Connection between Geometry

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Connection between Geometry Symmetry

• From reading some of the topics so far one might
  get an impression that theGeometry of the unit
  cell has no connection with the symmetry !!
• One may even be tempted to conclude (e.g.) that
  choice ofSquare Prism Unit Cell (Tetragonal
  UC) for the Tetragonal Crystal is purely
  coincidental
• Let us consider an example to clarify the matter

• The crux of the issue lies in the fact that many
  of the examples considered are ideal
  geometrical examples ? which have been used to
  illustrate basic concepts
• In real crystals with atomic entities ? nature
  decides the final outcome and we are left to
  analyze the outcome in the language of
  crystallography

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Let us consider a cubic unit cell decorated with
a two atom motif


UC of cubic lattice
This is an ideal geometrical example
If the entities are atomic a better picture would
be
We will use two views
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But then these atoms will not be hanging loosely
in space! ? The atoms would be touching each
other ? an even better picture would be
Side View
Front View
New Unit Cell

• As you can see this automatically leads to an
  unit cell in which a b ? ci.e. a Square Prism
  unit cell of Tetragonal crystal system
• Hence a lower symmetry motif can lead to an
  altered geometry of the unit cell (of lower
  symmetry)