# Find the translation vectors of the primitive cell

1. Feb 17, 2013

### Anisotrop

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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.

Last edited by a moderator: Feb 17, 2013
2. Feb 17, 2013

### ehild

Re: Find the translation vectors of the the primitive cell

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

ehild

3. Feb 17, 2013

### Anisotrop

Re: Find the translation vectors of the the primitive cell

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

#### Attached Files:

• ###### IMG_1641.jpg
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4. Feb 17, 2013

### Anisotrop

Re: Find the translation vectors of the the primitive cell

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

5. Feb 17, 2013

### ehild

Re: Find the translation vectors of the the primitive cell

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. Feb 17, 2013

### Anisotrop

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. Feb 18, 2013

### ehild

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. Feb 20, 2013

### Anisotrop

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. Feb 20, 2013

### ehild

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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