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1990

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Articles 1 - 30 of 193

Full-Text Articles in Physics

Power Law Exponents For A Spreading Front And Growing Interface In An Irreversible Wetting, Evan Willett, Ras B. Pandey Dec 1990

Power Law Exponents For A Spreading Front And Growing Interface In An Irreversible Wetting, Evan Willett, Ras B. Pandey

Faculty Publications

Using computer simulations, the power-law behavior of the interface growth of a spreading fluid is studied in a two-dimensional lattice model. The interface width exponent ν and the dynamical exponent k for the evolution of the front are consistent with their dynamical scaling relation. The magnitude of these exponents seems to depend upon the nature of the substrate and the concentration of the carriers of the wetting fluid.

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Relaxation Time Of The Order Parameter In A High-Temperature Superconductor, G.L. Eesley, J. Heremans, M.S. Meyer, G.L. Doll, Sy_Hwang Liou Dec 1990

Relaxation Time Of The Order Parameter In A High-Temperature Superconductor, G.L. Eesley, J. Heremans, M.S. Meyer, G.L. Doll, Sy_Hwang Liou

Sy-Hwang Liou Publications

We present femtosecond time-resolved measurements on the high-Tc superconductor Tl2Ba2Ca2Cu3O10. At temperatures below Tc, we observe a relaxation process which is distinct from the equilibration of hot carriers in the normal state. Our results demonstrate an increasing relaxation rate as the superconducting gap opens. This is consistent with the behavior of conventional metallic superconductors.

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Uniform Stationary-Phase Methods For Energy Spectra Resulting From Collisions In A Complex Potential: Penning And Associative Ionization Of He*(2³S)+He*(23s), Ronald James Bieniek, M. W. Muller, M. Movre Dec 1990

Uniform Stationary-Phase Methods For Energy Spectra Resulting From Collisions In A Complex Potential: Penning And Associative Ionization Of He*(2³S)+He*(23s), Ronald James Bieniek, M. W. Muller, M. Movre

Physics Faculty Research & Creative Works

Heavy-particle collisions involving strong electronic coupling can be conveniently described by using a complex (optical) potential in the entrance channel. Uniform JWKB stationary-phase techniques are used to evaluate T-matrix elements for transitions where an electron is ejected. The semi-analytic expressions for the resulting electron energy spectra are no more difficult to implement than corresponding ones for totally real potentials. Numerical results are reported for Penning and associative ionization from sub thermal He*(23S)+He*(23S) collisions. These are in excellent agreement with fully quantal, complex-potential computations. The stationary-phase expressions for T-matrix elements and differential cross sections are employed to elucidate the rapid and …

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Projectile- And Target-Charge Dependent Effects In Ionizing Collisions Of H ⁺ And He 2+ With He, Ne And Ar Atoms, Timothy James Gay, M. W. Gealy, M. E. Rudd Dec 1990

Projectile- And Target-Charge Dependent Effects In Ionizing Collisions Of H ⁺ And He 2+ With He, Ne And Ar Atoms, Timothy James Gay, M. W. Gealy, M. E. Rudd

Physics Faculty Research & Creative Works

The spectra of electrons emitted in collisions between H + and He 2+ projectiles and He, Ne and Ar targets at energies of 50 and 100 keV amu -1 have been studied. The data are in qualitative agreement with results of Irby el al., but are in disagreement with measurements of Bernardi et al. It is shown that the observed electron spectra have a dependence on both target-ion and projectile effective charge that can be understood qualitatively in terms of 'saddle-point' ionization. Several issues relevant to saddle-point ionization are discussed. © 1990 IOP Publishing Ltd.

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Laser Cvd And Plasma Cvd Of Cro2 Films And Cobalt Doped Cro2 Films Using Organometallic Precursors, Peter A. Dowben, Marshall Onellion Dec 1990

Laser Cvd And Plasma Cvd Of Cro2 Films And Cobalt Doped Cro2 Films Using Organometallic Precursors, Peter A. Dowben, Marshall Onellion

