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Phase Diagram

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Phase Diagram

  1. 1. Phase Diagrams Group 10
  2. 2. Introduction-Topics to be covered • • • • • • • Phase Diagrams Gibbs Phase Rule Binary phase diagrams Equilibrium Solidification Non-equilibrium solidification Fe-C Alloy Phase diagrams Intermediate Phases and reactions
  3. 3. Introduction-Topics to be covered • Development of Microstructure • Cu-Zn Phase Diagram • Stability of Hume-Rothery Phases in Cu-Zn alloys • Isothermal Transformation Diagram • Transformation Rate diagram
  4. 4. Phase Diagrams • A phase diagram is a type of chart used to show conditions at which thermodynamic distinct phases can occur at equilibrium. • It conveniently and concisely displays the control of phase structure of a particular system. • The three controllable parameters that will affect phase structure are temperature, pressure, and composition. Temperature-Composition phase diagram Pressure-Temperature phase diagram
  5. 5. Significance • To show phases are present at different compositions and temperatures under slow cooling (equilibrium) conditions. • To indicate equilibrium solid solubility of one element/compound in another. • To indicate temperature at which an alloy starts to solidify and the range of solidification. • To indicate the temperature at which different phases start to melt. • Amount of each phase in a two-phase mixture can be obtained. Classification • Phase diagrams are classified based on the number of components in the system Single component systems have unary diagrams. Two-component systems have binary diagrams and so on..
  6. 6. Examples Cu-Ni phase diagram Temperature- Composition Binary isomorphous diagram CO2 phase diagram Pressure-Temperature Unary diagram
  7. 7. Gibbs Phase Rule • A thermodynamic law which governs the conditions for phase equilibrium. • Useful in interpreting Phase Diagrams. P+F=C+N
  8. 8. Phase Diagram of CO2
  9. 9. Lever rule • Used to find the composition of phases. • Ws = Wo-Wl Ws-Wl • Wl = Ws-Wo Ws-Wl
  10. 10. For eutectic systems Wl = Wo-W1 W2-W1 Wα = W2-W0 W2-W1
  11. 11. Binary Phase Diagrams • A common phase diagram in which pressure is held constant whereas temperature and composition are kept variable parameters. • They represent the relationships between temperatures and compositions of phases at the equilibrium. • A common example for a binary isomorphous alloy is Cu-Ni system.
  12. 12. Equilibrium solidification Reference: William Callister - Materials Science and Engineering - An Introduction 7 edition Wiley figure 9.4
  13. 13. Non-equilibrium solidification In practical situations diffusion is not as slow to allow the readjustments in diffusion while maintaining the equilibrium. Its consequences? ● Segregation occurs where the concentration gradients are established across grains ● Formation of core-structure with center rich in high melting element whereas increase in concentration of low melting element on going towards grain boundary ● Melting below the equilibrium melting temperature of alloy may happen ● Loss in mechanical integrity due to thin liquid film that separates the grains. Reference: William Callister Materials Science and Engineering - An Introduction 7
  14. 14. Intermediate Phases & Reactions Intermediate Phases : ● Pure iron on heating undergoes two changes in the crystal structure before melting. ● At room temperature it exists in α-ferrite upto 1674 F, which has a BCC crystal structure. ● At 1185 F it get polymorphically transformed into FCC γ-austenite and it persists till 2541 F when it reverts back to BCC δ-ferrite. ● At 6.7% carbon concentration Cementite(Fe3C) is formed. ● Iron melts at 2800 F. Intermediate Reactions : ● Eutectic : • Eutectoid :
  15. 15. Development of MS in Fe-Fe3C system Case 1 : At Eutectoid composition >The above is the governing eqn. > The phase changes from a to b. 727.C > The pearlite structure forms due to the difference b/w parent & product phases. > This is called Pearlite because of its look of a pearl.
  16. 16. ) Diffusion through minimal distance by C-atoms leads to layered structure.
  17. 17. Case 2 : At Hypoeutectoid Composition
  18. 18. • • • • • • Composition left to the eutectoid, between 0.022 and 0.76 wt% C, is called hypoeutectoid alloy. At c, the microstructure consists entirely of γ-austenite grains. On cooling, at d, small α particles form along γ-grain boundaries. The composition becomes richer in carbon and α particles grow larger on cooling till 727.C. Once the temperature is lowered below 727.C all the γ-phase gets transformed into pearlite. α-phase is present as a continuous matrix phase surrounding the isolated pearlite colonies.
