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Help with Bravais lattice

  1. Mar 26, 2009 #1
    I have three primitive vectors a1,a2,a3 for the body-centered cubic (bcc) Bravais can be chosen as

    a1=ax
    a2=ay
    a3=(a/2)(x+y+z)

    or, for instance, as

    b1=(a/2)(y+z-x)
    b2=(a/2)(z+x-y)
    b3=(a/2)(x+y-z)

    where x,y,z are unit vectors.

    Now I should show that any vector of the form

    R=n1a1+n2a2+n3a3
    where n1,n2,n3 are integers

    can be presented as

    R=m1b1+m2b2+m3b3
    where m1,m2,m3 are integers

    Do anyone have an idea how I can do this?
    Does it help me if I construct reciprocal lattice?

    //
    Mythbusters - "Well, here's your problem"
     
  2. jcsd
  3. Mar 26, 2009 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    Hi Mythbusters!

    dunno wot a reciprockle lattice is :confused:

    but all you need to do is to express each a as a combination of bs :smile:

    Hint: to get you started, what is b1 + b2 + b3 ? :wink:
     
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