MTSE 3000: Fundamentals of Materials Science and
Engineering
Spring 2025, Quiz-04
Quiz Time: 65 Minutes to Answer
Time to Upload PDF File on CANVAS: 10 Minutes
Academic dishonesty is prohibited and considered a violation of
the Student Conduct Regulations. Cheating will not be tolerated
and will be referred to the Office of Student Conduct for
disciplinary action
 Closed book and closed notes quiz.
 Upload your answers on CANVAS as a single PDF file.
 Answer all the questions. An effective answer often uses a
combination of words, equations, simple sketches, and/or
examples.
 Show all work for full credit (if appropriate)
 You may use a calculator (if needed)
 Use the ruler as required
Multiple Choice Questions. CIRCLE ALL the correct
choice(s)/statements(s).
A. Multiple Choice Questions
(10 points)
50
1. The following are relevant to a homogeneous nucleation process.
(a) Water vapor condensation on dust particles.
(b) Uniform formation of nuclei throughout the liquid.
(c) Addition of inoculants to casting.
(d) Higher energy barrier for nucleation.
2. The addition of carbon to the surface layer of a gear during carburizing is an example of
(a) Work hardening.
(b) Interstitial diffusion mechanism.
(c) Hardening the surface.
(d) Hall-Petch strengthening.
3. Select true statements related to phase diagrams
(a) Mixing two elements always lowers the overall liquidus temperature.
(b) Isomorphous systems show complete solubility in liquid and solid phases over the
range of compositions.
(c) Changes in pressure can shift the phase transformation temperature.
(d) The Lever rule can be applied in single-phase regions of the phase diagram.
4. Heat treatments can
(a) Enhance the strength of a material.
(b) Relieve stresses.
(c) Improve the toughness of a material.
(d) Shape a component for applications.
5. Select statements applicable to the materials index
(a) It combines the objectives and constraints of the design.
(b) It provides a framework for process selection.
(c) It gives a slope for a selection line in an Ashby chart.
(d) It is only confined to the mechanical properties of the materials.
B. Conceptual Questions
(15 points)
6. Explain what is meant by materials index. Material indices for a light-weight spring for
𝛔𝟐
maximum energy storage per unit volume without failing is given by 𝐌 = 𝐟 . Here, E, f, and
𝐄
a are respectively the Young’s modulus, tensile strength, and linear thermal expansion
coefficient of a material. Answer the following questions. You need not select specific
materials.
a) What property will you plot on the X and Y-axes respectively? 𝜎𝐹 on Y axis and E on X axis
b) Will the axes be linear or logarithmic? Logarithmic
c) What is the slope of the selection line? 1/2
C. Numerical Questions
(25 points)
7. At 400°C, the fraction of lattice vacancies in FCC aluminum was 2.29x10-5. Calculate the
fraction of vacancies at 660°C (just below the melting point of aluminum). The Boltzmann
constant is 8.62x10-5 eV/K and activation energy for vacancy formation in aluminum is 0.76
eV.
Nv
N
−Q
−0.76
= exp kT = exp 8.62 ×10−5×933 = 7.87 × 10−5
T = 660 +273 = 933 K.
8. Fe-C phase diagram
(given on the right)
shows that the Fe3C
phase has 6.7 wt.% C
and 4.3 wt.% C is
dissolved in -Fe at
just below the eutectic
temperature (1147°C).
Consider 1 kg of a 98 wt.%
Fe–4.3 wt.% C alloy.
Determine the following
for this alloy.
(a) List the equilibrium
phases at (i) 1550°C
(liquid), (ii) 1300°C
(liquid); (iii) 1000°C (γ
Fe and Fe3C); (iv) 400
°C (α-Fe and Fe3C).
(b) At just below the
eutectic temperature,
(i) Calculate the chemical composition of cementite (Fe3C) and alpha (ii) The quantity
(fraction) of cementite in grams that forms per 1000 g of steel. (iii) Draw a schematic
microstructure of this alloy.
Fe3C =6.67 wt%, γ-Fe is ~2.1%
Just below the eutectic temperature (1147°C),
Quantity of γ-Fe = (6.67-4.3)/(6.67-2.1) = 51.85 %
Quantity of Fe3C = 48.1%
There is no ferrite (-Fe) phase just below eutectic temperature
For 1 kg, γ-Fe = 518.5 g, Fe3C = 481.5 g, and -Fe = 0 g.
(iii) The two phases will form the classical eutectic microstructure we discussed in the
class!