Mean-speed measurements in two-dimensional, incompressible, fully-developed turbulent channel flow

Mean velocity profiles were measured in the 5” x 60” wind channel of the turbulence laboratory at the GALCIT, by the use of a hot-wire anemometer. The repeatability of results was established, and the accuracy of the instrumentation estimated. Scatter of experimental results is a little, if any, beyond this limit, although some effects might be expected to arise from variations in atmospheric humidity, no account of this factor having been taken in the present work. Also, slight unsteadiness in flow conditions will be responsible for some scatter.

Irregularities of a hot-wire in close proximity to a solid boundary at low speeds were observed, as have already been found by others.

That Kármán’s logarithmic law holds reasonably well over the main part of a fully developed turbulent flow was checked, the equation u/u_t = 6.0 + 6.25 log₁₀ y^ut/v being obtained, and, as has been previously the case, the experimental points do not quite form one straight line in the region where viscosity effects are small. The values of the constants for this law for the best over-all agreement were determined and compared with those obtained by others.

The range of Reynolds numbers used (based on half-width of channel) was from 20,000 to 60,000.

Black holes in the early universe, in compact binaries, and as energy sources inside solar-type stars

This thesis consists of three separate studies of roles that black holes might play in our universe.

In the first part we formulate a statistical method for inferring the cosmological parameters of our universe from LIGO/VIRGO measurements of the gravitational waves produced by coalescing black-hole/neutron-star binaries. This method is based on the cosmological distance-redshift relation, with "luminosity distances" determined directly, and redshifts indirectly, from the gravitational waveforms. Using the current estimates of binary coalescence rates and projected "advanced" LIGO noise spectra, we conclude that by our method the Hubble constant should be measurable to within an error of a few percent. The errors for the mean density of the universe and the cosmological constant will depend strongly on the size of the universe, varying from about 10% for a "small" universe up to and beyond 100% for a "large" universe. We further study the effects of random gravitational lensing and find that it may strongly impair the determination of the cosmological constant.

In the second part of this thesis we disprove a conjecture that black holes cannot form in an early, inflationary era of our universe, because of a quantum-field-theory induced instability of the black-hole horizon. This instability was supposed to arise from the difference in temperatures of any black-hole horizon and the inflationary cosmological horizon; it was thought that this temperature difference would make every quantum state that is regular at the cosmological horizon be singular at the black-hole horizon. We disprove this conjecture by explicitly constructing a quantum vacuum state that is everywhere regular for a massless scalar field. We further show that this quantum state has all the nice thermal properties that one has come to expect of "good" vacuum states, both at the black-hole horizon and at the cosmological horizon.

In the third part of the thesis we study the evolution and implications of a hypothetical primordial black hole that might have found its way into the center of the Sun or any other solar-type star. As a foundation for our analysis, we generalize the mixing-length theory of convection to an optically thick, spherically symmetric accretion flow (and find in passing that the radial stretching of the inflowing fluid elements leads to a modification of the standard Schwarzschild criterion for convection). When the accretion is that of solar matter onto the primordial hole, the rotation of the Sun causes centrifugal hangup of the inflow near the hole, resulting in an "accretion torus" which produces an enhanced outflow of heat. We find, however, that the turbulent viscosity, which accompanies the convective transport of this heat, extracts angular momentum from the inflowing gas, thereby buffering the torus into a lower luminosity than one might have expected. As a result, the solar surface will not be influenced noticeably by the torus's luminosity until at most three days before the Sun is finally devoured by the black hole. As a simple consequence, accretion onto a black hole inside the Sun cannot be an answer to the solar neutrino puzzle.

Three-dimensional models of mantle convection : influence of phase transitions and temperature-dependent viscosity

Two of the most important questions in mantle dynamics are investigated in three separate studies: the influence of phase transitions (studies 1 and 2), and the influence of temperature-dependent viscosity (study 3).