Peter Dowben Publications

Chromium dioxide is deposited as a ferromagnetic layer onto selected portions of a substrate or over the entire substrate. Chromium hexacarbonyl vapor is introduced into a vacuum deposition chamber at e.g. 10 milliTorr and oxygen is introduced at e.g. 15 to 100 milliTorr. A UV laser beam is focused onto the substrate to form the CrO2 layer photolytically. The CrO2 layer can also be deposited by RF plasma deposition. This technique can also be employed for depositing MoC2, WC2, Mo2φ3, MoO2 or WO2. Magnetic recording or memory devices are …

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The Relationship Of The Virtual Orbitals Of Self-Consistent-Field Theory To Temporary Negative Ions In Electron Scattering From Molecules, Donghai Chen, Gordon A. Gallup Dec 1990

The Relationship Of The Virtual Orbitals Of Self-Consistent-Field Theory To Temporary Negative Ions In Electron Scattering From Molecules, Donghai Chen, Gordon A. Gallup

Gordon Gallup Publications

The theory given here shows how certain of the virtual orbitals of self-consistent field (SCF) theory provide a natural ingredient for constructing basis functions to study the shape resonances associated with temporary molecular ions. We give specific calculations of resonant behavior in H2, N2, ethylene, cyclopropene, and cyclobutene. In addition, we show how the theory can rationalize the relationship between Koopmans' theorem values of the energy of a resonance and the experimental values. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

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Magnetism Of Rare-Earth–Transition-Metal Nanoscale Multilayers. Ii. Theoretical Analysis Of Magnetization And Perpendicular Magnetic Anisotropy, Z.S. Shan, David J. Sellmyer, Sitaram Jaswal, Y.J. Wang, J.X. Shen Dec 1990

Magnetism Of Rare-Earth–Transition-Metal Nanoscale Multilayers. Ii. Theoretical Analysis Of Magnetization And Perpendicular Magnetic Anisotropy, Z.S. Shan, David J. Sellmyer, Sitaram Jaswal, Y.J. Wang, J.X. Shen

David Sellmyer Publications

Systematic studies of rare-earth–transition-metal amorphous compositionally modulated films (CMF) permit the development of a detailed model for understanding the magnetization and perpendicular magnetic anisotropy and their distributions along the film normal. It is shown that the single-ion anisotropy of rare-earth ions with orbital angular momentum is the major contributor to the perpendicular anisotropy for this class of CMF. The calculated results agree well with the experimental data for Dy/Co and Tb/Fe CMF when the individual layer thicknesses are small enough (<10 Å); these films have structures which can be characterized as compositionally modulated amorphous alloys.

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Magnetism Of Rare-Earth–Transition-Metal Nanoscale Multilayers. I. Experiments On Dy/Co, Dy/Fe, And Tb/Fe, Z.S. Shan, David J. Sellmyer Dec 1990

Magnetism Of Rare-Earth–Transition-Metal Nanoscale Multilayers. I. Experiments On Dy/Co, Dy/Fe, And Tb/Fe, Z.S. Shan, David J. Sellmyer

David Sellmyer Publications

Experimental investigations of magnetic and structural properties for rare-earth–transition-metal (RE-TM) compositionally modulated films (CMF) are presented in this paper. In particular, ARE/BTM including ARE=Dy and Tb and BTM=Fe, Co, and Ni, are studied. The layer thickness and temperature dependence of magnetic properties, which can be interpreted in terms of the antiferromagnetic coupling of RE and TM moments and their atomic distributions, are reported. These ARE/BTM CMF with nanoscale layer thicknesses exhibit perpendicular magnetic anisotropy (PMA) and the range of the layer thickness required for PMA is determined. The …

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Elastic Magnetic Electron Scattering From 'Ca, H Baghaei, A Cichocki, J B. Flanz, M Frodyma, Y Han, R S. Hicks, R A. Miskimen, Gerald Alvin Peterson, S H. Rokni Dec 1990

Elastic Magnetic Electron Scattering From 'Ca, H Baghaei, A Cichocki, J B. Flanz, M Frodyma, Y Han, R S. Hicks, R A. Miskimen, Gerald Alvin Peterson, S H. Rokni

Gerald Alvin Peterson

The elastic magnetic form factor of 41Ca has been determined by 180° electron scattering in the momentum-transfer range 0.9–2.0 fm-1. An analysis of the data indicates that the amplitudes of the M3 and M5 multipoles are quenched by factors of 0.57±0.16 and 0.68±0.07 relative to the simple shell model. In contrast, the magnitude of the M7 form factor is in good accord with this model. Calculations that include multiparticle-multihole configurations in the 1f7/2 and 1d3/2 subshells, first-order core polarization to higher excited orbitals, and meson exchange currents give reasonable agreement with the data for all multipoles. The rms radius of …

