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crystal symmetry

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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 More
Image
Published: 01 November 1995
Fig. 31 Classification scheme for properties based on crystal symmetry More
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
... 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...
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
... 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...
Image
Published: 01 January 1986
Fig. 11 Kikuchi pattern from [111] single-crystal silicon. The three-fold symmetry is visible in the pattern. The crystal orientation is such that each set of ( hkl ) planes parallel to the beam deviates from the Bragg condition through exactly the Bragg angle. The symmetry of the Kikuchi More
Image
Published: 01 December 2009
Fig. 2 Fundamental region for cubic symmetry crystals showing several orientations differing only by rotations about (a) a 001 axis of rotation and (b) a 1 11 axis of rotation. The crystal axes are shown in gray scale. The 1 11 axis of rotation is colored red. More
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005532
EISBN: 978-1-62708-197-9
..., which means that peaks that are less than approximately 2° apart tend to overlap at high tilt angles and should therefore not be used. For high-symmetry crystal types, such as the cubic metals, the first three reflections are adequate, for example, 111, 200, and 220 for face-cubic centered (fcc...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0004028
EISBN: 978-1-62708-185-6
... Abstract This article outlines several polycrystal formulations commonly applied for the simulation of plastic deformation and the prediction of deformation texture. It discusses the crystals of cubic and hexagonal symmetry that constitute the majority of the metallic aggregates used...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005424
EISBN: 978-1-62708-196-2
... crystal plasticity deforming crystals polycrystals elastic behaviour plastic behavior SOLID METALLIC MATERIALS typically are crystalline, existing with well-defined lattice structures. The lattices possess certain symmetries dependent on the packing arrangements of atoms. Accompanying...
Image
Published: 15 December 2019
Fig. 3 Illustration of symmetry operations and elements: (a) reflection and mirror plane; (b) a general lattice, showing inversion at ½, ½, ½; (c) 6-fold axis in the beryl crystal model, point group 6/ mmm ; (d) 2-fold axis in the struvite crystal model, point group mm 2; (e) glide reflection More
Image
Published: 15 December 2019
Fig. 7 Stereographic triangle color keys for cubic and hexagonal crystal structures. (a) Cubic m3m symmetry. (b) Hexagonal 6/mmm symmetry More
Series: ASM Handbook Archive
Volume: 10
Publisher: ASM International
Published: 01 January 1986
DOI: 10.31399/asm.hb.v10.a0001759
EISBN: 978-1-62708-178-8
.... Figure 9 shows the Euler space. For cubic materials with rolling symmetry only the range of 0 to π/2 need be considered for each of the three Euler angles. All possible orientations are in this range. In addition, because of the high degree of symmetry exhibited in cubic crystals, only a portion...
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
... of diffracted intensities Single crystal Refinement of whole pattern Powder Symmetry Moving crystal-spot pattern Single crystal Stationary crystal-spot pattern Single crystal Identification of compound Identification of cell parameters Single crystal Matching of d-I set Powder...
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
..., the arrangement of atoms depends on the types of atoms, the nature of their bonds, and their tendency to minimize the free energy by a high degree of organization. This organization usually results in some degree of geometric symmetry and unit-cell shapes reflecting this symmetry. The crystal as a whole...
Image
Published: 15 December 2019
Fig. 7 Polyhedral representation of the Cs 2 [(UO 2 ) 2 (SeO 4 ) 3 ] crystal structure: (a) view along the layers, and (b) projection of the uranyl-selenate layer, with symmetry elements overlaid. Legend: U polyhedra = yellow, SeO 4 tetrahedra = orange, Cs atoms = cyan, O atoms = red More
Book Chapter

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
... atoms per unit cell). Space-Group Notation Space-group notation is a symbolic description of the space lattice and symmetry of a crystal. It consists of the symbol for the space lattice followed by letters and numbers that designate the symmetry of the crystal. The space-group notation for each...
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
... electron volts. The limited penetration of electrons in this energy range provides the sensitivity to the surface. Low-energy electron diffraction measurements are conducted using a monoenergetic beam of electrons that impinges on the crystal surface. Diffraction of electrons occurs because...
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
... electron volts. The limited penetration of electrons in this energy range provides information from a very top surface. The first experimental observation of electron diffraction by a crystal lattice was performed by Davisson and Germer in 1927. After an accidental explosion of a bottle containing...
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
... by symmetry considerations and by convenience. Crystal Systems Crystallography uses seven different systems of axes, each with a specified equality or inequality to others of axial lengths and interaxial angles. These are the basis of the following crystal systems—triclinic (anorthic), monoclinic...
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
... cells stacked tightly together, each identical in size, shape, and orientation with all others. The choice of the boundaries of a unit cell is somewhat arbitrary, being conditioned by symmetry considerations and by convenience. Crystal Systems Crystallography uses seven different systems of axes...