(1) Numerical modeling of mantle convection in a three-dimensional spherical shell incorporating the two major mantle phase transitions reveals an inherently three-dimensional flow pattern characterized by accumulation of cold downwellings above the 670 km discontinuity, and cylindrical 'avalanches' of upper mantle material into the lower mantle. The exothermic phase transition at 400 km depth reduces the degree of layering. A region of strongly-depressed temperature occurs at the base of the mantle. The temperature field is strongly modulated by this partial layering, both locally and in globally-averaged diagnostics. Flow penetration is strongly wavelength-dependent, with easy penetration at long wavelengths but strong inhibition at short wavelengths. The amplitude of the geoid is not significantly affected.

(2) Using a simple criterion for the deflection of an upwelling or downwelling by an endothermic phase transition, the scaling of the critical phase buoyancy parameter with the important lengthscales is obtained. The derived trends match those observed in numerical simulations, i.e., deflection is enhanced by (a) shorter wavelengths, (b) narrower up/downwellings (c) internal heating and (d) narrower phase loops.

(3) A systematic investigation into the effects of temperature-dependent viscosity on mantle convection has been performed in three-dimensional Cartesian geometry, with a factor of 1000-2500 viscosity variation, and Rayleigh numbers of 10^5-10^7. Enormous differences in model behavior are found, depending on the details of rheology, heating mode, compressibility and boundary conditions. Stress-free boundaries, compressibility, and temperature-dependent viscosity all favor long-wavelength flows, even in internally heated cases. However, small cells are obtained with some parameter combinations. Downwelling plumes and upwelling sheets are possible when viscosity is dependent solely on temperature. Viscous dissipation becomes important with temperature-dependent viscosity.

The sensitivity of mantle flow and structure to these various complexities illustrates the importance of performing mantle convection calculations with rheological and thermodynamic properties matching as closely as possible those of the Earth.

Part I. Influence of membrane morphology on ion-exchange and charge propagation in composite polyelectrolyte electrode coatings. Part II. Dynamic surface tension measurements of polarization relaxation at mercury pool electrodes by the method of Wilhelmy.

Part I. Novel composite polyelectrolyte materials were developed that exhibit desirable charge propagation and ion-retention properties. The morphology of electrode coatings cast from these materials was shown to be more important for its electrochemical behavior than its chemical composition.

Part II. The Wilhelmy plate technique for measuring dynamic surface tension was extended to electrified liquid-liquid interphases. The dynamical response of the aqueous NaF-mercury electrified interphase was examined by concomitant measurement of surface tension, current, and applied electrostatic potential. Observations of the surface tension response to linear sweep voltammetry and to step function perturbations in the applied electrostatic potential (e.g., chronotensiometry) provided strong evidence that relaxation processes proceed for time-periods that are at least an order of magnitude longer than the time periods necessary to establish diffusion equilibrium. The dynamical response of the surface tension is analyzed within the context of non-equilibrium thermodynamics and a kinetic model that requires three simultaneous first order processes.

Solar photospheric and coronal abundances from solar energetic particle measurements

Observations of solar energetic particles (SEPs) from 22 solar flares in the 1977-1982 time period are reported. The observations were made by the Cosmic Ray Subsystem on board the Voyager 1 and 2 spacecraft. SEP abundances have been obtained for all elements with 3 ≤ Z ≤ 30 except Li, Be, B. F, Sc, V, Co and Cu. for which upper limits have been obtained. Statistically meaningful abundances of several rare elements (e.g., P, Cl, K, Ti, Mn) have been determined for the first time, and the average abundances of the more abundant elements have been determined with improved precision, typically a factor of three better than the best previous determinations.

Previously reported results concerning the dependence of the fractionation of SEPs relative to photosphere on first ionization potential (FIP) have been confirmed and amplified upon with the new data. The monotonic Z-dependence of the variation between flares noted by earlier studies was found to be interpretable as a fractionation, produced by acceleration of the particles from the corona and their propagation through interplanetary space, which is ordered by the ionic charge-to-mass ratio Q/ M of the species making up the SEPs. It was found that Q/M is the primary organizing parameter of acceleration and propagation effects in SEPs, as evidenced by the dependence on Q/M of time, spatial and energy dependence within flares and of the abundance variability from flare to flare.

