ch10-Phase_Diagramsbsnsbbbsbsbsbbwbwbwb.ppt
- 2. Chapter 10 (part 1) • Introduction • Solubility Limits • Phases • Phase Equilibrium • Interpretation of Phase Diagrams • Binary Isomorphous Systems (Cu-Ni) • Development of Microstructure • Mechanical Properties • Binary Eutectic Systems • Development of Eutectic Alloy Microstructure
- 3. 3 • Components: The elements or compounds that are mixed initially (Al and Cu). • Phases: A phase is a homogenous, physically distinct and mechanically separable portion of the material with a given chemical composition and structure ( and ). (darker phase) (lighter phase) Components and Phases Aluminum- Copper Alloy
- 4. Phase Equilibria: Solubility Limit • Solution – solid, liquid, or gas solutions, single phase • Mixture – more than one phase Question: What is the solubility limit for sugar in water at 20°C? Answer: 65 wt% sugar. At 20°C, if C < 65 wt% sugar: syrup At 20°C, if C > 65 wt% sugar: syrup + sugar 65 • Solubility Limit: Maximum concentration for which only a single phase solution exists. Sugar/Water Phase Diagram Sugar Temperature (°C) 0 20 40 60 80 100 C = Composition (wt% sugar) L (liquid solution i.e., syrup) Solubility Limit L (liquid) + S (solid sugar) 20 40 60 80 100 Water
- 5. 5 Equilibrium • A system is at equilibrium if its free energy is at a minimum, given a specified combination of temperature, pressure and composition. • The (macroscopic) characteristics of the system do not change with time — the system is stable. • A change in T, P or C for the system will result in an increase in the free energy and possible changes to another state whereby the free energy is lowered.
- 6. One Component Phase Diagram 6
- 7. 7 Phase Diagrams • Indicate phases as a function of Temp, Comp and Pressure. • Focus on: - binary systems: 2 components. - independent variables: T and C (P = 1 atm is almost always used). Cu-Ni system • 2 phases: L (liquid) (FCC solid solution) • 3 different phase fields: L L + wt% Ni 20 40 60 80 100 0 1000 1100 1200 1300 1400 1500 1600 T(°C) L (liquid) (FCC solid solution) L + liquidus solidus
- 8. 8 • Changing T can change # of phases: path A to B. • Changing Co can change # of phases: path B to D. Effect of Temperature & Composition (Co) wt% Ni 20 40 60 80 100 0 1000 1100 1200 1300 1400 1500 1600 T(°C) L (liquid) (FCC solid solution) L + liquidus solidus A B D Cu Cu-Ni system
- 9. 9 • Rule 1: If we know T and Co, then we know: --how many phases and which phases are present. • Examples: wt% Ni 20 40 60 80 100 0 1000 1100 1200 1300 1400 1500 1600 T(°C) L (liquid) (FCC solid solution) L + liquidus solidus A(1100,60) B(1250,35) Cu-Ni phase diagram A(1100, 60): 1 phase: B(1250, 35): 2 phases: L + Determination of phase(s) present Melting points: Cu = 1085°C, Ni = 1453 °C Solidus - Temperature where alloy is completely solid. Above this line, liquefaction begins. Liquidus - Temperature where alloy is completely liquid. Below this line, solidification begins.
