Unit cell interactions of non-local active acoustic media

This article introduces a numerical formulation for studying frequency band structure in multi-periodic acoustic composite structures. Herein, multi-periodic acoustic composite structures are defined as periodically-layered acoustic media wherein each layer is composed of periodically-repeated unit fluid cells, especially those arising from the study of rigid-frame porous materials. Hence, at least two periodic scales (microscopic and mesoscopic, respectively) comprise the macroscopic acoustic media. Under the Floquet-Bloch’s condition, exploitation of the multi-periodicity allows for efficient generation of dispersion curves via a multi-scale asymptotic method (for homogenizing the mesoscale) coupled to original acoustic transfer matrix methods (for the macroscale). The combined numerical formulation results in a general analysis procedure for evaluating complex dispersion relationships. The dispersion curves can be used to reveal frequency stop bands wherein the wave vector is highly imaginary—i.e., plane waves experience rapid attenuation. The formulation is applied to four infinite, multi-periodic acoustic composite structures in order to demonstrate the formulation’s utility and to reveal novel properties, particularly those which can be influenced by design of the mesoscopic unit cell.

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High-resolution structure determination by ALCHEMI

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100074707 ◽

1983 ◽

Vol 41 ◽

pp. 178-181 ◽

Cited By ~ 1

Author(s):

Peter G. Self ◽

Peter R. Buseck

Keyword(s):

Site Occupancy ◽

Real Space ◽

Unit Cell ◽

Bragg Angle ◽

Electron Current ◽

High Resolution Structure ◽

Beam Incident ◽

Crystallographic Planes ◽

Electron Beam Incident ◽

Resolution Structure

ALCHEMI (Atom Location by CHanneling Enhanced Microanalysis) enables the site occupancy of atoms in single crystals to be determined. In this article the fundamentals of the method for both EDS and EELS will be discussed. Unlike HRTEM, ALCHEMI does not place stringent resolution requirements on the microscope and, because EDS clearly distinguishes between elements of similar atomic number, it can offer some advantages over HRTEM. It does however, place certain constraints on the crystal. These constraints are: a) the sites of interest must lie on alternate crystallographic planes, b) the projected charge density on the alternate planes must be significantly different, and c) there must be at least one atomic species that lies solely on one of the planes.An electron beam incident on a crystal undergoes elastic scattering; in reciprocal space this is seen as a diffraction pattern and in real space this is a modulation of the electron current across the unit cell. When diffraction is strong (i.e., when the crystal is oriented near to the Bragg angle of a low-order reflection) the electron current at one point in the unit cell will differ significantly from that at another point.

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The External Shape of Human γ GI Immunoglobulin from Crystal Sections

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010006619x ◽

1971 ◽

Vol 29 ◽

pp. 428-429

Author(s):

L. W. Labaw

Keyword(s):

Molecular Weight ◽

Sodium Phosphate ◽

Osmium Tetroxide ◽

Unit Cell ◽

Monoclinic Space Group ◽

X Ray ◽

Large Molecular Weight ◽

Cell Dimensions ◽

Unit Cell Dimensions ◽

Crystallographic Axes

Crystals of a human γGl immunoglobulin have the external morphology of diamond shaped prisms. X-ray studies have shown them to be monoclinic, space group C2, with 2 molecules per unit cell. The unit cell dimensions are a = 194.1, b = 91.7, c = 51.6Å, 8 = 102°. The relatively large molecular weight of 151,000 and these unit cell dimensions made this a promising crystal to study in the EM.Crystals similar to those used in the x-ray studies were fixed at 5°C for three weeks in a solution of mother liquor containing 5 x 10-5M sodium phosphate, pH 7.0, and 0.03% glutaraldehyde. They were postfixed with 1% osmium tetroxide for 15 min. and embedded in Maraglas the usual way. Sections were cut perpendicular to the three crystallographic axes. Such a section cut with its plane perpendicular to the z direction is shown in Fig. 1.This projection of the crystal in the z direction shows periodicities in at least four different directions but these are only seen clearly by sighting obliquely along the micrograph.

