Showing papers on "Scattering published in 1989"

Advanced engineering electromagnetics

Abstract: Time--Varying and Time--Harmonic Electromagnetic Fields. Electrical Properties of Matter. Wave Equation and Its Solutions. Wave Propagation and Polarization. Reflection and Transmission. Auxiliary Vector Potentials, Contruction of Solutions, and Radiation and Scattering Equations. Electromagnetic Theorems and Principles. Rectangular Cross--Section Waveguides and Cavities. Circular Cross--Section Waveguides and Cavities. Spherical Transmission Lines and Cavities. Scattering. Integral Equations and the Moment Method. Geometrical Theory of Diffraction. Greena s Functions. Appendices. Index.

Thermal boundary resistance

Abstract: The thermal boundary resistance present at interfaces between helium and solids (Kapitza resistance) and the thermal boundary resistance at interfaces between two solids are discussed for temperatures above 0.1 K. The apparent qualitative differences in the behavior of the boundary resistance at these two types of interfaces can be understood within the context of two limiting models of the boundary resistance, the acoustic mismatch model, which assumes no scattering, and the diffuse mismatch model, which assumes that all phonons incident on the interface will scatter. If the acoustic impedances of the two media in contact are very different, as is the case for helium (liquid or solid) in contact with a solid, then phonon scattering at the interface will reduce the boundary resistance. In the limiting case of diffuse mismatch, this reduction is typically over 2 orders of magnitude. Phonons are very sensitive to surface defects, and therefore the Kapitza resistance is very sensitive to the condition of the interface. For typical solid-solid interfaces, at which the acoustic impedances are less different, the influence of diffuse scattering is relatively small; even for the two limiting cases of acoustic mismatch and diffuse mismatch the predicted boundary resistances differ by very little (\ensuremath{\lesssim} 30%). Consequently, the experimentally determined values are expected to be rather insensitive to the condition of the interface, in agreement with recent observations. Subsurface (bulk) disorder and imperfect physical contact between the solids play far more important roles and led to the irreproducibilities observed in the early measurements of the solid-solid thermal boundary resistance.

Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties.

Abstract: When a picosecond light pulse is incident on biological tissue, the temporal characteristics of the light backscattered from, or transmitted through, the sample carry information about the optical absorption and scattering coefficients of the tissue. We develop a simple model, based on the diffusion approximation to radiative transfer theory, which yields analytic expressions for the pulse shape in terms of the interaction coefficients of a homogeneous slab. The model predictions are in good agreement with the results of preliminary in vivo experiments and Monte Carlo simulations.