An unfractionated coronal composition was derived by applying a simple Q/M fractionation correction to the observed average SEP composition, to simultaneously correct for all Q/M-correlated acceleration/propagation fractionation of SEPs. The resulting coronal composition agrees well with current XUV/X-ray spectroscopic measurements of coronal composition but is of much higher precision and is available for a much larger set of elements. Compared to spectroscopic photospheric abundances, the SEP-derived corona appears depleted in C and somewhat enriched in Cr (and possibly Ca and Ti).

An unfractionated photospheric composition was derived by applying a simple FIP fractionation correction to the derived coronal composition, to correct for the FIP-associated fractionation of the corona during its formation from photospheric material. The resulting composition agrees well with the photospheric abundance tabulation of Grevesse (1984) except for an at least 50% lower abundance of C and a significantly greater abundance of Cr and possibly Ti. The results support the Grevesse photospheric Fe abundance, about 50% higher than meteoritic and earlier solar values. The SEP-derived photospheric composition is not generally of higher precision than the available spectroscopic data, but it relies on fewer physical parameters and is available for some elements (C, N, Ne, Ar) which cannot be measured spectroscopically in the photosphere.

The Equation of State and Petrogenesis of Komatiite

(1) Equation of State of Komatiite

The equation of state (EOS) of a molten komatiite (27 wt% MgO) was detennined in the 5 to 36 GPa pressure range via shock wave compression from 1550°C and 0 bar. Shock wave velocity, U_S, and particle velocity, U_P, in km/s follow the linear relationship U_S = 3.13(±0.03) + 1.47(±0.03) U_P. Based on a calculated density at 1550°C, 0 bar of 2.745±0.005 glee, this U_S-U_P relationship gives the isentropic bulk modulus K_S = 27.0 ± 0.6 GPa, and its first and second isentropic pressure derivatives, K'_S = 4.9 ± 0.1 and K"_S = -0.109 ± 0.003 GPa^-1.

The calculated liquidus compression curve agrees within error with the static compression results of Agee and Walker [1988a] to 6 GPa. We detennine that olivine (FO₉₄) will be neutrally buoyant in komatiitic melt of the composition we studied near 8.2 GPa. Clinopyroxene would also be neutrally buoyant near this pressure. Liquidus garnet-majorite may be less dense than this komatiitic liquid in the 20-24 GPa interval, however pyropic-garnet and perovskite phases are denser than this komatiitic liquid in their respective liquidus pressure intervals to 36 GPa. Liquidus perovskite may be neutrally buoyant near 70 GPa.

At 40 GPa, the density of shock-compressed molten komatiite would be approximately equal to the calculated density of an equivalent mixture of dense solid oxide components. This observation supports the model of Rigden et al. [1989] for compressibilities of liquid oxide components. Using their theoretical EOS for liquid forsterite and fayalite, we calculate the densities of a spectrum of melts from basaltic through peridotitic that are related to the experimentally studied komatiitic liquid by addition or subtraction of olivine. At low pressure, olivine fractionation lowers the density of basic magmas, but above 14 GPa this trend is reversed. All of these basic to ultrabasic liquids are predicted to have similar densities at 14 GPa, and this density is approximately equal to the bulk (PREM) mantle. This suggests that melts derived from a peridotitic mantle may be inhibited from ascending from depths greater than 400 km.

The EOS of ultrabasic magmas was used to model adiabatic melting in a peridotitic mantle. If komatiites are formed by >15% partial melting of a peridotitic mantle, then komatiites generated by adiabatic melting come from source regions in the lower transition zone (≈500-670 km) or the lower mantle (>670 km). The great depth of incipient melting implied by this model, and the melt density constraint mentioned above, suggest that komatiitic volcanism may be gravitationally hindered. Although komatiitic magmas are thought to separate from their coexisting crystals at a temperature =200°C greater than that for modern MORBs, their ultimate sources are predicted to be diapirs that, if adiabatically decompressed from initially solid mantle, were more than 700°C hotter than the sources of MORBs and derived from great depth.

We considered the evolution of an initially molten mantle, i.e., a magma ocean. Our model considers the thermal structure of the magma ocean, density constraints on crystal segregation, and approximate phase relationships for a nominally chondritic mantle. Crystallization will begin at the core-mantle boundary. Perovskite buoyancy at > 70 GPa may lead to a compositionally stratified lower mantle with iron-enriched mangesiowiistite content increasing with depth. The upper mantle may be depleted in perovskite components. Olivine neutral buoyancy may lead to the formation of a dunite septum in the upper mantle, partitioning the ocean into upper and lower reservoirs, but this septum must be permeable.

