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Miller indices
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Image
Published: 01 January 2005
Fig. 3 Miller indices for planes and directions of a cube. Indices in parentheses define planes, while bracketed indices, such as [100], indicate directions. An overbar is shorthand for a minus sign, indicating a negative Miller coordinate relative to the origin at the center of the cube
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Image
Published: 01 January 1986
Fig. 2 Unit meshes and two-dimensional Miller indices. (a) The five two-dimensional Bravais nets. (b) Examples of families of rows with Miller indices referenced to the unit mesh vectors. (11) and (31) families of rows are shown.
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Image
Published: 01 December 1998
Image
Published: 15 December 2019
Fig. 2 Unit meshes and two-dimensional Miller indices. (a) The five two-dimensional Bravais nets. (b) Examples of families of rows with Miller indices referenced to the unit mesh vectors. (11) and (31) families of rows are shown.
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Image
Published: 01 December 2004
Fig. 5 Orientation parameterizations. (a) Axis-angle description. (b) Euler angles (Bunge notation). (c) Miller indices
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Image
Published: 15 December 2019
Fig. 14 Example of card in Hanawalt search method for compound tentatively identified as Al 2 O 3 . The information on the card enables identification of the Miller indices of the planes associated with each diffraction peak, shown in the last column of Table 2 .
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Image
Published: 01 December 1998
Fig. 3 Various planes of atoms defined in simple two-dimensional “crystals.” Each plane is defined by its Miller indices, computed from the reciprocals of its intersections with the x - and y -axes. Each plane has a characteristic interplanar spacing. Source: Ref 1
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Image
Published: 01 January 1986
Fig. 3 Examples of crystal symmetry in the tetragonal system. (a) Unit cell type. (b) Phloroglucinol diethyl ether, class 4/ m. (c) Wulfenite (PbMoO 4 ), class 4. (d) Anatase (TiO 2 ), class 4/ mmm. (e) Zircon (ZrSiO 4 ), class 4/ mmm. The three digit codes are the Miller indices, hkl
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Image
Published: 01 November 1995
Fig. 6 Plot of intensity vs. twice the angle of incidence, 2θ, to show powder diffraction pattern obtained for face-centered-cubic (fcc) phase magnesium oxide using a copper target and a nickel filter. Acceleration voltage was 50 kV at a current of 20 mA. Numbers in parentheses are Miller
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Series: ASM Desk Editions
Publisher: ASM International
Published: 01 December 1998
DOI: 10.31399/asm.hb.mhde2.a0003251
EISBN: 978-1-62708-199-3
.... Fig. 3 Various planes of atoms defined in simple two-dimensional “crystals.” Each plane is defined by its Miller indices, computed from the reciprocals of its intersections with the x - and y -axes. Each plane has a characteristic interplanar spacing. Source: Ref 1 Crystal planes...
Abstract
X-ray diffraction (XRD) is the most extensively used method for identifying and characterizing various aspects of metals related to the arrangements and spacings of their atoms for bulk structural analysis. XRD techniques are also applicable to ceramics, geologic materials, and most inorganic chemical compounds. This article describes the operating principles and types of XRD analyses, along with information about the threshold sensitivity and precision, limitations, sample requirements, and capabilities of related techniques. The necessary instrumentation for XRD analyses include the Debye-Scherrer camera and the X-ray diffractometer. The article also describes the uses of XRD analyses, such as the identification of phases or compounds in metals and ceramics; detection of order and disorder transformation; determination of lattice parameters and changes in lattice parameters due to alloying and temperature effects; measurement of residual stresses; characterization of crystallite size and perfection; characterization of preferred orientations; and determination of single crystal orientations.
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
.... If the imaginary plane corresponds to an ( hkl ) plane in the bulk crystal, the surface is defined as an ( hkl ) surface, using the usual 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...
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: 10
Publisher: ASM International
Published: 15 December 2019
DOI: 10.31399/asm.hb.v10.a0006655
EISBN: 978-1-62708-213-6
... to an ( hkl ) plane in the bulk crystal, the surface is defined as an ( hkl ) surface, using the usual 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...
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.
Book Chapter
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0004018
EISBN: 978-1-62708-185-6
.... In contrast, the bcc system is not a close-packed structure; in this case, nearly close-packed planes may serve as slip planes. Common slip systems for various metals are listed in Table 1 . Fig. 3 Miller indices for planes and directions of a cube. Indices in parentheses define planes, while...
