The hydro-kinetic theory of liquid helium II

In Part I the kinetic theory of excitations in flowing liquid He II is developed to a higher order than that carried out previously, by Landau and Khalatnikov, in order to demonstrate the existence of non-equilibrium terms of a new nature in the hydrodynamic equations. It is then shown that these terms can lead to spontaneous destabilization in counter currents when the relative velocity of the normal and super fluids exceeds a critical value that depends on the temperature, but not on geometry. There are no adjustable parameters in the theory. The critical velocities are estimated to be in the 14-20 m/sec range for T ≤ 2.0° K, but tend to zero as T → T_λ. The possibility that these critical velocities may be related to the experimentally observed "intrinsic" critical velocities is discussed.

Part II consists of a semi-classical investigation of rotonquantized vortex line interactions. An essentially classical model is used for the collision and the behavior of the roton in the vortex field is investigated in detail. From this model it is possible to derive the HVBK mutual friction terms that appear in the phenomenalogical equations of motion for rotating liquid He II. Estimates of the Hall and Vinen B and B' coefficients are in good agreement with experiments. The claim is made that the theory does not contain any arbitrary adjustable parameters.

Liquid silicate equation of state : using shock waves to understand the properties of the deep Earth

The equations of state (EOS) of several geologically important silicate liquids have been constrained via preheated shock wave techniques. Results on molten Fe₂SiO₄ (fayalite), Mg₂SiO₄ (forsterite), CaFeSi₂O₆ (hedenbergite), an equimolar mixture of CaAl₂Si₂O₈-CaFeSi₂O₆ (anorthite-hedenbergite), and an equimolar mixture of CaAl₂Si₂O₈-CaFeSi₂O₆-CaMgSi₂O₆(anorthite-hedenbergite-diopside) are presented. This work represents the first ever direct EOS measurements of an iron-bearing liquid or of a forsterite liquid at pressures relevant to the deep Earth (> 135 GPa). Additionally, revised EOS for molten CaMgSi₂O₆ (diopside), CaAl₂Si₂O₈ (anorthite), and MgSiO₃ (enstatite), which were previously determined by shock wave methods, are also presented.

The liquid EOS are incorporated into a model, which employs linear mixing of volumes to determine the density of compositionally intermediate liquids in the CaO-MgO-Al₂O₃-SiO₂-FeO major element space. Liquid volumes are calculated for temperature and pressure conditions that are currently present at the core-mantle boundary or that may have occurred during differentiation of a fully molten mantle magma ocean.

The most significant implications of our results include: (1) a magma ocean of either chondrite or peridotite composition is less dense than its first crystallizing solid, which is not conducive to the formation of a basal mantle magma ocean, (2) the ambient mantle cannot produce a partial melt and an equilibrium residue sufficiently dense to form an ultralow velocity zone mush, and (3) due to the compositional dependence of Fe2+ coordination, there is a threshold of Fe concentration (molar X_Fe ≤ 0.06) permitted in a liquid for which its density can still be approximated by linear mixing of end-member volumes.

Probing the thermodynamic properties of mantle rocks in solid and liquid states

Our understanding of the structure and evolution of the deep Earth is strongly linked to knowledge of the thermodynamic properties of rocky materials at extreme temperatures and pressures. In this thesis, I present work that helps constrain the equation of state properties of iron-bearing Mg-silicate perovskite as well as oxide-silicate melts. I use a mixture of experimental, statistical, and theoretical techniques to obtain knowledge about these phases. These include laser-heated diamond anvil cell experiments, Bayesian statistical analysis of powder diffraction data, and the development of a new simplified model for understanding oxide and silicate melts at mantle conditions. By shedding light on the thermodynamic properties of such ubiquitous Earth-forming materials, I hope to aid our community’s progress toward understanding the large-scale processes operating in the Earth’s mantle, both in the modern day and early in Earth’s history.

