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