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atomic coordination
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Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002460
EISBN: 978-1-62708-194-8
... Abstract This article focuses on the relationships among material properties and material structure. It summarizes the fundamental characteristics of metals, ceramics, and polymers. The article provides information on the crystal structure, the atomic coordination, and crystalline defects...
Abstract
This article focuses on the relationships among material properties and material structure. It summarizes the fundamental characteristics of metals, ceramics, and polymers. The article provides information on the crystal structure, the atomic coordination, and crystalline defects. It discusses the relevance of the properties to design. The article describes the common means for increasing low-temperature strength and presents an example that shows structure-property relationships in nickel-base superalloys for high-temperature applications. The relationships of microstructure with low-temperature fracture, high-temperature fracture, and fatigue failure are also discussed.
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Published: 01 December 2004
Fig. 32 The principle of operation of a 3D atom probe. The x and y coordinates of each atom are determined from the impact position on the position-sensitive detector. The z coordinate is determined from its position in the evaporation sequence. The mass-to-charge ratio and hence
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in The Liquid State and Principles of Solidification of Cast Iron
> Cast Iron Science and Technology
Published: 31 August 2017
Fig. 1 Number of atoms in the first coordination sphere obtained by neutron diffraction and x-ray. Source: Ref 2
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Published: 01 January 1986
Fig. 4 The experimental RDF curve obtained for silica glass and the corresponding curves calculated from the atomic coordinates of a 1412 atom model and spherical regions within the crystal structures of tridymite, cristobalite, and quartz. For the small details in G ( r ) at large r
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Series: ASM Handbook
Volume: 10
Publisher: ASM International
Published: 15 December 2019
DOI: 10.31399/asm.hb.v10.a0006631
EISBN: 978-1-62708-213-6
... The main application of single-crystal x-ray diffraction (XRD) is to characterize the crystal structure, including determining symmetry, unit cell parameters, atomic coordinates and thermal displacement parameters, bond lengths and angles between the atoms, and structural motive (or topology). During...
Abstract
This article provides a detailed account of the concepts of single-crystal x-ray diffraction (XRD). It begins with a historical review of XRD methods, followed by a description of the various factors involved in crystal symmetry. The article then focuses on the phase problem in x-ray structural analysis and validation of the structural model. Some of the factors to be considered for performing experimental procedure are provided. The article presents several examples of applications of single-crystal XRD. The following sections cover the crystallographic problem in terms of structural analysis, software programs for crystal structure solution and refinement, and visualization of crystal structures. The article ends with a discussion on various databases available for single-crystal XRD analysis.
Series: ASM Handbook Archive
Volume: 10
Publisher: ASM International
Published: 01 January 1986
DOI: 10.31399/asm.hb.v10.a0001758
EISBN: 978-1-62708-178-8
... diffraction has as its primary goal the determination of crystal structure, the arrangement of atoms within the unit cell. If the atoms are grouped into molecules, the molecular structure is an added benefit. Once the atoms are located, interatomic bond distances and angles can be calculated, coordination...
Abstract
The primary goal of single-crystal x-ray diffraction is to determine crystal structure and the arrangement of atoms in a unit cell. This article discusses the diffraction of light through line gratings and explains the significance of crystal symmetry, space groups, and diffraction intensities. It also addresses phase and crystallographic analysis along with related challenges, and presents several application examples highlighting various experimental techniques.
Series: ASM Handbook Archive
Volume: 10
Publisher: ASM International
Published: 01 January 1986
DOI: 10.31399/asm.hb.v10.a0001762
EISBN: 978-1-62708-178-8
... is the distance between the i th and j th atoms, N ij is the coordination number, and l ij is the disorder parameter. Elimination of spurious details due to termination effects from the RDF is based on the recognition that generally only the shortest distances contribute significantly...
Abstract
The diffraction pattern of any material contains structural and chemical property information that can be extracted using radial distribution function analysis. This article provides an introduction to the technique and presents several examples highlighting various ways in which it can be used. It begins with a discussion on the principles of diffraction and scattering and the effectiveness of x-ray, neutron, and electron energy sources for different types of measurements. It provides information on data collection and reduction and explains how to create atomic distribution plots from intensity and scattering angle data. The article also presents application parameters for defining short distances and background intensity and describes a procedure for generating pair distribution functions.
Book Chapter
Series: ASM Handbook
Volume: 10
Publisher: ASM International
Published: 15 December 2019
DOI: 10.31399/asm.hb.v10.a0006665
EISBN: 978-1-62708-213-6
... N j atoms (the coordination number). Lambda is the mean free path of the photoelectron. The second exponential containing σ j 2 is a Debye-Waller term in which σ j 2 is not the usual mean-square vibrational amplitude of an atom but the mean-square relative positional...
Abstract
This article provides a detailed account of extended x-ray absorption fine structure (EXAFS). It begins with a description of the fundamentals of EXAFS, providing information on the physical mechanism, single-scattering approximation, and multiple-scattering effects. This is followed by a discussion on the use of synchrotron radiation as an X-ray source for EXAFS. Data-reduction procedures used to extract EXAFS signals are then described. The article also provides information on the analysis of x-ray absorption near-edge structure spectrum and ends with a discussion on the unique features and applications of EXAFS.
Series: ASM Handbook Archive
Volume: 10
Publisher: ASM International
Published: 01 January 1986
DOI: 10.31399/asm.hb.v10.a0001765
EISBN: 978-1-62708-178-8
... to the refinement of atomic coordinates, increasingly it has been applied to the solution of structures by trial and error or Patterson methods. In addition to refinement of atomic coordinates and temperature factors, the original Rietveld code was established for the refinement of magnetic structures. Newer...