The Monte Carlo Method for Semiconductor Device Simulation

Abstract: 1 Introduction.- References.- 2 Charge Transport in Semiconductors.- 2.1 Electron Dynamics.- 2.2 Energy Bands.- 2.2.1 Relationship of Energy to Wavevector.- 2.2.2 Effective Masses.- 2.2.3 Nonparabolicity.- 2.2.4 Herring and Vogt Transformation.- 2.2.5 Actual Bands of Real Semiconductors.- 2.3 Scattering Mechanisms.- 2.3.1 Classification and Physical Discussion.- 2.3.2 Fundamentals of Scattering.- 2.4 Scattering Probabilities.- 2.4.1 Phonon Scattering, Deformation-Potential Interaction.- 2.4.2 Phonon Scattering, Electrostatic Interaction.- 2.4.3 Ionized Impurity Scattering.- 2.4.4 Carrier-Carrier Scattering.- 2.5 Transport Equation.- 2.6 Linear Response and the Relaxation Time Approximation.- 2.6.1 Relaxation Times for the Various Scattering Mechanisms.- 2.6.2 Carrier Mobilities in Various Materials.- 2.7 Diffusion, Noise, and Velocity Autocorrelation Function.- 2.7.1 Basic Macroscopic Equations of Diffusion.- 2.7.2 Diffusion, Autocorrelation Function, and Noise.- 2.7.3 Electron Lifetime and Diffusion Length.- 2.8 Hot Electrons.- 2.9 Transient Transport.- 2.10 The Two-dimensional Electron Gas.- 2.10.1 Subband Levels and Wavefunctions.- 2.10.2 Scattering Rates.- References.- 3 The Monte Carlo Simulation.- 3.1 Fundamentals.- 3.2 Definition of the Physical System.- 3.3 Initial Conditions.- 3.4 The Free Flight, Self Scattering.- 3.5 The Scattering Process.- 3.6 The Choice of the State After Scattering.- 3.6.1 Phonon Scattering, Deformation-Potential Interaction.- 3.6.2 Phonon Scattering, Electrostatic Interaction.- 3.6.3 Ionized Impurity Scattering.- 3.6.4 Carrier-Carrier Scattering.- 3.7 Collection of Results for Steady-State Phenomena.- 3.7.1 Time Averages.- 3.7.2 Synchronous Ensemble.- 3.7.3 Statistical Uncertainty.- 3.8 The Ensemble Monte Carlo (EMC).- 3.9 Many Particle Effects.- 3.9.1 Carrier-Carrier Scattering.- 3.9.2 Molecular Dynamics and Monte Carlo Method.- 3.9.3 Degeneracy in Monte Carlo Calculations.- 3.10 Monte Carlo Simulation of the 2DEG.- 3.11 Special Topics.- 3.11.1 Periodic Fields.- 3.11.2 Diffusion, Autocorrelation Function, and Noise.- 3.11.3 Ohmic Mobility.- 3.11.4 Impact Ionization.- 3.11.5 Magnetic Fields.- 3.11.6 Optical Excitation.- 3.11.7 Quantum Mechanical Corrections.- 3.12 Variance-reducing Techniques.- 3.12.1 Variance Due to Thermal Fluctuations.- 3.12.2 Variance Due to Valley Repopulation.- 3.12.3 Variance Related to Improbable Electron States.- 3.13 Comparison with Other Techniques.- 3.13.1 Analytical Techniques.- 3.13.2 The Iterative Technique.- 3.13.3 Comparison of the Different Techniques.- References.- 4 Review of Semiconductor Devices.- 4.1 Introduction.- 4.2 Historical Evolution of Semiconductor Devices.- 4.2.1 Evolution of Si Devices.- 4.2.2 Evolution of GaAs Devices.- 4.2.3 Technological Features.- 4.2.4 Scaling and Miniaturization.- 4.3 Physical Basis of Semiconductor Devices.- 4.3.1 p-n Junction.- 4.3.2 Bipolar Transistors.- 4.3.3 Heterojunction Bipolar Transistor.- 4.3.4 Metal-Semiconductor Contacts.- 4.3.5 Metal-Semiconductor Field-Effect Transistor.- 4.3.6 Metal-Oxide-Semiconductor Field-Effect Transistor.- 4.3.7 High Electron Mobility Transistor.- 4.3.8 Hot Electron Transistors.- 4.3.9 Permeable Base Transistor.- 4.4 Comparison of Semiconductor Devices.- 4.4.1 Device Parameters.- 4.4.2 Comparison of Semiconductor Devices.- References.- 5 Monte Carlo Simulation of Semiconductor Devices.- 5.1 Introduction.- 5.2 Geometry of the System.- 5.2.1 Boundary Conditions.- 5.2.2 Grid Definition.- 5.2.3 Superparticles.- 5.3 Particle-Mesh Force Calculation.- 5.3.1 Particle-Mesh Calculation in One Dimension.- 5.3.2 Charge Assignment Schemes in Two Dimensions.- 5.4 Poisson Solver and Field Distribution.- 5.4.1 Finite Difference Scheme.- 5.4.2 Matrix Methods.- 5.4.3 Rapid Elliptic Solvers (RES).- 5.4.4 Iterative Methods.- 5.4.5 Calculation of the Electric Field.- 5.4.6 The Collocation Method.- 5.5 The Monte Carlo Simulation of Semiconductor Devices.- 5.5.1 Initial Conditions.- 5.5.2 Time Cycles.- 5.5.3 Free Flight.- 5.5.4 Scattering.- 5.5.5 Carrier-Carrier Scattering.- 5.5.6 Degenerate Statistics.- 5.5.7 Statistics.- 5.5.8 Static Characteristics.- 5.5.9 A.C. Characteristics.- 5.5.10 Noise.- References.- 6 Applications.- 6.1 Introduction.- 6.2 Diodes.- 6.2.1 n+-n-n+ Diodes.- 6.2.2 Schottky Diode.- 6.3 MESFET.- 6.3.1 Short Channel Effects.- 6.3.2 Geometry Effects.- 6.3.3 Space-Charge Injection FET.- 6.3.4 Conclusions.- 6.4 HEMT and Heterojunction Real Space Transfer Devices.- 6.4.1 HEMT.- 6.4.2 Real-Space Transfer Devices.- 6.4.3 Velocity-Modulation Field Effect Transistor.- 6.5 Bipolar Transistor.- 6.6 HBT.- 6.7 MOSFET and MISFET.- 6.7.1 MOSFET.- 6.7.2 GaAs Injection-modulated MISFET.- 6.7.3 Conclusions.- 6.8 Hot Electron Transistors.- 6.8.1 The THETA Device.- 6.8.2 GaAs FET with Hot-Electron Injection Structure.- 6.8.3 Planar-doped-Barrier Transistors.- 6.9 Permeable Base Transistor.- 6.10 Comparison with Traditional Simulators.- References.- Appendix A. Numerical Evaluation of Some Integrals of Interest.- References.- Appendix B. Generation of Random Numbers.- References.

