# Mechanical Metallurgy Questions and Answers – Plastic Deformation – Concept of Crystal Geometry – 1

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This set of Mechanical Metallurgy Multiple Choice Questions & Answers (MCQs) focuses on “Plastic Deformation – Concept of Crystal Geometry – 1”.

1. Crystal Structure of NaCl is ______________
a) simple cubic
b) body-centered cubic
c) face-centered cubic
d) hexagonal closed packed structure

Explanation: NaCl and LiF are the most common examples of simple cubic structure material. In this structure, all the atoms of the element are arranged in the corner of a simple cube.

2. Miller indices of any crystallographic plane are specified with three indices. A crystallographic plane is defined in terms of the length of its intercepts on three axes, measured from the origin of the coordinate axes.
a) True
b) False

Explanation: The statement, Miller indices of any crystallographic plane defined with three indices. A crystallographic plane is specified in terms of the length of its intercepts on three axes, measured from the origin of the coordinate axes is true. To simplify the crystallographic formulas, the reciprocals of these intercepts are used. They are reduced to the lowest common denominator to give the Miller indices (hkl) of the plane.

3. Find the Miller indices of the given blue plane in the diagram, given that side of the cube, is equal to 1?

a) (1,0,0)
b) (0,1,0)
c) (0,0,1)
d) (1,1,1)

Explanation: A crystallographic plane is specified in terms of the length of its intercepts on three axes. Here plane cut x-axis at 1, and y and z-axis at infinity (because it is parallel to the plane).
The intercept on axes is (1,∞,∞).
Now, take reciprocal of this (1/1,1/∞,1/∞) = (1,0,0).

4. Find the Miller indices of the given blue plane in the diagram, given that side of the cube, is equal to 1?

a) (1,1,0)
b) (1,1,0)
c) (0,0,1)
d) (1,1,1)

Explanation: A crystallographic plane is specified in terms of the length of its intercepts on three axes. Here plane cut x-axis, y and z-axis at 1.
Intercept on axes is (1,1,1).
Now take reciprocal of this (1/1,1/1,1/1) = (1,1,1).

5. Find the Miller indices of the given blue plane in the diagram, given that side of the cube, is equal to 1?

a) $$(\bar{1},0,0)$$
b) $$(0,\bar{1},0)$$
c) $$(\bar{1},0,1)$$
d) $$(0,0,1)$$

Explanation: A crystallographic plane is specified in terms of the length of its intercepts on three axes. But in this case, the plane is passing through the origin. So, in this case, we have to shift the plane in the positive z-direction by 1 unit.
So, the plane will look like this after shifting:

The plane is intersecting the x-axis at –1 and z-axis at 1. It is parallel to the y-axis. The Miller indices of the plane will be (-1,0,1) in Miller indices negative is represented by the bar over the letter.

6. The family of plane for (1,0,0) plane is denoted as __________
a) (1,0,0)
b) [1,0,0]
c) {1,0,0}
d) <1,0,0>

Explanation: The family of plane represents all the crystallographic equivalent planes for (1,0,0). These are represented by the symbol {1,0,0}.

7. Integers indicate crystallographic directions in brackets: [u v w]. Reciprocals are not used in determining directions.
a) True
b) False

Explanation: The crystallographic direction is determined by enclosing a cube around the axes, and the intercept of the line at the cube edge along given direction determine the Miller indices of line. So, reciprocal is not taken in determining direction.

8. The miller indices of the given direction is equal to ______________

a) [100]
b) [010]
c) [110]
d) [101]

Explanation: The crystallographic direction is determined by enclosing a cube around the axes, and the intercept of the line at the cube edge along given direction determine the Miller indices of line. So, along the x and Z axis, the intercept is equal to 1, and along Y-axis it is zero. So, Miller indices of the direction will be equal to [101].

9. The family of crystallographic equivalent directions for [1,0,0] is denoted as __________
a) (100)
b) [100]
c) {100}
d) <100>

Explanation: The family of direction represent all the crystallographic equivalent direction for (1,0,0). These are $$[1\bar{0}0],[01\bar{1}],[00\bar{0}],[100],[010],[001]$$ and all of these planes are represented by the symbol <100>.

10. Which of the following statement is not true considering a cubic lattice system?
a) The crystallographic plane (uvw) and crystallographic direction [uvw] are not perpendicular to each other
b) Direction [uvw] is parallel to plane (hkl), when uh+vk+wl=0
c) Direction [uvw] is perpendicular to the plane (hkl) when u=h, v=k, w=l
d) Two planes (hkl) and (abc) are perpendicular to each other if h=a, k=b, l=c

Explanation: Only for cubic lattice the crystallographic plane (uvw) and crystallographic direction [uvw] are perpendicular to each other. Two planes (hkl) and (abc) are perpendicular to each other if:
=> ha+kb+lc=0.

11. Find the angle between plane (100) and (111)?
a) 45°
b) 90°
c) 54.7°
d) 37.3°

Explanation: If planes are (h1k1L1) and (h2k2L2) then angle between than is given by:
$$cos\theta=\frac{h1h2+k1k2+l1l2}{(h1^2+k1^2l1^2)^{(1/2)}*(h2^2+k2^2l2^2)^{(1/2)}}$$
So, for (100) and (111)
=> cos ϴ = 1*1+1*0+1*0/{(12+02+02)1/2*(12+12+12)1/2}
=> cos ϴ = 1/(1*√3)
=> cos ϴ = 1/√3
=> ϴ = 54.73.

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