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Unpinning Of Gaas Surface Fermi Level By 200 Degrees C Molecular Beam Epitaxial Layer, David C. Look, C. E. Stutz, K. R. Evans Dec 1990

Unpinning Of Gaas Surface Fermi Level By 200 Degrees C Molecular Beam Epitaxial Layer, David C. Look, C. E. Stutz, K. R. Evans

Physics Faculty Publications

Previous attempts to passivate the n‐type (100)GaAs surface have significantly reduced only the surface recombination centers, but not the surface acceptors which pin the Fermi level. Here we show that a 100 Å molecular beam epitaxial layer grown at 200 °C reduces the effective surface potential energy − eϕs from 0.70 to 0.17 eV, nearly eliminates light sensitivity, and permits nonalloyed ohmic contacts. After a 10 min, 450 °C anneal, − eϕs increases only to 0.22 eV.

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Fresnel And Fraunhofer Diffraction: Development Of An Advanced Laboratory Experiment, Jeff Adams Dec 1990

Fresnel And Fraunhofer Diffraction: Development Of An Advanced Laboratory Experiment, Jeff Adams

Senior Theses and Projects

The purpose of this lab is to help the student become more familiar with, or get a better feel for what is actually occurring, when observing the effects of double slit diffraction patterns. In most sophomore labs dealing with double slit diffraction, the student simply determines the diffraction angle, and slit spacing, from marking the positions of the maxima on the screen. No attempt is made to measure the relative intensity of the interference pattern, and see how the experimental data compare with the theory of interference and diffraction. In an attempt to further clarify this phenomena, we will attempt …

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Device For Dispersal Of Micrometer- And Submicrometer-Sized Particles In Vaccum, D. P. Sheehan, M. Carillo, W. Heidbrink Dec 1990

Device For Dispersal Of Micrometer- And Submicrometer-Sized Particles In Vaccum, D. P. Sheehan, M. Carillo, W. Heidbrink

Physics and Biophysics: Faculty Scholarship

A simple, versatile device for dispersing micrometer‐ and submicrometer-sized particles in vacuum is described. The source allows control of particle size (0.5 μm≤l≤200 μm) and particle flux density up to roughly 107 cm−2 s−1. Several types of microparticles were successfully dispersed.

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Single Transfer-Excitation Resonance Observed Via The Two-Photon Decay In He-Like Ge³⁰⁺, Paul H. Mokler, S. Reusch, A. Warczak, Zbigniew Stachura, T. Kambara, Alfred K. Muller, Reinhold S. Schuch, Michael Schulz Dec 1990

Single Transfer-Excitation Resonance Observed Via The Two-Photon Decay In He-Like Ge³⁰⁺, Paul H. Mokler, S. Reusch, A. Warczak, Zbigniew Stachura, T. Kambara, Alfred K. Muller, Reinhold S. Schuch, Michael Schulz

Physics Faculty Research & Creative Works

We measured the 2E1 decay of the 1s2s 1S0 →1s2 1S0 transition in He-like germanium for 12- to 19-MeV/u Ge31+ +H2 collisions. The resonant population of the 2s2p 1P1 state by transfer excitation was isolated due to its cascading to the 1s2s 1S0 state. The experimental cross sections compare well with calculations using dielectronic recombination rates. The method gives the unique possibility to populate selectively the 1S0 state in heavy He-like ions.

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Extension Of The Metal Light Pipe Infrared Spectroscopy Technique: Applications To Surface Adsorption And High Tc Superconductors, Torsten Will Dec 1990

Extension Of The Metal Light Pipe Infrared Spectroscopy Technique: Applications To Surface Adsorption And High Tc Superconductors, Torsten Will

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The development of an infrared instrument for the study of surface adsorption and high Tc superconductors is presented and its applicability is discussed. The use of and theoretical background for the metal light pipe multiple-reflection technique are discussed in comparison to other infrared devices. Measurements are carried out to determine its limitations with powdered substrates as well as its sensitivity limitation for thin films. The results of the two test measurements, adsorption of CO on MgO and investigation of the energy gap of high Tc superconductors, are presented. Comparisons of the spectra with the experimental and theoretical literature …

