# Phase Transformation Questions and Answers – Boundaries in Single Phase Solids – 2

This set of Phase Transformation Questions and Answers for Experienced people focuses on “Boundaries in Single Phase Solids – 2”.

1. When the two grains are related by a rotation about a <100> axis, it can be seen that most high-angle boundaries have _____
a) Almost same energy
b) Different energy
c) Highly ordered structure
d) Nothing can be said about their energies

Explanation: When the two grains are related by a rotation about a <100> axis it can be seen that most high-angle boundaries have about the same energy and should therefore have a relatively disordered structure characteristic of random boundaries.

2. When the two grains are related by a rotation about a <110> axis, there are several large-angle orientations which have significantly lower energies than the random boundaries.
a) True
b) False

Explanation: When the two grains are related by a rotation about a <110> axis, there are several large-angle orientations which have significantly lower energies than the random boundaries. When Θ = 70.5°, it corresponds to the coherent twin boundary, but low-energy boundaries are also found for several other values of Θ.

3. When two grains meet in a plane it is known as _____
a) Grain corner
b) Grain boundary
c) Grain edge
d) Grain center

Explanation: When two grains meet in a plane it is known as a grain boundary, when three grains meet in a line then it is called a grain edge and when four grains meet at a point then it is called a grain corner.

4. What is the need for a grain boundary in an annealed material?
a) To control the grain size
b) To maintain its shape
c) It can produce a stable equilibrium at the grain edges
d) During annealing it produce a metastable equilibrium at the grain boundary intersections

Explanation: The boundaries are all high-energy regions that increase the free energy of a polycrystal relative to a single crystal. It is the reason that a polycrystalline material is never a true equilibrium structure but it has the property to adjust themselves during annealing to produce a metastable equilibrium and this happens at the intersections of the grain boundary.

5. What will be the torque acting on the boundary if the boundary happens to be at the orientation of a cusp in the free energy?
a) 500 Nm
b) Greater than 500 Nm
c) Less than 500 Nm
d) Zero

Explanation: If the boundary happens to be at the orientation of a cusp in the free energy, there will be no torque acting on the boundary since the energy is a minimum in that orientation. However, the boundary will be able to resist a pulling force Fy (in the vertical direction) of up to (dγ/dΘ) cusp without rotating.
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6. Under which of the following circumstances the grain boundary behaves as a thin soap film?
a) When the boundary energy is dependent on the orientation
b) When boundary energy is 0
c) When the torque is greater than zero
d) When the boundary energy is independent on the orientation

Explanation: If the boundary energy is independent of orientation the torque term is zero (this must be applied to the ends of the boundary to prevent it rotating into a lower energy orientation) and the grain boundary behaves like a soap film. Under these conditions the requirement for metastable equilibrium at a junction between three grains.

7. Calculate the pulling force F, if the chemical potential and the molar volume is given as respectively?
a) ΔG-V
b) ΔG+V
c) ΔG/V
d) ΔG*V

Explanation: F = ΔG/V. In other words the force on the boundary is simply the free energy difference per unit volume of material. In case of grain growth ΔG arises from the boundary curvature, but this equation applies equally to any boundary whose migration causes a decrease in free energy.

8. Calculate the chemical potential if the molar volume is given as 5 mm3/mol? (Given the value of radius as 4mm and the interfacial energy γ is 8 kJ/mm2?
a) 10
b) 20
c) 24
d) 22

Explanation: The effect of the pressure difference caused by a curved boundary is to create a difference in free energy (ΔG) or chemical potential (Δμ) that drives the atoms across the boundary. In a pure metal ΔG and Δμ are identical and are given by ΔG = 2γV/r. This free energy difference can be thought of as a force pulling the grain boundary towards the grain with the higher free energy.

9. During recrystallization, the boundaries between the new strain-free grains and the original deformed grains are acted on by a force ΔG /V where, in this case, ΔG is due to the difference in dislocation strain energy between the two grains.
a) False
b) True

Explanation: Consider a dislocation- free recrystallized grain expanding into the heavily deformed surroundings. In this case the total grain-boundary area is increasing, therefore the driving force for recrystallization must be greater than the opposing boundary tension forces. Such forces are greatest when the new grain is smallest, and the effect is therefore important in the early stages of recrystallization.

10. For low mole fractions of solute in the matrix 0.5 (Xo), the boundary solute concentration Xb (in 10-12) is given by_____ (ΔG =105kJ/Mol, T =505K)
a) 6.94
b) 7.94
c) 6.14
d) 9.80

Explanation: For low mole fractions of solute in the matrix (Xo), the boundary solute concentration Xb is given by the equation Xb= Xo*exp(-ΔG/RT). Substituting the respective value we get 6.94*10-12 as the value of Xb.

11. It is possible that the higher mobility of special grain boundaries plays a role in the development of recrystallization textures.
a) True
b) False

Explanation: It is possible that the higher mobility of special grain boundaries plays a role in the development of recrystallization textures. If a polycrystalline metal is heavily deformed, by say rolling to a 90% reduction, a deformation texture develops such that the rolled material resembles a deformed single crystal.

12. On heating to a sufficiently high temperature, what happens to the new grains?
a) They fall off
b) They disperse
c) Velocity decreases
d) They grow and nucleate

Explanation: On heating to a sufficiently high temperature new grains nucleate and begin to grow. However, not all grains will grow at the same rate: those grains which are specially oriented with respect to the matrix should have higher mobility boundaries and should overgrow the boundaries of the randomly oriented grains.

13. If unit area of grain boundary advances a distance 4mm, the number of moles of material that enter in the grain B is 4* (1/ 8(mm3/mol)) and the free energy released is given by_______ (ΔG =10kJ/mol)
a) 5 kJ/mol*mm2
b) 20 kJ/mol*mm2
c) 10 kJ/mol*mm2
d) 40 kJ/mol*mm2

Explanation: ΔG, Free energy difference can be thought of as a force pulling the grain boundary towards the grain with the higher free energy. If unit area of grain boundary advances a distance dx, the number of moles of material that enter grain B is dx*(1/ Vm) and the free energy released is given by ΔG*(dx/Vm).

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