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Homework Help: Zigzag carbon nanotubes

  1. Sep 18, 2011 #1
    1. The problem statement, all variables and given/known data
    I'm trying to express the conditions for a zigzag carbon nanotube in a mathematical vector.


    2. Relevant equations

    B = na1 + ma2

    3. The attempt at a solution

    I want to say "either a=0 or b=0", but must I also say that it can't be a=b=0 or is that already excluded in the statement? I'm not sure of the mathematical logic at work.
    Thanks in advance
    P.S B, a1 and a2 are vectors, but I couldn't find the bold button.
     
    Last edited: Sep 18, 2011
  2. jcsd
  3. Jan 29, 2017 #2

    TeethWhitener

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    Science Advisor
    Gold Member

    You could say "either ##n=0## or ##m=0## but not both." Alternatively, since ##\mathbf{a}_1## and ##\mathbf{a}_2## are identical graphene unit cell vectors, they're interchangeable, so you could just say "##n=0## and ##m \neq 0##," which is equivalent to the first statement.
     
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