- 10. 10 • Rule 2: If we know T and Co, then we know: --the composition of each phase. • Examples: wt% Ni 20 1200 1300 T(°C) L (liquid) (solid) L + liquidus solidus 30 40 50 TA A D TD TB B tie line L + 43 35 32 Co CL C Cu-Ni system Phase Diagrams: composition of phases At TA = 1320°C: Only Liquid (L) present CL = C0 ( = 35 wt% Ni) At TB = 1250°C: Both and L present At TD = 1190°C: Only Solid () present C = C0 ( = 35 wt% Ni) CL = Cliquidus ( = 32 wt% Ni) C = Csolidus ( = 43 wt% Ni)
- 11. 11 • Rule 3: If we know T and Co, then we know: --the amount of each phase (given in wt%). Cu-Ni system • Examples: At TB: Both and L At TA: Only Liquid (L) WL = 100wt%, W = 0 At TD: Only Solid () WL = 0, W = 100wt% Co = 35wt%Ni wt% Ni 20 1200 1300 T(°C) L (liquid) (solid) L + liquidus solidus 30 40 50 TA A D TD TB B tie line L + 43 35 32 Co CL C R S Phase Diagrams: weight fractions of phases WL S R S W R R S 43 35 43 32 73wt% R R S S R S WL C Co C CL = 27wt % R R S W Co CL C CL WL S R S W R R S
- 12. 12 wt% Ni 20 1200 1300 30 40 50 1100 L (liquid) (solid) L + L + T(°C) A 35 C0 L: 35wt%Ni Cu-Ni system • Phase diagram: Cu-Ni system. • Consider microstuctural changes that accompany the cooling of a C0 = 35 wt% Ni alloy Ex: Equilibrium Cooling of a Cu-Ni Alloy 46 35 43 32 : 43 wt% Ni L: 32 wt% Ni B : 46 wt% Ni L: 35 wt% Ni C E L: 24 wt% Ni : 36 wt% Ni 24 36 D
- 13. • Development of microstructure during the non-equilibrium solidification of a 35 wt % Ni-65 wt% Cu alloy outcome: • Segregation- nonuniform distribution of elements within grains. • Weaker grain boundaries if alloy is reheated.
- 14. • C changes as it solidifies. • Cu-Ni case: • Fast rate of cooling: Cored structure • Slow rate of cooling: Equilibrium structure First to solidify has C = 46wt%Ni. Last to solidify has C = 35wt%Ni. First to solidfy: 46wt%Ni Uniform C: 35wt%Ni Last to solidfy: < 35wt%Ni Cored vs Equilibrium Phases • Coring can be eliminated by means of a homogenization heat treatment carried out at temperatures below the alloy’s solidus. During the process, atomic diffusion produces grains that are compositionally homogeneous.
- 15. 15 • Effect of solid solution strengthening on: --Tensile strength (TS) --Ductility (%EL,%AR) --Peak as a function of Co --Min. as a function of Co Mechanical Properties: Cu-Ni System Elongation (%EL) Composition, wt%Ni Cu Ni 0 20 40 60 80 100 20 30 40 50 60 %EL for pure Ni %EL for pure Cu Tensile Strength (MPa) Composition, wt%Ni Cu Ni 0 20 40 60 80 100 200 300 400 TS for pure Ni TS for pure Cu
- 16. 16 Binary Isomorphous Systems Cu-Ni system: • The liquid L is a homogeneous liquid solution composed of Cu and Ni. • The α phase is a substitutional solid solution consisting of Cu and Ni atoms with an FCC crystal structure. • At temperatures below 1080 C, Cu and Ni are mutually soluble in each other in the solid state for all compositions. • The complete solubility is explained by their FCC structure, nearly identical atomic radii and electro-negativities, and similar valences. • The Cu-Ni system is termed isomorphous because of this complete liquid and solid solubility of the 2 components.
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- 18. 18 Criteria for Solid Solubility Crystal Structure electroneg r (nm) Ni FCC 1.9 0.1246 Cu FCC 1.8 0.1278 • Both have the same crystal structure (FCC) and have similar electronegativities and atomic radii (W. Hume – Rothery rules) suggesting high mutual solubility. Simple system (e.g., Ni-Cu solution) • Ni and Cu are totally soluble in one another for all proportions.
- 19. 19 Cu-Ni phase diagram Isomorphous Binary Phase Diagram • Phase diagram: Cu-Ni system. • System is: -- binary 2 components: Cu and Ni. -- isomorphous i.e., complete solubility of one component in another; phase field extends from 0 to 100 wt% Ni. wt% Ni 20 40 60 80 100 0 1000 1100 1200 1300 1400 1500 1600 T(°C) L (liquid) (FCC solid solution) L + liquidus solidus
- 20. 20 Importance of Phase Diagrams • There is a strong correlation between microstructure and mechanical properties, and the development of alloy microstructure is related to the characteristics of its phase diagram. • Phase diagrams provide valuable information about melting, casting, crystallization and other phenomena.
