Dissemination of IT for the Promotion of Materials Science (DoITPoMS)

DoITPoMS Teaching & Learning Packages The Stereographic Projection Identifying poles on a stereogram through use of the Wulff net
The Stereographic Projection AimsBefore you startIntroductionBasic conceptDemonstration of projectionImportant properties of the stereographic projectionThe Wulff netUse of the Wulff net in constructing a stereogramPlotting poles on the stereogram through use of the Wulff netIdentifying poles on a stereogram through use of the Wulff netApplications of the Stereographic Projection - SlipInteractive Wulff netSummaryQuestionsGoing further
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Identifying poles on a stereogram through use of the Wulff net

To identify poles, find two great circles that intersect at the desired pole hkl. Find the two zone directions [u1v1w1] and [u2v2w2] of these two great circles by, in each case, identifying two poles lying in these zone directions, and then using the Weiss zone law condition to determine the two zone directions. The desired pole hkl is then the normal to the plane hkl which contains the directions [u1v1w1] and [u2v2w2]; this can also be determined from the Weiss zone law condition.

In general, directions such as [u1v1w1] and [u2v2w2] are referred to the real space lattice, while normals to planes (hkl) are referred to the reciprocal lattice.

However, since for cubic crystals, the normal to the plane hkl is parallel to the vector [hkl], the algebra required is equivalent to taking cross products to determine the zone directions [u1v1w1] and [u2v2w2], and then taking a cross product again to determine the desired pole hkl.

So, for cubic crystals and stereograms of cubic crystals, we can drop the distinction between the real lattice and the reciprocal lattice. Therefore, for example, we can identify poles on stereograms of cubic crystals using vector addition, e.g.:

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