Rapid calculation of radiative heating rates and photodissociation rates in inhomogeneous multiple scattering atmospheres

Abstract: The solution of the generalized two-stream approximation for radiative transfer in homogeneous multiple scattering atmospheres is extended to vertically inhomogeneous atmospheres in a manner which is numerically stable and computationally efficient. It is shown that solar energy deposition rates, photolysis rates, and infrared cooling rates all may be calculated with the simple modifications of a single algorithm. The accuracy of the algorithm is generally better than 10 percent, so that other uncertainties, such as in absorption coefficients, may often dominate the error in calculation of the quantities of interest to atmospheric studies.

Tunneling times: a critical review

Abstract: The old question of "How long does it take to tunnel through a barrier?" has acquired new urgency with the advent of techniques for the fabrication of semiconductor structures in the nanometer range. For the restricted problem of tunneling in a scattering configuration, a coherent picture is now emerging. The dwell time ${\ensuremath{\tau}}_{D}$ has the status of an exact statement of the time spent in a region of space, averaged over all incoming particles. The phase times ${\ensuremath{\tau}}_{T}^{\ensuremath{\phi}}$ and ${\ensuremath{\tau}}_{R}^{\ensuremath{\phi}}$ are defined separately for transmitted and reflected particles. They are asymptotic statements on completed scattering events and include self-interference delays as well as the time spent in the barrier. Consequently, neither the dwell time nor the phase times can answer the question of how much time a transmitted (alternatively, reflected) particle spent in the barrier region. Our discussion of this question relies on a few simple criteria: (1) The average duration of a physical process must be real. (2) Since transmission and reflection are mutually exclusive events, the times ${\ensuremath{\tau}}_{T}$ and ${\ensuremath{\tau}}_{R}$ spent in the barrier region are, if they exist, conditional averages. Consequently, they must obey the identity ${\ensuremath{\tau}}_{D}=T{\ensuremath{\tau}}_{T}+R{\ensuremath{\tau}}_{R}$, where $T$ and $R$ are the transmission and reflection probabilities, respectively. The existence of this identity distinguishes tunneling in a scattering configuration from tunneling out of a metastable state. (3) Any proposed ${\ensuremath{\tau}}_{T}$ and ${\ensuremath{\tau}}_{R}$ must meet every requirement that can be constructed from ${\ensuremath{\tau}}_{D}$. On the basis of (2), the naively extrapolated phase times, as well as the B\"uttiker-Landauer time, must be rejected. The local Larmor times, as introduced by Baz', satisfy (2), but not every criterion of type (3). The local Larmor clock is therefore unreliable. The asymptotic Larmor clock shows the phase times, as it should. Finally, the inverse characteristic frequency of an oscillating barrier cannot always be defined. It is shown not to represent the duration of the tunneling process. This leaves the dwell time and the phase times as the only well-established times in this context. It also leaves open the question of the length of time a transmitted particle spends in the barrier region. It is not clear that a generally valid answer to this question exists.

