Find the translation vectors of the primitive cell

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SUMMARY

The discussion focuses on finding the translation vectors of the primitive cell in crystallography, specifically addressing homework problems related to this topic. User "ehild" provides insights on the correct identification of vectors, emphasizing the importance of the basis and the correct placement of the origin. The conversation highlights the need for accurate vector definitions to avoid misrepresentation of atomic positions within the crystal structure. The participants discuss adjustments to the vectors based on visual representations of the primitive cell.

PREREQUISITES
  • Understanding of primitive cells in crystallography
  • Familiarity with vector mathematics in three-dimensional space
  • Knowledge of crystal structures and basis atoms
  • Experience with visual representations of geometric shapes, such as hexagons
NEXT STEPS
  • Study the concept of basis in crystal structures
  • Learn how to calculate translation vectors in crystallography
  • Explore the use of visualization tools for crystal structures
  • Research the implications of changing the origin point in vector calculations
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Students and researchers in materials science, crystallography, and solid-state physics who are working on understanding and calculating primitive cells and their translation vectors.

Anisotrop
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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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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
 


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

Attachments

  • IMG_1641.jpg
    IMG_1641.jpg
    56.2 KB · Views: 1,234


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


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
 
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).
 
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
 
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
 
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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  • cell.JPG
    cell.JPG
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