Volume Texture of a Deformed Quartzite Observed With U-Stage
Microscopy and Neutron Diffractometry

The volume texture of a naturally deformed quartzite from the Kaoko belt, North-West Namibia, has been analysed by both universal stage microscopy and neutron diffraction. Universal stage microscopy is restricted to the determination of the base pinacoid preferred orientation in quartzite. For a more complete description of the texture, the orientations of additional crystal planes, such as first and second order prisms as well as positive and negative rhombs, must be known. Neutron methods allow the evaluation of pole figures of all Bragg reflecting planes, of which those of the first order prisms being considered to be the most active slip planes, are of particular interest. Drawbacks of neutron diffraction, i.e. the faking of an eventually absent inversion centre and lack of resolution, can be overcome by pole figure inversion and subsequent calculation of desired pole figures. Both, universal stage microscopy and neutron diffraction yield well comparable results, of course only with respect to the pole figure of the c-axis.

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Energy Dispersive Diffractometry for Quantitative Texture Studies

Textures and Microstructures ◽

10.1155/tsm.12.243 ◽

1990 ◽

Vol 12 (4) ◽

pp. 243-247 ◽

Cited By ~ 2

Author(s):

J. A. Szpunar

Keyword(s):

Distribution Function ◽

Neutron Diffraction ◽

Pole Figure ◽

Orientation Distribution ◽

Energy Dispersive ◽

Rolled Steel ◽

Pole Figures ◽

Cold Rolled ◽

Expansion Coefficients

Energy dispersive diffractometry is becoming a useful tool for texture measurements. In this work we demonstrated that the intensity measured at points in four inverse pole figures for cold-rolled steel can be used to calculate the orientation distribution function (ODF) with an accuracy sufficient for the determination of about 12 series expansion coefficients. A pole figure generated from such a selective experiment agrees with the pole figure measured by neutron diffraction.

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An Analytical Method for the Quantitative Determination of the Volume Fractions in Fiber Textures

Texture of Crystalline Solids ◽

10.1155/tsm.3.73 ◽

1979 ◽

Vol 3 (2) ◽

pp. 73-83 ◽

Cited By ~ 8

Author(s):

Ivan Tomov ◽

H. J. Bunge

Keyword(s):

Quantitative Determination ◽

Pole Figure ◽

Angular Range ◽

Asymmetric Unit ◽

Normalization Factor ◽

Measured Intensity ◽

Volume Fractions ◽

Pole Figures ◽

Axis Of Symmetry

In order to evaluate pole-figure measurements quantitatively, one needs the normalization factor which reduces measured intensity values to multiples of the random density. This factor may be determined experimentally by measuring the intensities of a random sample or it may be calculated by integrating over the whole pole-figure or its asymmetric unit. If pole-figure values are not available in the whole angular range 0≤φ≤90° (incomplete pole-figures), then the calculation is in general much more difficult and it usually presumes the knowledge of several pole-figures.In the case of fiber textures (axial symmetry), consisting of only a few strongly preferred orientations with the crystal directions 〈uvw〉i parallel to the axis of symmetry, the normalization factor and hence the volume fractions of the components i may be calculated in a rather simple way requiring only one, possibly incomplete, pole figure.

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A Method for Obtaining a Quantitative Pole Figure of Stretched Rubber

Advances in X-ray Analysis ◽

10.1154/s0376030800000124 ◽

1957 ◽

Vol 1 ◽

pp. 131-142

Author(s):

Otto Renius

Keyword(s):

Pole Figure ◽

Alpha Angle ◽

Geiger Counter ◽

Rubber Latex ◽

X Ray ◽

Outer Portion ◽

Transmission Technique ◽

Pole Figures ◽

Orientation Pattern

AbstractWork at the Detroit Arsenal has shown that techniques similar to those employed for the determination of pole figures of metals can be utilized for studying organic materials such a a stretched rubber latex. The rubber, when stretched, forms a preferred orientation pattern which is proportional in intensity to the degree of elongation, and which can be used to plot a pole figure.A Geiger-counter spectrometer was used to study samples of rubber stretched 600 to 1000 per cent. Using a transmission technique, the specimens were tilted to the impinging X-ray beam in five degree increments while rotating through 360 degrees to allow the measurement of the diffracted beam from the selected atomic planes at various angles within the specimen. The intensities of the diffracted beam at these angles were plotted on a stereographic net to form the pole figures of the (002) and (012) planes of the stretched rubber. The geometry of the sample arrangements permitted the outer portion of the pole figure to be plotted from alpha angle 0 degrees to alpha angle 45 degrees.

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Minimal Pole Figure Ranges for Quantitative Texture Analysis

Textures and Microstructures ◽

10.1155/tsm.19.45 ◽

1992 ◽

Vol 19 (1-2) ◽

pp. 45-54 ◽

Cited By ~ 8

Author(s):

K. Helming

Keyword(s):

Texture Analysis ◽

Pole Figure ◽

Practical Interest ◽

Texture Measurement ◽

Pole Figures

The use of only a small number of incomplete pole figures for texture determinations is of practical interest for reducing the effort of texture measurement. The determination of minimal pole figure ranges (MPR) is explained and the use of MPR is demonstrated on an example.