Skin optics

Abstract: The current status of tissue optics is reviewed, distinguishing among the cases of dominant absorption, dominant scattering, and scattering about equal to absorption. Previously published data as well as some current unpublished data on (human) stratum corneum, epidermis, and dermis are collected and/or (re)analyzed in terms of absorption coefficient, scattering coefficient, and anisotropy scattering factor. It is found that the individual skin layers show strongly forward scattering (anisotropy factors between 0.7 and 0.9). The absorption and scattering data show that for all wavelengths considered, scattering is much more important than absorption. Solutions to the transport equation for a multilayer skin model and finite beam laser irradiation that take this into account are not yet available. Hence, any quantitative dosimetry for skin treated with (laser) light is inaccurate. >

Theory of giant magnetoresistance effects in magnetic layered structures with antiferromagnetic coupling.

Abstract: We present a simple theoretical description of recently measured giant magnetoresistance effects in Fe/Cr layered structures. The resistivity is calculated by solving the Boltzmann transport equation with spin-dependent scattering at the interfaces. The magnitude of the effect depends on the ratio of the layer thickness to the mean free path and on the asymmetry in scattering for spin-up and spin-down electrons. Good agreement with experiment is found for both sandwich structures and superlattices.

Unsupervised classification of scattering behavior using radar polarimetry data

Abstract: The use of an imaging radar polarimeter data for unsupervised classification of scattering behavior is described by comparing the polarization properties of each pixel in an image to that of simple classes of scattering such as even number of reflections, odd number of reflections, and diffuse scattering. For example, when this algorithm is applied to data acquired over the San Francisco Bay area in California, it classifies scattering by the ocean as being similar to that predicted by the class of odd number of reflections, scattering by the urban area as being similar to that predicted by the class of even number of reflections, and scattering by the Golden Gate Park as being similar to that predicted by the diffuse scattering class. It also classifies the scattering by a lighthouse in the ocean and boats on the ocean surface as being similar to that predicted by the even number of reflections class, making it easy to identify these objects against the background of the surrounding ocean. >

Trap creation in silicon dioxide produced by hot electrons

Abstract: Trap creation in both the bulk of silicon dioxide films and at its interfaces with silicon and metallic contacting electrodes is shown to depend on the presence of hot electrons in the oxide. For thick oxides (≥100 A), little trap creation is observed in the near‐thermal transport regime at electric field magnitudes less than 1.5 MV/cm. At these low fields, electrons travel in a streaming fashion close to the bottom of the oxide conduction band at energies less than that of the dominant optical phonon mode at 0.153 eV. At higher electric fields, the rate of bulk trap creation is proportional to the average energy of the hot electrons, which move in a dispersive manner and can reach energies as large as 4 eV. For thin oxides (<100 A) where electrons can travel ballistically (i.e., without scattering), traps are not produced unless injected electrons acquire more than 2 eV of kinetic energy from the applied electric field, regardless of the magnitude of this field. All data on both thin and thick oxides are shown to give a threshold for trap creation of about 2.3 eV by the hot electrons in the oxide conduction band. Also, trap creation is shown to be suppressed by lowering the lattice temperature below ≊150 K. Our results are discussed in terms of a model involving hydrogen‐related‐species release from defect sites near the anode by the hot electrons and the subsequent motion of these molecules to regions near the cathode where they can interact with the lattice and form the trapping sites which are measured.

