Engineering Quiz #2
38. 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: (2 3 1) Explanation: 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.
24. The void fraction is the ratio of unfilled volume to total volume of a structure. For ideal metallic FCC crystal, it is: a) 0.22 b) 0.26 c) 0.32 d) 0.38
Answer: 0.26 Explanation: Void fraction = 1 − packing efficiency Packing efficiency for FCC lattice is 0.74 and hence void fraction is 1 − 0.74.
15. Number of particles in primitive cubic unit cell is: a) 1 b) 2 c) 3 d) 4
Answer: 1 Explanation: In a primitive cubic cell, 8 atoms are present at the eight vertices of the cube. However, each atom is shared by eight unit cells. Hence, only one-eighth of each of the eight atoms is present in one primitive cubic cell.
33. 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: 1 1 1 Explanation: Since the opposite vertex is located at distances equal to the edge lengths along the coordinate axes.
49. In the powder method of XRD, the intensities of various bright lines are compared to determine the crystal structure. For simple cubic lattice the ratio of intensities at first two maxima are: a) 1⁄2 b) 3⁄4 c) 1⁄2 d) None of the mentioned
Answer: 1/2 Explanation: For simple cubic lattice, the intensities at subsequent maxima are in the ratio 1:2:3:4:5:6:8
21. Coordination number of HCP and FCC lattices respectively are: a) 12, 12 b) 4, 4 c) 12, 8 d) 8, 8
Answer: 12, 12 Explanation: Coordination number is the number of atoms that are in direct contact of any particular atom or it is the number of nearest neighbours.
27. The edge length of an FCC lattice is X times the atomic radius. Value of X is: a) 2 b) 2√2 c) 4/√3 d) 3/√2
Answer: 2√2 Explanation: In FCC unit cell, the atoms at face diagonal touch each other; thus diagonal is four times the atomic radius(r). Diagonal of the square faces is also equal to √ times of the edge length(a). Hence, √2a = 4r.
22. Number of particles in one unit cell of HCP lattice is: a) 1 b) 2 c) 4 d) 6
Answer: 6 Explanation: Consider the top and bottom layers. One-sixth of each of the 12(=6×2) atoms located at the vertices of the two hexagons belong to the cell. Also half of the atoms at the centre of each of the two hexagons are also part of the cell. Three more atoms are present between two hexagonal planes.
5. An octahedral void is surrounded by: a) 8 atoms b) 18 atoms c) 6 atoms d) 16 atoms
Answer: 6 atoms Explanation: An octahedral void resembles a regular octahedron with atoms situated at all the six vertices.
14. Coordination number for an ideal BCC metallic crystal is: a) 8 b) 6 c) 12 d) Varies for different metals
Answer: 8 Explanation: Consider the atom at the body center. It is touched by all the atoms present at the vertices of the cubic unit cell. We know that a cube has 8 vertices.
30. Which of the following quantities is larger in HCP as compared to FCC if the constituting atoms are similar? a) Number of particles per unit cell b) Volume per unit cell c) Mass per unit cell d) All of the mentioned
Answer: All of the mentioned Explanation: An HCP unit cell contains 6 atoms rather than only 4 present in FCC. Also, both structures are assumed to be comprised of similar atoms thus HCP being heavier. However the HCP unit cell is also larger in volume than an FCC one such that both have same packing efficiency.
47. Laue's model pictures XRD as reflection from parallel crystalline planes. Reflection is different from refraction as: a) diffraction occurs throughout the bulk b) intensity of diffracted beams is less c) diffraction in crystals occurs only at Bragg's angles d) all of the mentioned
Answer: All of the mentioned Explanation: Reflection is a surface phenomenon, and large portions of the incident waves can be reflected. Moreover, reflection can occur at any angle of incidence whereas diffraction patterns (alternative dark and bright bands) occur only at Bragg's angles.
16. In which of the following Bravais lattices none of the sides are equal? a) Triclinic b) Monoclinic c) Orthorhombic d) All of the mentioned
Answer: All of the mentioned Explanation: Each of the above mentioned lattices have all axial distances unequal. Moreover, triclinic, monoclinic, and orthorhombic lattices have none, two and all axial angles as right angles respectively.
28. Density is the ratio of mass of crystal to its volume. For a perfect FCC metallic crystal, mass of a unit cell is 4 times M0. M0 is: a) specific mass b) molar mass c) atomic mass d) none of the mentioned
Answer: Atomic mass Explanation: Mass of an ideal FCC metallic crystal unit cell is four times the atomic mass of the metal since there are four atoms per unit cell.
7. Which of the following is a crystalline solid? a) Copper wire b) Glass bottle c) Polythene bag d) Rubber ball
Answer: Copper wire Explanation: Copper wires are made of crystalline copper. In fact, most metallic objects are crystalline. However, research for large-scale production of amorphous metals is in progress.
1. Allotropes differ in which of the following properties: a) Atomic Number b) Atomic Mass c) Crystal Structure d) Electronegativity
Answer: Crystal Structure Explanation: Allotropes are different crystalline structures of the same element. Hence, they have same atomic number, atomic mass and electronegativity. For e.g., graphite and diamond are allotropes of carbon.
