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# Lecture 9 10 - PowerPoint PPT Presentation

Lecture 9 (10/11/2006) Crystallography Part 2: Multiple Symmetry Operations Crystal Morphology. Rotation with Inversion (Rotoinversion) Equivalency to other symmetry operations. Combination of Symmetry Elements – Multiple Rotational Axes.

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

Rotation with Inversion (Rotoinversion)Equivalency to other symmetry operations

• 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)

Combination of Symmetry Elements – Multiple Rotational Axes and Mirrors

A#

m

• mirror plane

• perpendicular

• to rotational

• axis

Hermann-Maugin notation Axes and Mirrorsfor Crystal Classes (Point Groups)

Relationship of Mirrors and Rotational Axes Axes and Mirrors

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

32 Crystal Classes grouped by Crystal System Axes and Mirrors

Least

Symmetry

Greatest

Symmetry

Crystal Morphology Axes and Mirrors

• 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

Steno’s Law of Interfacial Angles Axes and Mirrors

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

Paradox of the Growth of Crystal Faces Axes and Mirrors

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).

Next Lecture Axes and Mirrors

Crystal Symmetry (Continued)

• Crystallographic Axes

• Numerical Notation of Crystal Faces and Atomic Planes – Miller Indicies