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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 More
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. More
Image
Published: 01 December 1998
Fig. 4 Planes in three-dimensional crystals defined by their Miller indices. Source: Ref 2 More
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. More
Image
Published: 01 December 2004
Fig. 5 Orientation parameterizations. (a) Axis-angle description. (b) Euler angles (Bunge notation). (c) Miller indices More
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 . More
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 More
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. 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 More
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...
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...
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...
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...
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...
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...
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
... 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...
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...
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...
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...
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...