# Phase Transformation Questions and Answers – Boundaries in Single Phase Solids – 1

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This set of Phase Transformation Multiple Choice Questions & Answers (MCQs) focuses on “Boundaries in Single Phase Solids – 1”.

1. The lattices of any two grains can be made to coincide by ________
a) Twisting across the plane
c) Turning in the direction of grain boundary
d) Rotating one of them through a suitable angle about a single axis

Explanation: The nature of any given boundary depends on the disorientation of the two adjoining grains and the orientation of the boundary plane relative to them. The lattices of any two grains can be made to coincide by rotating one of them through a suitable angle about a single axis.

2. Which of the following boundary occurs when the axis of rotation is parallel to the plane of boundary?
a) Roll in boundary
b) Twist boundary
c) Tilt boundary
d) Roll out boundary

Explanation: There are two special types of boundary that are relatively simple. A tilt boundary occurs when the axis of rotation is parallel to the plane of the boundary, whereas a twist boundary is formed when the rotation axis is perpendicular to the boundary.

3. Which among the following boundary is an array of parallel edge dislocations?
a) Low angle twist boundary
b) High angle tilt boundary
c) High angle twist boundary
d) Low angle tilt boundary

Explanation: The low-angle tilt boundary is an array of parallel edge dislocations. These is an idealized boundary and are symmetric in nature. In this case the atoms in the regions between the dislocations fit almost perfectly into both adjoining crystals whereas the dislocation cores are regions of poor fit in which the crystal structure is highly distorted.
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4. Which of the following boundary is related to screw dislocation?
a) Low angle twist boundary
b) High angle tilt boundary
c) High angle cross boundary
d) Low angle tilt boundary

Explanation: The twist boundary is a cross-grid of two sets of screw dislocations. Here the disorientation occurs around the axis that is perpendicular to the boundary plane. And these dislocations in the boundary remain isolated and distinct.

5. Calculate the magnitude of Burgers vector for the BCC lattice expressed as ½<148>, where 1, 4, 8 are their respective components of Burgers vector and the value of “a’’ is given as 1?
a) 6.5
b) 4
c) 5.5
d) 4.5

Explanation: The magnitude is given by the equation ||b||= (1/2)*√(12+42+82) = 4.5.The direction of the vector depends on the dislocation plane and in most cases it is usually found on one of the closest packed crystallographic planes.

6. In the edge dislocations, the Burger vectors and dislocation line are _________
a) Parallel to each other
b) Perpendicular to each other
c) Close to each other
d) Far away from each other

Explanation: In the edge dislocations, the Burger vectors and dislocation line are perpendicular to each other whereas in case of the screw dislocations they are parallel to each other.

7. “α” is the angular misorientation across the boundary. At very small values of α, the dislocation spacing is very large and the grain boundary energy ꙋ is approximately proportional to the____
a) Position of dislocation
b) Density of dislocation
c) Type of dislocation
d) Volume of dislocation

Explanation: At very small values of α, the dislocation spacing is very large and the grain boundary energy ꙋ is approximately proportional to the density of dislocations in the boundary (1/D). However, as α increases the strain fields of the dislocations progressively cancel out so that ꙋ increases at a decreasing rate.

8. For simple arrays, the spacing of dislocation is given by the formula________ (where b is the Burgers vector of the dislocations and α is the angular misorientation across the boundary)
a) D = b/sinα
b) D = b/cosα
c) D = b*sinα
d) D = b*cosα

Explanation: The energy of a low-angle grain boundary is simply the total energy of the dislocations within unit area of boundary and this depends on the spacing of the dislocations which, for the simple arrays is given by D = b/sinα.

9. If the tilt boundary is unsymmetrical, dislocations with different Burgers vectors are required to accommodate the misfit.
a) True
b) False

Explanation: Here we require different Burgers vector to accommodate the misfit as the boundary is having unsymmetrical dislocation and in some cases the tilt boundary can be symmetrical with respect to the two adjoining crystals at that instance however we don’t need different Burgers vector to accommodate the misfit.

10. When α > 10-15° the boundary is known as a_______ (“α” is the angular misorientation across the boundary)
a) Random high-angle grain boundary
b) Random low-angle grain boundary
c) Super angle grain boundary
d) Axial grain boundary

Explanation: When α > 10-15° the boundary is known as a Random high-angle grain boundary. The difference in structure between low-angle and high-angle grain boundaries can be lucidly illustrated by the bubble-raft model. High angle boundaries contain large areas of poor fit and have a relatively open structure.

11. Which among the following is the property of a low angle boundary?
a) Areas of poor fit
b) Relatively open structure
c) Highly disordered
d) Areas of perfect fit

Explanation: The reason behind the perfect fit in the low-angle boundaries is that most of the atoms correctly fit into both lattices so that there is very less free volume and the interatomic bonds are only slightly distorted. The regions of poor fits are also observed but rarely and it is restricted to the dislocation cores.

12. What is most likely to happen to the grain boundary energy of a pure metal on alloying?
a) It increases
b) It reduces
c) It increases first and finally becomes constant
d) No effect

Explanation: Generally, the grain boundary energy of a pure metal changes on alloying. Often (though not always) it is reduced. Under these circumstances the concentration of alloying element in the boundary is higher than that in the matrix.

13. A recrystallization texture is sometimes an advantage.
a) True
b) False

Explanation: Yes, this statement is true. For example, the proper texture in Fe-3wt% Si alloys makes them much better soft magnets for use in transformers. Another application is in the production of textured sheet for the deep drawing of such materials as low-carbon steel.

14. When the boundary moves the solute atoms migrate along with the boundary and exert a drag that reduces the boundary velocity. The magnitude of the drag will depend on ______
a) Shape of the boundary
b) Texture
c) Concentration in the boundary
d) It is an independent property

Explanation: The magnitude of the drag will depend on the binding energy and the concentration in the boundary. The higher mobility of special boundaries can, therefore, possibly be attributed to a low solute drag on account of the relatively more c1ose-packed structure of the special boundaries.

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