  19. 19. Case 3: At Hyper Eutectoid Composition
  20. 20. • • • • • • Composition right to the eutectoid, between 0.76 and 2.14 wt% C, is called hyper eutectoid alloy. At g, the microstructure consists entirely of γ-austenite grains. On cooling, at h, small cementite particles starts forming along γgrain boundaries. Cementite composition remains constant as the temperature changes until 727.C. On lowering the temperature below 727.C all the γ-phase gets transformed into pearlite. The resulting microstructure consists of pearlite and proeutectoid cementite as microconstituents.
  21. 21. Cu-Zn phase diagram
  22. 22. Stability of Hume-Rothery Phases in Cu-Zn alloys ● Cu-Zn system displays a sequence of ● ● ● ● phases along the alloy composition called Hume-Rothery phases. The criterion for the stability is a contact of the Brillouin zone (BZ) plane with the Fermi surface (FS) where FS is considered to be a sphere within the nearly free electron approximation. Interaction between the BZ boundary & FS opens a pseudo-gap and reduces the electronic energy. The close-packed α and β-structures begin to transform to new high-pressure phases, and the vacant γ-structure is shown to be stable up to at least 50 GPa. The γ-phase shows an anomalous behaviour of some physical properties which were accounted for by the bandstructure effect associated with the BZ– FS interaction.
  23. 23. NUCLEATION During phase transformation normally at least one new phase is formed that has different physical or chemical characteristics or a different structure than parent phase. This is called as nucleation. Appearance of very small particles or nuclei of new phase involves in nucleation. Theory of nucleation involves thermodynamic parameter called free energy. There are two types of nucleation as follows. 1. Homogeneous nucleation. 2. Heterogeneous nucleation. HOMOGENEOUS NUCLEATION In case of homogeneous nucleation nuclei of new phase form uniformly through parent phase. Let us consider homogeneous nucleation, and study the impact of free energy involved in it.
  24. 24. Free energy change on nucleation  Reduction in bulk free energy  increasein surfaceenergy  increasein strain energy ΔG  (Volume).(G)  (Surface). ) (   4 3 ΔG   r .( Gv )  4r 2 .( ) 3  Gv  f (T ) r3 r2 1 Neglected in L → S transformations
  25. 25.   4  ΔG   r 3 .( Gv )  4r 2 .( ) 3   By setting d(G)/dr = 0 the critical values (corresponding to the maximum) are obtained (denoted by superscript *)  Reduction in free energy is obtained only after r0 is obtained dG 0 dr r 0 * 1 r2*   2 Gv As Gv is ve, r*is +ve Trivial G  0 2 Gv 16  3 G   3 Gv2 G  0 * r0   3 Gv G → r*   dG 0 dr r* Embryos Supercritical nuclei r →
  26. 26. Gv  f ( T ) The bulk free energy reduction is a function of undercooling Decreasing G* Turnbull approximation 2 Tm 16 3 G   3 T 2 H 2  G → Decreasing r* r →
  27. 27. Rate of nucleation = dN I dt No. of critical sized particles N *  Nt e  G *     kT    x Frequency with which they become supercritical  '  s * e No. of particles/volume in L  H d    kT    → lattice vibration frequency (~1013 /s) s* atoms of the liquid facing the nucleus Critical sized nucleus Jump taking particle to supercriticality → nucleated (enthalpy of activation = Hd) Critical sized nucleus
  28. 28. I  N t s*  e  G *  H d   kT       G* ↑  I ↓ T↑ I ↑ T = Tm → G* =  → I = 0 T (K) → Increasing T Tm T=0→I=0 0 I →
  29. 29. Heterogeneous nucleation • Heterogeneous nucleation occurs much more often than homogeneous nucleation. It forms at structural homogeneities such as phase boundaries, Impurities, container surfaces, grain boundaries or dislocations and require less energy than homogeneous nucleation. • Heterogeneous nucleation requires slight supercooling. •To understand heterogeneous nucleation, Let us consider nucleation on planer surface of inclusion , of  phase from  phase.
