# Metallurgical Thermodynamics

1. Why is Gibbs Free energy used instead of Helmholtz Free Energy as condition for equilibrium?

2. Why Q (heat) at constant temperature is H (enthalpy)?

3. In condensed systems, why is H approximately equal to U?

4. Why Entropy goes to zero at 0K? (Entropy comes from Heat capacity which comes from vibrations)1

5. Why entropy always increases with increasing temperature? (Since $\frac{dS}{dT} = \frac{C_{p}}{T}$ )

6. Why $\frac{dS}{dT}$ will always be positive? Why does it decrease with increasing T?

7. Show a perfectly ordered material will have a zero configurational entropy

8. Plot $C_{p}$ vs. T, H vs. T and S vs. T

9. Draw G vs. T curve. How do you decide its curvature?

10. Draw a G vs. T plot showing the curves for solid, liquid and gas on the same plot. How will their curvatures vary?

11. Draw a G vs. P plot showing the curves for solid, liquid and gas on the same plot. How will their curvatures vary?

12. Why $H_{liquid}$ is greater than $H_{solid}$ ? ($C_{p}$ is higher due to higher vibrations)

13. Why Enthalpy or Entropy cannot be used as a stability criterion?

14. What are the assumptions when deriving $\Delta G_{mix}$ for ideal solution? Is thermal entropy factored?

15. What is the assumptions regarding $\Delta H_{mix}$ when deriving $\Delta G_{mix}$ for regular solution? Is it valid for large values of $\Delta H_{mix}$?

16. Will entropy always be zero at 0K? (True only for thermal entropy not configurational)

17. How do H, S and G vary with increasing temperature? (First two increase, last one decreases)

18. Among solid, liquid, gas which has a higher $C_{p}$ and thus a higher H?

19. What is the effect of crystal structure of inoculants on surface energy term of nucleation?

20. How is 0001 hcp plane similar to the 111 fcc plane?

21. How are phase diagrams drawn using cooling curves?

22. Why is there is no shrinkage in case of grey cast iron? (Lower density of graphite)

23. Why is there a linear section in a T vs. t curve? (latent heat)

24. How is the cooling curve of a eutectic composition different from one at a hyper-eutectic composition?

25. How is the cooling curve for a eutectic composition similar to that of a pure metal?

26. How to calculate time required for cooling if enthalpy change of fusion and heat extraction rate are given? 2

27. How can Clausius Clapeyron equation be used for approximating vapour pressure of a gas at different temperatures?

28. Apply Clausius-Clapeyron equation to verify the sign of slopes in the phase diagrams of pure iron and water. Also find out invariant points in these phase diagrams

29. How can Clausius Clapeyron equation be derived from Gibbs Duhem equation?

30. How is Clausius Clapeyron equation used in secondary steel making?

31. What happens to melting point on increasing pressure? Why? Explain why a pressure cooker works using this idea

32. Find out slopes of the phase diagram of water. Apply Clausius Clapeyron equation. How does the equation predict the change in melting point in varying conditions?

33. Draw the phase diagram of $H_{2}O$ and show how the slopes will change during transformation if we increase pressure.

34. What are the models used to calculate $\Delta H_{mix}$ in non-ideal solutions? What determines the sign of 𝛀 in the model?

35. What happens in a phase diagram if the attraction is present i.e. $\Omega$ is negative? (Compounds, Inter-metallic Compounds)

36. What happens in a phase diagram if the attraction is present i.e. $\Omega$ is positive? (Miscibility Gaps)

37. How does congruent melting appear in a phase diagram? What determines the shape of such a phase diagram i.e. in which cases does the inversion happen in such phase diagrams?

38. If the higher temperature portion of the phase diagram opens downward, what type of behaviour will be observed at lower temperatures? Will there be phase separation or ordering?

39. Cu accepts Zn, but Zn does not accept Cu. How is this justified? (Valency factor, Hume Rothery rules, metallic bond accepts an increase in e/a ratio but not a decrease)

40. What does a higher melting point imply regarding the strength of the bonds?

41. What gap in understanding does a sub-regular model fill? What is the expression for the sub-regular model? What if $\Omega_{A}$ = $\Omega_{B}$ (The miscibility of A in B will not be same throughout the phase diagram)

42. What will be the signs of $\Delta H_{mix}$ and $\Delta S_{mix}$? How do the signs vary?

43. How will the G-X curve change when $\Delta H_{mix}$ is non-zero? Plot G-X curve for $\Omega$ < 0 and $\Omega$ > 0 cases and compare. What is the final expression for G?