Abstract
Plastic deformation can occur in metals from various mechanisms, such as slip, twinning, diffusion creep, grain-boundary sliding, grain rotation, and deformation-induced phase transformations. This article emphasizes on the mechanism of slip and twinning under cold working conditions. It discusses the factors on which the structures developed during plastic deformation depend. These factors include crystal structure, amount of deformation, composition, deformation mode, and deformation temperature and rate. The article illustrates the microstructural features that appear after substantial deformation when revealed through metallographic investigation.
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
... are typically given by either an axis and a rotation angle ( n ,θ), a triplet of Euler angles (φ 1 ,Φ,φ 2 ), or by a set of Miller indices { hkl }⟨ uvw ⟩. The axis-angle description defines an axis of rotation ( n ) about which a rotation of (θ) will result in the required transformation. The Euler angle...
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.
Book Chapter
Series: ASM Handbook
Volume: 10
Publisher: ASM International
Published: 15 December 2019
DOI: 10.31399/asm.hb.v10.a0006654
EISBN: 978-1-62708-213-6
..., which is also proposed by W.L. Bragg, is a very intuitive way of understanding diffraction. Fig. 5 Illustration of Bragg’s law. The path in red marks the extra length the x-rays go through when scattered by the second plane of atoms. Crystal planes are identified by Miller indices...
Abstract
This article discusses the techniques and applications of synchrotron x-ray diffraction, providing information on x-ray generation, monochromation, and crystallography. X-ray diffraction techniques covered include single-crystal and powder diffraction. Some of the factors involved in the construction and development of macromolecular x-ray crystallography are also described.
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
... is the volume of the unit cell, and N is Avogadro's number (6.022 × 10 23 ). Miller Indices for Planes and Direction Miller indices used for designating planes within a crystal are based on the intercepts of the plane with the crystal axes. If the unit-cell edges are of lengths a, b, and c...
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
... in the unit cell, A is their mean atomic weight (calculated with atomic percentages), V is the volume of the unit cell, and N is Avogadro's number (6.022 × 10 23 ). Miller Indices for Planes and Direction Miller indices used for designating planes within a crystal are based on the intercepts...
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: 4A
Publisher: ASM International
Published: 01 August 2013
DOI: 10.31399/asm.hb.v04a.a0005790
EISBN: 978-1-62708-165-8
... it is naïve to assume that a given time-temperature parameter applies to all of the subcritical annealing responses, some rough time-temperature trade-offs can be projected with the use of the Larson-Miller parameter, P , where: P = T ( log t + C ) where T is absolute temperature (most...
Abstract
This article describes the metallurgy and process specifics of subcritical annealing, which involves heating below the lower critical temperature such that austenite does not form during subcritical annealing. It provides information on the nominal subcritical annealing temperatures of plain carbon, low-alloy and high-alloy steels and temperature-time relations of subcritical annealing. Practical implications for induction annealing and induction normalizing are included. The article concludes by describing induction softening, which softens the threaded area on carburized components such as hypoid pinion gears, to prevent the occurrence of delayed fractures from occurring.
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
... ( sin ϕ c − sin ψ c ) where a , b , and c are the lattice repeats; n a , n b , and n c are the order numbers usually identified as the Miller indices h , k , and l ; and ϕ and ψ are the incident and diffracted angles, respectively. The three-dimensional lattice...
Abstract
X-ray diffraction techniques are useful for characterizing crystalline materials, such as metals, intermetallics, ceramics, minerals, polymers, plastics, and other inorganic or organic compounds. This article discusses the theory of x-rays and how they are generated and detected. It also describes the crystalline nature of certain materials and how the geometry of a unit cell, and hence crystal lattice, affects the direction and intensity of diffracted x-ray beams. The article concludes with several application examples involving measurements on single and polycrystalline materials.
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005405
EISBN: 978-1-62708-196-2
... micromechanics. Miller ( Ref 23 ) further indicated the importance of considering environmental effects in overcoming or eradicating MSC thresholds, although they are not indicated on Fig. 8 . Fig. 8 Hierarchical thresholds for propagating cracks in a plot of completely reversed applied stress amplitude...
Abstract
The purposes and methods of fatigue modeling and simulation in high-cycle fatigue (HCF) regime are to design either failsafe components or components with a finite life and to quantify remaining life of components with pre-existing cracks using fracture mechanics, with the intent of monitoring via an inspection scheme. This article begins with a discussion on the stages of the fatigue damage process. It describes hierarchical multistage fatigue modeling and several key points regarding the physics of crack nucleation and microstructurally small crack propagation in the HCF regime. The article provides a description of the microstructure-sensitive modeling to model fatigue of several classes of advanced engineering alloys. It describes the various modeling and design processes designed against fatigue crack initiation. The article concludes with a discussion on the challenges in microstructure-sensitive fatigue modeling.