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Lecture 8 (10/09/2006) Crystallography 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 geometrically-arranged smooth faces

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Lecture 8 (10/09/2006) Crystallography Part 1: Symmetry Operations

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  1. Lecture 8 (10/09/2006)CrystallographyPart 1: Symmetry Operations

  2. Crystallography The study of crystalline solids and the principles that govern their growth, external shape, and internal structure Crystal – a solid bounded by geometrically-arranged smooth faces Perfection of crystal face development: Euhedral – perfect crystal faces Subhedral – imperfectly developed crystal faces Anhedral – no crystal faces

  3. 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)

  4. External Symmetry ElementsCrystal Morphology Rotation Reflection Center of Symmetry Rotation with Inversion

  5. External Symmetry ElementsMotif Patterns Rotation Reflection Center of Symmetry Rotation with Inversion

  6. 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

  7. Rotation with Inversion (Rotoinversion)Equivalent to other symmetry operations Equivalent to Center of Symmetry

  8. 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)

  9. Combination of Symmetry Elements –Multiple Rotational Axes with 32 Symmetry • motif projections • do not require a • second set of 2-fold • axes

  10. Combination of Symmetry Elements – Multiple Rotational Axes in the Cubic System • 432 Point Group

  11. 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

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