Material Science - short answer questions from AMIE exams (Summer 2019)

What is the angle between the directions [001] and [111 ] of cubic crystal?

Cos\,\theta \,\, = \,\,\frac{{{h_1}{h_2} + {k_1}{k_2} + {l_1}{l_2}}}{{\sqrt {h_1^2 + k_1^2 + l_1^2} \,\,x\,\,\sqrt {h_2^2 + k_2^2 + l_2^2} }}

What is the degree of freedom of a system of one component when the number of phases is two?
F = 2 – 2 + 1 = 1.

What is congruent transformation?
  • Congruent transformation: It involves no change in composition (e.g., allotropic transformation such as α-Fe to γ-Fe or melting transitions in pure solids).
  • Incongruent transformation: Here at least one phase changes composition (e.g. eutectic, eutectoid, peritectic reactions).
Define devitrification.
Devitrification, the process by which glassy substances change their structure into crystalline solids. This devitrification process is very slow, but over millions of years, a glass will form a completely crystalline mass; thus, the occurrence of very old glassy rocks is rare.

What is mobility?
We define Mobility in Physics as the measurement of the ease with which charged particles move through a solid material under the influence of an applied electric field.

If we observe the working of an electric circuit when a potential difference is applied across the circuit, electrons get a push and they start mobilizing from one end to the other, and electricity generates, which is how we define mobility of charge carriers like electrons.

Write the expressions for permeability and susceptibility of a magnetic material.
  • Magnetic susceptibility Xm = I/H, where I is the intensity of magnetization and H is the intensity of the magnetizing field (magnetizing force of applied field)
  • Relative permeability μr = μ/μ0, where the permeability of the material is μ, and that of free space μ0
  • Relative permeability in terms of susceptibility: μr = (1 + Xm)
Define the term Tg.
Glass Transition Temperature (Tg) is the point at which a material alters state – going from a glass-like rigid solid to a more flexible, rubbery compound.

What is vulcanization?
Vulcanization, a chemical process by which the physical properties of natural or synthetic rubber are improved; finished rubber has higher tensile strength and resistance to swelling and abrasion, and is elastic over a greater range of temperatures. In its simplest form, vulcanization is brought about by heating rubber with sulphur.

Write the invariant reactions (a) monotectic (b) syntectic.
Monotectic reaction
  • In this case, the two liquid solutions are not soluble in each other over a certain
  • composition range, i.e., there is a miscibility gap in the liquid state between the two metals. In this type one liquid decomposes into another liquid solid. Cu and Pb form a monotectic system. 
  • It is shown as  L₁ ↔ L₂ + ɑ
Syntectic reaction: 
  • In this reaction, two liquid phases react to form a solid phase.
  • It is shown as L₁ + L₂ ↔ ɑ
State the Griffith criterion for the propagation of a crack.
The fracture strength of a real material is much lower than the theoretical minimum value for an ideal solid. It means that the stress at which a material fracture is much below the lower value of the ideal breaking strength calculated from the atomic strength. the theoretical strength of an ideal crystal having no imperfections in it is 100 to 1000 times the normal strength. This discrepancy between the strength normally observed and the theoretical strength led Griffith to postulate that the low observed strength was due to many fine cracks which act to concentrate the stress at their ends.

According to Griffith, such a crack will propagate and produce brittle fracture when an incremental increase in its length does not change the net energy of the system.

\sigma  = \sqrt {\frac{{2\gamma E}}{{\pi C}}}


The study material for AMIE/B Tech/Junior Engineer exams is available at