Name: Hexagonal Close Packing in 2D and 3D
Uploaded: 2019-07-19
Duration: 5 min 29 s
Description: When the rows of spheres are stacked over each other, a 2D closed packed structure is produced. Let’s see how the stacking is done to produce a hexagonal clo...

Question

A compound forms hexagonal close packed

(hcp)

structure. What is the total number of voids in

0.5 mol

of it? How many of these are tetrahedral voids?

Accepted Answer

Number of compound units in 1 mole of close-packed structure $= N_{A} = 6.022 \times 10^{23}$
Number of compound units in $0.5$ mole of close-packed structure $= 0.5 \times 6.022 \times 10^{23} = 3.011 \times 10^{23}$

We know that, one unit of hcp has atoms $= 6$

So, number of unit cells $= \frac{3.011 \times 10^{22}}{6} = 5.018 \times 10^{22}$

And if close packed structure has $6$ atoms then it will have $6$ octahedral voids and $12$ tetrahedral voids in one unit cell.
So, number of octahedral voids $= 6 \times 5 .018 \times 10^{22} = 3.011 \times 10^{23}$
And, number of tetrahedral voids $= 12 \times 5 .018 \times 10^{22} = 6.022 \times 10^{23}$
Therefore, total number of voids $=$ Octahedral voids $+$ Tetrahedral voids $= 3.011 \times 10^{23} + 6.022 \times 10^{23} = 9.033 \times 10^{23}$ .

A compound forms hexagonal close packed $(hcp)$ structure. What is the total number of voids in $0.5 mol$ of it? How many of these are tetrahedral voids?

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