FCC reciprocal to BCC

  • Thread starter Piano man
  • Start date
  • #1
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Homework Statement



The proof seems fairly straight forward, but after plugging in the primitive vectors to the equations for the reciprocal lattice vectors, I'm getting
[tex]2\pi\frac{\frac{a^2}{4}(x+y-z)}{\frac{a}{2}(y+z)\cdot(\frac{a^2}{4}(-x+y+z))}[/tex]

One proof I checked said that the bottom line's
[tex](y+z)\cdot(-x+y+z)=2[/tex]

I don't see how. Any ideas?
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
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Hi Piano man! :smile:

If this is a dot product then x.y = y.z = z.x = 0. :wink:
 
  • #3
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:blushing: :facepalm:

thanks I completely forgot that.
So it would reduce to y.y + z.z = 2

A tad embarrassing not to spot that :D
 

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