Oxidative chemisorption of SO_2 on γ - Al_2O_3 and deposition of H_2-permselective SiO_2 films

The interaction of SO_2 with γ - Al_2O_3 and the deposition of H_2 permselective SiO_2 films have been investigated. The adsorption and oxidative adsorption of SO_2 on γ - Al_2O_3 have been examined at temperatures 500-700°C by Fourier transform infrared spectroscopy (FTIR) and thermogravimetric analysis (TGA). At temperatures above 500°C most of SO_2 adsorbed on the strong sites on alumina. The adsorbed SO_2 species was characterized by an IR band at 1065 cm^(-1). The equilibrium coverage and initial rate of adsorption decreased with temperature suggesting a two-step adsorption. When γ - Al_2O_3 was contacted with a mixture of SO_2 and O_2, adsorption of SO_2 and oxidation of the adsorbed SO_2 to a surface sulfate characterized by broad IR bands at 1070 cm^(-1), 1390 cm^(-1) took place. The results of a series of TGA experiments under different atmospheres strongly suggest that surface SO_2 and surface sulfate involve the same active sites such that SO_2 adsorption is inhibited by already formed sulfate. The results also indicate a broad range of site strengths.

The desorption of adsorbed SO_2 and the reductive desorption of oxidatively adsorbed SO_2 have been investigated by microreactor experiments and thermogravimetric analysis (TGA). Temperature programmed reduction (TPR) of adsorbed SO_2 showed that SO_2 was desorbed without significant reaction with H_2 when H_2 concentration was low while considerable reaction occurred when 100% H_2 was used. SO_2 adsorbed on the strong sites on alumina was reduced to sulfur and H_2S. The isothermal reduction experiments of oxidatively adsorbed SO_2 reveal that the rate of reduction is very slow below 550°C even with 100% H_2. The reduction product is mainly composed of SO_2. TPR experiments of oxidatively adsorbed SO_2 showed that H_2S arose from a sulfate strongly chemisorbed on the surface.

Films of amorphous SiO_2 were deposited within the walls of porous Vycor tubes by SiH_4 oxidation in an opposing reactants geometry : SiH_4 was passed inside the tube while O_2 was passed outside the tube. The two reactants diffused opposite to each other and reacted within a narrow front inside the tube wall to form a thin SiO_2 film. Once the pores were plugged the reactants could not reach each other and the reaction stopped. At 450°C and 0.1 and 0.33 atm of SiH_4 and O_2, the reaction was complete within 15 minutes. The thickness of the SiO_2 film was estimated to be about 0.1 µm. Measurements of H_2 and N_2 permeation rates showed that the SiO_2 film was highly selective to H_2 permeation. The H_2:N_2 flux at 450°C varied between 2000-3000.

Thin SiO_2 films were heat treated in different gas mixtures to determine their stability in functioning as high-temperature hydrogen-permselective membranes. The films were heat-treated at 450-700°C in dry N_2, dry O_2, N_2-H_2O, and O_2-H_2O mixtures. The permeation rates of H_2 and N_2 changed depending on the original conditions of film formation as well as on the heat treatment. Heating in dry N_2 slowly reduced the permeation rates of both H_2 and N_2. Heating in a N_2-H_2O atmosphere led to a steeper decline of H_2 permeability. But the permeation rate of N_2 increased or decreased according to whether the film deposition had been carried out in the absence or presence of H_2O vapor, respectively. Thermal treatment in O_2 caused rapid decline of the permeation rates of H_2 and N_2 in films that were deposited under dry conditions. The decline was moderate in films deposited under wet conditions.

Investigations of charge-carrier dynamics at semiconductor/liquid interfaces

Theoretical and experimental investigations of charge-carrier dynamics at semiconductor/liquid interfaces, specifically with respect to interfacial electron transfer and surface recombination, are presented.

Fermi's golden rule has been used to formulate rate expressions for charge transfer of delocalized carriers in a nondegenerately doped semiconducting electrode to localized, outer-sphere redox acceptors in an electrolyte phase. The treatment allows comparison between charge-transfer kinetic data at metallic, semimetallic, and semiconducting electrodes in terms of parameters such as the electronic coupling to the electrode, the attenuation of coupling with distance into the electrolyte, and the reorganization energy of the charge-transfer event. Within this framework, rate constant values expected at representative semiconducting electrodes have been determined from experimental data for charge transfer at metallic electrodes. The maximum rate constant (i.e., at optimal exoergicity) for outer-sphere processes at semiconducting electrodes is computed to be in the range 10^-17-10^-16 cm⁴ s^-1, which is in excellent agreement with prior theoretical models and experimental results for charge-transfer kinetics at semiconductor/liquid interfaces.

