Institute of Metals Division - A Reflection Method for Pole-Figure Determination (TN)

SEVERAL methods are available for determining pole figures by X-ray means.' The earlier film methods have been replaced by techniques in which the intensities are measured by Geiger counters on an X-ray diffractometerZm7. These methods utilize either flat transmission or reflection samples,214°8 cylindrical specimens,3 or spherical specimens.7 A single transmission or reflection sample will not yield information over the complete pole figure. The cylindrical specimens suggested by Nortod and the spherical specimen of Jetter and Borie7 have the advantage of allowing the whole pole figure to be obtained without any corrections to the intensity for absorption, There is a lower limit to the size of sheet which can be conveniently studied, however, and sample preparation can be rather tedious. Probably the most common method today for determining the complete pole figure is that developed by Schulz. A flat reflection sample is used for determining the pole figure from the center out to about 70". Because of the geometry of the system used, little or no correction for absorption or irradiated volume is necessary.4'6 A separate transmission sample is used for the region near the edge of the pole figure. This procedure requires two separate samples, one of which must be a thin carefully-prepared transmission sample. Furthermore, since the reflection and transmission data are in different arbitrary intensity units, a region of overlap must be obtained, and the intensity data from one set of measurements converted to units of the other. These are serious disadvantages of this method, and they point out the need for a simplified procedure. Since the reflection technique can be used for planes whose normals lie up to about 70° from the sample surface normal, it is apparent that a complete pole figure can be obtained by reflection alone if sample surfaces are cut at oblique angles to the rolling plane Specifically, if a rolled sample is cut so that the normal to the surface formed lies equidistant (54" 44') from the rolling plane normal, rolling direction, and transverse direction, then complete information for one quadrant of the pole figure can be obtained by reflection from the surface. Fig. 1 shows this oblique surface, as well as the position of the pole of this surface in the pole figure. When a surface has been cut oblique to the rolling plane, the standard polar stereographic net is inconvenient to use, and it would be more desirable to have the center of the net coincide with the pole of the oblique plane. Fig. 2 shows such a net, where the center has been offset 54' 44' to correspond to a specimen cut as in Fig. 1. This net was in effect obtained by rotating a standard polar stereographic net 54" 44' with the help of a Wulff net. With the experimental setup used. a sample can be cut from plate of 1/2-in. thickness or br Gen- erally thinner sheet is under investigation, and a composite specimen must be used. A convenient procedure has been to bond together, using epoxy resin, sufficient sheets to form a cube. These are clamped in a vise, and when dry, the whole vise is rotated and a flat surface ground at the required angle. The sample is then mounted inside a larger steel ring using Koldmount, the backside ground flat and parallel to the approximate desired thickness. The sample is then polished and etched to remove any effects of cold working during grinding. With this method only one quadrant of the pole figure is obtained. Often pole figures show symmetry around the rolling and transverse directions, and any slight asymmetry is due to scatter. Should the pole figure not be symmetrical, four oblique surfaces, corresponding to the four quadrants of the pole figure, would have to be examined. In most cases there is symmetry at least around the rolling direction, which reduces to two the number of quadrants to be investigated. For many purposes all that is required is an average polefigure for the four quadrants. This canreadilybe obtained with composite specimens of sheet material, where sheets Corresponding to each of the four quadrants can be intermixed. The four quadrants can be obtained by considering sheet in the normal position, and by rotatiolls of 180" around the sheet normal, the rolling direction, and the transverse direction. If desired, the whole thickness of the sheet can be used, yielding an average of the surface and interior textures; or the surface material can be removed from each sheet, resulting in a pole figure for the center alone. Eugene S. Meieran of the Massachusetts Institute of Technology has independently developed the same method. His results, adapted to a pole figure goniometer with a specimen spiraler, will be described in another publication.