Question

Examine the given defective crystal.
\[{{\text{X}}^ + }{\text{ }}{{\text{Y}}^ - }{\text{ }}{{\text{X}}^ + }{\text{ }}{{\text{Y}}^ - }{\text{ }}{{\text{X}}^ + } \\
{{\text{Y}}^ - }{\text{ O }}{{\text{Y}}^ - }{\text{ }}{{\text{X}}^ + }{\text{ }}{{\text{Y}}^ - } \\
{{\text{X}}^ + }{\text{ }}{{\text{Y}}^ - }{\text{ }}{{\text{X}}^ + }{\text{ O }}{{\text{X}}^ + } \\
{{\text{Y}}^ - }{\text{ }}{{\text{X}}^ + }{\text{ }}{{\text{Y}}^ - }{\text{ }}{{\text{X}}^ + }{\text{ }}{{\text{Y}}^ - } \\\]
Answer the following questions:
(A) Is the above defect stoichiometric or non-stoichiometric?
(B) Write the term used for this type of defect. Give an example of the compound which shows this type of defect?
(C) How does this defect affect the density of the crystal?

Answer 1

Hint: The defects arise when an atom or ion goes missing or dislocates from the crystal lattice or any atom gets added to the crystal lattice. In stoichiometric defects, the ratio of cations and anions does not change. In non-stoichiometric defects, the ratio of cations and anions changes.

Complete step by step answer:
(A) Determine if the defect is stoichiometric or non-stoichiometric as follows:
The defective crystal is as follows:
\[{{\text{X}}^ + }{\text{ }}{{\text{Y}}^ - }{\text{ }}{{\text{X}}^ + }{\text{ }}{{\text{Y}}^ - }{\text{ }}{{\text{X}}^ + } \\
{{\text{Y}}^ - }{\text{ O }}{{\text{Y}}^ - }{\text{ }}{{\text{X}}^ + }{\text{ }}{{\text{Y}}^ - } \\
{{\text{X}}^ + }{\text{ }}{{\text{Y}}^ - }{\text{ }}{{\text{X}}^ + }{\text{ O }}{{\text{X}}^ + } \\
{{\text{Y}}^ - }{\text{ }}{{\text{X}}^ + }{\text{ }}{{\text{Y}}^ - }{\text{ }}{{\text{X}}^ + }{\text{ }}{{\text{Y}}^ - } \\\]
In the crystal, one cation $\left( {{{\text{X}}^ + }} \right)$ and one anion $\left( {{{\text{Y}}^ - }} \right)$ are missing. Thus, the ratio of cations and anion remains the same even after the defect. Such defects are known as stoichiometric defects.
In stoichiometric defects, the ratio of cations and anions does not change. Thus, the defect is stoichiometric defect.
(B) When an equal number of cations and anions are missing from the crystal lattice the defect is known as Schottky defect. In the Schottky defect, the electrical neutrality of the crystal is maintained.
The compounds that have a small difference in the size of cations and ions show Schottky defects.
The examples of compound showing Schottky defect are: sodium chloride $\left( {{\text{NaCl}}} \right)$ and potassium chloride $\left( {{\text{KCl}}} \right)$.
(C) When a Schottky defect occurs, the equal number of cations and anions go missing from the interstitial sites of the crystal lattice. As a result the density of the crystal lattice decreases.
Thus, the Schottky defect decreases the density of the crystal.

Note: The defect formed when the smaller atom or ion (usually cation) leaves its original place in the crystal lattice and creates a vacancy in the crystal lattice is known as Frenkel defect. The cation occupies another interstitial position in the crystal lattice. The density does not change when a Frenkel defect occurs.