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

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) Crystallography Part 2: Multiple Symmetry Operations Crystal Morphology

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

  2. Rotation with Inversion (Rotoinversion)Equivalency to other symmetry operations

  3. Combination of Symmetry Elements – Multiple Rotational Axes • 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)

  4. Combination of Symmetry Elements – Multiple Rotational Axes and Mirrors A# m • mirror plane • perpendicular • to rotational • axis

  5. Hermann-Maugin notationfor Crystal Classes (Point Groups)

  6. Relationship of Mirrors and Rotational Axes Line traced by intersecting of X mirrors corresponds to X-fold rotation axis

  7. 32 Point Groups (Crystal Classes)

  8. 32 Crystal Classes grouped by Crystal System Least Symmetry Greatest Symmetry

  9. Graphical Representation of Point Groups

  10. Crystal Morphology • 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

  11. Steno’s Law of Interfacial Angles • Angles between adjacent crystal faces will be constant, regardless of crystal shape and size.

  12. Paradox of the Growth of Crystal Faces 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).

  13. Next Lecture Crystal Symmetry (Continued) • Crystallographic Axes • Numerical Notation of Crystal Faces and Atomic Planes – Miller Indicies Read: Chapter 5, p. 192-201

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