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Lecture 9 (10/11/2006) Crystallography Part 2: Multiple Symmetry Operations Crystal Morphology

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Lecture 9 (10/11/2006)CrystallographyPart 2: Multiple Symmetry OperationsCrystal Morphology

- Axes at 90º (except 3-fold axes in cubic symmetry at 54º44’)
- Axes intersect at a point
- Possible symmetry combinations:
422, 622, 222, 32, 23, 432

(View 422 Symmetry.ai)

A#

m

- mirror plane
- perpendicular
- to rotational
- axis

Line traced by intersecting of X mirrors corresponds to X-fold rotation axis

Least

Symmetry

Greatest

Symmetry

- The angular relationships, size and shape of faces on a crystal
- Bravais Law – crystal faces will most commonly occur on lattice planes with the highest density of atoms

Planes AB and AC will be the most common crystal faces in this cubic lattice array

- Angles between adjacent crystal faces will be constant, regardless of crystal shape and size.

Lattice planes with the highest density are the most stable, but experience slow growth due to the abundance of atoms needed to construct them.

These stable faces will appear at the nucleation stages of growth (1), but then will diminish due to fast growth in these directions (2-4).

Crystal Symmetry (Continued)

- Crystallographic Axes
- Numerical Notation of Crystal Faces and Atomic Planes – Miller Indicies
Read: Chapter 5, p. 192-201