- 21. 21 Microstructure • In metal alloys, microstructure is characterized by the number of phases, their proportions, and the way they are arranged. • The microstructure depends on: – Alloying elements – Concentration – Heat treatment (temperature, time, rate of cooling)
- 22. 22 Eutectic • A eutectic or eutectic mixture is a mixture of two or more phases at a composition that has the lowest melting point. • It is where the phases simultaneously crystallize from molten solution. • The proper ratios of phases to obtain a eutectic is identified by the eutectic point on a binary phase diagram. • The term comes from the Greek 'eutektos', meaning 'easily melted.‘
- 23. 23 • The phase diagram displays a simple binary system composed of two components, A and B, which has a eutectic point. • The phase diagram plots relative concentrations of A and B along the X-axis, and temperature along the Y-axis. The eutectic point is the point where the liquid phase borders directly on the solid α + β phase; it represents the minimum melting temperature of any possible A B alloy. • The temperature that corresponds to this point is known as the eutectic temperature. • Not all binary system alloys have a eutectic point: those that form a solid solution at all concentrations, such as the gold-silver system, have no eutectic. An alloy system that has a eutectic is often referred to as a eutectic system, or eutectic alloy. • Solid products of a eutectic transformation can often be identified by their lamellar structure, as opposed to the dendritic structures commonly seen in non-eutectic solidification. The same conditions that force the material to form lamellae can instead form an amorphous solid if pushed to an extreme.
- 24. 24 2 components has a special composition with a min. melting T. Binary-Eutectic Systems • 3 single phase regions (L, , ) • Limited solubility: : mostly Cu : mostly Ag • TE : No liquid below TE : Composition at temperature TE • CE Cu-Ag system L (liquid) L + L+ C , wt% Ag 20 40 60 80 100 0 200 1200 T(°C) 400 600 800 1000 CE TE 8.0 71.9 91.2 779°C Ag) wt% 1.2 9 ( Ag) wt% .0 8 ( Ag) wt% 9 . 71 ( L cooling heating • Eutectic reaction L(CE) (CE) + (CE)
- 26. 26 Eutectic Reaction • An isothermal, reversible reaction between two (or more) solid phases during the heating of a system where a single liquid phase is produced. Eutectic reaction L(CE) (CE) + (CE) Ag) wt% 1.2 9 ( Ag) wt% .0 8 ( Ag) wt% 9 . 71 ( L cooling heating • Solvus – (solid solubility line) BC, GH • Solidus – AB, FG, BEG (eutectic isotherm) • Liquidus – AEF • Maximum solubility: α = 8.0 wt% Ag, β = 8.8 wt %Cu • Invariant point (where 3 phases are in equilibrium) is at E; CE = 71.9 wt% Ag, TE = 779C (1434F).
- 28. 28 Solidification of Eutectic Mixtures • Mixtures of some metals, such as copper & nickel, are completely soluble in both liquid and solid states for all concentrations of both metals. Copper & nickel have the same crystal structure (FCC) and have nearly the same atomic radii. The solid formed by cooling can have any proportion of copper & nickel. Such completely miscible mixtures of metals are called isomorphous. • By contrast, a mixture of lead & tin that is eutectic is only partially soluble when in the solid state. Lead & tin have different crystal structures (FCC versus BCT) and lead atoms are much larger. No more than 18.3 weight % solid tin can dissolve in solid lead and no more than 2.2% of solid lead can dissolve in solid tin (according to previous phase diagram). • The solid lead-tin alloy consists of a mixture of two solid phases, one consisting of a maximum of 18.3 wt% tin (the alpha phase) and one consisting of a maximum of 2.2 wt% lead (the beta phase).
