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Question: Examine the defective crystal given below and answer the question that follows: A.\[{A^ + }{B^ - }...

Examine the defective crystal given below and answer the question that follows:
A.A+B−A+B−A+{A^ + }{B^ - }{A^ + }{B^ - }{A^ + }
B.B−   B−A+B−{B^{ - \;}}{\text{ }}{B^ - }{A^ + }{B^ - }
C.A+B−A+   A+{A^ + }{B^ - }{A^ + }\;{\text{ }}{A^ + }
D.B−A+B−A+B−{B^ - }{A^ + }{B^ - }{A^ + }{B^ - }
State if the above defect is stoichiometric or non-stoichiometric. How does this type of defect affect the density of the crystal? Also, write the term used for this type of defect.

Explanation

Solution

Compounds having equal numbers of positive and negative ions are called stoichiometric compounds. The density of crystal is the ratio of the mass and volume of the crystal. Mainly two types of defects are present in crystals named as Schottky and Frenkel defects.

Complete step by step answer:
The defects which originate due to migration of ions from lattice to the surface creating vacancies of the site present in the crystal lattice. This is called the Schottky defect or valency defect. Equal number of cations and anions are missing from the lattice. This type of defect results in a decrease in density of the lattice.
The defects which result when cations leave the normal lattice sites and occupy interstitial sites are known as Frenkel defects. The density of the lattice does not change.
Let us examine the given lattice and evaluate the defect present.

A+{A^ + }B−{B^ - }A+{A^ + }B−{B^ - }A+{A^ + }
B−{B^ - }B−{B^ - }A+{A^ + }B−{B^ - }
A+{A^ + }B−{B^ - }A+{A^ + }A+{A^ + }
B−{B^ - }A+{A^ + }B−{B^ - }A+{A^ + }B−{B^ - }

An investigation of the crystal lattice indicated that one positive ion and one negative ion is missing from the structure, therefore the defect is stoichiometric.
The density of the defective crystal is lowered as the numbers of ions are less than the number of ions in pure form. The number of ions removed maintains the charge neutrality of the lattice.
This type of defect is known as Schottky defect.

Note:
Both these defects belong to the same category of defects called point defects. Line defects and planar defects are other types of defects. Large numbers of defects are present on real crystals. Non stoichiometric crystals have different stoichiometry over a wide range of lattice structures.