Abstract
Neutrons are a principal tool for the study of lattice vibrational spectra in materials. This article provides a detailed account of fission and spallation methods of neutron production that are capable of producing sufficient intensity to be useful in neutron scattering research. It describes the instrumentation required for, and advancements made in, neutron powder diffraction. The article further explains the texture and residual stress (macrostresses and microstresses) problems that are analyzed using the neutron powder diffraction method. It also outlines the single-crystal neutron diffraction technique, and provides examples of the applications of neutron diffraction.
Image
Published: 01 January 1986
by the small letters at the end of the label) to complete the coordination sphere around each atom. Source: Ref 14
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Published: 01 January 1986
at the origin with coordinates 0, 0, 0 has an equivalent at 1 2 , 1 2 , 1 2 (the center of the cell). More generally, an atom at x , y, z has an equivalent at 1 2 + x , 1 2 + y , 1 2 + z. Source: Ref 3
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Published: 01 January 1990
Fig. 3 The metallic radius for a coordination number (CN) of twelve versus the lanthanide atomic number
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in Crystallography and Engineering Properties of Ceramics
> Engineered Materials Handbook Desk Edition
Published: 01 November 1995
Fig. 2 The wurtzite (a) and zinc blende (b) structures illustrating two arrangements of atoms that result in tetrahedral coordination of both constituents
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Published: 01 December 2009
Series: ASM Handbook Archive
Volume: 10
Publisher: ASM International
Published: 01 January 1986
DOI: 10.31399/asm.hb.v10.a0001764
EISBN: 978-1-62708-178-8
... (the coordination number). Lambda is the mean free path of the photoelectron. The second exponential containing σ j 2 is a Debye-Waller term in which σ j 2 is not the usual mean-square vibrational amplitude of an atom, but the mean-square relative positional fluctuation of the central...
Abstract
This article provides an introduction to extended x-ray absorption fine structure (EXAFS). It describes the fundamentals of EXAFS with an emphasis on the physical mechanism, the single-scattering approximation, and multiple-scattering effects. The article discusses the use of synchrotron radiation as the x-ray source for EXAFS experiments. It also describes the typical EXAFS data analysis of pure nickel at 90 K, and explains the near-edge structure analysis of vanadium. The article presents a discussion on the unique features and applications of EXAFS.
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Published: 30 September 2015
Fig. 10 Relationship between x-ray line broadening and vibratory milling time for Nickel 123 powder. Numbers in parentheses refer to coordinates of atomic planes in face-centered cubic structure.
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Published: 01 January 1986
Fig. 7 Diffraction in a unit cell and the structure factor equation for the cell. The positions of atoms 1 and 2 are defined by their position coordinates based on fractions of the unit cell dimensions in directions a , b , and c . x 1 = X 1 / a , y 1 = Y 1 / b , and z 1 = Z
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Image
Published: 15 December 2019
Fig. 7 Diffraction in a unit cell and the structure factor equation for the cell. The positions of atoms 1 and 2 are defined by their position coordinates based on fractions of the unit-cell dimensions in directions a , b , and c . x 1 = X 1 / a , y 1 = Y 1 / b , and z 1 = Z
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Book Chapter
Book: Alloy Phase Diagrams
Series: ASM Handbook
Volume: 3
Publisher: ASM International
Published: 27 April 2016
DOI: 10.31399/asm.hb.v03.a0006292
EISBN: 978-1-62708-163-4
..., because different materials with the same type of atomic arrangement have atoms that differ in size, causing the lengths of the a , b , and c edges to differ. Similarly, the atom-position coordinates x , y , and z vary among different materials. Atom Positions The position of an atom...
Abstract
This article defines crystallographic terms and concepts, including crystal structure, unit cell, structure symbols, lattice, space-group notation, and atom position. It schematically illustrates the atom positions, prototypes, structure symbols, space-group notations, and lattice parameters for some of the simple metallic crystals. A table that lists the crystal structures of various metal elements is presented. The crystal structures are described by the Pearson symbols for crystal system, space lattice, total number of atoms per unit cell, and prototype structure. The article tabulates the assorted structure types of metallurgical interest arranged according to Pearson symbol. It also provides information on crystal defects, explaining some significant ones, such as point defects, line defects, stacking faults, and twins.
Book Chapter
Series: ASM Handbook
Volume: 9
Publisher: ASM International
Published: 01 December 2004
DOI: 10.31399/asm.hb.v09.a0003722
EISBN: 978-1-62708-177-1
..., causing the lengths of the a , b, and c edges to differ. Similarly, the atom-position coordinates x , y , and z vary among different materials. Atom Positions The position of an atom, or the lattice point, in a unit cell is expressed by three coordinates ( Ref 5 )—the three distances...
Abstract
This article describes crystallographic terms and concepts and illustrates various crystal structures. The crystallographic terms described include crystal structure, unit cell, crystal system, lattice, structure symbols, space-group notation, structure prototype, atom positions, point groups, and equivalent positions. The article presents a table of assorted structure types of metallurgical interest arranged according to the Pearson symbol. It also schematically illustrates atom positions, prototypes, structure symbols, space-group notations, and lattice parameters for some of the simple metallic crystals. The article concludes with a description of some of the most significant crystal defects such as point defects, line defects, and stacking faults.
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