- 29. 29 L + L+ + 200 T(°C) 18.3 C, wt% Sn 20 60 80 100 0 300 100 L (liquid) 183°C 61.9 97.8 • For a 40 wt% Sn-60 wt% Pb alloy at 150°C, determine: -- the phases present Pb-Sn system (Ex 1) Pb-Sn Eutectic System Answer: + -- the phase compositions -- the relative amount of each phase 150 40 C0 11 C 99 C Answer: C = 11 wt% Sn C = 99 wt% Sn W = C - C0 C - C = 99 - 40 99 - 11 = 59 88 = 0.67 W C0 - C C - C = = 29 88 = 0.33 = 40 - 11 99 - 11 Answer:
- 30. 30 Answer: C = 17 wt% Sn -- the phase compositions L+ + 200 T(°C) C, wt% Sn 20 60 80 100 0 300 100 L (liquid) L + 183°C • For a 40 wt% Sn-60 wt% Pb alloy at 220°C, determine: -- the phases present: (Ex 2) Pb-Sn Eutectic System -- the relative amount of each phase W = CL - C0 CL - C = 46 - 40 46 - 17 = 6 29 = 0.21 WL = C0 - C CL - C = 23 29 = 0.79 40 C0 46 CL 17 C 220 Answer: + L CL = 46 wt% Sn Answer:
- 31. 31 Pb-Sn • For lead & tin the eutectic composition is 61.9 wt% tin and the eutectic temperature is 183ºC -- which makes this mixture useful as solder. • At 183ºC, compositions of greater than 61.9 wt% tin result in precipitation of a tin- rich solid in the liquid mixture, whereas compositions of less than 61.9 wt% tin result in precipitation of lead-rich solid.
- 32. 32 • For alloys where C0 < 2 wt% Sn • Result at room temperature is a polycrystalline with grains of phase having composition C0 Microstructural Developments in Eutectic Systems - I 0 L+ 200 T(°C) C, wt% Sn 10 2 20 C0 300 100 L 30 + 400 (room T solubility limit) TE L L: C0 wt% Sn : C0 wt% Sn Pb-Sn system
- 33. 33 2 wt% Sn < C0 < 18.3 wt% Sn • Results in polycrystalline microstructure with grains and small -phase particles at lower temperatures. Microstructural Developments in Eutectic Systems - II L + 200 T(°C) C, wt% Sn 10 18.3 20 0 C0 300 100 L 30 + 400 (sol. limit at TE) TE 2 (sol. limit at Troom) L L: C0 wt% Sn : C0 wt% Sn Pb-Sn system
- 34. Microstructures in Eutectic Systems - III Pb-Sn system • Co = CE • Results in a eutectic microstructure with alternating layers of and crystals. Sn) wt% 7.8 9 ( Sn) wt% .3 8 (1 Sn) wt% 9 . 61 ( L cooling heating
- 35. 35 Lamellar Eutectic Structure A 2-phase microstructure resulting from the solidification of a liquid having the eutectic composition where the phases exist as a lamellae that alternate with one another. Formation of eutectic layered microstructure in the Pb-Sn system during solidification at the eutectic composition. Compositions of α and β phases are very different. Solidification involves redistribution of Pb and Sn atoms by atomic diffusion. Pb-rich Sn-rich
- 36. 36 Pb-Sn Microstructures The dark layers are Pb-rich α phase, the light layers are the Sn- rich β phase.
