# Physical Metallurgy

1. Write down the list of all crystal systems, geometrical conditions and symmetry conditions

2. What is the difference between crystal systems and crystal structure?

3. What is the difference between a unit cell and Bravais Lattice?

4. Why there are only 12 Bravais lattices? Why not 28? Why there is no base centered simple cubic lattice?

5. How are crystal systems defined on the basis of symmetry?

6. What is a primitive unit cell?

7. How to calculate Miller Indices in HCP (plane and direction)? (How to transform four axes system to three axes system)

8. How does an ABCABC stacking result in FCC structure?

9. What is a closed packed structure?

10. Prove c/a in hcp is 1.633

11. Find out packing fraction in case of BCC, HCP

12. What does the U-r curve show? How does it relate to the band gap in semiconductors? What happens to the U-r curve at higher temperatures?

13. How to calculate density when lattice parameter is given? Derive the relation. Explain Z-factor

14. How can thermal expansion be explained using the U-r curve? [Hint: mean inter-ionic distance]1

15. How does the shape of this curve for a given material relate to its coefficient of thermal expansion? (What will be the shape for lower CTE?)

16. Why are d-block elements called transition elements? (Hint: Write down the electronic configuration of Ca and Ga and see their position in the periodic table)

17. What is the difference between BCC and CsCl crystal structures?

18. What is anisotropy? Why is wood easier to cut along the grain than against it?

19. Why can’t a crystal have a 5-fold axis of symmetry? For what values of ‘n’ do crystals show n-fold symmetry?

20. What are point groups and space groups?

21. What is the radius ratio of void to atom for a tetrahedral and octahedral void in FCC? How is it different for BCC?

22. What is the location of voids in FCC, BCC?

23. Calculate structure factor. What are the different h,k,l conditions for identifying the crystal structure?2

24. How can you distinguish the XRD patterns for BCC and FCC based on spacing of peaks? (2 close peaks followed by a third for FCC, equally spaced peaks for BCC)

25. Show undercooling and recalescence on a Temperature vs. Time plot for solidification of a metal

26. Draw cooling curves for pure metal, alloy, hypoeutectoid, hyper-eutectoid, eutectic, eutectoid compositions

27. How do curves for with and without inoculation differ?

28. How can latent heat of fusion be explained in terms of potential energy of atoms?

29. How does varying concentration, cooling rate, undercooling bring variations in the microstructure?

30. What is the condition for nucleation?

31. Draw G, H, S with varying T in one plot? Do they start from the same point on y-axis or not? If yes or no, why?

32. How do cooling curves help in creating phase diagrams?

33. What is Richard’s Rule? What is Turnbull’s approximation?

34. Why does the T vs t curve for binary phase diagram open downwards? What affects this curvature? [Hint: Newton’s Law of Cooling?]

35. Draw the cooling curves for eutectic phase diagram at three different points (hyper, eutectoid, hypo)

36. What are sites for heterogeneous nucleation to occur? (inclusion, grain boundaries, dislocation, stacking faults)

37. How is strain energy stored by a system undergoing deformation?

38. Why does strain energy increase during solidification (nucleation)? Why is this negligible? [liquid melt can flow to accommodate volume change)

39. What are the maximum heterogeneous nucleation temperature and the homogeneous nucleation temperature? [Hint: Melting Point and Freezing Point of pure substance]

40. Derive Free Energy Change on Nucleation. Using the expression, show why undercooling is necessary for nucleation to take place during solidification. Justify why the shape of nuclei is assumed to be a sphere. Assuming isotropic interfacial energy, determine critical radius of the nuclei.

41. What equation governs the kinetics of nucleation?

42. Plot the variation of G against number of vacancies. Explain the thermodynamic cause of defects. Justify the trend of the plot (first G decreases then increases - why?)

43. Why point defects are equilibrium defects?

44. Why does having defects make a crystal more stable? (until a certain point after which G increases)

45. Derive the relation between ‘n’ (intrinsic defect concentration/ number of vacancies), ΔG and T from the above concept.3

46. What will be the nature of stress (tensile/compressive) in the extra half plane region?

47. Why dislocations cannot end inside the crystal? Are dislocations equilibrium defects? (Answer: As you may have probably guessed - No)

48. Why do dislocations form loops? What keeps dislocations loops stable?

49. Why slip happens only on closed packed planes?

50. Calculate stress fields in case of a hollow cylinder with radial and tangential displacement. How do these relate to stresses in case of edge and screw dislocations?

51. Why is climb non-conservative? (Hint: Just show how dislocation climb takes place because of vacancies)

52. Why does addition of salt to snow help clear it from the roads in cold countries? What is the difference between melting point and freezing point?

53. How to plot free energy curve when A and B mix? Why does $\Delta G_{mix}$ open upwards? (i.e. why is the curve ‘U-type’ ?)