34. 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] ? a) AD b) CH c) FB d) GE
Answer: FB Explanation: 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.
19. Which of the following unit cells do not exist for tetragonal lattices? a) Primitive centered unit cell b) Body centered unit cell c) Face centered unit cell d) All of the mentioned exist
Answer: Face centered unit cell Explanation: Tetragonal lattices exist only in primitive and body centered unit cells. Face centered unit cells occur only for cubic and orthorhombic lattices.
40. Miller indices for perpendicular planes are always the same. a) True b) False
Answer: False Explanation: It is true only for cubic lattices. For other systems, there is no simple relationship between planes with same Miller indices.
50. K-alpha x-rays have shorter wavelengths than K-beta x-rays? a) True b) False
Answer: False Explanation: K-alpha are formed from transfer of electrons from L shell to K while K-beta result from M-to-K transition. Hence K-alpha lines have lower energy (or longer wavelength).
29. A maximum of 74% packing efficiency can be achieved for crystalline solids. a) True b) False
Answer: False Explanation: 74% is the maximum packing efficiency for pure metallic crystals. However if there are particles of two or more different sizes, greater packing efficiency is possible by filling the tetrahedral and octahedral voids.
41. X-rays have larger wavelengths than which of the following? a) Gamma rays b) Beta rays c) Microwave d) Visible light
Answer: Gamma rays Explanation: Larger wavelengths mean less energy. Only gamma rays have higher energy (or shorter wavelengths) than x-rays. Beta rays are actually stream of particles and have much less energy than x-rays.
17. Graphite is a common allotrope of Carbon. Its crystal structure is: a) Cubic b) Monoclinic c) Orthorhombic d) Hexagonal
Answer: Hexagonal Explanation: Graphite crystals consist of several planar layers of Carbon atoms arranged in interconnected hexagonal rings. Each atom makes three &sigma bonds and one &pi bond. VSEPR theory predicts a trigonal planar molecular structure with respect to each Carbon atom.
4. HCP and BCC are called close-packed structures. Close packed structures have: a) Highest packing efficiency b) Highest void fraction c) Highest density d) All of the mentioned
Answer: Highest packing efficiency Explanation: Due to largest number of particles in a unit cell, close-packed structures have highest packing efficiency and hence, lest void fraction. Density is NOT a property of the crystal structure but the substance and depends also on molar mass.
6. Which of the following is a property of amorphous solids? a) Sharp melting point b) Isotropy c) Long range order d) Definite heat of fusion
Answer: Isotropy Explanation: Due to irregularity in structure, the average of physical properties like density, thermal and electrical conductivity etc. is same along any direction for a particular amorphous solid.
25. If N is the number of tetrahedral voids in a close-packed structure, then the number of octahedral voids is: a) N/4 b) 4N c) 2N d) N/2
Answer: N/2 Explanation: Tetrahedral voids are formed when triangular voids of one close-packed layer do not overlap while octahedral ones when they overlap. The above relation is valid for both ABAB type(HCP) and ABCABC type(FCC) packing.
23. Standard axial ratio for metallic HCP lattice is 2√( 2/3). It is the ratio of a) Atomic radius to hexagon edge length b) Hexagon height length to atomic radius c) Atomic radius to hexagon height d) None of the mentioned
Answer: None of the mentioned Explanation: Ratio of height of the hexagonal unit cell to its edge length is called the axial ratio, usually expressed as (c/a).
36. 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: None of these Explanation: 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.
2. Co-ordination number of a crystalline solid is: a) Number of particles in the unit cell b) Number of nearest neighbours of a particle c) Number of octahedral voids in a unit cell d) Number of tetrahedral voids in a unit cell
Answer: Number of nearest neighbours of a particle Explanation: Coordination number of a crystal structure is the number of particles with which a given particle is in direct contact.
26. An octahedral void is present at each edge of the FCC lattice. How much of each of these voids belong to each unit cell? a) One-eighth b) One-sixth c) One-fourth d) Half
Answer: One-fourth Explanation: In a cubic lattice, each edge is shared by four adjacent cubes. Hence, the octahedral voids present at these edges are equally divided among the four cells.
13. Which of the following Bravais lattices exist as face centered unit cell? a) Orthorhombic b) Monoclinic c) Tetragonal d) None of the mentioned
Answer: Orthorhombic Explanation: Orthorhombic lattice exists as all four types of unit cells. Besides primitive cell, monoclinic lattice exists only as end centered cell while tetragonal exists only as body centered lattices.
48. In Bragg's equation [nλ = 2.d.sinθ], θ is the angle between: a) specimen surface and incident rays b) normal to specimen surface and incident rays c) parallel lattice surfaces d distance apart and incident rays d) normal to parallel lattice surfaces d distance apart and incident rays
Answer: Parallel lattice surfaces d distance apart and incident rays Explanation: In the following figure, one can easily deduce that the path difference (PQ + QR) between the two incident waves is 2.d.sinθ using simple trigonometry.
