Find the translation vectors of the primitive cell

In summary, the figure shows the primitive cells and their content, the basis, repeated in the crystal. The basis is not necessarily a single atom. It can be two as in the first figure, or it can be a complicated molecule. The smallest shape you can use to "tile" the whole plane is the hexagons.
  • #1
Anisotrop
5
0

Homework Statement



Find the translation vectors of the primitive cell. The figures are provided.

nn-2012-02696v_0001.jpg


Homework Equations

The Attempt at a Solution



I found these are more difficult than what I am learning from Kittel. I did number 1, but not sure if it is correct. Answer or hint for any of the figures is appreciated.
 
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  • #2


Anisotrop said:
1. The figures are provided



2. Answer or hint for any of the figures is appreciated.
View attachment 55827


3. I did number 1 but not sure if it is correct

]

Show you work. How did you find the translation vectors in case 1?

ehild
 
  • #3


Here is the one 1 I did for number 1.
I also need to find the location of basis and generate the structure.
 

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  • #4


I think my vector a1= sqrt(3)*a in x-direction...
 
  • #5


Anisotrop said:
I think my vector a1= sqrt(3)*a in x-direction...

Yes, but a2 was not correct
The picture shows the primitive cells and its content, the basis, repeated in the crystal. The basis is not necessarily a single atom. It can be two as in the first figure, or it can be a complicated molecule.

ehild
 
  • #6
Thanks for response! Could you please tell me what I need to change in the a2? Or should I take a different reference point (origin).
 
  • #7
What are the vectors making the sides of the cell shown in the picture?

If you take the vector a2 you have shown, you would get atoms even at the empty places at the centres of the hexagons.

ehild
 
  • #8
Thank you Ehild for your great help. I have changed my origin to the vertex of the Rhombus provided. I will upload it once I am done with it. Thanks again! :)

Anisotrop
 
  • #9
Find the smallest shape you can use to "tile" the whole plane. In the first figure, you can cover the plane with the hexagons. You can put the vertex of the primitive cell at the centre of the hexagons, and the length of the primitive translation vectors are equal to the distance between the centres. The primitive translation vectors determine the primitive cell. The cell contains the basis, the group of atoms, that are repeated in the crystal.

ehild
 

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Related to Find the translation vectors of the primitive cell

1. What is a primitive cell?

A primitive cell is the smallest repeating unit in a crystal lattice that contains all the necessary information to describe the entire crystal structure. It is usually a parallelepiped shape and is used to define the unit cell of a crystal lattice.

2. Why is it important to find the translation vectors of the primitive cell?

Finding the translation vectors of the primitive cell allows us to understand the symmetry and periodicity of the crystal structure. It also helps us to determine the lattice parameters and the arrangement of atoms in the crystal lattice.

3. How do you find the translation vectors of the primitive cell?

The translation vectors of the primitive cell can be found by determining the shortest lattice vectors that connect equivalent points in the crystal lattice, such as the corners of the primitive cell. These vectors are known as lattice translation vectors.

4. What information do you need to find the translation vectors of the primitive cell?

To find the translation vectors of the primitive cell, you will need to know the crystal system, lattice parameters, and the positions of the atoms within the unit cell. This information can be obtained from X-ray diffraction data or other experimental techniques.

5. Can the translation vectors of the primitive cell be different for the same crystal structure?

No, the translation vectors of the primitive cell are unique for a given crystal structure. However, the choice of which vectors are used to define the primitive cell may vary, as long as they satisfy the requirements of being the shortest lattice vectors connecting equivalent points in the crystal lattice.

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