54. Why must the chemical potentials of a component be the same across phases for equilibrium?

55. How does the common tangent rule work for multiphase systems?

56. What is the free energy at constant P and T condition? What if P, T are not constant?

57. Why does recrystallisation lead to an increase in hardness?

58. What is the driving force for recrystallisation? How is recrystallisation temperature normally defined?

59. What factors affect the recrystallisation temperature?4

60. How do segregations affect the recrystallisation temperature?

61. In the case of Aluminium, grain size refinement is not done via cold working. Why? 5

62. If the temperature is continuously increased, will the grain size keep increasing? What is the limiting grain size? What does it depend on?

63. Why does electrical resistance increase during recovery?

64. Why is the hardness of martensite more than that of austenite?6

65. What is the most general form of Fick’s first “law”?

66. Why is Diffusivity a tensor?

67. How can Fick’s “second law” be derived from the first law?

68. What is the difference between gradient and divergence? How can it be shown visually?

69. How does nucleation happen during spinodal decomposition?7 Why not?

70. At what speed do the lens shaped regions shear during martensitic transformation?

71. In other systems, martensite is not hard and brittle, but it is so in Fe-C system. Why?

72. Why does shearing in martensite occur in lenticular regions? Why not spherical? Show how distortion creates new crystallographic arrangement.

73. Martensitic transformations are reversible geometrically but not thermodynamically. Why?

74. Why do carbides precipitate during tempering of martensite?

75. Will spinodal decomposition occur if the second derivative in G-X curve is positive?

76. In solid state transformation, what additional terms come into the picture?8

77. How is the kinetics of nucleation determined?

78. What are the two causes of precipitation hardening? (Orowan Bowing and Precipitate shearing)

79. What is the driving force for Ostwald ripening? How can this be shown using free energy curves?

80. Why solution treatment should be done at a temperature just below the eutectic temperature and not above it?

81. Will a lower precipitation temperature lead to higher hardness and strength? Why?

82. Why does the material softening with time? Does this lead to a decrease in strength?

83. Why does hardness increase with increasing concentration of Cu in Al-Cu alloys?

84. Explain precipitation hardening in Al-Cu alloys using free energy curves. Show the phase diagram with the metastable phases.

85. How do the contours around an edge dislocation look like? How does this lead to alignment of dislocations as low angle grain boundaries?

86. Explain how stress cores due to dislocations play a role in strain ageing?

87. Why do partial dislocation tend to pull towards one another?

88. A stacking fault acting like surface tension, tries to close the fault due to attraction, but this does not happen. Why?

89. What is the driving force for spheroidisation?

90. Why do martensitic transformation show twins in their microstructure?

91. Why are martensitic transformations athermal? What does this mean?

92. What are the different morphologies of martensite? What are the conditions in which they form?

93. Why does $M_{s}$ temperature decrease with increasing percentage of Carbon?

94. What is the difference between martempering and tempering?

95. Why do carbon atoms move to dislocation sites in first stage of tempering?

96. What is the basic difference in how pure metals grow versus how alloys grow during solidification?9

97. What does the rank of a tensor describe?

98. In Zone Refining, what keeps the molten liquid from falling out?

99. Will the critical radius (r*) change in heterogenous nucleation due to contact angle? Why not?

100. Where do the bubbles in a bottle of carbonated water originate? Why do crevices have a lower activation energy?

101. Why is AgCl added to promote rainfall via seedling? How does the process work?

102. Why does dendritic growth happen? What is the critical temperature gradient for which growth happens?

103. How does the solidification defer for a pure metal vs. for an alloy? Draw the section of the microstructure of an ingot for both cases.

104. How can solidification be represented mathematically? How can this representation explain segregation and zone refining?

105. What are the assumptions when computing the concentration as a function of fraction solidified and partition coefficient?

106. What is partitioning coefficient? Under what assumptions does can it be used?

107. Show how the purity increases with successive passes during zone refining

108. On what factors does the interlamellar spacing depend?

109. Why peritectic reactions usually never go to 100% completion? What is surrounding?

110. In eutectoid solidification, show how the liquid gives B atoms in the correct proportion to alpha and beta resulting in coupled growth.

111. Calculate the equation that gives the concentration of point defects as a function of temperature

112. If e/a increases on addition of solute, solubility increases. Why?

113. How are Kirkendall effect and porosity creation related?

114. What is the difference between a regular and a sub-regular solution model?

### Footnotes

1. Another way to think about it is when a metal bar expands upon heating, how can you explain the volume increase when no additional metal is added?

2. Refer to Anand Subramaniam’s slides on structure factor derivation

3. Refer to Anandh Subramaniam’s slides on defect concentration

4. Purity, prior cold work, prior grain size

5. Aluminium has high surface energy. Hence recovery and recrystallisation being competing processes, the refinement from recrystallisation is less. Hence, grain size refinement is done using inoculants

6. Geometry and Stresses

7. It does not.

8. Strain energy and grain boundary area terms

9. Dendritic growth