(2) Viscosity Measurement with Shock Waves

We have examined in detail the analytical method for measuring shear viscosity from the decay of perturbations on a corrugated shock front The relevance of initial conditions, finite shock amplitude, bulk viscosity, and the sensitivity of the measurements to the shock boundary conditions are discussed. The validity of the viscous perturbation approach is examined by numerically solving the second-order Navier-Stokes equations. These numerical experiments indicate that shock instabilities may occur even when the Kontorovich-D'yakov stability criteria are satisfied. The experimental results for water at 15 GPa are discussed, and it is suggested that the large effective viscosity determined by this method may reflect the existence of ice VII on the Rayleigh path of the Hugoniot This interpretation reconciles the experimental results with estimates and measurements obtained by other means, and is consistent with the relationship of the Hugoniot with the phase diagram for water. Sound waves are generated at 4.8 MHz at in the water experiments at 15 GPa. The existence of anelastic absorption modes near this frequency would also lead to large effective viscosity estimates.

(3) Equation of State of Molybdenum at 1400°C

Shock compression data to 96 GPa for pure molybdenum, initially heated to 1400°C, are presented. Finite strain analysis of the data gives a bulk modulus at 1400°C, K'_S. of 244±2 GPa and its pressure derivative, K'_OS of 4. A fit of shock velocity to particle velocity gives the coefficients of U_S = C_O+S U_P to be C_O = 4.77±0.06 km/s and S = 1.43±0.05. From the zero pressure sound speed, C_O, a bulk modulus of 232±6 GPa is calculated that is consistent with extrapolation of ultrasonic elasticity measurements. The temperature derivative of the bulk modulus at zero pressure, θK_OSθT|_P, is approximately -0.012 GPa/K. A thermodynamic model is used to show that the thermodynamic Grüneisen parameter is proportional to the density and independent of temperature. The Mie-Grüneisen equation of state adequately describes the high temperature behavior of molybdenum under the present range of shock loading conditions.

On Ultrafast Time-Domain TeraHertz Spectroscopy in the Condensed Phase: Linear Spectroscopic Measurements of Hydrogen-Bond Dynamics of Astrochemical Ice Analogs and Nonlinear TeraHertz Kerr Effect Measurements of Vibrational Quantum Beats

Much of the chemistry that affects life on planet Earth occurs in the condensed phase. The TeraHertz (THz) or far-infrared (far-IR) region of the electromagnetic spectrum (from 0.1 THz to 10 THz, 3 cm^-1 to 300 cm^-1, or 3000 μm to 30 μm) has been shown to provide unique possibilities in the study of condensed-phase processes. The goal of this work is to expand the possibilities available in the THz region and undertake new investigations of fundamental interest to chemistry. Since we are fundamentally interested in condensed-phase processes, this thesis focuses on two areas where THz spectroscopy can provide new understanding: astrochemistry and solvation science. To advance these fields, we had to develop new instrumentation that would enable the experiments necessary to answer new questions in either astrochemistry or solvation science. We first developed a new experimental setup capable of studying astrochemical ice analogs in both the TeraHertz (THz), or far-Infrared (far-IR), region (0.3 - 7.5 THz; 10 - 250 cm^-1) and the mid-IR (400 - 4000 cm^-1). The importance of astrochemical ices lies in their key role in the formation of complex organic molecules, such as amino acids and sugars in space. Thus, the instruments are capable of performing variety of spectroscopic studies that can provide especially relevant laboratory data to support astronomical observations from telescopes such as the Herschel Space Telescope, the Stratospheric Observatory for Infrared Astronomy (SOFIA), and the Atacama Large Millimeter Array (ALMA). The experimental apparatus uses a THz time-domain spectrometer, with a 1750/875 nm plasma source and a GaP detector crystal, to cover the bandwidth mentioned above with ~10 GHz (~0.3 cm^-1) resolution.

