a) by a pair of rapidly equilibrating classical radicals (the ring-opened allylcarbinyl-type radical 3 and the ring-closed cyclopropylcarbinyl-type 4), or (b) by a nonclassical radical such as homoallylic radical 7.

[Figure not reproduced.]

Entry to the radical system is gained via degassed thermal decomposition of peresters having the ring-opened and the ring-closed structures. The ratio of 6:5 is essentially independent of the hydrogen donor concentration for decomposition of the former at 125° in the presence of triethyltin hydrdride. A deuterium labeling study showed that the α and β methylene groups in 3 (or the equivalent) are rapidly interchanged under these conditions.

Existence of two (or more) product-forming intermediates is indicated (a) by dependence of the ratio 6:5 on the tin hydride concentration for decomposition of the ring-closed perester at 10 and 35°, and (b) by formation of cage products having largely or wholly the structure (ring-opened or ring-closed) of the starting perester.

Relative rates of hydrogen abstraction by 3 could be inferred by comparison of ratios of rate constants for hydrogen abstraction and ortho-ring cyclization:

[Figure not reproduced.]

At 100° values of k_a/k_r are 0.14 for hydrogen abstraction from 1,4-cyclohexadiene and 7 for abstraction from triethyltin hydride. The ratio 6:5 at the same temperature is ~0.0035 for hydrogen abstraction from 1,4-cyclohexadiene, ~0.078 for abstraction from the tin hydride, and ≥ 5 for abstraction from cyclohexadienyl radicals. These data indicate that abstraction of hydrogen from triethyltin hydride is more rapid than from 1,4-cyclohexadiene by a factor of ~1000 for 4, but only ~50 for 3.

Measurements of product ratios at several temperatures allowed the construction of an approximate energy-level scheme. A major inference is that isomerization of 3 to 4 is exothermic by 8 ± 3 kcal/mole, in good agreement with expectations based on bond dissociation energies. Absolute rate-constant estimates are also given.

The results are nicely compatible with a classical-radical mechanism, but attempted interpretation in terms of a nonclassical radical precursor of product ratios formed even from equilibrated radical intermediates leads, it is argued, to serious difficulties.

The roles played by hydrogen abstraction from 1,4,-cyclohexadiene and from the derived cyclohexadienyl radicals were probed by fitting observed ratios of 6:5 and 5:10 in the sense of least-squares to expressions derived for a complex mechanistic scheme. Some 30 to 40 measurements on each product ratio, obtained under a variety of experimental conditions, could be fit with an average deviation of ~6%. Significant systematic deviations were found, but these could largely be redressed by assuming (a) that the rate constant for reaction of 4 with cyclohexadienyl radical is inversely proportional to the viscosity of the medium (i.e., is diffusion-controlled), and (b) that k_a/k_r for hydrogen abstraction from 1,4-cyclohexadiene depends slightly on the composition of the medium. An average deviation of 4.4% was thereby attained.

Degassed thermal decomposition of the ring-opened perester in the presence of the triethyltin hydride occurs primarily by attack on perester of triethyltin radicals, presumably at the –O-O- bond, even at 0.01 M tin hydride at 100 and 125°. Tin ester and tin ether are apparently formed in closely similar amounts under these conditions, but the tin ester predominates at room temperature in the companion air-induced decomposition, indicating that attack on perester to give the tin ether requires an activation energy approximately 5 kcal/mole in excess of that for the formation of tin ester.