Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Derivation of lattice parameter of zinc blende crystal structure

  1. Mar 25, 2012 #1
    I need to derive the lattice parameter in terms of the Zn-S separation distance, l.

    I looked up the value and I've found it to be
    a = [itex]\frac{4}{\sqrt{3}}[/itex]l

    The way that I started my derivation was saying that each tetrahedron has a sulfide ion in the center, so then we can make a triangle from the center point, and two zinc adjacent atoms. This isosceles triangle will have an angle
    θ = cos-1[itex]\frac{1}{3}[/itex]
    with two equal sides of the separation distance l, and an opposite side of the angle θ, let's call it x. Finding x is then easy using the law of cosines.
    x2 = 2l2 – 2l2cosθ
    x = [itex]\frac{2}{\sqrt{3}}[/itex]l

    Now, I'm having a hard time relating x to a. And the only way it seems to work out to get the answer I looked up is by saying a = 2x. But from the crystal structure, my mind tells me [itex]\sqrt{2}a[/itex] = 2x.

    Does anyone know what's going on?

    Last edited: Mar 25, 2012
  2. jcsd
  3. Mar 26, 2012 #2
    Found my mistake! the bond angle is arcos(-⅓)!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook