MSE615: Structure and Characterization of Materials | IITK | Quiz 5 Solutions PDF
MSE615: Structure and Characterization of Materials | IITK | Quiz 5 Solutions PDF
MSE 615: Quiz-V
Date: November 12, 2025
Time: 50 minutes
Total Score: 60 Points
Question 1
Mention which of the following statements is/are correct.
(i) Which of the following is/are generally true regarding X-ray diffraction?
(a) Some of the diffractions predicted by Bragg equation do not occur in non-primitive unit cells.
(b) All the diffractions predicted by Bragg equation occur in primitive unit cells.
(c) Only for certain values of q, the reflections from all planes will add up in phase to give a strong reflected beam.
(d) All of the above.
(ii) Which of the following statements is/are true?
(a) Reciprocal lattice of BCC is FCC.
(b) Reciprocal lattice of FCC is BCC.
(c) For the square lattice, the shape of the lattice and the reciprocal lattice is the same and the rotation angle between them is 0 degrees.
(d) For the hexagonal lattice, the shape of the lattice and the reciprocal lattice is the same and the rotation angle between them is 0 degrees.
(iii) Which of the following statements is/are true?
(a) In order to satisfy Bragg’s condition, reciprocal lattice vector G must be located at the zone boundary of the first Brillouin zone.
(b) Whenever a reciprocal lattice point lies exactly on the Ewald sphere, Bragg’s equation is satisfied.
(c) Radius of the Ewald sphere changes with change in wavelength of X-rays.
(d) Only lattice points lying within the limiting sphere can diffract.
(e) All of the above.
(iv) Which of the following statements is/are true regarding XRD pattern analysis?
(a) Peak positions tell about the size and shape of the unit cell.
(b) Peak intensities provide information about location of atoms inside the unit cell.
(c) Peak widths and shapes give information on crystallite size.
(d) Peak intensity gives information on crystallite size.
(v) Which of the following statements is true?
(a) For positively charged impurity center, the defects are either anion vacancies or cation interstitials.
(b) For positively charged impurity center, the defects are either cation vacancies or anion interstitials.
(c) For negatively charged impurity centers, defects are either anion vacancies or cation interstitials.
(d) For negatively charged impurity centers, defects are either cation vacancies or anion interstitials.
Question 2
Short Questions. Answer in less than 200 words.
(a) When you receive a chest X-ray at a hospital, the X-rays pass through a series of parallel ribs in your chest. Do the ribs act as a diffraction grating for X-rays? Can you obtain an XRD pattern of your ribs similar to metals in laboratory experiments?
(b) In XRD the peak intensities drop off at higher diffraction angles. Do you expect the same behaviour in neutron diffraction? Explain.
(c) In the XRD pattern of simple cubic crystals, the (100) peak is observed, but for BCC and FCC structures no peak corresponding to (100) is detected. Explain why.
(d) Holding your hand at arm’s length, you can easily block sunlight from your eyes. Why can you not block sound from reaching your ears in the same way?
Question 3
A sample of BCC metal with lattice parameter a = 0.33 nm is placed in an X-ray diffractometer using incoming X-rays with wavelength λ = 0.1541 nm.
Using Bragg’s law (assume first order diffraction, n = 1), predict the positions of diffraction peaks (in 2θ) corresponding to the following planes:
{110}, {210}, {230}, {321}, and {431}.
Question 4
Calculate the Kroger-Vink diagram for WO3 if the oxide has Frenkel defects with oxygen interstitials dominating the intermediate PO2 levels.
Consider the Kroger-Vink diagram at low, intermediate, and high PO2 for both electronic and ionic defects.
Question 5
Consider the 2D lattice defined by primitive vectors:
a1 = (2, 0)a
a2 = (1, 1/2)a
(a) What kind of unit cell is this?
(b) What is the cell volume?
(c) Sketch the Wigner-Seitz primitive cell.
(d) What are the reciprocal lattice vectors?
(e) Sketch the reciprocal lattice and show the first Brillouin zone.
(f) What angles would the first X-ray diffraction ring occur at if λ = a/4?