Solar radiative transfer in cirrus clouds. I - Single-scattering and optical properties of hexagonal ice crystals. II - Theory and computations of multiple scattering in an anisotropic medium

Abstract: The light scattering and absorption programs of Cai and Liou (1982) and Takano and Jaweera (1985) are extended to include hexagonal ice crystals randomly and horizontally oriented in space. The scattering and polarization results for the ice crystals are calculated. The results are compared with measurement data. The single-scattering properties for horizontally oriented columns and plates are presented and used to explain halos and arcs observed in the atmopshere. In the second section, the theory and computations for multiple scattering in cirrus clouds containing oriented ice crystals are presented. The radiative transfer in clouds composed of horizontally oriented ice crystals is formulated. Also, reflected and transmitted intensities, planetary albedo, and polarization in multiple scattering by ice crystals are discussed.

Triply-differential cross sections for ionisation of hydrogen atoms by electrons and positrons

Abstract: A derivation is given of the exact form of the three-body Coulomb wavefunction in the asymptotic region where the separation of all particles tends to infinity. Using a modification of the method of Pluvinage (1951), an approximate three-body scattering wavefunction is derived that satisfies this boundary condition. Triply-differential cross sections (TDCS) for electron impact ionisation of atomic hydrogen calculated with this scattering wavefunction, which contains no free parameters, show excellent agreement with measurements at impact energies greater than 150 eV. The corresponding TDCS for positron impact ionisation are also presented.

Dynamic light scattering by non-ergodic media

Abstract: We consider dynamic light scattering (DLS) by non-ergodic media, such as glasses or gels, in which the scattering elements are able only to make limited Brownian excursions about fixed average positions. We point out that, for such media, the time-averaged correlation function of the intensity of scattered light, the quantity obtained from a single DLS measurement, is different from the ensemble-averaged function. An expression for this time-averaged intensity correlation function is derived and its properties and experimental analysis are discussed. Some of the literature on DLS by polymer gels is re-evaluated in the light of these new theoretical predictions.

Neutron reflectivity studies of the surface-induced ordering of diblock copolymer films

Abstract: Neutron reflectivity from annealed thin films of the poly(styrene-b-deuterated methylmethacrylate), P(S-b-D-MMA), reveals the formation of a multilayered morphology parallel to the film surface. This multilayer forms so that PS locates, preferentially, at the air/copolymer and D-PMMA at the substrate/copolymer interfaces with layer thicknesses at these interfaces one-half that found in the bulk. P(D-S-b-MMA) of lower molecular weight shows the first evidence of surface-induced ordering of copolymers in the phase mixed state characterized by an exponentially damped cosine function.

X Ray Scattering of Synthetic Polymers

Abstract: 1. The Theory of Coherent X-Ray Scattering. The scattering from one electron. The scattering from many electrons. Fourier transformation and reciprocal space. The Ewald sphere construction. The convolution operation. The Fourier transforms of convolutions and products of functions. General relations involving Fourier transforms. Diffraction by crystals. Powder patterns. Diffraction from non-crystalline substances. 2. Experimental Techniques. Properties of X-ray radiation. X-ray excitation. Absorption of X-ray radiation. X-ray detection. Apparatus. 3. Lattice Constants. Measurement of lattice constants by photographic methods. Measurement of lattice constants from diffractometer line profiles. Unit cell measurements in polymers. Interpretation of unit cell variations. 4. Line Breadth Measurements: Paracrystallinity. Lattice distortions. Distortions of the first kind. The concept of paracrystal: distortions of the second kind. Line broadening analysis. alpha-Relation: natural paracrystals. Fourier transform methods. Instrumental corrections. 5. The X-Ray Determination of the Crystallinity in Polymers. Methods based on external comparison. Methods based on internal comparison. 6. The X-Ray Determination of the Orientation in Polymers. Classification. The X-ray registration of the orientation of crystallites. Pole figures. Specification of orientation. The interpretation of orientation phenomena. 7. The Small-Angle X-Ray Scattering of Polymers. Primary data treatment. Two-phase structures. Particle scattering. Lamellar systems. The small-angle scattering of oriented polymers. (Chapters include an introduction and references). Author Index. Subject Index.

