Crystal-Bravis Lattice Definitions

In summary, during the conversation, it was discussed that there is a concept of an orthorhombic body centered crystal lattice. The selection of a unit cell with the highest symmetry and smallest area was mentioned, and it was noted that the red unit cell has a higher symmetry by 90 degrees. The green shape can be reflected vertically and horizontally, but the point of reflection is not the same, which explains the higher symmetry for the red unit cell. It was also clarified that all atoms in a lattice are identical, and the choice of centered cells is mainly a convention. The complexity of defining the different Bravais lattices was also mentioned. Finally, it was emphasized that the lattice is made up of simple points, not atoms
  • #1
SpartanG345
70
1
There is such thing as a orthorhombic body centered crystal lattice. I am wondering why this is the case

see the image bellow, we can find a repeating pattern which has a smaller area.

Orthorombic.png


A unit cell
- must be selected such that it has the highest symmetry and the smallest area, however i do not see how the red unit cell has a higher symmetry. According to our lecture the red unit cell has a higher symmetry by 90 degrees, therefore a orthorhombic cubic has a body centered from

The green shape can be reflected vertically and horizontally, however the point of reflection where the axis of symmetry passes through is not the same is this why there is a higher symmetry for the red ( default) unit cell?

The blue atom is from a neighboring unit cell
 
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  • #2
Are all atoms identical?
 
  • #3
yes all atoms are identical, the blue one is from a neighboring unit cell
 
  • #4
As you observed correctly, even in centered lattices it is always possible to chose a unit cell which only contains one lattice point.
The choice of the centered cells is mainly convention. I was astonished to find that it is quite involved to define mathematically in what sense the 14 Bravais lattices are different.
See, e.g., S. Sternberg, Group theory and physics.

I would only speak of lattice points and not of an atom as "crystal=lattice+cell". Hence the cell can be very complicated, e.g. a protein. Nevertheless the lattice is made up of simple points.
 
  • #5
Yes, atom was a wrong word. What I was asking about was whether all lattice points are equivalent. In ionic crystal nodes are occupied by different objects, so it can (?) be possible that the cell smallest in geometrical terms is not representative to whole crystal.
 

1. What is a Crystal-Bravis lattice?

A Crystal-Bravis lattice is a mathematical model used to describe the arrangement of atoms or molecules in a crystal structure. It is a repeating three-dimensional pattern that extends infinitely in all directions.

2. How is a Crystal-Bravis lattice defined?

A Crystal-Bravis lattice is defined by a set of lattice points, which represent the positions of the atoms or molecules in the crystal. These points are connected by lattice vectors, which define the length and direction of the lattice.

3. What is the importance of Crystal-Bravis lattices in crystallography?

Crystal-Bravis lattices are important in crystallography because they provide a way to classify and describe different types of crystals. They also allow scientists to predict the physical and chemical properties of crystals based on their lattice structure.

4. Are there different types of Crystal-Bravis lattices?

Yes, there are 14 different types of Crystal-Bravis lattices, also known as Bravis lattices. These include simple cubic, body-centered cubic, face-centered cubic, hexagonal, and many others. Each type has a unique arrangement of lattice points and lattice vectors.

5. How are Crystal-Bravis lattices used in materials science?

In materials science, Crystal-Bravis lattices are used to study the properties and behaviors of different materials. By understanding the lattice structure of a material, scientists can predict its strength, conductivity, and other important characteristics. Crystal-Bravis lattices also play a role in the design of new materials with specific properties.

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