Bravais latices and crystalographic group

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In summary, there are only 14 types of Bravais lattices because they describe the different symmetries of a set of points generated by three discrete translations. However, if we consider the internal structure of these points and the possibility of a base with more than one atom at each point, the extended lattice could have up to 230 different symmetry groups.
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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.
 

FAQ: Bravais latices and crystalographic group

1. What are Bravais lattices?

Bravais lattices are a set of 14 possible three-dimensional lattices that describe the geometric arrangement of atoms or molecules in a crystal. They are named after the French mathematician Auguste Bravais, who first described them in the 19th century.

2. How are Bravais lattices classified?

Bravais lattices are classified based on the shape and symmetry of their unit cell, which is the smallest repeating unit of the lattice. They are divided into 7 crystal systems (cubic, tetragonal, orthorhombic, hexagonal, rhombohedral, monoclinic, and triclinic) and further categorized into primitive and centered lattices.

3. What is a crystallographic group?

A crystallographic group is a mathematical concept used to describe the symmetry of a crystal lattice. It is a set of symmetry operations (such as rotations, reflections, and translations) that can be applied to a crystal lattice to generate an identical pattern. There are 230 possible crystallographic groups that can describe the symmetry of a crystal lattice.

4. How are Bravais lattices and crystallographic groups related?

Each Bravais lattice corresponds to a specific crystallographic group, which describes the symmetry of that lattice. This means that for each of the 14 Bravais lattices, there is a corresponding crystallographic group that contains all of the possible symmetry operations that can be applied to that lattice.

5. What is the importance of understanding Bravais lattices and crystallographic groups?

Understanding Bravais lattices and crystallographic groups is important in the study of crystallography, which is the science of determining the atomic and molecular structure of crystals. These concepts provide a framework for describing and understanding the symmetry and arrangement of atoms in a crystal, which is crucial in many industrial and scientific applications such as materials science, mineralogy, and crystal engineering.

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