MSE615: Structure and Characterization of Materials | IITK | Quiz 4 Solutions PDF
MSE 615: Quiz-IV
Date: September 11, 2025
Time: 50 minutes
Total Score: 60 Points
Question 1
Which of the following statements are TRUE and FALSE.
(i) Point defects are zero-dimensional defects.
(ii) Intrinsic point defects are always present in a crystalline material above absolute zero temperature.
(iii) All cation interstitials are Frenkel defects.
(iv) Non-equilibrium concentrations of point defects introduced by heat treatment can be classified as extrinsic defects.
(v) Point defects created by ion bombardment in a material can be classified as intrinsic defect.
Question 2
Using Kroger-Vink notation, considering only ionic defects in solids, write the defect reactions for the following compounds.
Please write two defect reactions for scenarios when cation and anion sublattice ideally filled.
(a) Li2O doped in TiO2
(b) Fe2O3 doped in Nb2O5
(c) Cr2O3 doped in Na2O
(d) AlF3 doped in Al2O3
Question 3
(a) Write the defect reaction for Schottky defect present in Nb2O5.
(b) Derive the expression for law of mass action, charge neutrality relationship and oxygen vacancy concentration arising from Schottky defect.
Question 4
Consider MgO having Rock-salt structure.
(a) Write the defect reaction corresponding to cation Frenkel disorder.
(b) Applying the law of mass action and charge neutrality condition derive the expression for various ionic defect concentrations possibly occurred due to this Frenkel disorder in MgO.
Question 5
Tungsten Oxide (WO3) has density of 7.16 g/cm3. Theoretical calculations indicate that the formation energy of a Schottky defect in WO3 is 2.6 eV.
(a) Derive the Schottky defect reaction corresponding to WO3.
(b) Calculate the number of Schottky defects per cm3 in WO3 at 1000 K ignoring the pre-exponential factor.
Given:
Atomic weight of Tungsten (W) = 184 g/mol
Atomic weight of Oxygen (O) = 16 g/mol
Boltzmann constant = 8.62 × 10⁻⁵ eV/atom-K
Avogadro’s number = 6.02 × 10²³ atoms/mol
MSE615: Structure and Characterization of Materials | IITK | Quiz 1 Solutions PDF