44. Why does the Free Energy curve make a W like pattern and not an M like pattern? How can this be explained physically? Why will the $\Delta S_{mix}$ term dominate at low temperatures leading to a W type curve?

45. If you add a small amount of A to B, free energy can never increase. Why? How does this explain the difficulty in purifying a metal?

46. If you draw a G-X curve for Mg-Si system, it will have two lines which intersect. What do the endpoints of these lines represent? (Hint: Think in terms of crystal structure)

47. How is chemical potential different from partial molar free energy? 3

48. How is equilibrium defined using chemical potential? Show equivalence between the different relations used for expressing Gibbs Free Energy. Show how activity gradient becomes zero in such a case.

49. Derive the condition for equilibrium using common tangent rule i.e. $\mu_{A}^{\alpha}=\mu_{A}^{\beta}$

50. Derive Stirling's Approximation

51. Explain uphill diffusion using the example of Steel and Cast Iron+Si. How does this extend to carbide formers? Discuss activity gradient in this case.

52. How will the G-X curve look like in case of uphill diffusion?

53. Is concentration gradient absolutely useful in determining the direction of diffusion? Why not?

54. In how many ways can you define or categorically show eutectic transformation?4 (Liquid becomes solid, invariant reaction, melting point decreases, difference in miscibility in liquid and solid states)

55. How does $\Omega$ relate to miscibility? Will $\Omega_{solid}$ be the same as $\Omega_{liquid}$ in case of a eutectic transformation?

56. How does $\Omega_{solid}$ and $\Omega_{liquid}$ look like in the case of isomorphous phase diagrams? Are they almost equal?

57. If $\Omega_{solid}$ = 0 and $\Omega_{liquid}$ < 0 what will the phase diagram look like? What will the reverse case look like? What is this phenomena called?5

58. What if $\Omega_{solid}$ > 0 and $\Omega_{liquid}$ = 0? What happens to the size of the miscibility gap with increasing $\Omega_{solid}$ ?

59. BCC can take in more strain but not FCC? How does this depend on packing and strain? Explain solubility of C in $\alpha$-Fe vs. that in $\gamma$-Fe

60. Explain why there cannot be an isomorphous phase diagram for an interstitial solid solution.

61. How are $\Omega$ and size factor related? How are size factor and miscibility gap related?

62. How does a eutectic phase diagram evolve from isomorphous system by merging of the miscibility gap with the liquidus line?6

63. Draw generic eutectic, peritectic, monotectic and synthetic phase diagrams

64. Take different case for variation of values of $\Omega_{solid}$ and $\Omega_{liquid}$ and show how the phase diagram evolves

65. How does free energy curve change with variation in Ω? (For $\Omega$ > 0 and $\Omega$ < 0)

66. Draw free energy curve at a temperature such that it cuts through the miscibility gap at binodal points. How do $α_{1}$ and $α_{2}$ precipitate?

67. How to convert from atomic % to weight % ? How much weight % of Fe is present in $Fe_{3}C$?

68. Why is the free energy of $Fe_{3}C$ represented by a point on the G vs. X plot?

69. What happens when %C increased? Does it become more Brittle/Ductile? Why?

70. Why do steels weld easily when their carbon content is low?

71. Draw free energy curves as a function of temperature to show transitions between alpha, gamma and delta iron

72. When you say liquid has been undercooled to T what does it say about the solidification of the liquid? Has the solidification started? When undercooled is the cooling rate higher or lower than equilibrium cooling?

73. What is $T_{o}$ curve? Why is there a zero in the subscript? What does it signify7?

74. How to calculate $\Delta T_{N}$ which is the temperature gradient for heterogeneous nucleation? (Refer Turnbull8, Nucleation, Reed-Hill)

75. Why does the TTT diagram have a ‘C’ shape? What are the two factors that affect nucleation?9 Show how the curvature comes in as the undercooling is increased. Compare this with S-curves or Avrami kinetics models.

76. What phase comes out in tempering of martensite?10

77. When we say that a higher undercooling leads to smaller sized grains, what is the assumptions we are taking?11 What mechanism dominates in the lower half of the C-curve?

78. What is the difference between tie line and lever rule?

79. If G vs. X diagram is plotted at $T=T_{eutectic}$ and then the temperature is increased, how will the curves move? Will they move up or down? Which will move faster? Will the move at the same rate?

