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Hexagional Bravais Latice Question

  1. Nov 6, 2009 #1


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    1. The problem statement, all variables and given/known data

    The hexagonal close-packed structure (hcp) is the hexagonal Bravais lattice with a basis of two identical atoms associated with each lattice point, one at (0,0,0) and the second at

    [tex] r = \frac{2}{3}a_1 + \frac{1}{3}a_2 + \frac{1}{2} a_3 [/tex]

    where [tex]\left|a_1\right|[/tex] = [tex]\left|a_2 \right|[/tex] and [tex]a_1[/tex] and [tex]a_2[/tex] are at 120 degrees in the basal plane and [tex]a_3[/tex] is parallel to the c-axis. By considering the atoms to be hard spheres with nearest neighbour contact, show that the “c/a” ratio [tex]\frac{a_3}{a_1}[/tex] is 1.633.

    2. Relevant equations

    3. The attempt at a solution

    I am not quite sure what to do with this question. I am not quite sure how to get a3 and a1.

    Any ideas?

    many thanks,

    Last edited: Nov 6, 2009
  2. jcsd
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