Crystallography Lecture 8 (10/09/2006) Part 1: Symmetry Operations
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Transcript Crystallography Lecture 8 (10/09/2006) Part 1: Symmetry Operations
Lecture 8 (10/09/2006)
Crystallography
Part 1: Symmetry
Operations
Crystallography
The study of crystalline solids and the
principles that govern their growth,
external shape, and internal structure
Crystal – a solid bounded by geometricallyarranged smooth faces
Perfection of crystal face development:
Euhedral – perfect crystal faces
Subhedral – imperfectly developed crystal faces
Anhedral – no crystal faces
Recognition of Mineral Symmetry
External Crystal Form (Morphology)
- macroscopic observations/measurements of
crystal faces
- 32 crystal classes (point groups) possible symmetry
elements or combinations of elements
- 1st Half of Chapter 5 (p. 170-213)
Internal Atomic Arrangement
-
determined from X-ray diffraction
takes into account 3D translation
14 lattice types (Bravais lattices)
Combination of 32 point groups and 14 lattice
types yields 230 space groups
- 2nd Half of Chapter 5 (p. 213-239)
External Symmetry Elements
Crystal Morphology
Rotation
Reflection
Center of Symmetry Rotation with
Inversion
External Symmetry Elements
Motif Patterns
Rotation
Center of
Symmetry
Reflection
Rotation with
Inversion
Rotational Axes
As an external symmetry element,
rotation increments (n) range from 1 to ∞
When considering the
limits of translation,
rotation increments are
limited to 1, 2, 3, 4,
and 6-fold
Rotation with Inversion
(Rotoinversion)
Equivalent to other symmetry
operations
Equivalent to Center
of Symmetry
Combination of Symmetry Elements –
Multiple Rotational Axes
Axes at 90º (except
3-fold axes in cubic
symmetry at 54º44’)
Axes intersect at
point
Possible symmetry
combinations:
422, 622, 222, 32,
23, 432
(View 422 Symmetry.ai)
Combination of Symmetry Elements –
Multiple Rotational Axes with 32 Symmetry
- motif projections
do not require a
second set of 2-fold
axes
Combination of Symmetry Elements –
Multiple Rotational Axes in the Cubic System
432 Point Group
Next Lecture
External Symmetry (Continued)
Combination of Rotation Axes and
Mirror Planes
32 Crystal Classes/Point Groups
6 Crystal Systems
Crystal Morphology
Read: Chapter 5, p. 181-192