1. Phase Transformation Chapter 9

2. Shiva-Parvati, Chola Bronze Ball State University Q: How was the statue made? A: Invest casting Liquid-to-solid transformation An example of phase transformation

3. Czochralski crystal pulling technique How does one produce single crystal of Si for electronic applications?

4. Quenching of steel components a solid->solid phase transformation How does one harden a steel component?

5. Liquid solidification evaporation sublimation Solid gas melting condensation Solid state phase transformation Solid 21

6. Thermodynamic driving force for a phase transformation? Decrease in Gibbs free energy Liquid-> solid g s - g l =  g = -ve

7. g gLgL gSgS g S < g L g L < g S Liquid is stable TmTm T Gibbs free energy as a function of temperature,Problem 2.3 gLgL gSgS gg Solid is stable T freezing Fig. 9.1

8. How does solidification begins? Usually at the walls of the container Why? To be discussed later. Heterogeneous nucleation.

9. Spherical ball of solid of radius R in the middle of the liquid at a temperature below T m Homogeneous nucleation g L = free energy of liquid per unit volume g S = free energy of solid per unit volume r  g = g S - g L

10. Change in free energy of the system due to formation of the solid ball of radius r : r +ve: barrier to nucleation r r*r*  2 4r 

11. r r*r*  2 4r  Solid balls of radius r < r* cannot grow as it will lead to increase in the free energy of the system !!! Solid balls of radii r > r* will grow r* is known as the CRITICAL RADIUS OF HOMOGENEOUS NUCLEATION

12. r r*r*  2 4r  Eqn. 9.5 Eqn. 9.4

13. T g TmTm gLgL gSgS T  g (T) Eqn. 9.7 Driving force for solidification

14.  2 4r   2 4r  ff r Eqn. 9.8 Eqn. 9.7 Fig. 9.3 r1*r1* f1*f1* f2*f2* r2*r2* T1T1 T 2 <

15. 15 S V G=S+V R R* NucleationCapillary Rise Unstable EquilibriumStable Equilibrium H* S E=S+V V H Comparison of Nucleation & Capillary Rise

16. 16 NucleationCapillary Rise Driving Force Volume free energy (R 3 ) Surface energy (H) Opposing Force Surface energy (R 2 ) Volumetric gravitational potential (H 2 ) Equilibrium UnstableStable R. Prasad, “On Capillary Rise and Nucleation”, Journal of Chemical Education, Vol. 85, No. 10, October 2008, p1389

17. 17 Journal of Chemical Education, Vol. 85, No. 10, October 2008, p1389

18. 18 Nucleation is often aided by some preexisting surfaces, e.g., container walls, grain boundaries etc. Such nucleation is called HETEROGENEOUS NUCLEATION HETEROGENEOUS NUCLEATION Pepsi experiment

19. 19 Orthophosphoric Acid Demonstration Homogeneous vs. heterogeneous nucleation Cloud seeding and artificial rain Phosphoric acid, used in many soft drinks (primarily cola), has been linked to lower bone density in epidemiological studies.cola -Wikipedia

20. 20

21. Critical particle Fig. 9.4 Formation of critical nucleus by statistical fluctuation Atoms surrounding the critical particle Diffuse jump of a surrounding atom to the critical particle makes it a nucleation

22.         

23.          

24. Plot of S(  )

26. s*= no. of liquid phase atoms facing the critical sized particle  H d = activation energy for diffusive jump from liquid to the solid phase = atomic vibration frequency The rate of successful addition of an atom to a critical sized paticle Eqn. 9.10 Eqn. 9.9

27. Rate of nucleation, I, (m 3 s -1 ) With decreasing T 1. Driving force increases 2. Atomic mobility decreases = No. of nucleation events per m 3 per sec = number of critical clusters per unit volume (N*) x rate of successful addition of an atom to the critical cluster ( ’) T I TmTm

28. Growth Increase in the size of a product particle after it has nucleated T U

29. Overall Transformation Kinetics U I dX/dt T I :Nucleation rate (m -3 s -1 ) U : Growth rate (ms -1 ) Overall transformation rate (fraction trans- formed per second, s -1 ) X=fraction of product phase

30. Fraction transformed as a function of time tsts tftf X t Slow due to very few nuclei Slow due to final impingement

31. TTT Diagram for liquid-to-solid transformation T Stable liquid Under Cooled liquid crystal Crystallization begins L+  Crystallization ends dX/dt T log t X tsts tftf 0 1 TmTm C- curves

