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Plotting poles by the intersection of great circles

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We have already seen certain poles on the Wulff net, so these will be assumed.

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Suppose we wish to plot the poles of the form {101}. We need to find zones which contain these poles.

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011 is in the same zone as 010 and 001, and is also in the same zone as 111 and

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So, we can plot the zone containing 010 and 001 by joining the two along a great circle.

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So, we can plot the zone containing 010 and 001 by joining the two along a great circle.

We then join

11 and 111 along a great circle, and so plot the zone containing them.0

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We then join

11 and 111 along a great circle, and so plot the zone containing them.0

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The 011 pole is at the intersection of these two zones.

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This can be repeated for all the other relevant poles, with rotation of the Wulff net if necessary.

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We can plot more general poles by making use of the Weiss
zone law: (*hU* + *kV* + *lW* = 0).

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For example, for the pole *U*, *V* and *W*, which
produce a scalar product of 0 with the pole. Several possibilites come
to mind, but the simplest are [101] and [ 1].

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We therefore need to plot the great circles corresponding
to the zones of [101] and [*hkl*] will plot at the same position
on the stereogram as the *hkl* pole. Therefore, for cubic crystals
the required great circles also each represent the equivalent plane
*hkl* in real space perpendicular to the plane normal represented
by the pole *hkl*.

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We do this by measuring 90° from the pole along the Wulff net, and then look at the great circle we have reached, i.e. for [101].

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We then do the same for the [

1] zone, with rotation of the Wulff net first.0

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The point where the two great circles cross defines the pole

21.
21

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The point where the two great circles cross defines the pole

21.