First slide

Crystal lattices and unit cells

Question

In cubic ZnS,the radii of the Znand S atoms are 0.83 $\overset{o}{A}$ and 1.74 $\overset{o}{A}$ respectively. What is the edge length of the unit cell of ZnS?

Moderate

A

2.57 $\overset{o}{A}$
B

3.64 $\overset{o}{A}$
C

2.97 $\overset{o}{A}$
D

5.935 $\overset{o}{A}$

Solution

This figure shows one part of eight cubic components of a unit cell of ZnS.
Let edge length of the unit cell = a
$\sqrt{3} \times \frac{a}{2} \times \frac{1}{2} = r_{{Zn}^{2 +}} + r_{S^{2 -}}$
or $\sqrt{3} \frac{a}{4} = 0.83 + 1.74 = 2.57$
or $a = 2.57 \times \frac{4}{\sqrt{3}} = 5.935 Å$

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