How Many Bravais Lattices Exist?

  • Thread starter MagnusBL
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In summary, The conversation discusses the topic of the number of Bravais lattices, specifically whether there are exactly 14 or 15. One person asks for a proof or reference to support the claim that there are 14, to which another person responds with a suggested reading and a rebuttal to the idea of 15 lattices. Another person suggests looking in solid state textbooks or seeking input from mathematicians, as crystallography has roots in pure mathematics.
  • #1
MagnusBL
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Hi

Anyone who can tell me how to proove that there consists exactly 14 Bravais lattices or can point me to a reference where this is prooven?



Magnus
 
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  • #2
Not a proof, but you may enjoy Nussbaum's "The mystery of the fifteenth Bravais lattice," Am J Phys 68(10) (2000) and Azaroff's rebuttal "No! to a fifteenth Bravais lattice," Am J Phys 70(2) (2002).
 
  • #3
Any solid state textbook, Tinkham comes to mind as well as Kittel.
 
  • #4
I haven't seen this proof in any solid state text, including Kittel (unless you mean his more advanced 'Quantum Theory of Solids' - haven't had to pleasure to read this yet). I would think this question is better suited for the mathematicians. Crystallography, although definitely an applied subject today, began as a pure mathematical subject.
 

1. What is Bravais' 14 lattices?

Bravais' 14 lattices are a set of 14 unique three-dimensional lattice structures that describe the possible arrangements of points in a crystal. These lattices are named after Auguste Bravais, a French mathematician who first described them in 1848.

2. Why is it important to prove Bravais' 14 lattices?

Proving Bravais' 14 lattices is important because it provides a comprehensive understanding of the possible arrangements of atoms in a crystal. This knowledge is crucial in fields such as materials science, solid state physics, and crystallography.

3. How are Bravais' 14 lattices classified?

Bravais' 14 lattices are classified based on the symmetry of the lattice structure. They are divided into seven crystal systems (cubic, tetragonal, orthorhombic, monoclinic, triclinic, hexagonal, and trigonal) and further grouped into primitive and non-primitive lattices.

4. What are the methods used to prove Bravais' 14 lattices?

There are two main methods used to prove Bravais' 14 lattices: geometric and group theoretical approaches. The geometric approach involves analyzing the crystal structure's symmetry elements and constraints. The group theoretical approach uses mathematical groups to describe the symmetry of the lattice structure.

5. Are there any exceptions to Bravais' 14 lattices?

Yes, there are exceptions to Bravais' 14 lattices. These exceptions occur when a crystal structure has additional symmetry elements, which result in a lattice that is not one of the 14 described by Bravais. These exceptions are known as non-Bravais lattices.

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