Undergrad Drawing a reciprocal lattice, also basis

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SUMMARY

This discussion focuses on the process of drawing a reciprocal lattice, specifically for a 2D rectangular lattice. The reciprocal lattice vectors are defined as G = h(2π/a1) + k(2π/a2), where a1 and a2 are the lattice vectors of the original lattice. Additionally, the conversation addresses the difference in the number of basis atoms in face-centered cubic (FCC) and body-centered cubic (BCC) lattices, with FCC having four bases and BCC having two. The concept of a "primitive cell" is also highlighted as essential for understanding lattice structures.

PREREQUISITES
  • Understanding of lattice vectors in crystallography
  • Familiarity with reciprocal lattice concepts
  • Knowledge of primitive cells in solid-state physics
  • Basic vector notation and operations
NEXT STEPS
  • Study the calculation of reciprocal lattice vectors for different lattice types
  • Learn about the significance of primitive cells in crystallography
  • Explore the differences between FCC and BCC structures in detail
  • Investigate vector notation and its implications in crystallographic calculations
USEFUL FOR

Students and professionals in materials science, solid-state physics, and crystallography, particularly those interested in lattice structures and their reciprocal forms.

thegirl
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Hey could anyone please explain how you go about drawing a reciprocal lattice? For example a 2d rectangular lattice to it's reciprocal form?

Also... I don't know if this is correct but if you have a 2d rectangular lattice with lattice vectors L=n1a1 + n2a2

would the reciprocal lattice vectors be G = h(2pi/a1) + k (2pi/a2) ?

Another question I have is why do fcc's have 4 bases whereas a bcc only has 2? How would you go about calculating the bases vectors of any lattice?
 
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thegirl said:
Another question I have is why do fcc's have 4 bases whereas a bcc only has 2? How would you go about calculating the bases vectors of any lattice?

I think any lattice can be spanned by only 3 (in 2-D 2) lattice vectors, independently whether the lattice is centered or not. Look for "primitive cell".
 
thegirl said:
Heycould anyone please explain how you go about drawing a reciprocal lattice? For example a 2d rectangular lattice to it's reciprocal form?

Also... I don't know if this is correct but if you have a 2d rectangular lattice with lattice vectors L=n1a1 + n2a2

would the reciprocal lattice vectors be G = h(2pi/a1) + k (2pi/a2) ?
I think you are basically right, but you should be careful about vector notation. I.e. if a1 is a vector, then you can't form (2pi/a1).
 

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