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Electron Emission From Both Target And Projectile In C⁺ + He Collisions, C. O. Reinhold, D. R. Schultz, Ronald E. Olson, L. H. Toburen, R. (Robert) D. Dubois Dec 1990

Electron Emission From Both Target And Projectile In C⁺ + He Collisions, C. O. Reinhold, D. R. Schultz, Ronald E. Olson, L. H. Toburen, R. (Robert) D. Dubois

Physics Faculty Research & Creative Works

The first classical trajectory Monte Carlo calculation of the electronic spectra arising from both target and projectile ionization is presented and compared with experimental measurements of the differential cross section for electrons emitted in C++He collisions. The theoretical treatment is based on an independent-electron model in which the interactions between the electrons are approximated by quantum model potentials. Good agreement is obtained between theory and experiment and structures appearing in the measurements can be explained in terms of the electron emission from either, or both, target and projectile. Further, the relative importance of the electron capture to the continuum and …

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Tunable Lasers At 1080 Nm For Helium Optical Pumping, Laird D. Schearer, Padetha Tin Dec 1990

Tunable Lasers At 1080 Nm For Helium Optical Pumping, Laird D. Schearer, Padetha Tin

Physics Faculty Research & Creative Works

We describe the current status of tunable, cw, solid-state lasers in the infrared region of the spectrum which may be tuned to the helium resonance transition near 1083 nm. The principal use for these laser devices is the optical pumping of 3He and 4He atoms via the 23S1 metastable state. The tunable lasers we have examined include Nd3+-doped YAlO3, LaxNd1-xMgAl11O19 (x ∼0.15), Nd:LiNbO3, and Nd:silica glass fibers. Power outputs from these lasers range from a milliwatt to more than 1 W at …

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A High Power, Tunable, Arc-Lamp Pumped Nd-Doped Lanthanum-Hexaluminate Laser, Padetha Tin, Laird D. Schearer Dec 1990

A High Power, Tunable, Arc-Lamp Pumped Nd-Doped Lanthanum-Hexaluminate Laser, Padetha Tin, Laird D. Schearer

Physics Faculty Research & Creative Works

An LNA (Nd-doped lanthanum-hex aluminate) crystal has been pumped with a cw, krypton arc lamp in a commercial Nd:YAG cavity. The cw output power greater than 6 W is obtained in a 28-cm long, plane mirror cavity. The free-running wavelength is near 1083 nm and has a width of about 0.8 nm. Inserting a 0.25 mm thick, uncoated solid etalon in the cavity permits the laser output to be continuously tuned from 1082 to 1084 nm by tilting the etalon. The laser bandwidth is reduced to below 0.016 nm. Over 3 W are obtained at the helium resonance transition. The …

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United States Patent: Metaginsulator Composites Having Improved Properties And Method For Their Preparation, Chia-Ling Chien, Gang Xiao, Sy-Hwang Liou Nov 1990

United States Patent: Metaginsulator Composites Having Improved Properties And Method For Their Preparation, Chia-Ling Chien, Gang Xiao, Sy-Hwang Liou

Sy-Hwang Liou Publications

Improved cermets having superior properties comprising a ferromagnetic metal and an insulator. By controlling process conditions, cermets having high magnetization and high coercivity as well as chemical stability, wear resistance and corrosion resistance are prepared. The cermets of this invention find particular utility as high density recording media.

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Anomalous Dimensions Of Anisotropic Gauge Theory Operators, David G. Robertson, Frank Wilczek Nov 1990

Anomalous Dimensions Of Anisotropic Gauge Theory Operators, David G. Robertson, Frank Wilczek

Physics Faculty Scholarship

The anomalous dimensions of the anisotropic dimension four operators in SU(N) gauge theory coupled to fermions are calculated to lowest order. The possibility of comparison with numerical simulations is pointed out.