  30. 30. Consider the nucleation of  from  on a planar surface of inclusion      Interfacial Energies Created   A lens  Created A circle  Surface tension force balance      Cos       Cos       Lost ΔG  (Vlens )Gv  (A lens )   ( Acircle )    ( Acircle )   Vlens = h2(3r-h)/3 Alens = 2rh h = (1-Cos)r A circle  r circle = r Sin
  31. 31. dG 0 dr * hetero r  2  G * hetero Gv    1 * * Ghetero  Ghomo 2  3Cos  Cos 3 4 G*hetero (0o) = 0 no barrier to nucleation 1 3 4     2  3Cos  Cos3 3 Gv2 0.75  G*hetero (180o) = G*homo no benefit 0.5 G*hetero (90o) = G*homo/2 0.25 0 0 30 Complete wetting 60 90 120 150 180  (degrees) → Partial wetting No wetting      Cos   
  32. 32. I hom o  I 0 hom o e *  Ghom o      kT    0 I hetero  I hetero e *  Ghetero      kT    = f(number of nucleation sites) = f(number of nucleation sites) ~ 1026 ~ 1042 BUT the exponential term dominates I hetero > I homo
  33. 33.    Choice of heterogeneous nucleating agent  Small value of .     Cos   Choosing a nucleating agent with a low value of  (low energy  interface).  (Actually the value of (  ) will determine the effectiveness of the heterogeneous nucleating agent → high  or low ).  low value of  → Crystal structure of  and  are similar and lattice parameters are as close as possible.  for example, Ni (FCC, a = 3.52 Å) is used a heterogeneous nucleating agent in the production of artificial diamonds (FCC, a = 3.57 Å) from graphite       
  34. 34. Isothermal transformation diagram Iron-Iron carbide eutectoid reaction: Temperature plays an important role in the rate of the austenite-to-pearlite transformation . The temperature dependence for an iron–carbon alloy of eutectoid composition is indicated in Figure. which plots S-shaped curves of the percentage transformation versus the logarithm of time at three different temperatures. For each curve, data were collected after rapidly cooling a specimen composed of 100% austenite to the temperature indicated; that temperature was maintained constant throughout the course of the reaction.
  35. 35. ISOTHERMAL TRANSFORMATION DIAGRAMS  A more convenient way of representing both the time and temperature dependence of this transformation is in the bottom portion of Figure.  The dashed curve corresponds to 50% of transformation completion.  In interpreting this diagram, note first that the eutectoid temperature (1341F)is indicated by a horizontal line; at temperatures above the eutectoid.  The austenite-to-pearlite transformation will occur only if an alloy is super cooled to below the eutectoid; as indicated by the curves, the time necessary for the transformation to begin and then end depends on temperature.
  36. 36. ISOTHERMAL TRANSFORMATION DIAGRAMS  The transformation rate increases with decreasing temperature such that at ( 1000 F) only about 3 s is required for the reaction to go to 50% completion.
  37. 37. ISOTHERMAL TRANSFORMATION DIAGRAMS  In previous graph Very rapid cooling of austenite to a temperature is indicated by the near-vertical line AB, and the isothermal treatment at this temperature is represented by the horizontal segment BCD.  The transformation of austenite to pearlite begins at the intersection, point C (after approximately 3.5 s), and has reached completion by about 15 s, corresponding to point D. Figure 10.14 also shows schematic microstructures at various times during the progression of the reaction.  The thickness ratio of the ferrite and cementite layers in pearlite is approximately 8 to 1. However, the absolute layer thickness depends on the temperature at which the isothermal transformation is allowed to occur. At temperatures just below the eutectoid, relatively thick layers of both the -ferrite and Fe3C phases are produced; this microstructure is called coarse pearlite (shown in next slide) and the region at which it forms is indicated to the right of the completion curve on Figure 10.14
  38. 38. ISOTHERMAL TRANSFORMATION DIAGRAMS  The thin-layered structure produced in the vicinity 540C of is termed fine pearlite; is the dependence of mechanical properties on lamellar thickness. Photomicrographs of coarse and fine pearlite for a eutectoid composition are shown in Figure .  For iron–carbon alloys of other compositions, a proeutectoid phase (either ferrite or cementite) will coexist with pearlite, Thus additional curves corresponding to a proeutectoid transformation also must be included on the isothermal transformation diagram. A portion of one such diagram for a 1.13 wt% C alloy
  39. 39. Summary
  40. 40. Acknowledgements • Materials Science and Engineering by William Callister(Chapter 9: Phase Diagrams & Chapter 10: Phase Transformations: Development of Microstructure and Alteration of Mechanical Properties) • Mechanical metallurgy by Dieter • Stability of Hume-Rothery phases in Cu–Zn alloys at pressures up to 50 GPa by V F Degtyareva and O Degtyareva
  41. 41. Group Members Kumar Ishu 120100056 Paresh Raut 120100022 Pratik Koche 120100019 Anand Kumar 120100048 Pramod Kumar 120100044 Sunil Kumawat 120100042 Sunil Tandi 120100046 Hitesh Sahare 120100020 Vijay Thyagraj 120100066 Aniruddha Rajendra Kanere 120100026 Rajendra Thate 120100023
  42. 42. THANK YOU!

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