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Homework Help: Lattice Parameter c of HCP

  1. Feb 10, 2010 #1
    1. The problem statement, all variables and given/known data
    I'm trying to figure out the lattice parameter, c, of the HCP crystal structure.

    Here are a couple links showing the structure: http://images.google.com/imgres?img...agonal+close+packed&hl=en&safe=off&sa=N&um=1"


    2. Relevant equations
    I know that a=2r, where r is the atomic radius of whatever atoms make up the structure. I'm not really sure what else is relevant, it seems to be a problem of geometry and I'm having trouble working it out.


    3. The attempt at a solution
    I can't really type out my math that I've attempted to do since I am having trouble conceptually. I think that the way to go about doing it is with a triangular pyramid, since with the way that the atoms sit on top of each other you will get an equilateral triangle as your base (sides=a) and then the height is c/2. However I can't seem to get this to work out mathematically. I got c to be 2*sqrt(3)*r, which is incorrect.

    Thanks for the help.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited by a moderator: Apr 24, 2017
  2. jcsd
  3. Feb 12, 2010 #2

    Lok

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    If the height of a triangular piramid is what you seek then a simple method is pytagora with a being the distance between 2 corners.

    that is the height of a equilateral triangle is (3^0.5)/2 which means that the pyramid triangle will have a base of 2/3 of the height. That is (3^0.5)/3 so:

    Pytagora : a^2(1-3/9)=a^2*c^2 where c=(6/9)^0.5=0.8164
     
    Last edited: Feb 12, 2010
  4. Feb 12, 2010 #3

    Astronuc

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    Staff Emeritus
    Science Advisor

    c/a must > 1, and a ~ 2r.
     
    Last edited: Feb 12, 2010
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