Pole figures

Texture Analysis with GADDS. With a conventional detector, a data collection for a pole figure analysis with a powder diffractometer with a texture attachment could take 12 h or more. With an area detector, it is possible to collect enough data for several pole figures (required for an ODF analysis) ia a few minutes. 

Figure 7. 5. Time evolution of crystallographic texture [(0002) pole figures] along the axis of an explosively driven, hemispherical, titanium liner [66]. A high density of contours near the center of the circle indicate the c-axes of individual crystals are all normal to liner surface.

The discovery of ozone holes over Antarctica in the mid-1980s was strong observational evidence to support the Rowland and Molina hypothesis. The atmosphere over the south pole is complex because of the long periods of total darkness and sunlight and the presence of a polar vortex and polar stratospheric clouds. However, researchers have found evidence to support the role of CIO in the rapid depletion of stratospheric ozone over the south pole. Figure 11-3 shows the profile of ozone and CIO measured at an altitude of 18 km on an aircraft flight from southern Chile toward the south pole on September 21, 1987. One month earlier the ozone levels were fairly uniform around 2 ppm (vol). 

Simple eombinations of eomponents produee responses whieh are ealledpoles and zeros. A single pole (Figure B-1) produees a flat gain response from de to... 

K.Pawlik, J. Pospiech and K. Liicke, "The ODF approximation from pole figures with the aid of the ADC method" Textures and Microstructures 14-18, 66,1991,... 

An Automated Apparatus for X-ray Pole Figure Studies of Polymers... 

We have adapted a commercially available x-ray diffractometer normally used for structure determinations on single crystals to operate as a very flexible device for performing x-ray pole figure determinations and related studies on polymeric materials. Descriptions of crystallite orientations, as provided by pole figures, are useful in studying many aspects of the behavior of products made from semicrystalline polymers. This paper describes the software that we have written for our pole figure facility. Except for some vendor-provided routines to drive the hardware Interface all of our software is written in FORTRAN. Menu driven operation is provided to maximize user convenience. 

Figure 1. Hardware block diagram for NBS Polymer Pole Figure Facility.

Figure 2. Software modules for Pole Figure Facility.

The user has no control over the size of the x grid that is sampled in the Standard Pole Figure data collection task. The default angular ranges and step sizes have been found to be convenient for many applications. The data in Figure 4 were obtained using the Standard Pole Figure data collection function. 

Figure 4. A set of pole figures for three reflections of a highly oriented linear polyethylene specimen. The concentric circles are parallels of latitude, which represent constant values of x from 0 deg (outermost circle) to 90 deg (north pole) in 15 deg steps. The straight lines are meridians of longitude, which represent constant values of < > from 180 degrees to +180 degrees.

There are three subroutines for making contour plots using various map projections and a subroutine for making x-y plots. The contour plotting routines are used with the Standard Pole Figure and Area Scan diffraction data files, while the x-y plot is used for data from x scans, scans, 28 scans, and layer line plots. 

Figure 4 is a set of contour plots of data derived from three Standard Pole Figure scans on a highly oriented specimen of linear polyethylene. The contour plotting software establishes a set of intensity levels that span the data in the diffraction data file. 

Whenever we are considering orientation, we are dealing with anisotropic scattering data. Orientation is most frequently analyzed in 2D scattering data with fiber symmetry or in pole-figure data recorded by means of a texture goniometer. 

Definition Pole Figure. A pole figure, ghki(scattering intensity of the reflection... 

Figure 9.2. Reflection 4m (s) smeared by misorientation of the ensemble of crystallites (structural entities). The center of gravity is found at s/jd- Definitions of polar coordinates Dashed lines indicate the radial direction of the integration that leads to a projection onto the orientation sphere resulting in the pole figure g kl ([Pg.208]

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