Understanding the Properties of Ionic Liquids: Electrostatics, Structure Factors, and Their Sum Rules

AbstractThe structure of a υ component liquid or amorphous alloy is analyzed in terms of υ(υ+1)/2 independent partial structure factors which are associated to the different correlations between the numbers of particles of all chemical species. This formalism, which is specially adapted to the study of alloys of more than two components, is related to Fournet-Faber-Ziman and extended Bhatia-Thornton theory. Sum rules, inequality relations and limiting values are calculated in the static approximation and Debye pair expressions of the structure factors are derived in the isotropic approximation.

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Numerical evaluation of frequency-moment sum rules for dynamical structure factors

Physical Review B ◽

10.1103/physrevb.53.11543 ◽

1996 ◽

Vol 53 (17) ◽

pp. 11543-11549 ◽

Cited By ~ 5

Author(s):

A. Fledderjohann ◽

M. Karbach ◽

K.-H. Mütter

Keyword(s):

Numerical Evaluation ◽

Sum Rules ◽

Dynamical Structure ◽

Structure Factors

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A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

International Astronomical Union Colloquium ◽

10.1017/s025292110010805x ◽

1988 ◽

Vol 102 ◽

pp. 343-347

Author(s):

M. Klapisch

Keyword(s):

Perturbation Theory ◽

Small Parameter ◽

Classification Scheme ◽

Sum Rules ◽

Energy Levels ◽

Natural Classification ◽

Quantum Numbers ◽

Formal Expansion ◽

Atomic Energy Levels ◽

As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

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Some Applications of the U. S. Steel MVEM

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100070461 ◽

1973 ◽

Vol 31 ◽

pp. 4-5

Author(s):

J. S. Lally ◽

L. E. Thomas ◽

R. M. Fisher

Keyword(s):

Electron Diffraction ◽

Debye Temperature ◽

Metals And Alloys ◽

Critical Voltage ◽

Dynamical Diffraction ◽

Phase Structures ◽

Structure Factors ◽

Local Bonding ◽

Diffraction Phenomenon ◽

Multi Phase

A variety of materials containing many different microstructures have been examined with the USS MVEM. Three topics have been selected to illustrate some of the more recent studies of diffraction phenomena and defect, grain and multi-phase structures of metals and minerals.(1) Critical Voltage Effects in Metals and Alloys - This many-beam dynamical diffraction phenomenon, in which some Bragg resonances vanish at certain accelerating voltages, Vc, depends sensitively on the spacing of diffracting planes, Debye temperature θD and structure factors. Vc values can be measured to ± 0.5% in the HVEM ana used to obtain improved extinction distances and θD values appropriate to electron diffraction, as well as to probe local bonding effects and composition variations in alloys.

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Isomorphous replacement in electron diffraction of wet crystals of rat hemoglobin

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100075968 ◽

1983 ◽

Vol 41 ◽

pp. 446-447

Author(s):

William F. Tivol ◽

Murray Vernon King ◽

D. F. Parsons

Keyword(s):

Electron Diffraction ◽

Heavy Atom ◽

Isomorphous Substitution ◽

X Ray Diffraction ◽

Salt Solutions ◽

X Ray ◽

Isomorphous Replacement ◽

Structure Factors ◽

Diffraction Structure ◽

The Mean

Feasibility of isomorphous substitution in electron diffraction is supported by a calculation of the mean alteration of the electron-diffraction structure factors for hemoglobin crystals caused by substituting two mercury atoms per molecule, following Green, Ingram & Perutz, but with allowance for the proportionality of f to Z3/4 for electron diffraction. This yields a mean net change in F of 12.5%, as contrasted with 22.8% for x-ray diffraction.Use of the hydration chamber in electron diffraction opens prospects for examining many proteins that yield only very thin crystals not suitable for x-ray diffraction. Examination in the wet state avoids treatments that could cause translocation of the heavy-atom labels or distortion of the crystal. Combined with low-fluence techniques, it enables study of the protein in a state as close to native as possible.We have undertaken a study of crystals of rat hemoglobin by electron diffraction in the wet state. Rat hemoglobin offers a certain advantage for hydration-chamber work over other hemoglobins in that it can be crystallized from distilled water instead of salt solutions.

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Computer processing of high-resolution images of periodic specimens

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100141834 ◽

1986 ◽

Vol 44 ◽

pp. 2-5

Author(s):

W. Chiu ◽

M.F. Schmid ◽

T.-W. Jeng

Keyword(s):

High Resolution ◽

Fourier Transforms ◽

Complex Structure ◽

Distribution Functions ◽

Multiple Image ◽

Cryo Electron Microscopy ◽

Structure Factors ◽

Unit Cells ◽

High Resolution Images ◽

Phase Probability Distribution

Cryo-electron microscopy has been developed to the point where one can image thin protein crystals to 3.5 Å resolution. In our study of the crotoxin complex crystal, we can confirm this structural resolution from optical diffractograms of the low dose images. To retrieve high resolution phases from images, we have to include as many unit cells as possible in order to detect the weak signals in the Fourier transforms of the image. Hayward and Stroud proposed to superimpose multiple image areas by combining phase probability distribution functions for each reflection. The reliability of their phase determination was evaluated in terms of a crystallographic “figure of merit”. Grant and co-workers used a different procedure to enhance the signals from multiple image areas by vector summation of the complex structure factors in reciprocal space.

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