- 37. 37/57 Ni-Al Pb-Sn Copper phosphorus eutectic 20mol% CeO2-80mol% CoO. Ir-Si
- 38. 38 • For alloys with18.3 wt% Sn < C0 < 61.9 wt% Sn • Result: phase particles and a eutectic microconstituent Microstructures in Eutectic Systems - IV 18.3 61.9 97.8 eutectic eutectic WL = (1- W) = 0.50 C = 18.3 wt% Sn CL = 61.9 wt% Sn W = = 0.50 • Just above TE : • Just below TE : C = 18.3 wt% Sn C = 97.8 wt% Sn W = = 0.727 W = 0.273 wt% Sn Pb-Sn system L+ 200 T(°C) C, wt% Sn 20 60 80 100 0 300 100 L L+ 40 + TE L: C0 wt% Sn L L CL - C0 CL - C Cβ - C0 Cβ - C Primary α
- 39. 39 Chapter 10 (part 2) • Equilibrium Diagrams with Intermediate Phases or Compounds • Eutectoid and Peritectic Reactions • Ceramic Phase Diagrams • The Gibbs Phase Rule • The Iron-Iron Carbide Phase Diagram • Development of Microstructures in Iron-Carbon Alloys • Hypoeutectoid Alloys • Hypereutectoid Alloys • Influence of Other Alloying Elements
- 40. 40 Intermetallic Compounds Mg2Pb Note: intermetallic compounds exist as a line on the diagram - not a phase region. The composition of a compound has a distinct chemical formula. 19 wt% Mg-81 wt% Pb
- 41. Cu-Zn System (Brass) Cartridge brass: 70 wt% Cu
- 42. 42 Eutectoid & Peritectic Cu-Zn Phase diagram Eutectoid transformation + Peritectic transformation + L
- 43. 43 • Eutectoid – one solid phase transforms to two other solid phases Solid1 ↔ Solid2 + Solid3 + Fe3C (For Fe-C, 727C, 0.76 wt% C) Eutectic, Eutectoid, & Peritectic • Eutectic - liquid transforms to two solid phases L + (For Pb-Sn, 183C, 61.9 wt% Sn) cool heat • Peritectic - liquid and one solid phase transform to a 2nd solid phase Solid1 + Liquid ↔ Solid2 + L ε (For Cu-Zn, 598°C, 78.6 wt% Zn) cool heat cool heat
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- 45. 45 Ceramic Phase Diagrams MgO-Al2O3 diagram:
- 46. 46 • Need a material to use in high temperature furnaces. • Consider Silica (SiO2) - Alumina (Al2O3) system. • Phase diagram shows: mullite, alumina and crystobalite (made up of SiO2) are candidate refractories. Composition (wt% alumina) T(°C) 1400 1600 1800 2000 2200 20 40 60 80 100 0 alumina + mullite mullite + L mullite Liquid (L) mullite + crystobalite crystobalite + L alumina + L 3Al2O3-2SiO2 APPLICATION: REFRACTORIES
- 47. 47 Ceramic Phases and Cements
- 48. 48 Gibbs Phase Rule • Phase diagrams and phase equilibria are subject to the laws of thermodynamics. • Gibbs phase rule is a criterion that determines how many phases can coexist within a system at equilibrium. P + F = C + N P: # of phases present F: degrees of freedom (temperature, pressure, composition) C: components or compounds N: noncompositional variables For the Cu-Ag system @ 1 atm for a single phase P: N=1 (temperature), C = 2 (Cu-Ag), P= 1 (, L) F = 2 + 1 – 1= 2 This means that to characterize the alloy within a single phase field, 2 parameters must be given: temperature and composition. If 2 phases coexist, for example, L L, then according to GPR, we have 1 degree of freedom: F = 2 + 1 – 2= 1. So, if we have Temp or composition, then we can completely define the system. If 3 phases exist (for a binary system), there are 0 degrees of freedom. This means the composition and Temp are fixed. This condition is met for a eutectic system by the eutectic isotherm.
- 49. 49 Iron-Carbon System • Pure iron when heated experiences 2 changes in crystal structure before it melts. • At room temperature the stable form, ferrite ( iron) has a BCC crystal structure. • Ferrite experiences a polymorphic transformation to FCC austenite ( iron) at 912 ˚C (1674 ˚F). • At 1394˚C (2541˚F) austenite reverts back to BCC phase ferrite and melts at 1538 ˚C (2800 ˚F). • Iron carbide (cementite or Fe3C) an intermediate compound is formed at 6.7 wt% C. • Typically, all steels and cast irons have carbon contents less than 6.7 wt% C. • Carbon is an interstitial impurity in iron and forms a solid solution with the phases
- 51. Though carbon is present in relatively low concentrations, it significantly influences the mechanical properties of ferrite: (a) α ferrite, (b) austenite.
