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Bravais lattices
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in Introduction to the Mechanical Behavior of Nonmetallic Materials
> Mechanical Testing and Evaluation
Published: 01 January 2000
Fig. 9 The 14 Bravais lattices illustrated by a unit cell of each: 1, triclinic, primitive; 2, monoclinic, primitive; 3, monoclinic, base centered; 4, orthorhombic, primitive; 5, orthorhombic, base centered; 6, orthorhombic, body centered; 7, orthorhombic, face centered; 8, tetragonal
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Published: 01 December 1998
Fig. 3 The 14-space (Bravais) lattices illustrated by a unit cell of each: (1) triclinic, primitive; (2) monoclinic, primitive; (3) monoclinic, base centered; (4) orthorhombic, primitive; (5) orthorhombic, base centered; (6) orthorhombic, body centered; (7) orthorhombic, face centered; (8
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Published: 15 December 2019
Series: ASM Desk Editions
Publisher: ASM International
Published: 01 December 1998
DOI: 10.31399/asm.hb.mhde2.a0003084
EISBN: 978-1-62708-199-3
... Abstract Crystal structure is the arrangement of atoms or molecules in the solid state that involves consideration of defects, or abnormalities, in idealized atomic/molecular arrangements. The three-dimensional aggregation of unit cells in the crystal forms a space lattice or Bravais lattice...
Abstract
Crystal structure is the arrangement of atoms or molecules in the solid state that involves consideration of defects, or abnormalities, in idealized atomic/molecular arrangements. The three-dimensional aggregation of unit cells in the crystal forms a space lattice or Bravais lattice. This article provides a brief review of the terms and basic concepts associated with crystal structures. It also discusses some of the significant defects obstructing plastic flow in real crystals, namely point defects, line defects, stacking faults, twins, and cold work. Several tables in the article provide information on the crystal structures and lattice parameters of allotropes of metallic elements.
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Published: 01 January 2005
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in Introduction to the Mechanical Behavior of Nonmetallic Materials
> Mechanical Testing and Evaluation
Published: 01 January 2000
Fig. 10 Schematic illustration of the construction of NaCl from two interpenetrating fcc Bravais lattices
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in Introduction to the Mechanical Behavior of Nonmetallic Materials
> Mechanical Testing and Evaluation
Published: 01 January 2000
Fig. 2 Schematic representation of ionically bonded NaCl. Note that this structure consists of Na + and Cl − ions sitting on interpenetrating fcc Bravais lattices.
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Book Chapter
Book: Corrosion: Materials
Series: ASM Handbook
Volume: 13B
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v13b.a0006544
EISBN: 978-1-62708-183-2
... of which form the a , b , and c axes of the crystal. The three-dimensional aggregation of unit cells in the crystal forms a space lattice, or Bravais lattice ( Fig. 1 ). Fig. 1 A space (Bravais) lattice Crystal Systems Seven different crystal systems are recognized in crystallography...
Abstract
The crystal structure of a material is an important aspect of corrosion and oxidation processes. This article provides a general introduction to the crystal structure of materials, providing information on the crystal systems, lattice dimensions, nomenclature, and solid-solution mechanisms used to characterize structures. It illustrates the unit cells and ion positions for some simple metal crystals, arranged alphabetically according to the Pearson symbol. The space lattice and crystal system, space-group notation, and prototype for each crystal are also illustrated.
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0003255
EISBN: 978-1-62708-176-4
... to have little tolerance for alloying. Fig. 2 Schematic representation of ionically bonded NaCl. Note that this structure consists of Na + and Cl − ions sitting on interpenetrating fcc Bravais lattices. Covalent bonding occurs in compounds containing electronegative elements. Covalent...
Abstract
This article reviews the fundamental relationships between microstructure and mechanical properties for major classes of nonmetallic engineering materials: metals, ceramics and glasses, intermetallic compounds, polymers, and composites. It details the structures of inorganic crystalline solids, inorganic noncrystalline solids, and polymers. The article describes the various strengthening mechanisms of crystalline solids, namely, work hardening, solid-solution hardening, particle/precipitation hardening, and grain size hardening. Deformation and strengthening of composite materials, polymers, and glasses are reviewed. The article concludes with information on the two important aspects of the mechanical behavior of any class of engineering material: fatigue response and fracture resistance.
Book Chapter
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
... on the points of a Bravais lattice or in a fixed relation to those points ( Ref 11 ). A Bravais lattice is a set of points in space such that each point has identical surroundings. There are 14 possible arrangements or crystal structures ( Table 4 and Fig. 4 ). The name of the crystal structure...
Abstract
This article presents common conventions and definitions in corrosion, electrochemical cells, cathodic protection (CP), electricity, and oxidation. Evans diagrams for impressed current CP in neutral or basic environment and galvanic or sacrificial CP, in both neutral or basic environment and acidic environment, are illustrated.
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
... of the directions of the symmetry axes and translational symmetry element arrangement. Bravais Lattices A lattice where the nodes are located only at the corners of a unit cell ( Fig. 2 ) is called primitive ( P ). In the presence of translations that link the vertexes of cells with equivalent nodes inside...
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.
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
...° As; Sb; Bi; calcite Cubic a = b = c α = β = γ = 90° Cu; Ag; Au; Fe; NaCl (a) Rhombohedral crystals (sometimes called trigonal) can also be described by using hexagonal axes (rhombohedral-hexagonal). Lattice A lattice (space lattice or Bravais lattice) is a regular, periodic...
