A Computerized Technique of Plotting a Complete Pole Figure by an X-Ray Reflection Method

1971 ◽  
Vol 15 ◽  
pp. 365-372
Author(s):  
J. J. Klappholz ◽  
S. Waxman ◽  
C. Feng
Keyword(s):  
Computer Program ◽  
Pole Figure ◽  
Rate Of Change ◽  
Reflection Method ◽  
Time Rate ◽  
X Ray ◽  
Present Technique ◽  
Rectangular Coordinates ◽  
Data Points ◽  
Intensity Loss

The technique of plotting a complete pole figure composed of data points in both longitude and latitude from 0 to 180 degrees by a computer program is described. X-ray data were obtained by a reflection method from a specimen cut into three sections mutually perpendicular to one another. The computer program calculates each position in the pole figure based on the time rate of change of the tilt angle ϕ and the spin angle α which are transformed into rectangular coordinates.The advantage of the present technique is to minimize the x-ray intensity loss due to geometric defocusing, since each section of a given specimen is required to tilt not more than 55 degrees. Due to the fact that a complete pole figure is plotted, one is allowed to examine the symmetry or lack of symmetry in a given specimen with respect to a set of references axes.

Elaboration on the hexagonal grid and spiral trace schemes for pole figure data collection

2008 ◽  
Vol 23 (2) ◽  
pp. 87-91 ◽  
Author(s):  
Anthony C. Rizzie ◽  
Thomas R. Watkins ◽  
E. Andrew Payzant
Keyword(s):  
Data Collection ◽  
Pole Figure ◽  
Aluminum Foil ◽  
Hexagonal Grid ◽  
Equal Area ◽  
X Ray ◽  
Pole Figures ◽  
Area Sampling ◽  
Data Points ◽  
Pole Figure Data

A practical description of the mathematics required to implement the hexagonal grid and spiral trace pole figure data collection schemes is presented. Applying the concepts of stereographic and equal area projections with geometry, spreadsheets were created to calculate the angular settings of the goniometer. Using the generated settings, the hexagonal grid and spiral trace schemes were programmed into the existing X-ray software and employed to collect data for a sample of aluminum foil. The resulting (111) pole figures were similar to those collected with the conventional 5°χ×5°ϕ grid. The hexagonal grid has been shown by others to reduce the number of data points and time needed to complete a pole figure, while providing equal area sampling. Although not optimized, the spiral method was also investigated as another alternative to the 5°χ×5°ϕ grid.

Direct Printout X-Ray Pole Figures from Digital Computers

1968 ◽  
Vol 12 ◽  
pp. 391-403 ◽  
Author(s):  
Hung-Chi Chao
Keyword(s):  
Computer Program ◽  
Pole Figure ◽  
Sheet Metal ◽  
Digital Computer ◽  
Stereographic Projection ◽  
X Ray Diffraction ◽  
X Ray ◽  
Pole Figures ◽  
Time Required ◽  
Digital Computers

AbstractThe texture of sheet metal Is best described, by means of pole figures, which are very expensive and time-consuming to prepare. About 8 to 12 hours of effort by a specially trained, and. highly skilled technician are needed to prepare each pole figure. Accordingly, pole figures are not used as extensively in research studies as they would, be if they could be obtained more easily.A method has been developed for automatically producing pole figures by printing results directly from a digital computer. This method does not require the use of additional plotting attachments and, is therefore less expensive and time consuming than other methods. With this method, any laboratory with access to a digital computer can produce pole figures automatically.X-ray diffraction intensities are recorded on punched tape or on punched cards and are fed into the digital computer. A computer program corrects X-ray data obtained, by either transmission or reflection X-ray techniques, maps the stereographic projection, and prints pole figures directly. The time required, to prepare an accurate pole figure is reduced from 8 to 12 hours to 20 minutes or less depending on the type of digital computer used.

