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1. Which of the following is not true for crystallographic axes?
a) They must be parallel to the edges of the unit cell
b) They must be perpendicular to each other
c) They must originate at one of the vertices of the cell
d) They form a right-handed co-ordinate system

Answer: b [Reason:] The axes must be parallel to the edges of the unit cell, which in case of some crystal systems like monoclinic, hexagonal etc. are not mutually perpendicular.

2. The point coordinate indices q, r, and s are multiples of:
a) Unit cell edge lengths
b) Distance between nearest neighbours
c) Cosine of angles between unit cell edges
d) None of the mentioned

Answer: a [Reason:] Point coordinate indices are the fractions which when multiplied by the corresponding unit cell edge lengths, provide the location of a given point in the crystallographic coordinate system.

3. The point coordinates of the vertex just opposite to the origin are
a) 0 0 0
b) 0 0 1
c) 0 1 1
d) 1 1 1

Answer: d [Reason:] Since the opposite vertex is located at distances equal to the edge lengths along the coordinate axes.

4. If x, y, and z are three positive axes of the crystallographic coordinate system with origin at point A, then which line points in the direction [1 0 1̅] ? b) CH
c) FB
d) GE

Answer: c [Reason:] Moving 1 unit along positive x-axis, 0 units along positive y-axis, 1 unit along negative z-axis points in a direction parallel to line FB.

5. In the following diagram, what is the direction cosine of the line EB? a) [1 1̅ 1̅]
b) [1̅ 1̅ 1̅]
c) [1 1 1]
d) [1 0 0]

Answer: a [Reason:] One can reach from point E to B by traversing 1 unit along each of positive x, negative y, and negative z-axis, where one unit along any axis equals the corresponding edge length.

6. In cubic crystals, crystallographic directions are arranged in families. Which of the following directions does not belong to the family <110> ?
a) [1 0 1]
b) [1̅ 1 0]
c) [1̅ 0 1̅]
d) None of these

Answer: d [Reason:] Since the cubic lattice is symmetrical about all the three axes, the above directions are equivalent irrespective of order & sign and are part of same direction family.

7. Convert [2 1̅ 1̅ 1] from four-index system to three-index system.
a) [2 1 0]
b) [3 0 1]
c) [1̅ 1̅ 1]
d) [1̅ 2 1]

Answer: b [Reason:] [u v t w] can be converted to [U V W] using the formulae: i) U = 2u+v ii) V = 2v+u iii) W = w. Four-index systems are generally used for hexagonal lattices.

8. Miller indices of the hatched plane in the following figure are: a) (2 3 1)
b) (3 2 1)
c) (3 2 0)
d) (1 1 1)

Answer: a [Reason:] If a plane intercepts the coordinate axes at distances A, B, and C from the origin, then Miller indices are given by multiplying (a/A b/B c/C) by a suitable factor so as to obtain integers.

9. Which of the following is a property of Miller indices?
a) They uniquely identify a plane
b) They are always positive
c) They are not fractions
d) None of the mentioned

Answer: c [Reason:] Two or more planes can have same Miller indices which can be negative, zero or positive depending on the intercept on the axes. If the ratios of intercepts to lattice constants come out be fractional, then they are scaled to lowest integers to be represented as Miller indices.

10. Miller indices for perpendicular planes are always the same.
a) True
b) False