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

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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 notationfor Crystal Classes (Point Groups)


Relationship of mirrors and rotational axes

Relationship of Mirrors and Rotational Axes

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


32 point groups crystal classes

32 Point Groups (Crystal Classes)


32 crystal classes grouped by crystal system

32 Crystal Classes grouped by Crystal System

Least

Symmetry

Greatest

Symmetry


Graphical representation of point groups

Graphical Representation of Point Groups


Crystal morphology

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


Steno s law of interfacial angles

Steno’s Law of Interfacial Angles

  • 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

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

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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