Question

What are Schottky defects and Frenkel defects? Face centered cubic crystal lattice of copper has the density of $8.966\text{ }g\text{ }c{{m}^{-3}}$. Calculate the volume of the unit cell. Given molar mass of copper is \[63.54\text{ }g\text{ }mol{{e}^{-1}}\]and the Avogadro’s number N is $6.02\times {{10}^{23}}$ $\text{mol}{{\text{e}}^{-1}}$.

Answer 1

Hint: Schottky defect is due to the absence of ions and on the contrary Frenkel defect is due to the occupation of the interstitial sites by the ions and we can find the volume of the copper cubic crystal by applying the density as: $\dfrac{\text{ZM}}{{{\text{a}}^{3}}\times {{\text{N}}_{\text{0}}}}$. Now answer the statement accordingly.

Complete step by step answer:
We will discuss the Frenkel and the Schottky defect in the tabular form. It is easy to discuss these in the tabular form as well as the easy to differentiate between them.

Serial no.	Schottky defect	Frenkel defect
1.	This defect is produced by the missing ions.	This defect is produced when the ion moves to the interstitial sites.
2.	In this, density is lowered.	In this, density remains the same.
3.	Both the anion and the cation have the same size.	Anions are larger in size than the cations.
4.	It is shown by the compounds having high coordination numbers.	It is shown by the compounds having low coordination numbers.
5.	Example: NaCl, CsCl etc.	Example : AgCl, ZnS etc.

Now, coming to the next part of the statement;
We can find the volume of the Cu crystal by applying the density formula as;
density =$\dfrac{\text{ZM}}{{{\text{a}}^{3}}\times {{\text{N}}_{\text{0}}}}$
here, Z represents what type of crystal it is i.e. simple cube, face centered cubic or body centered cube, M is the mass of the crystal, ${{a}^{3}}$ is the volume of the crystal and ${{N}_{a}}$ is the Avogadro’s number.
Now, we know that Cu crystal occupies face -centered cubic lattice,
Then For face centered, Z=4
Atomic mass of Cu=\[63.54\text{ }g\text{ }mol{{e}^{-1}}\] (given)
${{\text{N}}_{a}}$=$6.02\times {{10}^{23}}$ $\text{mol}{{\text{e}}^{-1}}$(given),
Density= $8.966\text{ }g\text{ }c{{m}^{-3}}$ then;
Put all these values in equation (1), we get;
$\begin{align}
& 8.966=\dfrac{4\times 63.5}{{{a}^{3}}\times 6.023\times {{10}^{23}}} \\
& {{a}^{3}}=\dfrac{4\times 63.5}{8.966\times 6.023\times {{10}^{23}}} \\
& \text{ =}\dfrac{254}{53.99\times {{10}^{23}}} \\
& {{a}^{3}}\text{ =4}\text{.70}\times {{10}^{-23}}\text{ }c{{m}^{3}} \\
\end{align}$
So, the volume of the copper crystal lattice is $4.70\times {{10}^{-23}}\text{ }c{{m}^{3}}$.

Note: Both the Schottky and Frenkel defect comes under the category of the defects in the stoichiometric crystals in which the positive and the negative ions are exactly in the same ratio as indicated by their chemical formula.