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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 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...
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
... ¯ m Fm 3 ¯ m Fm 3 ¯ c Fd 3 ¯ m Fd 3 ¯ c Im 3 ¯ m   Ia 3 ¯ d Source: Ref 1 , 9 , 12 Atomic coordinates and isotropic displacement parameters, Å<sup>2</sup>, for Cs<sub>2</sub>[(UO<sub>2</sub>)<sub>2</sub>(SeO<sub>4</sub>)<sub>3</sub>...
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
... of positional parameters, temperature factors, etc., as well as the half-width, zero point, and cell parameters and (2) calculating, in a least squares method, the difference between observed and calculated intensities. Although such a method is most often applied to the refinement of atomic coordinates...
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
... | F c | and therefore D are dependent on the atomic coordinates. By a combination of least squares refinement and electron density maps, most crystal structures can be solved and refined quickly. Atoms undergo vibrational motions. For example, one atom may be moving to the left as its...
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
... oxygen-oxygen distances. Therefore, interpretation of the first two peaks yields information concerning the oxygen-silicon-oxygen bond angles. Thus, the RDF provides information on bond distances and angles and the number of atoms in various coordination spheres. Fig. 1 The radial distribution...
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
... of Fig. 12b ) characteristic of the fcc structure and consists of four resolved peaks associated with the first four coordination shells about the central atom (compare with Fig. 7 for nickel at 90 K). Like Ni 3 C, Ni 3 B has a cementite structure (Schoenflies symbol V h 16 , Hermann...
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
... that are at a distance r j from the absorbing atom and that contain 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...
Series: ASM Handbook
Volume: 10
Publisher: ASM International
Published: 15 December 2019
DOI: 10.31399/asm.hb.v10.a0006667
EISBN: 978-1-62708-213-6
... measured observables (the individual reflections) is much greater than the unknowns (the atomic coordinates). For large structural units and macromolecular materials, the resolution is often not sufficient to refine an atomic- or molecular-level model with only 2 Å resolution. Data analysis for inorganic...
Book Chapter

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...
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...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005429
EISBN: 978-1-62708-196-2
... the structure designations, the atomic basis and the Wyckoff positions are listed in terms of the atom type, the number of atoms at each symmetry distinct point, and the internal coordinate. All the required information is now determined. The International Tables for X-Ray Crystallography has more information...
Series: ASM Handbook
Volume: 10
Publisher: ASM International
Published: 15 December 2019
DOI: 10.31399/asm.hb.v10.a0006678
EISBN: 978-1-62708-213-6
... X-Ray Diffraction” in this Volume explains how single-crystal x-ray diffraction is used 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...
Series: ASM Handbook
Volume: 10
Publisher: ASM International
Published: 15 December 2019
DOI: 10.31399/asm.hb.v10.a0006662
EISBN: 978-1-62708-213-6
... Laboratories. Normal-coordinate analysis begins by describing a molecular structure as a collection of balls and massless springs. This is a reasonable model based on chemical intuition. The balls represent atoms, and the springs are the forces or chemical bonds between atoms. The problem would be simple...
Series: ASM Handbook Archive
Volume: 10
Publisher: ASM International
Published: 01 January 1986
DOI: 10.31399/asm.hb.v10.a0001735
EISBN: 978-1-62708-178-8
... of atoms in the molecule. It is assumed that there is no coupling of the vibrational degrees of freedom with the rotations and translations. Of the parameters necessary to begin a normal-coordinate analysis, only the atomic masses are always easily obtained. The molecular geometry can often be acquired...
Series: ASM Handbook
Volume: 10
Publisher: ASM International
Published: 15 December 2019
DOI: 10.31399/asm.hb.v10.a0006650
EISBN: 978-1-62708-213-6
... ratio (γ), nuclear spin ( I ), and quadrupole moment ( Q ) Several atoms are shown with more than one NMR-active isotope. Element Isotope γ/2π, MHz/T I Natural abundance, % Q , barns Hydrogen 1 H 42.577 1/2 99.9885 … 2 H 6.536 1 0.0115 0.00286 Helium 3...
Series: ASM Handbook
Volume: 10
Publisher: ASM International
Published: 15 December 2019
DOI: 10.31399/asm.hb.v10.a0006655
EISBN: 978-1-62708-213-6
... to create a surface. The coordination number defines the number of nearest neighbors of any atom in the crystal structure. The necessity of breaking bonds to create a surface implies a coordination number for surface atoms that is lower than that of atoms in the bulk. Surfaces can be singular or vicinal...
Series: ASM Handbook Archive
Volume: 10
Publisher: ASM International
Published: 01 January 1986
DOI: 10.31399/asm.hb.v10.a0001769
EISBN: 978-1-62708-178-8
... Miller indices. Bonds between atoms must be broken to create a surface. The coordination number defines the number of nearest neighbors of any atom in the crystal structure. The necessity of breaking bonds to create a surface implies a coordination number for surface atoms that is lower than...
Series: ASM Handbook Archive
Volume: 10
Publisher: ASM International
Published: 01 January 1986
DOI: 10.31399/asm.hb.v10.a0001756
EISBN: 978-1-62708-178-8
.... Figure 7 shows a unit cell containing two atoms. The positions of these atoms are described by their position coordinates based on the fractions of the unit-cell dimensions in the three principal directions from some origin. The choice of origin is not critical; it is usually selected on some symmetry...
Series: ASM Handbook
Volume: 13A
Publisher: ASM International
Published: 01 January 2003
DOI: 10.31399/asm.hb.v13a.a0003709
EISBN: 978-1-62708-182-5
... or current density values on logarithmic coordinates, absolute values of the current or current density are used and the cathodic values are clearly indicated. The direction of conventional current in an external circuit is defined by the cell type: Cell type Direction of conventional current...
Series: ASM Handbook
Volume: 10
Publisher: ASM International
Published: 15 December 2019
DOI: 10.31399/asm.hb.v10.a0006643
EISBN: 978-1-62708-213-6
... differences among the diffracted beams, decreasing the amplitude of the total diffracted beam. 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...