The Construction Of Quantitative Inverse Pole Figures Using the Available Odf Data

1993 ◽  
Vol 37 ◽  
pp. 465-471
Author(s):  
Charles Peng ◽  
Lu Ting
Keyword(s):  
Computer Program ◽  
Pole Figure ◽  
Plastic Flow ◽  
Flow Behavior ◽  
Inverse Pole Figure ◽  
Cold Forming ◽  
X Ray ◽  
Bcc Metals ◽  
Pole Figures ◽  
Polycrystalline Aggregates

AbstractThe ODF calculation is, to a large extent, responsible for the increased interest in texture analysis. Accurate pole figures and ODF plots can be routinely obtained in the laboratory from x-ray units equipped with precision controlling devices. For studies of the plastic flow behavior of polycrystalline aggregates, it is important to present the texture results in a manner readily usable for these analyses. For samples having a simple concentrated texture, the presentation of the data in terms of conventional pole figures and ODF plots is usually adequate. Additional work however is frequently needed when the analysis is involved with a more complex texture. A method is described for constructing the quantitative inverse pole figure using the available ODF data. Attention is focused on the construction of inverse pole figures for FCC and BCC metals. Examples are given of the plastic flow analyses for copper and tantalum which were produced by different cold-forming processes to yield a multitude of texture elements. The modification and rearrangement of the computer program necessary to accomplish this task will be discussed.

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.

THE GEOPHYSICIST AS A FORECASTER

Geophysics ◽  
1943 ◽  
Vol 8 (3) ◽  
pp. 273-289
Author(s):  
Paul Weaver
Keyword(s):  
Critical Point ◽  
Physical Property ◽  
Economic Importance ◽  
Rate Of Change ◽  
Time Rate ◽  
Great Economic Importance ◽  
Present Technique ◽  
Non Equilibrium

The commercial geophysicist has hitherto been little concerned with a realm of geophysics which deals with the detection of non‐equilibrium by measuring the time‐rate of change of a physical property in a localized area, in order to forecast when a critical point will appear in the system, and what magnitude of transition is probable. The author has selected some examples of such geophysical problems, which he considers of great economic importance, and which would appear amenable to our present technique or to some modification thereof.

point-Analysis Using the Extrapolation Method in the Analytical Electron microscope

1990 ◽  
Vol 48 (2) ◽  
pp. 430-431
Author(s):  
Zenji Horita ◽  
Ryuzo Nishimachi ◽  
Takeshi Sano ◽  
Minoru Nemoto
Keyword(s):  
Electron Microscope ◽  
Extrapolation Method ◽  
X Ray ◽  
Absorption Correction ◽  
Point Analysis ◽  
Analytical Electron ◽  
Analytical Electron Microscope ◽  
Data Points ◽  
Identical Composition ◽  
X Ray Absorption

Absorption correction is often required in quantitative x-ray microanalysis of thin specimens using the analytical electron microscope. For such correction, it is convenient to use the extrapolation method[l] because the thickness, density and mass absorption coefficient are not necessary in the method. The characteristic x-ray intensities measured for the analysis are only requirement for the absorption correction. However, to achieve extrapolation, it is imperative to obtain data points more than two at different thicknesses in the identical composition. Thus, the method encounters difficulty in analyzing a region equivalent to beam size or the specimen with uniform thickness. The purpose of this study is to modify the method so that extrapolation becomes feasible in such limited conditions. Applicability of the new form is examined by using a standard sample and then it is applied to quantification of phases in a Ni-Al-W ternary alloy.The earlier equation for the extrapolation method was formulated based on the facts that the magnitude of x-ray absorption increases with increasing thickness and that the intensity of a characteristic x-ray exhibiting negligible absorption in the specimen is used as a measure of thickness.

STUDY OF PHASE PROPAGATION IN SUPERCONDUCTING ALUMINUM BY ULTRASONIC ATTENUATION MEASUREMENTS

1959 ◽  
Vol 37 (5) ◽  
pp. 614-618 ◽  
Author(s):  
K. L. Chopra ◽  
T. S. Hutchison
Keyword(s):  
Magnetic Field ◽  
Eddy Current ◽  
Ultrasonic Attenuation ◽  
Cylindrical Specimen ◽  
Current Theory ◽  
Superconducting Phase ◽  
Rate Of Change ◽  
Time Rate ◽  
Phase Propagation ◽  
The Magnetic Field

The phase propagation in superconducting aluminum has been studied by measuring the time rate of change of ultrasonic attenuation. The time taken for the destruction of the superconducting phase in a cylindrical specimen, by means of a magnetic field, H, greater than the critical field, Hc, is approximately proportional to{H/(H–Hc)} in agreement with eddy-current theory. In the converse case, where the superconducting phase is restored by switching off the magnetic field H (>Hc), the total time taken is nearly independent of the temperature (or Hc) as well as H. The superconducting phase grows at a non-uniform volume rate which is considerably less than the uniform rate of collapse.

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