80. Explain how coring occurs during cooling?

81. Why do S, H and V when plotted as a function of T show a step?

82. How is glass formation explained using $T_{o}$ curves? How is it related to viscosity variation with temperature?

83. In a eutectic formation, the grain boundaries are technically called analogous to grain boundaries?12

84. How do you differentiate between steels and cast irons? What is so sacrosanct about the 2% as a differentiator? How is easy castability related to a eutectic?

85. Show eutectics in an Al-Si phase diagram. Where are these used widely?

86. If you add sand to Al liquid while it is nucleating, will it lead to effective heterogeneous nucleation?13

87. What are examples of eutectics which form lamellae in their microstructure?

88. Why TiB2 acts as good nucleating agent in case of Al? Which plane of fcc and hcp are similar?14 Why? Is lattice parameter also important apart from crystal structure?

89. What decides if alpha or beta nucleates first in case of solidification of a eutectic?15 What factors decide whether you get lamellar structure or embedded structure? Is structure important?

90. Why do grain boundaries look black? Why are they visible distinctly after etching?

91. The closest packed plane will have the highest surface energy. Why?

92. Does phase diagram give you weight fraction or volume fraction?

93. How can peritectic transformation be explained as a summation of two different eutectic transformations? Why is a peritectic transformation slower than a eutectic one?16 Why does a peritectic transformation slow down with time?

94. How do you define solidus and liquidus in a phase diagram? Show the solidus in eutectic and peritectic systems.

95. Why can the curvature of the solvous line in a typical eutectic phase diagram NOT be opening up?

96. Draw an $Fe-Fe_{3}C$ phase diagram to scale

97. In case of Fe-Carbon (Graphite) diagram, the eutectoids shift. Why? Why don't the other lines change?

98. In a plot of G vs. T if bulk material is replaced by nano-particle what will happen to the intersection of solid and liquid G curves?

99. What are the different types of solid state transformation?17

100. If beta precipitates out of alpha on solidification, where will the nucleation occur?18 Why does it start especially at the junctions? In what order will the tendency of nucleation be amongst surface, tri-junctions, grain boundaries, stacking fault, dislocation and vacancies? Why is this order in this particular fashion?

101. What is the driving force and activation barrier in case of precipitation?19

102. What is the additional barrier in case of solid state transformation?20 When strain energy is considered, how does the r* value change?

103. How can you show $\Delta$G on a G vs. T curve? What about a G vs. X curve?

104. Why are GP Zones important when we talk about precipitation at lower temperature? How can formation of GP Zones be explained using the high interfacial energy for FCC to orthorhombic transformation in case of Al-Cu system?

105. Show how Cu rich clusters become GP Zones. What is the driving force for this transformation. Why does not alpha easily transform into theta phase?

106. What is the simplest way to understand strain energy?21 In which case will it be higher: sphere, cuboid or needlelike?

107. How does incoherency between precipitate and matrix help create misfit dislocations?

108. What is the Ostwald Step Rule that is seen in transformation of alpha to theta via GP Zones, $\theta$’’, $\theta$’ and finally to $\theta$ ? Why does this happen?

109. What will be the free energy curve for GP Zones? Will the free energy curve be different for the same crystal structure?

110. What is the condition for precipitation to occur? What should the composition be? For a fixed composition at what temperatures will the precipitation take place?22

111. Why is maximum hardness shown in some region between $\theta$’’ and $\theta$’?

112. What is the relation between coherence and strength? How does the size of precipitates influence the hardness? How does this explain the shape of the Hardness vs. time curve?

113. What happens to the curve at higher temperatures? Will the peak be now reached at a lesser time or more time? What will happen to the peak height at higher temperatures?

114. As temperature is increased will the amount of precipitates increase or decrease?

115. For a given alloy composition, how will you calculate the driving force for nucleation of a particular phase?

116. How are crystals, quasi-crystals and amorphous materials distinguished on the basis of symmetry?

117. How does G vary with the size of precipitate? Will smaller sized precipitate have a higher G? Why?

118. How can the decomposition be explained using a waveform like system? How does this relate to uphill diffusion?

119. Draw a phase diagram with a miscibility gap. Then draw G vs. X for a particular temperature that cuts through the miscibility gap. At that temperature, then draw the G’ vs. X and G’’ vs. X curves. (where ‘ and ‘’ are first and second derivatives respectively) Using these curves, show the position of spinodal points. What is the significance of these points? What is the shape of the G vs. X curve between these points?

120. Show how the spinodal curve is drawn using the binodal and spinodal points at different temperatures

121. Why can XRD be used to identify miscibility gaps? What do the peaks for $\alpha_{1}$ and $\alpha_{2}$ look like? Why does the splitting of peaks take place? How to identify crystal structure based on groupings of peaks?