Double-layer corrections have been evaluated for semiconductor electrodes in both depletion and accumulation conditions. In conjuction with the Gouy-Chapman-Stern model, a finite difference approach has been used to calculate potential drops at a representative solid/liquid interface. Under all conditions that were simulated, the correction to the driving force used to evaluate the interfacial rate constant was determined to be less than 2% of the uncorrected interfacial rate constant.

Photoconductivity decay lifetimes have been obtained for Si(111) in contact with solutions of CH₃OH or tetrahydrofuran containing one-electron oxidants. Silicon surfaces in contact with electrolyte solutions having Nernstian redox potentials > 0 V vs. SCE exhibited low effective surface recombination velocities regardless of the different surface chemistries. The formation of an inversion layer, and not a reduced density of electrical trap sites on the surface, is shown to be responsible for the long charge-carrier lifetimes observed for these systems. In addition, a method for preparing an air-stable, low surface recombination velocity Si surface through a two-step, chlorination/alkylation reaction is described.

A multi-scale approach to shaping carbon nanotube structures for hollow microneedles

The concept of a carbon nanotube microneedle array is explored in this thesis from multiple perspectives including microneedle fabrication, physical aspects of transdermal delivery, and in vivo transdermal drug delivery experiments. Starting with standard techniques in carbon nanotube (CNT) fabrication, including catalyst patterning and chemical vapor deposition, vertically-aligned carbon nanotubes are utilized as a scaffold to define the shape of the hollow microneedle. Passive, scalable techniques based on capillary action and unique photolithographic methods are utilized to produce a CNT-polymer composite microneedle. Specific examples of CNT-polyimide and CNT-epoxy microneedles are investigated. Further analysis of the transport properties of polymer resins reveals general requirements for applying arbitrary polymers to the fabrication process.

The bottom-up fabrication approach embodied by vertically-aligned carbon nanotubes allows for more direct construction of complex high-aspect ratio features than standard top-down fabrication approaches, making microneedles an ideal application for CNTs. However, current vertically-aligned CNT fabrication techniques only allow for the production of extruded geometries with a constant cross-sectional area, such as cylinders. To rectify this limitation, isotropic oxygen etching is introduced as a novel fabrication technique to create true 3D CNT geometry. Oxygen etching is utilized to create a conical geometry from a cylindrical CNT structure as well as create complex shape transformations in other CNT geometries.

CNT-polymer composite microneedles are anchored onto a common polymer base less than 50 µm thick, which allows for the microneedles to be incorporated into multiple drug delivery platforms, including modified hypodermic syringes and silicone skin patches. Cylindrical microneedles are fabricated with 100 µm outer diameter and height of 200-250 µm with a central cavity, or lumen, diameter of 30 µm to facilitate liquid drug flow. In vitro delivery experiments in swine skin demonstrate the ability of the microneedles to successfully penetrate the skin and deliver aqueous solutions.

An in vivo study was performed to assess the ability of the CNT-polymer microneedles to deliver drugs transdermally. CNT-polymer microneedles are attached to a hand actuated silicone skin patch that holds a liquid reservoir of drugs. Fentanyl, a potent analgesic, was administered to New Zealand White Rabbits through 3 routes of delivery: topical patch, CNT-polymer microneedles, and subcutaneous hypodermic injection. Results demonstrate that the CNT-polymer microneedles have a similar onset of action as the topical patch. CNT-polymer microneedles were also vetted as a painless delivery approach compared to hypodermic injection. Comparative analysis with contemporary microneedle designs demonstrates that the delivery achieved through CNT-polymer microneedles is akin to current hollow microneedle architectures. The inherent advantage of applying a bottom-up fabrication approach alongside similar delivery performance to contemporary microneedle designs demonstrates that the CNT-polymer composite microneedle is a viable architecture in the emerging field of painless transdermal delivery.

I. Spectroscopic observation of discrete sites in simple liquids. II. Infrared intensity perturbations of hydrogen halide fundamentals in liquid xenon. III. Rotation of HCl in solid rare gases.

Part I

The spectrum of dissolved mercury atoms in simple liquids has been shown to be capable of revealing information concerning local structures in these liquids.

