Bravais latices and crystalographic group

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SUMMARY

The discussion clarifies that there are 14 types of Bravais lattices, which represent distinct symmetries generated by three discrete translations in three-dimensional space. In contrast, there are 230 different crystallographic groups due to the potential internal structure of points within the Bravais lattices. Each point in a Bravais lattice can have a base consisting of multiple atoms, leading to a variety of symmetry groups. This relationship between Bravais lattices and crystallographic groups is well-established and accurately described in the discussion.

PREREQUISITES
  • Understanding of Bravais lattices
  • Knowledge of crystallographic groups
  • Familiarity with symmetry operations in three dimensions
  • Basic concepts of atomic structure in crystallography
NEXT STEPS
  • Study the 14 types of Bravais lattices in detail
  • Explore the 230 crystallographic groups and their classifications
  • Learn about symmetry operations in three-dimensional space
  • Investigate the role of atomic bases in crystal structures
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Students and professionals in materials science, crystallography, and solid-state physics who seek to deepen their understanding of lattice structures and symmetry in crystals.

paweld
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I'm not sure why there are only 14 types of Bravais latices whereas there are
as many as 230 different crystalographic groups (in 3 dimensions).
I think that it maybe related to the fact that Bravais latices describe
different symetries of the set of points generated by a set of three discrete translations.
In general these point might have some internal structure which changes the symmetry group.
If we took into account the fact that at each point of Bravais lattice we can have a so
called base consisting of more then one atom, then this extended latice might have as many
as 230 different symmetry groups. Is this explanation resonable?
 
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Yes, that's correct.
 

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