scholarly journals Indexing of icosahedral quasiperiodic crystals

1986 ◽  
Vol 1 (1) ◽  
pp. 13-26 ◽  
Author(s):  
John W. Cahn ◽  
Dan Shechtman ◽  
Denis Gratias
Keyword(s):  
Fourier Transform ◽  
Electron Diffraction ◽  
Single Crystal ◽  
Coordinate System ◽  
Powder Diffraction ◽  
Simple Application ◽  
Coordinate Systems ◽  
Diffraction Patterns ◽  
Definition Of ◽  
Crystal Electron

Since the definition of quasiperiodicity is intimately connected to the indexing of a Fourier transform, for the case of an icosahedral solid, the step necessary to prove, using diffraction, that an object is quasiperiodic, is described. Various coordinate systems are discussed and reasons are given for choosing one aligned with a set of three orthogonal two-fold axes. Based on this coordinate system, the main crystallographic projections are presented and several analyzed single-crystal electron diffraction patterns are demonstrated. The extinction rules for three of the five icosahedral Bravais quasilattices are compared, and some simple relationships with the six-dimensional cut and projection crystallography are derived. This analysis leads to a simple application for indexing powder diffraction patterns.

Compositional variation within some sedimentary chlorites and some comments on their origin

1985 ◽  
Vol 49 (352) ◽  
pp. 375-386 ◽  
Author(s):  
C. D. Curtis ◽  
C. R. Hughes ◽  
J. A. Whiteman ◽  
C. K. Whittle
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Electron Diffraction ◽  
Single Crystal ◽  
Compositional Variation ◽  
Analytical Transmission Electron Microscopy ◽  
Decomposition Reactions ◽  
Transmission Electron ◽  
Diffraction Patterns ◽  
Crystal Electron

AbstractA range of authigenic sedimentary chlorites from sandstones has been studied by analytical transmission electron microscopy. Selected area (single crystal) electron diffraction patterns are of the Ib (β = 90°) polytype confirming the earlier observations of Hayes (1970).TEM analyses show all samples to be relatively rich in both Al and Fe. In the general formula (Mg,Fe,Al)n [Si8−xAlxO20](OH)16, x varies between 1.5 and 2.6; Fe/(Fe + Mg) between 0.47 and 0.83 and n between 10.80 and 11.54. Octahedral Al is close to 3 in this formulation and Fe2+ predominates over Fe3+. Swelling chlorites have significantly different compositions which are consistent with smectite/chlorite interstratifications.The Ib (β = 90°) polytype appears to be stable under conditions of moderate to deep burial. It replaces berthierine and swelling chlorites formed at lower temperatures. As commonly seen in grain coatings, however, it precipitates from porewater; solutes probably being contributed from several mineral decomposition reactions.

Electron-optical data for crystals of scarbroite

1960 ◽  
Vol 32 (248) ◽  
pp. 363-365 ◽  
Author(s):  
G. W. Brindley ◽  
J. J. Comer
Keyword(s):  
Electron Diffraction ◽  
Single Crystal ◽  
Electron Micrographs ◽  
Optical Data ◽  
Diffraction Patterns ◽  
Crystal Electron

SummaryElectron micrographs of scarbroite show thin platy crystals of about 1 μ size, having rhombic outlines with angles 66° ± 1° and 113° ± 1°. Single-crystal electron-diffraction patterns show rectangular net patterns, with d100 = 9·90 Å., d010 = 14·67 Å., γ* = 90° ± 0·05°. Strong hk0 reflections show a pseudohexagonal arrangement, but true symmetry is probably orthorhombic or monoclinic. Faces outlining rhombic forms are of type {11l}, .

