Volume 10 - Materials Characterization Part 9 ppsx

Adams, Department of Mechanical Engineering, Brigham Young University... Adams, Department of Mechanical Engineering, Brigham Young University... Adams, Department of Mechanical Engineer

Richard L Harlow, E.I DuPont de Nemours

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Richard L Harlow, E.I DuPont de Nemours

Richard L Harlow, E.I DuPont de Nemours

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Table 2 Fractional coordinates x, y, and z (× 10,000) and isotropic thermal parameters Biso for Cu6Mo5O18

ORTEP illustration of the basic structural unit of Cu6Mo5O18 Each atom is represented by an oval, a two-dimensional projection of its ellipsoidal thermal motion The unique atoms have been labeled, and some of the symmetry-equivalent atoms have been added (as indicated by the small letters at the end of the label) to complete the coordination sphere around each atom Source: Ref 14

Copper tetrahedra and molybdenum octahedra as packed into the unit cell All the equivalent units are included Source: Ref 14

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Table 3 Positional and thermal parameters for Rb2 [Pt(CN)4](FHF)0.40

Perspective view of the unit cell of Rb2[Pt(CN)4](FHF)0.4 The small circles are the partially filled fluorine atom positions The platinum-platinum spacing is the shortest known for any −1-D metal complex The corresponding platinum-chain conductivity is the highest (~2000 Ω-1 cm-1 at 298 K) for any known complex of this type Source: Ref 16

Stacking of square-planar [Pt(CN)4]x- groups showing the overlapping of platinum d orbitals Source: Ref 16

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Richard L Harlow, E.I DuPont de Nemours

Richard L Harlow, E.I DuPont de Nemours

Brent L Adams, Department of Mechanical Engineering, Brigham Young University

Estimated Analysis Time

Brent L Adams, Department of Mechanical Engineering, Brigham Young University

Construction of the stereographic projection A point P on the surface of the reference sphere is projected to point P' on the projection plane

Crystal axes using the stereographic projection

Spherical polar angles defining directions in the RD-TD-ND coordinate system

Three consecutive Euler rotations defining an orientation

The complete set of angles for Roe's analysis of orientation The index i denotes different pole figures The angles and fix the diffracting plane normal, r i , to specimen axes x, y, and z The angles i and i fix

this direction to the crystal axes X, Y, and Z Also shown are the Euler angles , θ, and

Eulerian cradle mounted on the -axis of a diffractometer The unit vectors S0 and S depict the source and diffracted beams, respectively The angles χ and η correspond to those shown in Fig 2

Expected pole orientations of preferred orientations in Cu-3Zn (a) Expected positions of <111> poles for three specific variants of the preferred orientations (b) Expected <111> orientations when two mirror planes are introduced Figure 8 shows the measured <111> pole figure for the same alloy; note similarities between Fig 7(b) and 8

Measured (111) pole figure for Cu-3Zn Source: Ref 2

Euler space in Roe's notation Points in the cube represent discrete orientations For materials of cubic symmetry, regions I, II, and III represent equivalent orientations

Orientation distribution function for copper 10100 tubing using method of Euler plots and vary as shown in lower right-hand corner The value of for each slice is given in each rectangle

Brent L Adams, Department of Mechanical Engineering, Brigham Young University

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Brent L Adams, Department of Mechanical Engineering, Brigham Young University

(111) pole figure for copper 10100 tubing taken from the midwall

(111) pole figure for copper 10100 tubing taken from the inside wall

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- and β -fibers in rolled copper Courtesy of Jürgen Hirsch, Aachen

Orientation distribution function along fiber lines as a function of percent rolling reduction (a) -fiber (b) β-fiber (Courtesy of Jürgen Hirsch, Aachen)

Brent L Adams, Department of Mechanical Engineering, Brigham Young University

Brent L Adams, Department of Mechanical Engineering, Brigham Young University

Robert N Pangborn, Department of Engineering Science and Mechanics, The Pennsylvania State University

Arrangements for x-ray topography (a) Reflection topography (the Bragg case) (b) Transmission topography (the Laue case.) P, primary beam; R, diffracted beam; n, normal to diffraction planes; θB, Bragg angle

Two methods for obtaining reflection topographs (a) Polychromatic x-rays from a point source The misoriented crystal domains are numbered 1 to 3 and separated by tilt boundaries I and II (b) Top and side views of the line source of characteristic x-rays