Using the above instrumentation, experimental spectra of astrochemical ice analogs of water and carbon dioxide in pure, mixed, and layered ices were collected at different temperatures under high vacuum conditions with the goal of investigating the structure of the ice. We tentatively observe a new feature in both amorphous solid water and crystalline water at 33 cm^-1 (1 THz). In addition, our studies of mixed and layered ices show how it is possible to identify the location of carbon dioxide as it segregates within the ice by observing its effect on the THz spectrum of water ice. The THz spectra of mixed and layered ices are further analyzed by fitting their spectra features to those of pure amorphous solid water and crystalline water ice to quantify the effects of temperature changes on structure. From the results of this work, it appears that THz spectroscopy is potentially well suited to study thermal transformations within the ice.

To advance the study of liquids with THz spectroscopy, we developed a new ultrafast nonlinear THz spectroscopic technique: heterodyne-detected, ultrafast THz Kerr effect (TKE) spectroscopy. We implemented a heterodyne-detection scheme into a TKE spectrometer that uses a stilbazoiumbased THz emitter, 4-N,N-dimethylamino-4-N-methyl-stilbazolium 2,4,6-trimethylbenzenesulfonate (DSTMS), and high numerical aperture optics which generates THz electric field in excess of 300 kV/cm, in the sample. This allows us to report the first measurement of quantum beats at terahertz (THz) frequencies that result from vibrational coherences initiated by the nonlinear, dipolar interaction of a broadband, high-energy, (sub)picosecond THz pulse with the sample. Our instrument improves on both the frequency coverage, and sensitivity previously reported; it also ensures a backgroundless measurement of the THz Kerr effect in pure liquids. For liquid diiodomethane, we observe a quantum beat at 3.66 THz (122 cm^-1), in exact agreement with the fundamental transition frequency of the υ4 vibration of the molecule. This result provides new insight into dipolar vs. Raman selection rules at terahertz frequencies.

To conclude we discuss future directions for the nonlinear THz spectroscopy in the Blake lab. We report the first results from an experiment using a plasma-based THz source for nonlinear spectroscopy that has the potential to enable nonlinear THz spectra with a sub-100 fs temporal resolution, and how the optics involved in the plasma mechanism can enable THz pulse shaping. Finally, we discuss how a single-shot THz detection scheme could improve the acquisition of THz data and how such a scheme could be implemented in the Blake lab. The instruments developed herein will hopefully remain a part of the groups core competencies and serve as building blocks for the next generation of THz instrumentation that pushes the frontiers of both chemistry and the scientific enterprise as a whole.

Experimental study on inertial effects in liquid-solid flows

This thesis presents experimental measurements of the rheological behavior of liquid-solid mixtures at moderate Reynolds (defined by the shear rate and particle diameter) and Stokes numbers, ranging from 3 ≤ Re ≤ 1.6 × 10³ and 0.4 ≤ St ≤ 195. The experiments use a specifically designed Couette cylindrical rheometer that allows for probing the transition from transporting a pure liquid to transporting a dense suspension of particles. Measurements of the shear stress are presented for a wide range of particle concentration (10 to 60% in volume) and for particle to fluid density ratio between 1 and 1.05. The effective relative viscosity exhibits a strong dependence on the solid fraction for all density ratios tested. For density ratio of 1 the effective viscosity increases with Stokes number (St) for volume fractions (φ) lower than 40% and becomes constant for higher φ. When the particles are denser than the liquid, the effective viscosity shows a stronger dependance on St. An analysis of the particle resuspension for the case with a density ratio of 1.05 is presented and used to predict the local volume fraction where the shear stress measurements take place. When the local volume fraction is considered, the effective viscosity for settling and no settling particles is consistent, indicating that the effective viscosity is independent of differences in density between the solid and liquid phase. Shear stress measurements of pure fluids (no particles) were performed using the same rheometer, and a deviation from laminar behavior is observed for gap Reynolds numbers above 4× 10³, indicating the presence of hydrodynamic instabilities associated with the rotation of the outer cylinder. The increase on the effective viscosity with Stokes numbers observed for mixtures with φ ≤ 30% appears to be affected by such hydrodynamic instabilities. The effective viscosity for the current experiments is considerably higher than the one reported in non-inertial suspensions.

