Lecture 9 10 11 2006 crystallography part 2 multiple symmetry operations crystal morphology
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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

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


Rotation with inversion rotoinversion equivalency to other symmetry operations
Rotation with Inversion (Rotoinversion)Equivalency to other symmetry operations


Combination of symmetry elements multiple rotational axes
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)


Combination of symmetry elements multiple rotational axes and mirrors
Combination of Symmetry Elements – Multiple Rotational Axes and Mirrors

A#

m

  • mirror plane

  • perpendicular

  • to rotational

  • axis


Hermann maugin notation for crystal classes point groups
Hermann-Maugin notation Axes and Mirrorsfor Crystal Classes (Point Groups)


Relationship of mirrors and rotational axes
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
32 Crystal Classes grouped by Crystal System Axes and Mirrors

Least

Symmetry

Greatest

Symmetry



Crystal morphology
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
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
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
Next Lecture Axes and Mirrors

Crystal Symmetry (Continued)

  • Crystallographic Axes

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

    Read: Chapter 5, p. 192-201