Materials Science and Metallurgy

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Part II Materials Science and Metallurgy Course
C6 Crystallography
Professor Harry Bhadeshia
Lecture 4 point groups
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Point Group Symmetry
Self-consistent set of symmetry elements relating
vectors from a single point.
Excludes translations
Describes macroscopic symmetry
e.g., shape of crystal or thermal expansivity
along different directions
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Symmetry elements of a point group pass through a
single point, hence a single pole on a stereogram
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• Possible symmetry elements
• rotation axes (1, 2, 3, 4, 6)
• mirror planes (m)
• centre of symmetry
• inversion axes (1, 2, 3, 4, 6)

_ _ _ _ _
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_
1 (centre of symmetry)
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2 (mirror plane)
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We now study the shapes of crystals, illustrating
all the faces of the same form hkl
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_
3
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_
4
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_
6
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mt
t
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32 point groups
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rotation or inversion axis perpendicular
diad perpendicular mirror parallel mirror
monoclinic
tetragonal
orthorhombic
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all cubic
four triads diads tetrads mirrors
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centres of symmetry?
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Nucleation of Pb embedded in Zn (Goswani et al.
(1992)
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truncated hexagonal bi-prism of lead inside zinc
point group symmetry 6/mmm same as zinc
Pb particle
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