Pole figures
A pole figure is simply a stereogram with its axes defined by an external frame of reference with particular hkl poles plotted onto it from all of the crystallites in the polycrystal. Typically, the external frame is defined by the normal direction, the rolling direction, and the transverse direction in a sheet (ND, RD and TD respectively. Occasionally, CD meaning cross direction is used instead of TD.)
The animation below shows the relationship between the orientation of the crystal and the stereographic projection obtained for the <100> poles. Up to five unit cells can be added to the projection. Try altering their orientations so that all five are similar and then different, and notice how the positions of the poles change.
Note: This animation requires Adobe Flash Player 8 and later, which can be downloaded here.
A pole figure for a polycrystalline aggregate, which shows completely random orientation, does not necessarily appear as might naively be expected. Angular distortions inherent in the stereographic projection result in the accumulation of points close to the centre of the pole figure as shown in the image below.
If the material shows a degree of texture, the resultant pole figure will show the accumulation of poles about specific directions.
A 100 pole figure showing “cube” texture – the {100} poles of the crystallites are oriented so that they are aligned with the axes defined by the rolling, transverse, and normal directions.
A single crystal can be plotted on the pole figure and there is no ambiguity regarding its orientation. However, as more crystallite poles are plotted onto the pole figure, the specific orientation of a particular crystallite can no longer be defined.
For a large number of grains in a polycrystal, poles may overlap on the pole figure, so that the true orientation density is not clearly represented. In this case, contours tend to be used instead. Regions of high pole density have a high number of contours, while regions with low pole density have a few, greatly spaced contours.
100 pole figure showing “cube” texture and pole density represented using contours rather than discrete points.
Inverse pole figures
Instead of plotting crystal orientations with respect to an external frame of reference, inverse pole figures can be produced which show the rolling, transverse, and normal directions (RD, TD and ND respectively) with respect to the crystallographic axes. Typically, these are plotted on a standard stereographic triangle as shown below
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