A 1/f noise technique to extract the oxide trap density near the conduction band edge of silicon

Abstract: The use of 1/f noise measurements in n-channel MOSFETs to extract the oxide trap density in space and energy near and above the conduction band edge of silicon is investigated. The conventional carrier number fluctuation model of 1/f noise that attributes 1/f noise to the trapping and detrapping of inversion layer carriers by oxide traps is reviewed. It is shown that oxide band bending in devices with a nonuniform oxide trap distribution leads to a gate voltage dependence in the magnitude and exponent gamma (V/sub gs/) of the 1/f/sup gamma / noise spectrum. An extension of the 1/f noise number fluctuation model that includes both carrier number fluctuations and correlated mobility fluctuations is then studied. Correlated mobility fluctuations are attributed to the coulombic scattering of inversion layer carriers by the fluctuating trapped charge. It is shown that the correlated fluctuation model predicts a gate voltage dependence in the magnitude and exponent gamma of the 1/f/sup gamma / noise spectrum even for a uniform oxide trap distribution. By analyzing the 1/f noise magnitude and exponent data in n-channel MOSFETs having various oxide thicknesses, both models are used to extract the oxide trap density over a wide range of space and energy. >

Evaluation of some scattering times for electrons in unbiased and biased single- and multiple-quantum-well structures

Abstract: We report on calculations of scattering times for electrons in single or multiple quantum wells subjected to a longitudinal electric field. Static scatterers (Coulombic impurities and interface defects) as well as acoustical or optical phonons are considered. Intrasubband and intersubband contributions in single quantum wells as well as the intrawell and interwell ones in multiple quantum wells are analyzed and compared. We find that it is usually an excellent approximation to assume that intrasubband and/or intrawell relaxations are faster than intersubband and interwell ones. The variations of the relaxation times upon the strength of an electric field applied along the growth axis make evident the part played by the polarization of the carrier wave function.

Diffusion of light in turbid material

Abstract: This paper discusses some of the present knowledge of the mathematical techniques used to describe light diffusion in turbid material such as tissues. Attention will be paid to the usefulness and limitations of various techniques. First, we review the transport theory, radiance, radiant energy fluence rate, phase functions, boundary conditions, and measurement techniques. We then discuss the first-order solution, multiple scattering, diffusion approximation, and their limitations. The plane wave, spherical wave, beam wave, and pulse wave excitations are discussed followed by a brief review of the surface scattering effects due to rough interfaces.

A high-resolution diffuse X-ray scattering study of defects in dislocation-free silicon crystals grown by the float-zone method and comparison with Czochralski-grown crystals

Abstract: Point-defect aggregates in (111) dislocation-free silicon single crystals grown by the float-zone (FZ) method have been studied by diffuse X-ray scattering (DXS) and compared with those in the Czochralski-grown (CZ) crystals. A two-axis X-ray diffractometer was used. It employs three monochromators in (+, −, −) setting to obtain a highly collimated and monochromatic Mo Kα1 beam. DXS measurements were made around the 111 reciprocal-lattice point (r.l.p.) with K* along ±[111] and ±[01{\bar 1}]; K is the vector which joins the elemental volume of the reciprocal space under investigation to the nearest r.l.p. For FZ crystals for a given K* the DXS intensity was higher for θ θB showing that the anisotropy (DXS Iθ > θB − DXS Iθ < θB) is negative, as expected for vacancy clusters. For CZ crystals the anisotropy was positive, owing to the presence of interstitial clusters. The magnitude of anisotropy in the FZ crystals was smaller than that observed in the CZ crystals. The DXS intensity varies approximately as K−2 near Bragg peaks (Huang scattering) and as K*−4 (Stokes–Wilson scattering) away from it. From the K* values where the changeover from Huang to Stokes–Wilson scattering takes place the size of the clusters assumed to be the origin of the observed DXS is estimated as ~ 2 × 10−4 and 2.6 × 10−3 mm for FZ and ~ 5.5 × 10−4 and 3 × 10−3 mm for CZ crystals. The experimental data were compared with theoretically calculated DXS distributions assuming the defects to be dislocation loops. The number of point defects in a loop has been estimated.

