Question

A compound forms a hexagonal close-packed structure. What is the total number of voids in 0.5 many of these are tetrahedral voids?

Answer 1

In HCP, two voids are included that are octahedral voids and tetrahedral voids. The number of tetrahedral voids that are in the lattice is always twice the number of close-packed particles. The number of octahedral voids formed is the same as the number of close-packed particles.

Complete answer:
The layers of the sphere are packed in a way that spheres in alternating layers overlap one another. It is a slip system and is a close-packed structure.
This structure is common for metals like Beryllium, Cadmium, Magnesium, Titanium, Zinc, and Zirconium. The atoms in the crystal lattice are closely packed and don’t have any space between them. There are two ways in which three-dimensional solid packing could occur i.e Cubical close packing and hexagonal close packing.
Let’s solve the numerical :
Number of atoms in close packing = 0.5 mol
1 mole has $6.022\times {{10}^{23}}$particles
Therefore,
Number of atoms in close packing = $0.5\times 6.022\times {{10}^{23}}=3.01\times {{10}^{23}}$
Number of tetrahedral voids = 2$\times$Number of atoms in close-packed particles
Put the values in the formula
Number of tetrahedral voids = $2\times 3.011\times {{10}^{23}}$
= $6.022\times {{10}^{23}}$
Number of octahedral voids = Number of atoms in close packaging
Therefore,
Number of octahedral voids = $3.011\times {{10}^{23}}$
So, Total Number of voids = Number of tetrahedral void + Number of octahedral void
= $6.022\times {{10}^{23}}$+ $3.011\times {{10}^{23}}$
= $9.03\times {{10}^{23}}$

Note:
Crystalline solids contain a repeating and regular pattern of constituent particles. The three-dimensional arrangements of particles are represented by a diagram in a crystal in a manner that every particle is arranged as a point in the space, This lattice is called a crystal lattice.