I need to derive the lattice parameter in terms of the Zn-S separation distance,(adsbygoogle = window.adsbygoogle || []).push({}); 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 distancel, and an opposite side of the angle θ, let's call itx. Findingxis then easy using the law of cosines.

x^{2}= 2l^{2}– 2l^{2}cosθ

then

x= [itex]\frac{2}{\sqrt{3}}[/itex]l

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

Does anyone know what's going on?

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# Derivation of lattice parameter of zinc blende crystal structure

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