Part II

Infrared intensity perturbations in simple solutions have been shown to involve more detailed interaction than just dielectric polarization. No correlation has been found between frequency shifts and intensity enhancements.

Part III

Evidence for perturbed rotation of HCl in rare gas matrices has been found. The magnitude of the barrier to rotation is concluded to be of order of 30 cm^(-1).

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.

Photoelectrochemistry of GaAs and Si liquid junctions

A quantitative study has been performed on the stability of GaAs surfaces in a 0.10 M K₂Se-0.01 M K₂Se₂ aqueous solution. In this electrolyte, n-type GaAs electrodes displayed significant photocorrosion in competition with faradaic charge transfer to Se^2-. Chemisorption of group VIIIB metal ions onto the GaAs surfaces yielded improved current-voltage behavior of the GaAs photoanodes, and also resulted in a significant reduction in photocorrosion. This behavior implies that the chemisorbed metal ions act to increase the rate of hole transfer to the Se^2- species. Related experiments on n-GaAs, pGaAs, and Sn-doped In₂O₃ electrodes in Te^2-/- aqueous solutions have also been performed.

The majority carrier (electrons) transfer rate constant at a highly doped n⁺-Si/Co(Cp)₂Cl-methanol junction has been measured directly using the chronoamperometry electrochemical technique. The reduction reaction rate of Co(Cp)₂+ was 0.03 cm-s^-1 at the Si electrode, and was more than 100 times slower than at a hanging mercury electrode. The slower rate was attributed to the smaller optical and static dielectric constants, and the lower density of electrons of the semiconductor. The experimental results were compared to the Marcus theory of charge transfer.

The unique properties of high purity Si/liquid junctions have been investigated under illumination conditions in which the photogenerated carrier concentration exceeds the dopant concentration. Under these high injection conditions, negligible electric fields exist at the semiconductor/liquid interface, and carrier motion is driven by diffusion. Studies of the current-voltage properties of the Si in methanol solutions containing various redox couples suggested that high efficiency photoelectrochemical cells could be established through selective collection of carriers at the semiconductor/liquid junction. The quasi-Fermi levels of electrons and holes were measured directly against the solution potential. Steady-state and transient photovoltage measurements, and theoretical modeliug of the carrier transport, generation, and recombination dynamics indicated that the quasi-Fermi levels were flat across the semiconductor sample. The recombination velocities at the Si/liquid junctions have also been measured, and were shown to vary with the solution potential following the Shockley-Read-Hall theory on recombination.

Equilibration of a liquid droplet-vapor-gas mixture downstream of a shock wave

The equations of motion for the flow of a mixture of liquid droplets, their vapor, and an inert gas through a normal shock wave are derived. A set of equations is obtained which is solved numerically for the equilibrium conditions far downstream of the shock. The equations describing the process of reaching equilibrium are also obtained. This is a set of first-order nonlinear differential equations and must also be solved numerically. The detailed equilibration process is obtained for several cases and the results are discussed.

Sputtering of the gallium-indium eutectic alloy in the liquid phase

We have measured sputtering yields and angular distributions of sputtered atoms from both the solid and liquid phases of gallium, indium, and the gallium-indium eutectic alloy. This was done by Rutherford backscattering analysis of graphite collector foils. The solid eutectic target shows a predominance of indium crystallites on its surface which have to be sputtered away before the composition of the sputtered atoms equals the bulk target composition. The size of the crystallites depends upon the conditions under which the alloy is frozen. The sputtering of the liquid eutectic alloy by 15 keV Ar⁺ results in a ratio of indium to gallium sputtering yields which is 28 times greater than would be expected from the target stoichiometry. Furthermore, the angular distribution of gallium is much more sharply peaked about the normal to the target surface than the indium distribution. When the incident Ar⁺ energy is increased to 25 keV, the gallium distribution broadens to the same shape as the indium distribution. With the exception of the sharp gallium distribution taken from the liquid eutectic at 15 keV, all angular distributions from liquid targets fit a cos² θ function. An ion-scattering-spectroscopy analysis of the liquid eutectic alloy reveals a surface layer of almost pure indium. A thermodynamic explanation for this highly segregated layer is discussed. The liquid eutectic alloy provides us with a unique target system which allows us to estimate the fraction of sputtered material which comes from the first monolayer of the surface.