32. L+  T Stable liquid Under Cooled liquid log t TmTm TTT Diagram for liquid-to-solid transformation U I T Coarse grained crystals Fine grained crystals glass

33. T log t t s metals t s SiO 2  H d ∝ log (viscosity) Metals: high  h m, low viscosity SiO 2 : low  h m, high viscosity Silica glass Metallic glass Eqn. 9.11 Eqn. 9.8

34. Cooling rate 10 6 ºC s -1 From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002) http://Materials.Usask.Ca Melt Spinning for metallic glass ribbons

35. L+  T log t TmTm T TmTm TgTg Log (viscosity Pa-s) 12 18 crystal Stable liquid Undercooled liquid glass 30 Fig. 9.17

36. TmTm Specific volume Stable liquid Undercooled liquid Fast cool Slow cool T gs T gf crystal Fig. 9.18 T

37. log t U I T L+  T Stable liquid Undercooled liquid TmTm devitrification time T Glass ceramics nucleation growth glass Glass ceramic Liquid glass crystal Very fine crystals TUTU TITI Fig. 9.16

38. Corning’s new digital hot plates with Pyroceram TM tops. Corningware Pyroceram TM heat resistant cookware ROBAX® was heated until red- hot. Then cold water was poured on the glass ceramic from above - with NO breakage.

39. Czochralski crystal pulling technique for single crystal Si SSPL: Solid State Physics Laboratory, N. Delhi J. Czochralski, (1885-1953) Polish Metallurgist

40. A Steel Hardness Rockwell C 150.8 Wt% C Micro- structure Coarse pearlite fine pearlite bainite Tempered martensite martensite 0.8 30 45 55 65 Heat treatment Annealing normalizing austempering tempering quenching B C D E TABLE 9.2

41. HEAT TREATMENT Heating a material to a high temperature, holding it at that temperature for certain length of time followed by cooling at a specified rate is called heat treatment

42. A N AT T Q heating holding time T AnnealingFurnace coolingRC 15 NormalizingAir coolingRC 30 QuenchingWater coolingRC 65 TemperingHeating after quenchRC 55 AustemperingQuench to an inter-RC 45 mediate temp and hold

43. Eutectoid Reaction 0.80.026.67 cool Pearlite Ammount of Fe 3 C in Pearlite Red Tie Line below eutectoid temp

44. Phase diagrams do not have any information about time or rates of transformations. We need TTT diagram for austenite-> pearlite transformation

45. Stable austenite unstable austenite TTT diagram for eutectoid steel start finish

46. Stable austenite unstable austenite start finish Annealing: coarse pearlite Normalizing: fine pearlite U I T TTT diagram for eutectoid steel

47. Callister

48. Stable austenite unstable austenite start finish TTT diagram for eutectoid steel A+M M MsMs MfMf M s : Martensite start temperature M f : Martensite finish temperature  ’: martensite (M) QUENCHING Hardness R C 65 Extremely rapid, no C-curves

49. BCT Amount of martensite formed does not depend upon time, only on temperature. Atoms move only a fraction of atomic distance during the transformation: 1. Diffusionless (no long-range diffusion) 2. Shear (one-to-one correspondence between  and  ’ atoms) 3. No composition change Martensitic transformation

50. Problem 3.1 BCT unit cell of  (austenite) BCT unit cell of  ’ (martensite) 0% C (BCC)1.2 % C Contract ~ 20% Expand ~ 12% Martensitic transformation (contd.) Fig. 9.12

51. Hardness of martensite as a function of C content Wt % Carbon → 20 40 60 0.2 0.40.6 Hardness, R C Hardness of martensite depends mainly on C content and not on other alloying additions Fig. 9.13 Martensitic transformation (contd.)

52. A N AT T Q heating T

53. Heating of quenched steel below the eutectoid temperature, holding for a specified time followed by ar cooling. TEMPERING T<T E ?

54. Tempering (contd.)  +Fe 3 CPEARLITE A distribution of fine particles of Fe 3 C in  matrix known as TEMPERED MARTENSITE. Hardness more than fine pearlite, ductility more than martensite. Hardness and ductility controlled by tempering temperature and time. Higher T or t -> higher ductility, lower strength

55. Tempering Continued Callister

56. Austempering Bainite Short needles of Fe 3 C embedded in plates of ferrite

57. Problems in Quenching Quench Cracks High rate of cooling: surface cooler than interior Surface forms martensite before the interior AustenitemartensiteVolume expansion When interior transforms, the hard outer martensitic shell constrains this expansion leading to residual stresses

58. But how to shift the C-curve to higher times? Solution to Quench cracks Shift the C-curve to the right (higher times) More time at the nose Slower quenching (oil quench) can give martensite

59. By alloying All alloying elements in steel (Cr, Mn, Mo, Ni, Ti, W, V) etc shift the C-curves to the right. Exception: Co Substitutional diffusion of alloying elements is slower than the interstitial diffusion of C

60. Plain C steel Alloy steel Alloying shifts the C-curves to the right. Separate C-curves for pearlite and bainite Fig. 9.10

61. Hardenability Ability or ease of hardening a steel by formation of martensite using as slow quenching as possible Alloying elements in steels shift the C-curve to the right Alloy steels have higher hardenability than plain C steels.