18. Which of the following lattices has the highest void fraction? a) Hexagonal close packed b) Body centered cubic c) Face centered cubic d) Primitive cubic
Answer: Primitive cubic Explanation: Void fraction = 1 − packing efficiency Since primitive cubic unit cell has least packing efficiency out of those mentioned above, hence it has highest void fraction of (1 − 0.52 = ) 0.48 or 48% .
11. Most Bravais lattice are of the type: a) Primitive unit cell b) Body centered unit cell c) End centered unit cell d) Face centered unit cell
Answer: Primitive unit cell Explanation: Out of 14 naturally occurring Bravais lattices, 7 are primitive. Remaining seven consist of 3 body centered, 2 face centered and 2 end centered unit cells.
12. In which of the following Bravais lattices, not all axial angles are right angles? a) Tetragonal b) Rhombohedral c) Orthorhombic d) Cubic
Answer: Rhombohedral Explanation: A rhombohedral is a prism whose base is shaped as a non-square rhombus. Hence two of its six faces are rhombuses while others are rectangles. This results in a geometry for which two of the axial angles are right angles but the third is not.
31. 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: The must be perpendicular to each other Explanation: 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.
42. X-ray diffraction patterns are used for studying crystal structure of solids because a) They have very high energy, hence they can penetrate through solids b) They are electromagnetic radiation, and hence do not interact with matter (crystals) c) Their wavelengths are comparable to inter-atomic distances d) Their high frequency enables rapid analysis
Answer: Their wavelengths are comparable to inter-atomic distances Explanation: For diffraction to occur, the obstacle size should be comparable to wavelength of the incident radiation.
39. 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: They are not fractions Explanation: 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.
9. Which of the following is not a property of metal glass? a) Transparent b) Poor thermal conductivity c) High magnetic susceptibility d) None of the mentioned
Answer: Transparent Explanation: Metal glass is a form of metal which like glass, is amorphous but not transparent. Most of the metal glasses are alloys, having high yield strength and high elastic strain limits. High magnetic susceptibility, low coercivity and comparatively higher electrical resistance than their crystalline counterparts make them ideal material for power transformers.
20. Most unsymmetrical Bravais lattice in terms of axial distances and angles is: a) Monoclinic b) Triclinic c) Rhombohedral d) Hexagonal
Answer: Triclinic Explanation: For triclinic lattice, none of the adjacent sides are equal in length; neither are any axial angles equal. Hydrated copper (II) sulphate and boric acid have triclinic crystals.
10. Grain boundaries are one of the causes of corrosion of metals? a) True b) False
Answer: True Explanation: Grain boundaries are the regions that separate two grains in polycrystalline metallic solids. Absence of properly defined structure results in residual stresses. Hence, grain boundaries are the weak spots in the structure and are often the site of fracture.
44. Bragg's law is not a sufficient condition for diffraction by crystalline solids. a) True b) False
Answer: True Explanation: Atoms present at non-corner positions may result in out-of-phase scattering at Bragg angles.
8. The smallest portion of a crystal which when repeated in different directions generates the entire crystal is called: a) Lattice points b) Crystal lattice c) Unit cell d) None of the mentioned
Answer: Unit cell Explanation: Unit cell is the smallest unit of a crystal which repeats itself to generate the crystal. Lattice point represents the centres of atoms in a unit cell. Crystal lattice refers to the entire structure of a crystalline solid.
32. 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 View answer
Answer: Unit cell edge lengths Explanation: 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. Packing efficiency of a crystal structure is the ratio of: a) Volume occupied by particles to total volume of unit cell b) Volume occupied by particles to that by voids c) Total volume of unit cell to volume occupied by particles d) Volume occupied by voids to that by particles
Answer: Volume occupied by particles to total volume of unit cell Explanation: Packing efficiency represents the fraction of the unit cell volume that is utilized to hold the particles.
35. 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: [1 1̅ 1̅] Explanation: 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.
37. 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: [3 0 1] Explanation: [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.
45. The Miller indices h, k, and l of parallel planes in a BCC lattice should satisfy which of the following X-ray diffraction reflection rules? a) h + k + l should be even b) h, k, and l should all be either even or odd c) h, k, and l should form Pythagoras triplet d) all planes allow reflections
Answer: h + k + l should be even Explanation: If the sum of Miller indices becomes odd for a BCC lattice, destructive interference occurs.
43. For destructive interference to take place, the path difference between the two waves should be: a) nλ b) 2nλ c) (n + 1/2)λ d) (2n + 1)λ where n is any natural number
Answer: nλ Explanation: Constructive interference occurs when the phase difference between two interfering waves is an integral multiple of 2π. Also, ratio of path difference to wavelength equals that of phase difference to 2π.
46. Minimum interplanar spacing required for Bragg's diffraction is: a) λ/4 b) λ/2 c) λ d) 2λ
Answer: λ/2 Explanation: Maximum value of incident angle can be 90° for which sine is 1. Hence d = λ/2 ( nλ = 2.d.sinθ)
