17plane groups

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17-plane groups

• When the three symmetry elements, mirrors,
  rotation axis and glide planes are shown on the
  five nets, 17-plane groups are derived.

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17-plane groups
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17-plane groups
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17-plane groups
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17-plane groups
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17-plane groups
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17-plane groups
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17-plane groups
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17-plane groups
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17-plane groups
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17-plane groups
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17-plane groups
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17-plane groups
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17-plane groups
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17-plane groups
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17-plane groups
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17-plane groups
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The 14 Bravavis Lattices.

• There are 14 ways to combine to stack the 5 nets
  in 3D to give us 14 unique ways to translate a
  point in 3 dimensions.

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The 14 Bravavis Lattices.

• Stacking of the five nets (plane lattices) in
  various ways leads to the 14-possible lattices.
  These 14 lattices types are known as 14-Bravais
  lattices.
• The orthogonallity gained by the use of these
  (14-Bravais lattices) is of considerable aid in
  visualizing and describing space lattices.
• Multiple cells have lattice points on their
  faces, interiors (body), and their corners
• Cells with interior points are calledBody
  centered lattice (I) or (R) space lattice
• Cells with Face centered lattice are called
  A-B-C-or F-centered space lattice.

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The 14 Bravais Lattices

• When we add a third translation t3 to the 17
  plane groups, we only get 14 space lattice that
  are know as 14 Bravais Lattices.

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The 14 Bravais Lattices

• Monoclinic and Triclinic

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The 14 Bravais Lattices

• Tetragonal

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The 14 Bravais Lattices

• Orthorhombic

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The 14 Bravais Lattices

• Cubic

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The 14 Bravais Lattices

• The 14 Bravais Lattices can also be grouped into
  6(7) groups that are known as Crystal systems.

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The 6 (7) Crystal Systems

• The seven crystal systems will be very important
  in our discussion of optical properties (and
  other physical properties) of crystals and in our
  discussion of phase transitions. You must know
  this table very well.

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Relation between, Crystal System, Space and Plane
Lattices.
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The Six Crystal Systems
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The Six Crystal Systems
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The 32 Crystallographic Point Groups

• There are 32 ways to combine the symmetry
  elements, 1, -1, m, 2, 3, 4, and 6 that are
  internally consistent. Each combination is
  called a point group.
• The 32 point groups fall into the seven different
  crystal systems. These you must know.

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Significance of the Unit Cell Point Groups

• The External symmetry of the crystal will have
  the same symmetry as the Unit Cell. (Note The
  form of shape of the crystal may be different
  from that of the unit cell, however).

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Summary

• The 14 Bravais Lattices
• The 6 (7) Crystal Systems
• The 32 Point Groups (Crystal Classes)

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Summary

• The 32 point groups are combinations of
  inversion, rotation and mirrors
• If in addition, we allow glide and screw we come
  up with 230 space groups and form the basis of
  mineralogical description.

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Summary

• Space Groups, therefore reflect the point group
  and lattice type. Space group notation includes
  reference to both.

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Summary

• P432 primitive, 4-fold, 3-fold, 2-fold, isometric
• In as much as X-ray work is needed to determine
  space groups we will not dwell on it here.

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Relation of the crystal lattice to the crystal

• A) The 32 crystal classes (point groups)
  correspond to 32 unique combinations of symmetry
  elements (n, m, i).
• B) From observations of natural crystals find
  that only 32 possible combinations of symmetry
  elements are needed to describe their morphology.
  (Calcite overhead)

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Relation of the crystal lattice to the crystal

• Infer
• A) That crystal morphology is an expression of
  the point group (crystal class).
• B) The plane surfaces that bound natural
  crystals develop parallel to certain sets of net
  planes in the crystal lattice of a specific
  mineral.

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Summary

• 1. morphology tells us of point group (crystal
  class).
• 2. crystal class tells us of crystal system (iso,
  ortho, mono, etc.)
• 3. Crystal system specifies certain possible
  lattices (P, I, F, R etc.)
• 4. X-rays needed to identify lattice type.

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Summary

• But even without x-rays we have learned a lot!
  We can break down miriads of crystals into 32
  crystal classes, and these into 6 (7) crystal
  systems.