Are All Periodic Lattice Arrangements Bravais Lattices?

In summary: Essentially, it refers to the regular, repeating pattern of lattice points in a crystal structure. This is important because it helps us understand the symmetry and properties of crystals. There are only 5 Bravais lattices in 2D and 14 in 3D because these are the only unique and distinct ways in which lattice points can be arranged in a periodic manner. It may seem complicated, but understanding Bravais lattices is crucial in understanding the structure of crystals.
  • #1
Slimy0233
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or Are all naturally occurring crystals with periodic arrangement of lattices Bravais lattices?

From two days, I have been trying to understand Bravais lattices and what it's importance is and after a lot of research, I came to know that they are a periodic arrangement of lattice points with translational symmetry. Now, I want to write notes and I don't know why there are only 5 Bravais lattices in 2d and 14 in 3d (like WHY?) and I am of the believe that the actual derivation is pretty hard and unnecessary. Now, I have one doubt, Can all possible periodic arrangements of lattices be arranged as a Bravais lattice?

Because if they are, I can finally stop looking for answer and write, it has been observed that all possible periodic lattice arrangements can be expressed as Bravais lattices and close the chapter on this on and move on to the next topic.

Also, I believe this 10 year answer is right, but I just wanted to ask you all with the context I am in.
 
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  • #2
What the heck is a periodic arrangement of lattices?
Crystals are a periodic repetition of some motiv. Due to periodicity, there is some flexibility in defining where one motiv ends and the next one begins, hence the different types of elementary cells. However, if you chose one point of the motiv and take all vectors to the translationally equivalent points in other motivs, these vectors define the lattice (uniquely). There is only one lattice for a crystal and this lattice will belong to 1 of the 14 Bravais types.
 
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  • #3
DrDu said:
What the heck is a periodic arrangement of lattices?
Crystals are a periodic repetition of some motiv. Due to periodicity, there is some flexibility in defining where one motiv ends and the next one begins, hence the different types of elementary cells. However, if you chose one point of the motiv and take all vectors to the translationally equivalent points in other motivs, these vectors define the lattice (uniquely). There is only one lattice for a crystal and this lattice will belong to 1 of the 14 Bravais types.
> What the heck is a periodic arrangement of lattices?

I am sorry, I meant, periodic arrangement of lattice points.
 

FAQ: Are All Periodic Lattice Arrangements Bravais Lattices?

1. What is a Bravais lattice?

A Bravais lattice is a set of points in space that are arranged in a periodic manner, where each point has an identical environment. In three-dimensional space, there are 14 distinct types of Bravais lattices, which can be categorized based on their symmetry and dimensions. These lattices serve as the foundational building blocks for crystal structures in solid-state physics and materials science.

2. Are all periodic lattice arrangements considered Bravais lattices?

No, not all periodic lattice arrangements are considered Bravais lattices. A Bravais lattice must have translational symmetry such that each point in the lattice can be translated to any other point by a combination of lattice vectors. Some periodic arrangements, like those with additional internal structures or varying environments, do not meet the criteria to be classified as Bravais lattices.

3. How many types of Bravais lattices are there?

There are 14 distinct types of Bravais lattices in three-dimensional space. These include cubic, tetragonal, orthorhombic, hexagonal, rhombohedral, and monoclinic lattices, each characterized by unique arrangements of points and symmetry properties. Each type can further be classified into primitive and non-primitive lattices based on their unit cell structure.

4. What is the significance of Bravais lattices in crystallography?

Bravais lattices are significant in crystallography because they provide a framework for understanding the arrangement of atoms in crystalline solids. They help in classifying crystal structures and predicting their physical properties, such as symmetry, density, and electronic behavior. By studying Bravais lattices, scientists can gain insights into the material's characteristics and potential applications.

5. Can a single crystal have multiple Bravais lattice types?

Generally, a single crystal will exhibit only one type of Bravais lattice throughout its structure, as the definition of a Bravais lattice is based on a uniform periodic arrangement. However, different regions of a polycrystalline material may consist of grains that belong to different Bravais lattices. In such cases, the overall material may display complex behavior due to the presence of multiple lattice types at the grain boundaries.

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