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Effects Of Magnetic Field And Temperature On The Critical Current Hysteresis In Tl-Ca-Ba-Cu-O Thin Films, Hung-Lun Chang, Jenh-Yih Juang, Sy_Hwang Liou, Tzeng-Ming Uen, Yih-Shun Gou Nov 1990

Effects Of Magnetic Field And Temperature On The Critical Current Hysteresis In Tl-Ca-Ba-Cu-O Thin Films, Hung-Lun Chang, Jenh-Yih Juang, Sy_Hwang Liou, Tzeng-Ming Uen, Yih-Shun Gou

Sy-Hwang Liou Publications

The behavior of the critical current density of Tl-Ca-Ba-Cu-O superconducting thin films in a cycling magnetic field was investigated. The hysteresis of the transport Jc manifested similar features to those found in polycrystalline Y-Ba-Cu-O and granular Nb, Al thin films in zero-field cooling. However, a novel result of the transport Jc in field-cooled samples has been observed. The results were attributed to the presence of a saturated trapped magnetic flux in the weaklink network. The effects of temperature on both the trapped flux and the transport Jc suggest the existence of various states of the trapped flux …

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Coincident Charge State Production In F⁶⁺+Ne Collisions, D. R. Schultz, Ronald E. Olson, C. O. Reinhold Nov 1990

Coincident Charge State Production In F⁶⁺+Ne Collisions, D. R. Schultz, Ronald E. Olson, C. O. Reinhold

Physics Faculty Research & Creative Works

Total cross sections are presented for the production of various stages of multiple ionization of the target in coincidence with the final projectile charge state for collisions of F6+ with Ne at 10 and 15 MeV. In particular, the current measurements are compared with the results of a classical trajectory Monte Carlo method in which electrons are included explicitly on both target and projectile (nCTMC) and with those based on the conventional independent electron model (IEM). It is shown by the good agreement with experiment that the nCTMC model simultaneously represents well the ionization, charge transfer and excitation channels …

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Average Reaction Cross Sections For 74- To 112-Mev Α Particles On 127I And 133Cs, R. E. Warner, H. W. Wilschut, W. F. Rulla, Gary Felder Nov 1990

Average Reaction Cross Sections For 74- To 112-Mev Α Particles On 127I And 133Cs, R. E. Warner, H. W. Wilschut, W. F. Rulla, Gary Felder

Physics: Faculty Publications

The average reaction cross section for 74- to 112-MeV α particles on 127I and 133Cs was measured by a new method using a magnetic spectrograph and a CsI scintillation detector. The result, σR=2220±50 mb, is in good agreement with optical model calculations and finite-range microscopic calculations. Zero-range microscopic calculations underpredict σR by about 10%, while strong absorption theories overpredict σR by large amounts.

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Radiative Transfer In Astronomical Masers. I. The Linear Maser, Moshe Elitzur Nov 1990

Radiative Transfer In Astronomical Masers. I. The Linear Maser, Moshe Elitzur

Physics and Astronomy Faculty Publications

This is the first in a series of three papers presenting a comprehensive, unified approach for radiative transfer in astronomical maser sources. This paper provides the general formalism and presents the detailed analytic solution of the linear maser, including the case of a source illuminated by background radiation.

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Controlled Biosynthesis Of Greigite (Fe3S4) In Magnetotactic Bacteria, Brigid R. Heywood, Dennis A. Bazylinski, Anthony J. Garratt-Reed, Stephen Mann, Richard B. Frankel Nov 1990

Controlled Biosynthesis Of Greigite (Fe3S4) In Magnetotactic Bacteria, Brigid R. Heywood, Dennis A. Bazylinski, Anthony J. Garratt-Reed, Stephen Mann, Richard B. Frankel

Physics

No abstract provided.

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Predictions Of Cell Damage Rates For Lifesat Missions, Francis A. Cucinotta, William Atwell, Alva C. Hardy, Michael J. Golightly, John W. Wilson, Lawrence W. Townsend, Judy Shinn, John E. Nealy, Robert Katz Nov 1990

Predictions Of Cell Damage Rates For Lifesat Missions, Francis A. Cucinotta, William Atwell, Alva C. Hardy, Michael J. Golightly, John W. Wilson, Lawrence W. Townsend, Judy Shinn, John E. Nealy, Robert Katz

Robert Katz Publications

Radiological experiments with cell cultures are expected to be performed on Lifesat to study possible gravitational dependence on cellular response. Predictions of cell damage rates for well-studied systems are expected to help guide in the selection of orbits and the design of experiments. In this report we estimate the fractions of cell death and neoplastic transformation of C3H10T1/2 cells (cultured mouse cells) for the proposed Lifesat orbits. The parametric cellular track model of Katz et al. (refs. 1 and 2) is employed using cellular response parameters derived from the experiments of Yang et al. (refs. 3 and 4). The contributions …