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The orientation of sickle hemoglobin fibers within fascicles

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100104066 ◽

1988 ◽

Vol 46 ◽

pp. 400-401

Author(s):

Christopher A. Miller ◽

Bridget Carragher ◽

William A. McDade ◽

Robert Josephs

Keyword(s):

Sickle Cell ◽

Sickle Cell Anemia ◽

Relative Orientation ◽

Unit Cell ◽

Red Cell ◽

High Ph ◽

Sickle Hemoglobin ◽

Polar Crystal ◽

Helical Configuration

Highly ordered bundles of deoxyhemoglobin S (HbS) fibers, termed fascicles, are intermediates in the high pH crystallization pathway of HbS. These fibers consist of 7 Wishner-Love double strands in a helical configuration. Since each double strand has a polarity, the odd number of double strands in the fiber imparts a net polarity to the structure. HbS crystals have a unit cell containing two double strands, one of each polarity, resulting in a net polarity of zero. Therefore a rearrangement of the double strands must occur to form a non-polar crystal from the polar fibers. To determine the role of fascicles as an intermediate in the crystallization pathway it is important to understand the relative orientation of fibers within fascicles. Furthermore, an understanding of fascicle structure may have implications for the design of potential sickling inhibitors, since it is bundles of fibers which cause the red cell distortion responsible for the vaso-occlusive complications characteristic of sickle cell anemia.

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Toward High-Resolution Low-Voltage SEM

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100103152 ◽

1988 ◽

Vol 46 ◽

pp. 218-219

Author(s):

Zhifeng Shao

Keyword(s):

Low Voltage ◽

Spherical Aberration ◽

Chromatic Aberration ◽

Limiting Factor ◽

Operating Voltage ◽

Probe Radius ◽

Non Local ◽

Electron Microscopes ◽

Image Position ◽

Scanning Electron Microscopes

Recently, low voltage (≤5kV) scanning electron microscopes have become popular because of their unprecedented advantages, such as minimized charging effects and smaller specimen damage, etc. Perhaps the most important advantage of LVSEM is that they may be able to provide ultrahigh resolution since the interaction volume decreases when electron energy is reduced. It is obvious that no matter how low the operating voltage is, the resolution is always poorer than the probe radius. To achieve 10Å resolution at 5kV (including non-local effects), we would require a probe radius of 5∽6 Å. At low voltages, we can no longer ignore the effects of chromatic aberration because of the increased ratio δV/V. The 3rd order spherical aberration is another major limiting factor. The optimized aperture should be calculated as

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Chromatic aberration and low-voltage SEM

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100127293 ◽

1987 ◽

Vol 45 ◽

pp. 546-547

Author(s):

Zhifeng Shao ◽

A.V. Crewe

Keyword(s):

Electron Energy ◽

Low Voltage ◽

Spherical Aberration ◽

Chromatic Aberration ◽

Primary Electron ◽

Probe Size ◽

Non Local ◽

Optical Treatment ◽

Electron Microscopes ◽

Scanning Electron Microscopes

For scanning electron microscopes, it is plausible that by lowering the primary electron energy, one can decrease the volume of interaction and improve resolution. As shown by Crewe /1/, at V0 =5kV a 10Å resolution (including non-local effects) is possible. To achieve this, we would need a probe size about 5Å. However, at low voltages, the chromatic aberration becomes the major concern even for field emission sources. In this case, δV/V = 0.1 V/5kV = 2x10-5. As a rough estimate, it has been shown that /2/ the chromatic aberration δC should be less than ⅓ of δ0 the probe size determined by diffraction and spherical aberration in order to neglect its effect. But this did not take into account the distribution of electron energy. We will show that by using a wave optical treatment, the tolerance on the chromatic aberration is much larger than we expected.

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Kinematical and Dynamical CBED Pattern Models: Increasing the Accuracy of the Unit-Cell Parameter Measurements Based on CBED Patterns

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100136301 ◽

1990 ◽

Vol 48 (2) ◽

pp. 540-541

Author(s):

I.N. Yadhikov ◽

S.K. Maksimov

Keyword(s):

Reciprocal Lattice ◽

Unit Cell ◽

Reciprocal Lattice Vector ◽

Unit Cell Parameters ◽

Lattice Vector ◽

Cell Parameters ◽

Accuracy Of Measurements ◽

The Difference ◽

Image Position ◽

Convergent Beam

Convergent beam electron diffraction (CBED) is widely used as a microanalysis tool. By the relative position of HOLZ-lines (Higher Order Laue Zone) in CBED-patterns one can determine the unit cell parameters with a high accuracy up to 0.1%. For this purpose, maps of HOLZ-lines are simulated with the help of a computer so that the best matching of maps with experimental CBED-pattern should be reached. In maps, HOLZ-lines are approximated, as a rule, by straight lines. The actual HOLZ-lines, however, are different from the straights. If we decrease accelerating voltage, the difference is increased and, thus, the accuracy of the unit cell parameters determination by the method becomes lower.To improve the accuracy of measurements it is necessary to give up the HOLZ-lines substitution by the straights. According to the kinematical theory a HOLZ-line is merely a fragment of ellipse arc described by the parametric equationwith arc corresponding to change of β parameter from -90° to +90°, wherevector, h - the distance between Laue zones, g - the value of the reciprocal lattice vector, g‖ - the value of the reciprocal lattice vector projection on zero Laue zone.

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