scholarly journals The Determination of Complete Pole Figures Using the Reflection Method

1984 ◽  
Vol 6 (2) ◽  
pp. 125-135 ◽  
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.

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

1999 ◽  
Vol 31 (4) ◽  
pp. 239-248 ◽  
Author(s):  
H. Ghildiyal ◽  
E. Jansen ◽  
A. Kirfel
Keyword(s):  
Neutron Diffraction ◽  
Pole Figure ◽  
North West ◽  
Pole Figures ◽  
Slip Planes ◽  
Subsequent Calculation ◽  
Kaoko Belt ◽  
Universal Stage ◽  
Active Slip

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.

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

1979 ◽  
Vol 3 (2) ◽  
pp. 73-83 ◽  
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.

A Method for Obtaining a Quantitative Pole Figure of Stretched Rubber

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.

Helium Path Diffractometry and its Application to Determination of Retained Austenite and Macrostress in Steel

1962 ◽  
Vol 6 ◽  
pp. 85-90
Author(s):  
Robert A. McCune
Keyword(s):  
Retained Austenite ◽  
Intensity Increase ◽  
X Rays ◽  
X Ray ◽  
Long Wavelength ◽  
Gauge Block ◽  
Background Ratio ◽  
Ray Path

AbstractThe helium X-ray path has long been used, in spectrography to increase the intensity of the long-wavelength X-rays. The same principle has been applied to diflractometry. Up to threefold intensity increase is observed with chromium Ka radiation with very little increase In background. The peak to background ratio, therefore, is Improved by almost the same factor as the increase in intensity. Application of the technique is illustrated by analysis of gauge block steel for retained austcnite and macrostress.

scholarly journals Minimal Pole Figure Ranges for Quantitative Texture Analysis

1992 ◽  
Vol 19 (1-2) ◽  
pp. 45-54 ◽  
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.

scholarly journals The structure of the diamond

1913 ◽  
Vol 89 (610) ◽  
pp. 277-291 ◽  
Keyword(s):  
Wave Length ◽  
Main Beam ◽  
X Rays ◽  
Reflection Method ◽  
Glancing Angle ◽  
Whole Number ◽  
The Subject ◽  
Nickel Tungsten ◽  
Considerable Intensity

There are two distinct methods by which the X-rays may be made to help to a determination of crystal structure. The first is based on the Laue photograph and implies the reference of each spot on the photograph to its proper reflecting plane within the crystal. It then yields information as to the positions of these planes and the relative numbers of atoms which they contain. The X-rays used are the heterogeneous rays which issue from certain bulbs, for example, from the commonly used bulb which contains a platinum anticathode. The second method is based on the fact that homogeneous X-rays of wave-length λ are reflected from a set of parallel and similar crystal planes at an angle θ (and no other angle) when the relation n λ = 2 d sin θ is fulfilled. Here d is the distance between the successive planes, θ is the glancing angle which the incident and reflected rays make with the planes, and n is a whole number which in practice so far ranges from one to five. In this method the X-rays used are those homogeneous beams which issue in considerable intensity from some X-ray bulbs, and are characteristic radiations of the metal of the anticathode. Platinum, for example, emits several such beams in addition to the heterogeneous radiation already mentioned. A bulb having a rhodium anticathode, which was constructed in order to obtain a radiation having about half the wave-length of the platinum characteristic rays, has been found to give a very strong homogeneous radiation consisting of one main beam of wave-length 0.607 x 10 -8 cm.,*, and a much less intense beam of wave-length 0.533 x 10 -8 cm. It gives relatively little hetero­geneous radiation. Its spectrum, as given by the (100) planes of rock-salt, is shown in fig. 1. It is very convenient for the application of the second method. Bulbs having nickel, tungsten, or iridium anticathodes have not so far been found convenient; the former two because their homogeneous radiations are relatively weak, the last because it is of much the same wave-length as the heterogeneous rays which the bulb emits, while it is well to have the two sets of rays quite distinct. The platinum homogeneous rays are of lengths somewhat greater than the average wave-length of the general heterogeneous radiation; the series of homogeneous iridium rays are very like the series of platinum rays raised one octave higher. For convenience, the two methods may be called the method of the Laue photograph, or, briefly, the photographic method, and the reflection method. The former requires heterogeneous rays, the latter homogeneous. The two methods throw light upon the subject from very different points and are mutually helpful.

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

1983 ◽  
Vol 6 (1) ◽  
pp. 45-61 ◽  
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.

Simultaneous Spiral Recording of Pole Figures on Polaroid Film for Texture Goniometers

1971 ◽  
Vol 15 ◽  
pp. 499-503
Author(s):  
H. Ebel ◽  
M. F. Ebel
Keyword(s):  
Pole Figure ◽  
Photographic Film ◽  
List Type ◽  
Pole Density ◽  
Reflection Method ◽  
X Ray ◽  
Contour Lines ◽  
Pole Figures

The X-ray reflection method according to Schulz is used for investigations of textures in rolled materials. The pole figures are measured either along spirals or along circles. Points of equal intensity are transposed from the record of X-ray intensity to a spiral diagram. Finally contour lines are delineated, pointing out regions of equal pole density. Three ways are known for simplification of the evaluation. a)The results of the measurement are stored, evaluated by a computer and the pole figure is plotted. Points of equal pole density are represented by equal symbols (2 ,3 ).b)The pole figure is recorded synchronously with the X-ray measurement along circles or spirals. Ranges of different pole density are characterized by different colors (4 ,5 ).c)The pole figure is recorded on a photographic film along a spiral. The blackening depends on the measured countrate (6 ,7 ).An outline on different instruments using photographic registration is given.

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

1986 ◽  
Vol 6 (4) ◽  
pp. 289-313 ◽  
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.

Approximation of pole figures for the determination of crystal orientation in polymeric solids

1990 ◽  
Vol 23 (2) ◽  
pp. 88-93 ◽  
Author(s):  
P. Sajkiewicz ◽  
A. Wasiak
Keyword(s):  
Crystal Orientation ◽  
Linear Optimization ◽  
Orientation Distribution ◽  
Important Application ◽  
X Rays ◽  
Distribution Characteristics ◽  
Optimization Program ◽  
Pole Figures ◽  
Oriented Polycrystalline

The approximation of experimentally measured angular intensity distributions of X-rays diffracted by oriented polycrystalline specimens is suggested as a method for the determination of orientation distribution characteristics for uniaxially oriented polymeric fibres. A non-linear optimization program based on a Hook–Jeeves algorithm is elaborated and incorporated into the method. As an example, the interpretation of the data from polyethylene specimens having various degrees of orientation is given. An important application of the method is the analysis of distributions (pole figures) using a superposition of two identical or similar functions with different parameters.

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