Pulsed neutron measurements in two adjacent finite media

The pulsed neutron technique has been used to investigate the decay of thermal neutrons in two adjacent water-borated water finite media. Experiments were performed with a 6x6x6 inches cubic assembly divided in two halves by a thin membrane and filled with pure distilled water on one side and borated water on the other side.

The fundamental decay constant was measured versus the boric acid concentration in the poisoned medium. The experimental results showed good agreement with the predictions of the time dependent diffusion model. It was assumed that the addition of boric acid increases the absorption cross section of the poisoned medium without affecting its diffusion properties: In these conditions, space-energy separability and the concept of an “effective” buckling as derived from diffusion theory were introduced. Their validity was supported by the experimental results.

Measurements were performed with the absorption cross section of the poisoned medium increasing gradually up to 16 times its initial value. Extensive use of the IBM 7090-7094 Computing facility was made to analyze properly the decay data (Frantic Code). Attention was given to the count loss correction scheme and the handling of the statistics involved. Fitting of the experimental results into the analytical form predicted by the diffusion model led to

Ʃ_av = 4721 sec^-1 (±150)

D_o = 35972 cm²sec^-1 (±800) for water at 21˚C

C (given) = 3420 cm⁴sec^-1

These values, when compared with published data, show that the diffusion model is adequate in describing the experiment.

Mass measurements of some proton-rich nuclei

The Q values and 0^o cross sections of (He³, n) reactions forming seven proton-rich nuclei have been measured with accuracies varying from 6 to 18 keV. The Q values (in keV) are: Si²⁶ (85), S³⁰ (-573), Ar³⁴ (-759), Ti⁴² (-2865), Cr⁴⁸ (5550), Ni⁵⁶ (4513) and Zn⁶⁰ (818). At least one excited state was found for all but Ti⁴². The first four nuclei complete isotopic spin triplets; the results obtained agree well with charge-symmetry predictions. The last three, all multiples of the α particle, are important in the α and e-process theories of nucleo-synthesis in stars. The energy available for β decay of these three was found by magnetic spectrometer measurements of the (He³, p) Q values of reactions leading to V⁴⁸, Co⁵⁶, and Cu⁶⁰. Many excited states were seen: V⁴⁸ (3), Co⁵⁶ (15), Cu⁶⁰ (23). The first two states of S³⁰ are probably 0⁺ and 2⁺ from (He³, n) angular distribution measurements. Two NaI γ-ray measurements are described: the decay of Ar³⁴ (measured ^Ƭ1/2 = 1.2 ± 0.3s) and the prompt γ-ray spectrum from Fe⁵⁴(He³, nγ)Ni⁵⁶. Possible collective structure in Ni⁵⁶ and Ca⁴⁰, both doubly magic, is discussed.

The (He³, n) neutron energy and yield measurements utilized neutron-induced nuclear reactions in a silicon semiconductor detector. Cross sections for the most important detection processes, Si²⁸ (n, α) Mg²⁵ and Si²⁸ (n, p) Al²⁸, are presented for reactions leading to the first four states of both residual nuclei for neutron energies from 7.3 to 16.4 MeV. Resolution and pulse-height anomalies associated with recoil Mg²⁵ and Al²⁸ ions are discussed. The 0^o cross section for Be⁹ (α, n) C¹², used to provide calibration neutrons, has been measured with a stilbene spectrometer for n_o (5.0 ≤ E_α ≤ 12 MeV), n₁ (4.3 ≤ E_α ≤ 12.0 MeV) and n₂ (6.0 ≤ E_α ≤ 10.1 MeV). Resonances seen in the n_o yield may correspond to nine new levels in C¹³.

Total cross section measurements for ^3He(^3He, 2p)^4He at low energies

Precise measurements of the total reaction cross section for ³He(³He,2p)⁴He He have been made in the range of center-of-mass energies between 1100 keV and 80 keV. A differentially pumped gas target modified to operate with a limited quantity of the target gas was employed to minimize the uncertainties in the primary energy and energy straggle. Beam integration inside the target gas was carried out by a calorimetric device which measures the total energy spent in a heat sink rather than the total charge in a Faraday cup. Proton energy spectra have been obtained using a counter telescope consisting of a gas proportional counter and a surface barrier detector and angular distributions of these protons have been measured at seven bombarding energies. Cross section factors, S(E), have been calculated from the total cross sections and fitted to a linear function of energy over different ranges of energy. For E_cm < 500 keV

S(E_cm) = S₀ + S₁ E_cm

where S₀ = (5.0 ^+0.6_-0.4) MeV - barns and S₁ = (-1.8 ± 0.5) barns.