Pollutant Identification by Selected Area Electron Diffraction. II. The Limitations

1974 ◽  
Vol 32 ◽  
pp. 534-535
Author(s):  
R. E. Ferrell ◽  
G. G. Paulson ◽  
C. W. Walker
Keyword(s):  
Electron Diffraction ◽  
Single Crystal ◽  
Close Agreement ◽  
Straightforward Manner ◽  
Selected Area Electron Diffraction ◽  
The Subject ◽  
Diffraction Patterns ◽  
Crystal Electron

Single crystal electron diffraction patterns can be interpreted in a fairly straightforward manner because with a little knowledge of crystallography one can predict the kind of image to be formed by certain minerals. Close agreement between observed and theoretical patterns identifies the particles. However, in practice, electron diffraction patterns can be rather ambiguous or difficult to unravel. Most of the errors are inherent characteristics of certain samples and cannot be corrected easily. The most common of these are the subject of this discussion.

Electron Diffraction Studies of Pure SiC Polytypes

1969 ◽  
Vol 27 ◽  
pp. 162-163
Author(s):  
Donald L. Gibbon
Keyword(s):  
Electron Diffraction ◽  
Single Crystal ◽  
Single Crystals ◽  
X Ray ◽  
Carbon Substrates ◽  
Diffraction Patterns ◽  
Crystal Electron

Single crystal electron diffraction patterns have been obtained for three pure SiC polytypes, 4H, 6H, and 15R. The purity of the samples was determined by optical and x-ray techniques (Hannum and Shaffer, 1969). Diffracted intensity distributions for single crystals of these polytypes have been computed using the Busing-Levy ORFLS program. The samples were prepared by crushing and dispersing the powders on carbon substrates, shadowed with Pt. In scanning these dispersions, crystals were sought which were oriented with an a axis vertical.

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

1975 ◽  
Vol 26 ◽  
pp. 21-26
Keyword(s):  
Coordinate System ◽  
Working Group ◽  
General Character ◽  
Coordinate Systems ◽  
Reference Coordinate System ◽  
Group 2 ◽  
Definition Of ◽  
Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

scholarly journals The Celestial Reference System in Relativistic Framework

1990 ◽  
Vol 141 ◽  
pp. 99-110
Author(s):  
Han Chun-Hao ◽  
Huang Tian-Yi ◽  
Xu Bang-Xin
Keyword(s):  
Coordinate System ◽  
Reference Frame ◽  
Reference System ◽  
Light Deflection ◽  
Coordinate Systems ◽  
Definition Of ◽  
Celestial Sphere ◽  
Celestial Reference System ◽  
Relativistic Framework

The concept of reference system, reference frame, coordinate system and celestial sphere in a relativistic framework are given. The problems on the choice of celestial coordinate systems and the definition of the light deflection are discussed. Our suggestions are listed in Sec. 5.

Applications of the Global Coordinate System

2011 ◽  
Author(s):  
Yves Balasko
Keyword(s):  
Coordinate System ◽  
Critical Points ◽  
Global Coordinate System ◽  
Coordinate Systems ◽  
Analytical Characterization ◽  
Equilibrium Manifold ◽  
System P ◽  
Definition Of

The global coordinate system for the equilibrium manifold follows from: (1) the determination of the unique fiber F(b) through the equilibrium (ρ‎, ω‎) where b = φ‎((ρ‎, ω‎) = (ρ‎, ρ‎ · ρ‎1, …, ρ‎ · ρ‎m); and (2) the determination of the location of the equilibrium (ρ‎, ω‎) within the fiber F(b) viewed as a linear space of dimension (ℓ − 1)(m − 1) and, therefore, parameterized by (ℓ − 1)(m − 1) coordinates. If there is little leeway in determining the fiber F(b) through the equilibrium (ρ‎, ω‎), there are different ways of representing the equilibrium (ρ‎, ω‎) within its fiber F(b). This leads to the definition of coordinate systems (A) and (B) for the equilibrium manifold. This chapter defines these two coordinate systems and applies them to obtain an analytical characterization of the critical equilibria, i.e., the critical points of the natural projection.

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