Drawing a reciprocal lattice, also basis

[thegirl]

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?

 

[DrDu]

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".

 

[DrDu]

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).