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Microscopic Calculations Of Low-Energy Reaction Cross Sections, R. E. Warner, Gary Felder Nov 1990

Microscopic Calculations Of Low-Energy Reaction Cross Sections, R. E. Warner, Gary Felder

Physics: Faculty Publications

Microscopic calculations of nuclear reaction cross sections and total reaction probabilities are compared with measurements for the d+Si, 3,4He+Si, and d+Ge systems at energies ranging from 2 to 53 MeV/nucleon. Good agreement is obtained, except for 3He+Si at the very lowest energies, when zero-range nucleon-nucleon forces are assumed and realistic nuclear density distributions are used in the tail regions, where the models are most sensitive. The agreement is less good for finite-range forces. A strong absorption model gives much poorer agreement with the recent 4He+Si measurements than do the microscopic models.

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Some "Do's" And "Don't'S" For Using Computers In Science Instruction, Glenn A. Sowell, Robert Fuller Nov 1990

Some "Do's" And "Don't'S" For Using Computers In Science Instruction, Glenn A. Sowell, Robert Fuller

Robert G. Fuller Publications

As science researchers and professors, we have had a fairly broad collection of experiences in using computers, from batch-processing and number crunching in large computer systems using FORTRAN and symbolic languages to teaching problem-solving courses for nonscience students using personal computers. While we claim no special computer expertise, we both own computers and are frequently called upon to offer advice to our colleagues who are greater novices than we are. Hence, on the basis of reflections on our experiences and observations of what we have seen other people and institutions do, we have compiled a list of “Do’s” and “Don’ts” …

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Ab Initio Studies Of The Phase Transitions In K2Seo4, H. M. Lu, John R. Hardy Nov 1990

Ab Initio Studies Of The Phase Transitions In K2Seo4, H. M. Lu, John R. Hardy

John R. Hardy Papers

An ab initio model is developed for the potentials in ionic molecular solids in which the electron covalency within the molecular ions substantially affects the interionic interactions. By treating the intermolecular and intramolecular interactions on the basis of the true electron charge densities of the molecular ions, this new model leads to an accurate parameter-free description of the potentialenergy surfaces for such crystals. We performed first-principles static structural relaxation, supercell molecular-dynamics simulation, and lattice-dynamics studies for the room-temperature paraelectric phase and the lower-temperature ferroelectric superstructure of K2SeO4 and predicted with good accuracy the transition from the former …

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Synchrotron Radiation Induced Chemical Vapor Deposition Of Thin Films From Metal Hexacarbonyls*, Derrick C. Mancini, Shikha Varma, John K. Simons, Richard A. Rosenberg, Peter A. Dowben Nov 1990

Synchrotron Radiation Induced Chemical Vapor Deposition Of Thin Films From Metal Hexacarbonyls*, Derrick C. Mancini, Shikha Varma, John K. Simons, Richard A. Rosenberg, Peter A. Dowben

Peter Dowben Publications

We have studied the initial stages of synchrotron radiation [SR] induced chemical vapor deposition [CVD] of metal-containing thin films from metal hexacarbonyl gases. We have measured the dependence of the initial deposition rate upon gas pressure at room temperature. Substrates were exposed to SR for single fills of the electron storage ring at constant pressure of Mo(CO)6, Cr(CO)6, or W(CO) 6 gas. Deposition was monitored in situ by Auger electron spectroscopy using the SW as the excitation source. The presence of metal, carbon, and oxygen in the deposited films was observed, and the results are consistent …

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Simple Overdense Rf Plasma Source, R. Mcwilliams, D. Edrich, R. C. Platt, D. P. Sheehan Nov 1990

Simple Overdense Rf Plasma Source, R. Mcwilliams, D. Edrich, R. C. Platt, D. P. Sheehan

Physics and Biophysics: Faculty Scholarship

A simple, gas‐fed, radio‐frequency‐driven plasma source is described. By use of lower hybrid waves, noble gas plasmas were produced with electron densities up to 10^12 cm -3 over a range of magnetic fields from 400 G to 1.5 kG and rf frequencies from 2–220 MHz.

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