Heteroepitaxy of Group IV and Group III-V semiconductor alloys for photovoltaic applications

Photovoltaic energy conversion represents a economically viable technology for realizing collection of the largest energy resource known to the Earth -- the sun. Energy conversion efficiency is the most leveraging factor in the price of energy derived from this process. This thesis focuses on two routes for high efficiency, low cost devices: first, to use Group IV semiconductor alloy wire array bottom cells and epitaxially grown Group III-V compound semiconductor alloy top cells in a tandem configuration, and second, GaP growth on planar Si for heterojunction and tandem cell applications.

Metal catalyzed vapor-liquid-solid grown microwire arrays are an intriguing alternative for wafer-free Si and SiGe materials which can be removed as flexible membranes. Selected area Cu-catalyzed vapor-liquid solid growth of SiGe microwires is achieved using chlorosilane and chlorogermane precursors. The composition can be tuned up to 12% Ge with a simultaneous decrease in the growth rate from 7 to 1 μm/min^-1. Significant changes to the morphology were observed, including tapering and faceting on the sidewalls and along the lengths of the wires. Characterization of axial and radial cross sections with transmission electron microscopy revealed no evidence of defects at facet corners and edges, and the tapering is shown to be due to in-situ removal of catalyst material during growth. X-ray diffraction and transmission electron microscopy reveal a Ge-rich crystal at the tip of the wires, strongly suggesting that the Ge incorporation is limited by the crystallization rate.

Tandem Ga_1-xIn_xP/Si microwire array solar cells are a route towards a high efficiency, low cost, flexible, wafer-free solar technology. Realizing tandem Group III-V compound semiconductor/Si wire array devices requires optimization of materials growth and device performance. GaP and Ga_1-xIn_xP layers were grown heteroepitaxially with metalorganic chemical vapor deposition on Si microwire array substrates. The layer morphology and crystalline quality have been studied with scanning electron microscopy and transmission electron microscopy, and they provide a baseline for the growth and characterization of a full device stack. Ultimately, the complexity of the substrates and the prevalence of defects resulted in material without detectable photoluminescence, unsuitable for optoelectronic applications.

Coupled full-field optical and device physics simulations of a Ga_0.51In_0.49P/Si wire array tandem are used to predict device performance. A 500 nm thick, highly doped "buffer" layer between the bottom cell and tunnel junction is assumed to harbor a high density of lattice mismatch and heteroepitaxial defects. Under simulated AM1.5G illumination, the device structure explored in this work has a simulated efficiency of 23.84% with realistic top cell SRH lifetimes and surface recombination velocities. The relative insensitivity to surface recombination is likely due to optical generation further away from the free surfaces and interfaces of the device structure.

Finally, GaP has been grown free of antiphase domains on Si (112) oriented substrates using metalorganic chemical vapor deposition. Low temperature pulsed nucleation is followed by high temperature continuous growth, yielding smooth, specular thin films. Atomic force microscopy topography mapping showed very smooth surfaces (4-6 Å RMS roughness) with small depressions in the surface. Thin films (~ 50 nm) were pseudomorphic, as confirmed by high resolution x-ray diffraction reciprocal space mapping, and 200 nm thick films showed full relaxation. Transmission electron microscopy showed no evidence of antiphase domain formation, but there is a population of microtwin and stacking fault defects.

1. Ultrasonic studies of binary liquid structure in the critical region. Theory and experiment for the 2,6-lutidine/water system. 2. Hartree-Fock calculations of electric polarizabilities of some simple atoms and molecules, and their practicality. 3. Calculation of vibrational transition probabilities in collinear atom-diatom and diatom-diatom collisions with Lennard-Jones interaction