Light transport in tissue

Abstract: The propagation of light in tissue may be calculated by exact transport theory, or the approximate diffusion theory, provided the optical properties are known at the source wavelength. Optical properties for the exact methods are the absorption coefficient, scattering coefficient, and angular distribution of scattering. Appropriate properties for diffusion theory are the diffusion length and diffusion coefficient (corrected for anisotropic scattering). Computer programs and analytical solutions (for some simple geometries) exist, but the optical properties have to be determined experimentally and are not well defined as yet. The radiant energy fluence rate and the diffuse transmittance and reflectance have been measured in several tissues and in a few geometries, but there are gaps in the data as a function of wavelength. Calculations and measurements reveal that very large errors can result if the optical properties (for example, the diffusion length) are inaccurate, if anisotropic scattering is neglected, or if the finite size of the irradiating light beam is not taken into account. Furthermore, the radiant energy fluence and transmittance are perturbed by local regions of lesser or greater absorption, although recovery of the fluence and transmittance occurs beyond some three diffusion lengths.

Thermal conductivity of thin films: Measurements and understanding

Abstract: Several techniques are reviewed with which thermal conductivity and phonon scattering can be measured in films of thicknesses ranging from angstroms to millimeters. Recent experimental results are compared critically with previous measurements. It is shown that phonons are very sensitive probes of the structural perfection of the films.

Quantum reactive scattering via the S‐matrix version of the Kohn variational principle: Differential and integral cross sections for D+H2 →HD+H

Abstract: A comprehensive survey of the quantum scattering methodology that results from applying the S‐matrix version of the Kohn variational principle to the reactive scattering formulation given by Miller [J. Chem. Phys. 50, 407 (1969)] is presented. Results of calculations using this approach are reported for the reaction D+H2 →HD+H. The 3‐d calculations include total angular momentum values from J=0 up to 31 in order to obtain converged integral and differential cross sections over a wide range of energy (0.4–1.35 eV total energy). Results are given for reaction probabilities for individual values of J, integral and differential cross sections for a number of energies, and state‐to‐state rate constants (i.e., a Boltzmann average over translational energy), and comparisons are made to a variety of different experimental results. A particularly interesting qualitative feature which is observed in the calculations is that the energy dependence of the differential cross section in the backward direction (θ=180°) s...

Complete phase diagram of a charged colloidal system: A synchro- tron x-ray scattering study.

Abstract: High-resolution, small-angle, synchrotron x-ray-scattering techniques were used to determine the phase diagram, structure factor, and pair distribution function for a charged colloidal suspension from 6% to 30% volume fraction. The expected correlated liquid and fcc and bcc solid phases were observed along with a glass phase at high concentration with structure similar to metallic glasses. At high volume fractions the finite core size leads to substantial deviation from predictions resulting from a screened Coulomb interaction.

Phase modulated spectrophotometry

Abstract: An apparatus and method to determine the concentration of an absorptive constituent in a scattering medium. A light source (10) is coupled to a scattering medium (20) and is detected by a detector (16) after migrating through the medium. A reference signal (18) is mixed with the detected signal resulting in a phase shifted detected signal (22) from which the concentration is determined (26).