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The Determination of Crystallographic Textures From Selected Areas of a Specimen by Electron Diffraction

Textures and Microstructures ◽

10.1155/tsm.6.45 ◽

1983 ◽

Vol 6 (1) ◽

pp. 45-61 ◽

Cited By ~ 24

Author(s):

F. J. Humphreys

Keyword(s):

Electron Microscope ◽

Electron Diffraction ◽

Diffraction Pattern ◽

Pole Figure ◽

Single Phase ◽

Angular Resolution ◽

Thin Foil ◽

Two Phase ◽

Pole Figures

A technique for the determination of partial pole figures with an angular resolution of <3°, from selected areas of a thin foil, is described. A microcomputer, interfaced to an unmodified JEOL 100 CX TEMSCAN electron microscope is used to scan a diffraction pattern over a detector, tilt the specimen in steps of 1.5° over a range of ±50°, and plot the resulting data as a semiquantitative pole figure. The application of the technique to the study of materials which deform inhomogeneously is discussed, and examples are given of pole figures obtained from deformed single phase and two phase aluminium specimens.

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Determination of the Complete Orientation Distribution Function by the Zero-Range Method

Textures and Microstructures ◽

10.1155/tsm.6.289 ◽

1986 ◽

Vol 6 (4) ◽

pp. 289-313 ◽

Cited By ~ 1

Author(s):

H. P. Lee ◽

H. J. Bunge ◽

C. Esling

Keyword(s):

Distribution Function ◽

Pole Figure ◽

Orientation Distribution Function ◽

Statistical Error ◽

Orientation Distribution ◽

Positivity Condition ◽

Additional Information ◽

Pole Figures ◽

Zero Range

Because of the superposition of pole figures corresponding to symmetrically equivalent crystal directions, only the reduced orientation distribution function f∼(g) can be obtained directly by pole figure inversion. The additional information contained in the positivity condition of the ODF allows, however, the determination of an approximation to the “indeterminable” part and hence of the complete ODF f(g), if the texture has sufficiently large zero-ranges. The application of the method and the accuracy of the results was tested using two theoretical and one experimental textures. The accuracy of the complete ODF depends on the size of the zero-range, the errors in its determination, and on the errors, experimental and truncational, of the reduced ODF. The “physical zero” used in order to determine the zero-range is defined according to the statistical error of the pole figure measurement.

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The Determination of Complete Pole Figures Using the Reflection Method

Textures and Microstructures ◽

10.1155/tsm.6.125 ◽

1984 ◽

Vol 6 (2) ◽

pp. 125-135 ◽

Cited By ~ 2

Author(s):

Fan Xiong ◽

B. A. Parker

Keyword(s):

Pole Figure ◽

Outer Region ◽

Metal Sheet ◽

X Rays ◽

Reflection Method ◽

Background Ratio ◽

Pole Figures

A method is described which enables complete pole figures of metal sheet to be obtained using the reflection technique alone. A small known displacement of the sample from the centre of the texture goniometer is made and this significantly reduces absorption at high tilt angles (the outer region of the pole figure). The displacement introduced requires a wider receiving slit in order to collect an adequate fraction of the diffracted x-rays. The overall improvement in peak-to-background ratio is such that reproducible, complete pole figures can be produced. No loss in the detail contained in the pole figures has been observed due to the misalignment of the goniometer geometry.

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Neutron Texture Analysis of Melt-Textured YBCO Bulk Samples

Textures and Microstructures ◽

10.1155/tsm.33.75 ◽

1999 ◽

Vol 33 (1-4) ◽

pp. 75-92

Author(s):

Lothar Schmidt ◽

Martin Ullrich ◽

Werner F. Kuhs

Keyword(s):

Quantitative Analysis ◽

Texture Analysis ◽

Pole Figure ◽

Error Estimation ◽

Superconducting Phase ◽

Ybco Bulk ◽

Pole Figures ◽

Counting Statistics

Neutron texture measurements on YBCO bulk samples show a very sharp texture of the superconducting phase YBa2Cu3O7-x with half-widths of less than 5°. Even with a rather coarse measurement grid of only 722 points per complete pole figure, satisfactory results for the recalculated (002) pole figures could be obtained. However, for a reliable calculation of a complete ODF, finer grids will have to be used. Due to the importance of a good alignment of the c-axes in the material, a quantitative analysis of the (002) pole figures, including an error estimation due to measurement grid and counting statistics, was made. An outline for the determination of a reliable background estimate is given.

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A method to obtain orientation curves in Euler space for a seccond diffraction process in polycrystals

Revista Mexicana de Física ◽

10.31349/revmexfis.64.375 ◽

2018 ◽

Vol 64 (4) ◽

pp. 375

Author(s):

Jesús Palacios Gómez ◽

R.S. Salat Figols ◽

T. Kryshtab

Keyword(s):

Neutron Diffraction ◽

Pole Figure ◽

Incident Beam ◽

Mathematical Methods ◽

General Orientation ◽

Pole Figures ◽

Euler Space

A method is presented to obtain the orientation curve in the Eulerian space, of crystallites which diffract in one point of a Debye-Scherer ring in a second diffraction process. The incident beam is therefore the reflected beam of a previous diffraction process, and the sample has a general orientation for a pole figure measurement, given as usual by two angles, χ around the sample Y axis, and φ around the sample normal. Two solutions are found for all secondary reflections. The method proposed here was outlined somewhere else for the measurement of pole figures by neutron diffraction [1], and here important improvements are made, especially regarding the mathematical methods.

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