Diffraction in a near-perfect crystal (a) Reflected intensity distribution (rocking curve) for a near-perfect absorptionless crystal rotated through its angle for Bragg reflection, θB (b) Attenuation of the incident beam by

simple (Rh) and multiple (R0) reflection R'0 is 180° out of phase with R0

The flow of x-ray energy in crystals of different thicknesses (a) Borrmann fan in a thin crystal (b) Fan with reduced effective width in a thick crystal P is the primary beam defined by slits S; 0 and h are the

outermost wave vectors; R0 and Rh, the transmitted and reflected directions (toward the reciprocal lattice origin

and the reciprocal lattice point n(hkl) Reduced effective absorption in (b) results in anomalous transmission

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Origin of direct (1), dynamical (2), and intermediate (3) image contrast for a dislocation Source: Ref 8

Origin of fringes caused by a fault plane between crystals I and II Source: Ref 9, 10

Robert N Pangborn, Department of Engineering Science and Mechanics, The Pennsylvania State University

Schulz x-ray topograph of a niobium single crystal revealing its intrinsic microstructure 8× Source: Ref

13

Camera for Berg-Barrett topography Sample is mounted on a tilting stage (right), and the film plate is held close to the sample surface by a supporting plate that also screens the film plate from scattered incident radiation Source: Ref 15

Berg-Barrett topographs of a Vickers hardness indentation on MgO cleavage surface (a) (022) reflection (b) (202) reflection Both 45× Source: Ref 17

Configurations for transmission topography (a) Using white radiation from a point source (b) Using characteristic radiation from a line source Source: Ref 18

Defect imaging with transmission topography (a) Lang arrangement (b) Borrmann arrangement

Topograph of a 1-mm (0.04-in.) thick dolomite plate with an inclined stacking fault near the exit surface Source: Ref 9

Lang topograph of a silicon crystal showing dislocations, including a Frank-Read source and thickness fringes Source: Ref 20

X-ray topographs of a wedge-shaped silicon crystal showing Pendellösung fringes (a) Section topograph of the undeformed crystal (b) Traverse (projection) topograph of the undeformed crystal (c) Topograph of the notched crystal bent at elevated temperature Source: Ref 21

Borrmann (anomalous transmission) topograph of a silicon crystal showing contrast caused by dislocations Source: Ref 22

Divergent beam anomalous transmission method of x-ray topography Source: Ref 24

X-ray interferometer Source: Ref 25

Double crystal diffractometer arrangements (a) (+, -) setting (b) (+, +) setting Source: Ref 27

Intensity profiles (rocking curves) (a) Bent crystal (b) Crystal composed of misaligned independently reflecting domains (c) Crystal containing a tilt boundary Source: Ref 28, 29

Double crystal diffractometer (a) and beam expansion by reflection from two asymmetrically cut crystals in succession (b) Source: Ref 24, 38

Rocking curve and topographs of a gold single crystal (a) Rocking curve with (311)<123> orientation strained 5% in tension (b) Topographs taken at angular positions 1 through 5

Double crystal diffractometer for polycrystalline samples Source: Ref 40, 41

Outward tracing of individual grain reflections from the surface to the diffraction pattern (a) At the sample surface (b) 2.5 mm (0.1 in.) from the surface (c) 27.5 mm (1.1 in.) from the surface

Rocking curves for individual grains of a polycrystalline sample Arrays of spots correspond to reflection

range of each grain and are obtained by multiple exposures after incremental sample rotations of 3 arc minutes each (a) Annealed and undeformed type 304 stainless steel (b) Same sample after subjection to stress-corrosion (c) Detail of rock curve of grain 3 in (a) (d) Detail of rocking curve in grain 3 in (b)

Basic principle of polycrystal scattering topography

Two arrangements for polycrystal scattering topography (a) Cross Soller slit method (b) Soller slit oscillating method Source: Ref 49, 50

Robert N Pangborn, Department of Engineering Science and Mechanics, The Pennsylvania State University

Illustration of rocking curve profiles for epitaxial films of different thicknesses (a) Relatively thin film (b) Relatively thick film Peak positions and breadths, peak separations, number and spacing of subsidiary peaks, and interpeak intensities yield information useful in characterizing the junction

