Materials Science and Metallurgy

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Part II Materials Science and Metallurgy Course
C6 Crystallography
Professor Harry Bhadeshia
Lecture 2 Stereograms
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Understand the content DURING lectures Interact
during lectures Take notes Books Question
sheets Example Classes Supervisions
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great circles diameter equal to that of sphere
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great circles diameter less than that of sphere
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• To represent angles and planes

001
010
100
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(north)
001
010
100

• Representing a plane normal

(south)
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(north)
001
010
100

• Representing a plane normal

(south)
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(north)
001
010
100

• Representing a plane normal

(south)
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• Great circles project as the arcs of circles
• Vertical great circles project as straight lines

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p at 90 to a, b, C
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Small circles project as circles but geometric
centre of the projected circle does not coincide
with the projected centre P.
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Using small circles

• To locate a pole at angles ?1 from p1 and ?2 from
  p2 draw the two small circles with angular
  centres on the two poles.
• Solutions at intersections.

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Wulff net
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Measuring from the centre

• Similarly measure the angular distance from the
  centre along either of the diagonal scales -
  these are equivalent but you will need to rotate
  the net so one passes through the pole of interest

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• To measure the angle between two poles rotate the
  Wulff net until both lie on a common great
  circle. The angle required is measured along the
  great circle using the scale on the net.

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Small circles

• To plot a small circle position the angular
  centre on the diagonal, mark the two extremes of
  the small circle at equal angles from the centre,
  locate the geometrical centre at half the linear
  distance between the two and draw the circle with
  compasses

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Locating plane normals
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Angle between two planes
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Cubic symmetry
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Full cubic stereogram

• Weiss zone law
• Locating zones
• Calculating angles