62. HardnenabilityHardness Ability or ease of hardening a steel Resistance to plastic deformation as measured by indentation Only applicable to steelsApplicable to all materials Alloying additions increase the hardenability of steels but not the hardness. C increases both hardenability and hardness of steels.

63. High Speed steel Alloy steels used for cutting tools operated at high speeds Cutting at high speeds lead to excessive heating of cutting tools This is equivalent to unintended tempering of the tools leading to loss of hardness and cutting edge Alloying by W gives fine distribution of hard WC particles which counters this reduction in hardness: such steels are known as high speed steels.

64.   +   : solid solution of Cu in FCC Al  : intermetallic compound CuAl 2 4 T solvus  supersaturated  saturated +  FCC Tetragonal 4 wt%Cu0.5 wt%Cu54 wt%Cu Precipitation of  in 

65. Stable  unstable  T solvus As- quench ed   start  finsh  +  Aging TTT diagram of precipitation of  in  A fine distribution of  precipitates in  matrix causes hardening Completion of precipitation corresponds to peak hardness

66.  -grains As quenched  -grains +  AgedPeak aged Dense distribution of fine  overaged Sparse distribution of coarse  Driving force for coarsening  /  interfacial energy

67. 0.1 1 10100 hardness Aging time (days) 180ºC 100ºC 20ºC Aging temperature Peak hardness is less at higher aging temperature Peak hardness is obtained in shorter time at higher aging temperature Fig. 9.15

68. U I T Stable  unstable  As- quenched   start  finsh  +  Aging T solvus 1 hardness 180ºC 100ºC 20ºC 100 ºC 180 ºC

69. Recovery, Recrystallization and grain growth Following slides are courtsey Prof. S.K Gupta (SKG) Or Prof. Anandh Subramaniam (AS)

70. Cold work ↑ dislocation density ↑ point defect density Plastic deformation in the temperature range above(0.3 – 0.5) T m → COLD WORK  Point defects and dislocations have strain energy associated with them  (1 -10) % of the energy expended in plastic deformation is stored in the form of strain energy AS

71. Cold work ↑ Hardness ↑ Strength ↑ Electrical resistance ↓ Ductility AS

72. Cold work Anneal Recrystallization Recovery Grain growth AS

73. Recovery, Recrystallization and Grain Growth During recovery 1. Point Defects come to Equilibrium 2. Dislocations of opposite sign lying on a slip plane annihilate each other (This does not lead to substantial decrease in the dislocation density) SKG

74. POLYGONIZATION Bent crystal Low angle grain boundaries Polygonization AS

75. Recrystallization Strained grains Strain-free grains Driving force for the Process = Stored strain energy of dislocations SKG

76. Recrystallization Temperature: Temperature at which the 50% of the cold-worked material recrystallizes in one hour Usually around 0.4 T m (m.p in K) SKG

77. Factors that affect the recrystallization temperature: 1. Degree of cold work 2. Initial Grain Size 3. Temperature of cold working 4. Purity or composition of metal Solute Drag Effect Pinning Action of Second Phase Particle SKG

78. Solute Drag Effect SKG

79. Grain Boundary Pinning SKG

80. Grain Growth Increase in average grain size following recrystallization Driving Force reduction in grain boundary energy Impurities retard the process SKG

81. Grain growth  Globally ► Driven by reduction in grain boundary energy  Locally ► Driven by bond maximization (coordination number maximization) AS

82. Bonded to 4 atoms Bonded to 3 atoms Direction of grain boundary migration Boundary moves towards its centre of curvature JUMP AS

83. Hot Work and Cold Work  Hot Work  Plastic deformation above T Recrystallization  Cold Work  Plastic deformation below T Recrystallization Cold Work Hot Work Recrystallization temperature (~ 0.4 T m ) AS

84. Cold work Recovery Recrystallization Grain growth Tensile strength Ductility Electical conductivity Internal stress Fig. 9.19 %CW Annealing Temperature AS