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
... called trigonal) can also be described by using hexagonal axes (rhombohedral-hexagonal). Lattice A lattice (space lattice or Bravais lattice) is a regular, periodic array of points (lattice points) in space, at each of which is located the same kind of atom or a group of atoms of identical...
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.
Series: ASM Handbook
Volume: 10
Publisher: ASM International
Published: 15 December 2019
DOI: 10.31399/asm.hb.v10.a0006681
EISBN: 978-1-62708-213-6
... little. Inelastic scattering events generate SEs; Auger electrons; characteristic and continuum x-rays; long-wavelength electromagnetic radiation in the visible, ultraviolet, and infrared regions; electron-hole pairs; lattice vibrations (phonons); and electron oscillations (plasmons), as shown in Fig...
Abstract
Transmission electron microscopy (TEM) approach enables essentially simultaneous examination of microstructural features through imaging from lower magnifications to atomic resolution and the acquisition of chemical and crystallographic information from small regions of the thin specimen. This article discusses fundamentals of the technique, especially for solving materials problems. Background information is provided to help understand basic operations and principles, including instrumentation, the physics of signal generation and detection, image formation, electron diffraction, and spectrometry techniques with data analysis.
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
... analog of the unit cell. Primitive unit meshes contain one lattice point per mesh; nonprimitive, more than one lattice point per mesh. Figure 2(a) shows the five two-dimensional Bravais nets. The unit mesh vectors are conventionally defined, as shown, with the angle between the unit vectors ≥90...
Abstract
Low-energy electron diffraction (LEED) is a technique for investigating the crystallography of surfaces and overlayers adsorbed on surfaces. This article describes the principles of diffraction from surfaces, and elucidates the method of sample preparation to achieve diffraction patterns. The article describes the limitations of surface sensitive electron diffraction and discusses the applications of LEED with examples.
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0003254
EISBN: 978-1-62708-176-4
..., a crystal lattice is formed (see Fig 2 .). Although the arrangement of atoms in space can be of fourteen different types (or Bravais lattices), most metals have face-centered cubic (fcc) (e.g., nickel, aluminum, copper, lead), body-centered cubic (bcc) (e.g., iron, niobium, tungsten, molybdenum...
Abstract
Mechanical properties are described as the relationship between forces (or stresses) acting on a material and the resistance of the material to deformation (i.e., strains) and fracture. This article briefly introduces the typical relationships between metallurgical features and the mechanical behavior of metals. It explains the deformation and fracture mechanisms of these metals. Typical properties measured during mechanical testing related to these deformation mechanisms and the microstructures of metals are discussed. The article reviews the various factors that affect the deformation response of the metal: strain rate, temperature, nature of loading, stress-corrosion cracking, and presence of notches.
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
.... Primitive unit meshes contain one lattice point per mesh; nonprimitive contain more than one lattice point per mesh. Figure 2(a) shows the five two-dimensional Bravais nets. The unit mesh vectors are conventionally defined, as shown, with the angle between the unit vectors ≥90°, a denoting the shorter...
Abstract
Low-energy electron diffraction (LEED) is a technique for investigating the crystallography of surfaces and overlayers adsorbed on surfaces. This article provides a brief account of LEED, covering the principles and measurements of diffraction from surfaces. Some of the processes involved in sample preparation are described. In addition, the article discusses the limitations of surface-sensitive electron diffraction and the applications of LEED with examples.
Series: ASM Handbook
Volume: 9
Publisher: ASM International
Published: 01 December 2004
DOI: 10.31399/asm.hb.v09.a0003744
EISBN: 978-1-62708-177-1
... with an fcc Bravais lattice often exhibit alignment of {111} poles with the film normal direction. Such a texture is commonly termed a (111) fiber texture. X-ray rocking curves are often used to characterize such textures when the assumption is reasonably made that no additional texture components exist...
Abstract
This article describes the mechanisms involved in creating texture for various metal-fabrication processes, namely, solidification, deformation, recrystallization and grain growth, thin-film deposition, and imposition of external magnetic fields. It discusses two experimental and analytical approaches for experimental determination of texture: one using classical diffraction and pole figure measurement techniques and the other using individual orientation measurements. The article also provides information on microtexture, grain-boundary character, and texture gradients. It concludes with information on texture evolution through modeling.
Series: ASM Handbook
Volume: 9
Publisher: ASM International
Published: 01 December 2004
DOI: 10.31399/asm.hb.v09.9781627081771
EISBN: 978-1-62708-177-1
Series: ASM Handbook
Volume: 4D
Publisher: ASM International
Published: 01 October 2014
DOI: 10.31399/asm.hb.v04d.a0005959
EISBN: 978-1-62708-168-9
... and the radiation used for diffraction investigation. An investigation of homogenous nitrogen-expanded austenite with adjusted contents of nitrogen as controlled by gaseous nitriding showed that nitrogen-expanded austenite has a face-centered cubic (fcc) Bravais lattice and that systematic hkl-dependent peak shifts...
Abstract
Low-temperature surface hardening is mostly applied to austenitic stainless steels when a combination of excellent corrosion performance and wear performance is required. This article provides a brief history of low-temperature surface hardening of stainless steel, followed by a discussion on physical metallurgy, including crystallographic identity, thermal stability and decomposition, nitrogen and carbon solubility in expanded austenite, and diffusion kinetics of interstitials. It provides a description of low-temperature nitriding and nitrocarburizing processes for primarily austenitic and, to a lesser extent, other types of stainless steels along with practical examples and industrial applications of these steels.
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