122. How does $\alpha_{1}$ precipitate out of $\alpha_{2}$ when we consider an alloy composition such that it lies within the miscibility curve but outside the spinodal region?

123. What is the mechanism of decomposition when we consider an alloy composition such that it lies within the spinodal region?

124. What is the coherent spinodal? How is it different from the chemical spinodal?

125. Why is the burger’s vector in ordered structure greater than in disordered structures?

126. Why is the free energy requirement for transformations involving transient phases (eg. GP Zone formation) lower than eutectoid transformations?

127. Why does Co decrease hardenability? Why does the TTT curve shift to the right? When an alloy dissolves into austenite why does the curve shift to the right? What happens to the diffusivities in such cases?

128. What are non-lamellar ferrite-cementite mixtures called?23

129. What will nucleate first in a eutectoid transformation? Why?

130. How is the shifting of TTT determined by considering if the alloy element dissolves or does not dissolve in austenite?

131. How does upper bainite form from a austenite-austenite interface? What is the role of diffusion here? Why does the acicular nature of bainite come into the picture?

132. At eutectoid composition, what will be the differences in microstructure of annealed sample vs. normalized sample?

133. Will you get pearlite+martensite in the lower part of the C-curve? Why not?24

134. Why is $A_{cm}$ line steeper than $A_{3}$ line?

135. Why can perlite not transform into martensite?

136. What are the habit planes in Bainite?

137. If you increase carbon content where will the C-curve shift? What if % C is > 0.8? Why will the shift not be significant?

138. In Eutectoid transformation, how does parent phase selectively supply atoms to alpha and beta such that coupled growth takes place? How is this linked to Diffusion? How does the growth rate vary with the degree of undercooling?

139. What is the role of having a curve for proeutectoid phase in a TTT diagram?

140. How do austenite and ferrite stabilizers work?

141. In Al-Cu precipitation, the discs do not grow along the coherent sides (faces) but along the incoherent sides (edges). Why?25

142. How does the difference in growth velocities of coherent and incoherent surfaces lead to widmanstatten structures?

143. What are the essential conditions to choose a unit cell?26

144. When FCC becomes BCT, what is the c/a ratio? Show how this is calculated.

145. What happens to c/a ratio with increasing carbon content? Does it increase? Why?

146. When austenite is cooled to get ferrite, in-principle how does the transformation happen?27 How do the atoms move from face centered positions to body centred positions? How does martensite increase the strength in steels?

147. Will FCC and BCC unit cells have the symmetry?28

148. On what factors does the M~s~ temperature depend?29

149. What is the influence of stresses on martensite formation? What is an example of stress induced martensitic transformations?

150. What is the influence of stresses on Free Energy of a system?

151. How can systems be classified on the basis of order?

152. Assuming regular solution model, find out the temperature at which the miscibility in an isomorphous phase diagram closes.

153. Assuming regular solution model, find out the temperature at which an equilibrium exists between order-disorder transition.

154. How do you determine the solubility when the Gibbs Free Energy is given as a function? Can this be used to determine the solvus line? How?

155. How is the degree of ordering or clustering determined?

### Footnotes

1. Thermal Entropy, of course.

2. $time = \frac{\Delta H}{(\frac{dQ}{dt})}$

3. Trick question! Both are the same

4. In other words, what are the distinct features/characteristics of a eutectic reaction?

5. Congruent melting

6. You get a peritectic when melting points of A and B have a large difference

7. Tendency to undergo partitionless solidification

8. Turnbull is the ‘Father of Undercooling’

9. Change in Free Energy and Diffusivity

10. epsilon-carbide

11. That the temperature range is in the upper half of the C curve and diffusion component is constant

12. Grain boundaries are for a single phase, these are eutectic colonies

13. No, structural compatibility is important too

14. [111] of FCC and basal plane of Al

15. Interfacial energies of alpha-beta, alpha-liquid and beta-liquid

16. Diffusion

17. Based on Diffusion and long/short range order

18. Grain Boundaries

19. Gibbs Free Energy and Interfacial Energy

20. Strain energy

21. Compatibility of the precipitate with the matrix

22. Below solvus temperature

23. Spheroidite, Bainite

24. Difference is in what nucleates first - cementite in upper region and alpha in lower regions

25. Diffusion of course

26. Highest symmetry, lowest lattice points

27. Short range diffusion

28. Trick question! Symmetry is for crystal systems not unit cells

29. Carbon content, initial grain size