Photographs from video monitor of Laue transmission patterns of aluminum (a) During recrystallization (b) During coarsening Enlargement of Laue spot in lower right hand corner of (b) shows structure of recrystallized grains Source: Ref 62

Topographs showing equi-inclination contours in a niobium crystal containing β-niobium hydride precipitates Plate 0 is a multiple exposure Plates 1 to 16 are single exposures taken 140 arc minutes of rotation about the [110] direction OM is an optical micrograph showing hydride locations Source: Ref 11

Fracture surface of a molybdenum crystal (a) Synchrotron topograph of the fracture [(001) cleavage] surface; ( 2) reflection Dark band at the top of the image shows the crack initiation site, gray band through the midsection of the crystal corresponds to the path of fast fracture, and dark banding at the bottom of the image is the location of twinning (b) Optical micrograph (c) Scanning electron micrograph of the cleavage surface

Traverse x-ray topographs of a silicon sample deformed in tension at 800 °C (1470 °F) showing distribution of microplastic zones; AgK 1, (200) reflection (a) Without surface removal (b) After removal of a 125- m surface layer by chemical polishing Source: Ref 66

Robert N Pangborn, Department of Engineering Science and Mechanics, The Pennsylvania State University

Paul S Prevey, Lambda Research, Inc

Paul S Prevey, Lambda Research, Inc

Principles of x-ray diffraction stress measurement (a) = 0 (b)ψ = ψ(sample rotated through some known angle ψ) D, x-ray detector; S, x-ray source; N, normal to the surface

Table 1 Recommended diffraction techniques, x-ray elastic constants, and bulk values for various ferrous and nonferrous alloys

hkl

Paul S Prevey, Lambda Research, Inc

Plane-stress elastic model

A d(311) versus sin2 ψ plot for a shot peened 5056-O aluminum alloy having a surface stress of -148 MPa (-21.5 ksi)

Basic geometry of the single-angle technique for x-ray diffraction residual stress measurement Np,

normal to the lattice planes; Ns, normal to the surface See text for a discussion of other symbols Source: Ref

2

ψ

Paul S Prevey, Lambda Research, Inc

Range of K doublet blending for a simulated steel (211) Cr K peak at 156.0° A, fully annealed; B and

C, intermediate hardness; D, fully hardened

Comparison of d (21.3) versus sin2 ψ data taken 0.176 mm (0.0069 in.) below the surface for a ground Ti-6Al-4V sample using two diffraction-peak location methods

Comparison of residual stress patterns derived using Cauchy and parabolic peak location for a ground 6Al-4V sample using a six-angle sin2 ψ technique Errors in stress measurement by two methods of diffraction-peak location are shown

Diffraction-peak breadth at half height for the (211) peak for M50 high-speed tool steel as a function of Rockwell hardness

Diffraction-peak breadth at half height for the (420) peak for René 95 as a function of cold-working percentage

Paul S Prevey, Lambda Research, Inc

X-ray elastic constant determination for Inconel 718, (220) planes Δψ= 45°, do = 1.1272 o

Paul S Prevey, Lambda Research, Inc

Effect of the stress gradient correction on the measurement of near-surface stresses for ground 4340

steel, 50 HRC

Longitudinal residual stress distribution with and without correction for removal of the carburized case from a 16-mm ( -in.) diam 1070 steel shaft

Paul S Prevey, Lambda Research, Inc

Longitudinal residual stress distribution in an induction-hardened 1070 carbon steel shaft

Hardness (Rockwell C scale) distribution in an induction-hardened 1070 carbon steel shaft

Longitudinal residual stress and percent cold work distributions in belt-polished Inconel 600 tubing

Longitudinal residual stress as a function of the quantity (1 + cos θ) for a 63-mm (2.5-in.) Inconel 600 U-bend

Variations in longitudinal surface residual stress produced by surface grinding 4340 alloy steel (50 HRC) samples

Subsurface residual stress profiles produced in burned and unburned regions of abusively ground 4340 alloy steel (50 HRC)

Longitudinal residual stress distribution across a flash butt welded induction-hardened railroad rail head

Minimum and maximum principal residual stress profiles and their orientation relative to the longitudinal direction in a turned Inconel 718 cylinder

Paul S Prevey, Lambda Research, Inc

J.H Konnert, J Karle, and P D'Antonio, Laboratory for the Structure of Matter, Naval Research Laboratory