Part 1. Many interesting visual and mechanical phenomena occur in the critical region of fluids, both for the gas-liquid and liquid-liquid transitions. The precise thermodynamic and transport behavior here has some broad consequences for the molecular theory of liquids. Previous studies in this laboratory on a liquid-liquid critical mixture via ultrasonics supported a basically classical analysis of fluid behavior by M. Fixman (e. g., the free energy is assumed analytic in intensive variables in the thermodynamics)--at least when the fluid is not too close to critical. A breakdown in classical concepts is evidenced close to critical, in some well-defined ways. We have studied herein a liquid-liquid critical system of complementary nature (possessing a lower critical mixing or consolute temperature) to all previous mixtures, to look for new qualitative critical behavior. We did not find such new behavior in the ultrasonic absorption ascribable to the critical fluctuations, but we did find extra absorption due to chemical processes (yet these are related to the mixing behavior generating the lower consolute point). We rederived, corrected, and extended Fixman's analysis to interpret our experimental results in these more complex circumstances. The entire account of theory and experiment is prefaced by an extensive introduction recounting the general status of liquid state theory. The introduction provides a context for our present work, and also points out problems deserving attention. Interest in these problems was stimulated by this work but also by work in Part 3.

Part 2. Among variational theories of electronic structure, the Hartree-Fock theory has proved particularly valuable for a practical understanding of such properties as chemical binding, electric multipole moments, and X-ray scattering intensity. It also provides the most tractable method of calculating first-order properties under external or internal one-electron perturbations, either developed explicitly in orders of perturbation theory or in the fully self-consistent method. The accuracy and consistency of first-order properties are poorer than those of zero-order properties, but this is most often due to the use of explicit approximations in solving the perturbed equations, or to inadequacy of the variational basis in size or composition. We have calculated the electric polarizabilities of H₂, He, Li, Be, LiH, and N₂ by Hartree-Fock theory, using exact perturbation theory or the fully self-consistent method, as dictated by convenience. By careful studies on total basis set composition, we obtained good approximations to limiting Hartree-Fock values of polarizabilities with bases of reasonable size. The values for all species, and for each direction in the molecular cases, are within 8% of experiment, or of best theoretical values in the absence of the former. Our results support the use of unadorned Hartree-Pock theory for static polarizabilities needed in interpreting electron-molecule scattering data, collision-induced light scattering experiments, and other phenomena involving experimentally inaccessible polarizabilities.

Part 3. Numerical integration of the close-coupled scattering equations has been carried out to obtain vibrational transition probabilities for some models of the electronically adiabatic H₂-H₂ collision. All the models use a Lennard-Jones interaction potential between nearest atoms in the collision partners. We have analyzed the results for some insight into the vibrational excitation process in its dependence on the energy of collision, the nature of the vibrational binding potential, and other factors. We conclude also that replacement of earlier, simpler models of the interaction potential by the Lennard-Jones form adds very little realism for all the complication it introduces. A brief introduction precedes the presentation of our work and places it in the context of attempts to understand the collisional activation process in chemical reactions as well as some other chemical dynamics.

The structure of liquid argon as determined by x-ray diffraction

X-ray diffraction measurements and subsequent data analyses have been carried out on liquid argon at five states in the density range of 0.91 to 1.135 gm/cc and temperature range of 127 to 143°K. Duplicate measurements were made on all states. These data yielded radial distribution and direct correlation functions which were then used to compute the pair potential using the Percus-Yevick equation. The potential minima are in the range of -105 to -120°K and appear to substantiate current theoretical estimates of the effective pair potential in the presence of a weak three-body force.

The data analysis procedure used was new and does not distinguish between the coherent and incoherent absorption factors for the cell scattering which were essentially equal. With this simplification, the argon scattering estimate was compared to the gas scattering estimate on the laboratory frame of reference and the two estimates coincided, indicating the data normalized. The argon scattering on the laboratory frame of reference was examined for the existence of the peaks in the structure factor and the existence of an observable third peak was considered doubtful.

Numerical studies of the effect of truncation, normalization, the subsidiary peak phenomenon in the radial distribution function, uncertainties in the low angle data relative to errors in the direct correlation function and the distortion phenomenon are presented.

The distortion phenomenon for this experiment explains why the Mikolaj-Pings argon data yielded pair potential well depths from the Percus-Yevick equation that were too shallow and an apparent slope with respect to density that was too steep compared to theoretical estimates.

The data presented for each measurement are: empty cell and cell plus argon intensity, absorption factors, argon intensity, smoothed argon intensity, smoothed argon intensity corrected for distortion, structure factor, radial distribution function, direct correlation function and the pair potential from the Percus-Yevick equation.