Isotope shift measurements using k x-rays in Sn, Sm, and W

Electronic Kαl x-ray isotope shifts have been measured for Sn 116-124, Sm 148-154, W 182-184, W 184-186, and W 182-186 using a curved crystal Cauchois spectrometer. The analysis of the measurements has included the electrostatic volume effect, screening by the transition electron as well as the non-transition electrons, normal and specific mass shifts, dynamical nuclear qudrupole polarization, and a radiative correction effect of the electron magnetic moment in the nuclear charge radii are obtained. Where other experimental data are available, the agreement with the present measurements is satisfactory. Comparisons with several nuclear model predictions yield only partial agreement.

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.

New measurements on the absolute cosmic ray ionization from sea level to 1540 kilometers altitude

An air filled ionization chamber has been constructed with a volume of 552 liters and a wall consisting of 12.7 mg/cm² of plastic wrapped over a rigid, lightweight aluminum frame. A calibration in absolute units, independent of previous Caltech ion chamber calibrations, was applied to a sealed Neher electrometer for use in this chamber. The new chamber was flown along with an older, argon filled, balloon type chamber in a C-135 aircraft from 1,000 to 40,000 feet altitude, and other measurements of sea level cosmic ray ionization were made, resulting in the value of 2.60 ± .03 ion pairs/cm³ sec atm) at sea level. The calibrations of the two instruments were found to agree within 1 percent, and the airplane data were consistent with previous balloon measurements in the upper atmosphere. Ionization due to radon gas in the atmosphere was investigated. Absolute ionization data in the lower atmosphere have been compared with results of other observers, and discrepancies have been discussed.

Data from a polar orbiting ion chamber on the OGO-II, IV spacecraft have been analyzed. The problem of radioactivity produced on the spacecraft during passes through high fluxes of trapped protons has been investigated, and some corrections determined. Quiet time ionization averages over the polar regions have been plotted as function of altitude, and an analytical fit is made to the data that gives a value of 10.4 ± 2.3 percent for the fractional part of the ionization at the top of the atmosphere due to splash albedo particles, although this result is shown to depend on an assumed angular distribution for the albedo particles. Comparisons with other albedo measurements are made. The data are shown to be consistent with balloon and interplanetary ionization measurements. The position of the cosmic ray knee is found to exhibit an altitude dependence, a North-South effect, and a small local time variation.

Measurements of mantle velocities of P waves with a large array

A large array has been used to investigate the P-wave velocity structure of the lower mantle. Linear array processing methods are reviewed and a method of nonlinear processing is presented. Phase velocities, travel times, and relative amplitudes of P waves have been measured with the large array at the Tonto Forest Seismological Observatory in Arizona for 125 earthquakes in the distance range of 30 to 100 degrees. Various models are assumed for the upper 771 km of the mantle and the Wiechert-Herglotz method applied to the phase velocity data to obtain a velocity depth structure for the lower mantle. The phase velocity data indicates the presence of a second-order discontinuity at a depth of 840 km, another at 1150 km, and less pronounced discontinuities at 1320, 1700 and 1950 km. Phase velocities beyond 85 degrees are interpreted in terms of a triplication of the phase velocity curve, and this results in a zone of almost constant velocity between depths of 2670 and 2800 km. Because of the uncertainty in the upper mantle assumptions, a final model cannot be proposed, but it appears that the lower mantle is more complicated than the standard models and there is good evidence for second-order discontinuities below a depth of 1000 km. A tentative lower bound of 2881 km can be placed on the depth to the core. The importance of checking the calculated velocity structure against independently measured travel times is pointed out. Comparisons are also made with observed PcP times and the agreement is good. The method of using measured values of the rate of change of amplitude with distances shows promising results.