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Coordination Number and Geometry

  1. May 29, 2005 #1
    I am trying to understand a sample problem in this text I have about materials science. The question is to calculate the minimum radius ration for a coordination number of 8. The coordination geometry is cubic. What I don't understand in this problem is one of the two equations they use to solve the for the ratio.

    [tex]R[/tex] is the larger ion radius, [tex]r[/tex] is the smaller ion radius and [tex]l[/tex] is the cube length edge.

    Now what I don't get is how the book comes up with this relationship.

    [tex] 2R + 2r = \sqrt{3}\ l [/tex]

    The second expression [tex] l = 2R [/tex], I understand since the two large ions are touching eachother, their radius will make up the length of the cube edge. They substitute this equation in the other and solve for [tex]\frac{r}{R}[/tex] It's just that I don't understand where that first equation comes from.
     
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  3. May 29, 2005 #2

    OlderDan

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    [tex] \sqrt{3}\ l [/tex] is the diagonal of the cube. Each corner is occupied by the larger ion, with the smaller ion fitting in the space between the large ions.
     
  4. May 29, 2005 #3
    Ok. Great I understand it now. Thanks a lot OlderDan
     
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