- 52. 4 Solid Phases
- 53. Iron carbide (Cementite or Fe3C) • Forms when the solubility limit of carbon in ferrite is exceeded at temperatures below 727 ˚C. • Mechanically, cementite is very hard and brittle. • For ferrous alloys there are 3 basic types, based on carbon content: Iron (ferrite phase): <0.008 wt% C room temp Steel ( + Fe3C phase): 0.008 to 2.14 wt% C Cast iron: 2.14 to 6.70 wt% C 53
- 54. 54 Iron-Carbon (Fe-C) Phase Diagram • 2 important points - Eutectoid (B): +Fe3C - Eutectic (A): L ↔ +Fe3C Fe 3 C (cementite) 1600 1400 1200 1000 800 600 400 0 1 2 3 4 5 6 6.7 L (austenite) +L +Fe3C +Fe3C + (Fe) C, wt% C 1148°C T(°C) 727°C = Teutectoid 4.30 Result: Pearlite = alternating layers of and Fe3C phases, not a separate phase. 120 m 0.76 B A L+Fe3C Fe3C (cementite-hard) (ferrite-soft) ↔
- 55. Pearlite Eutectoid reaction: ↔ + Fe3C Austenite – 0.76 wt% C Ferrite - 0.022 wt% C Cementite - 6.70 wt% C Redistribution of carbon by diffusion
- 56. Fe 3 C (cementite) 1600 1400 1200 1000 800 600 400 0 1 2 3 4 5 6 6.7 L (austenite) +L + Fe3C + Fe3C L+Fe3C (Fe) C, wt% C 1148°C T(°C) 727°C C0 0.76 Hypoeutectoid Steel W = W =(1 - W) pearlite pearlite = + Fe3C W’ = W = (1 – W’) pearlite Microstructures for iron-iron carbide alloys that are below the eutectoid with compositions between 0.022 and 0.76 wt% Carbon are hypoeutectoid. C - C0 C - C CFe3C - C0 CFe3C - C
- 57. 57 Fe 3 C (cementite) 1600 1400 1200 1000 800 600 400 0 1 2 3 4 5 6 6.7 L (austenite) +L + Fe3C + Fe3C L+Fe3C (Fe) C, wt% C 1148°C T(°C) 727°C C0 0.76 Hypoeutectoid Steel pearlite
- 58. 58 Proeutectoid • Formed before the eutectoid • Ferrite that is present in the pearlite is called eutectoid ferrite. • The ferrite that is formed above the Teutectoid (727°C) is proeutectoid.
- 59. 59
- 60. Fe 3 C (cementite) 1600 1400 1200 1000 800 600 400 0 1 2 3 4 5 6 6.7 L (austenite) +L +Fe3C +Fe3C L+Fe3C (Fe) C, wt%C 1148°C T(°C) Hypereutectoid Steel 0.76 C0 pearlite Fe3C x v V X Wpearlite = W W = X/(V +X) W =(1 - W) Fe3C’ W =(1-W) W =x/(v + x) Fe3C Microstructures for iron-iron carbide alloys that have compositions between 0.76 and 2.14 wt% carbon are hypereutectoid (more than eutectoid).
- 61. 61 Hypereutectoid Steel Fe 3 C (cementite) 1600 1400 1200 1000 800 600 400 0 1 2 3 4 5 6 6.7 L (austenite) +L +Fe3C +Fe3C L+Fe3C (Fe) C, wt%C 1148°C T(°C) 0.76 C0 Fe3C pearlite
- 62. Hypereutectoid Steel (1.2 wt% C) Proeutectoid: formed above the Teutectoid (727°C) pearlite
- 63. 63 L+ L+ + 200 C, wt% Sn 20 60 80 100 0 300 100 L TE 40 (Pb-Sn System) Hypoeutectic & Hypereutectic 160 m eutectic micro-constituent hypereutectic: (illustration only) 175 m hypoeutectic: C0 = 50 wt% Sn T(°C) 61.9 eutectic eutectic: C0 =61.9wt% Sn
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- 65. 65 Example Problem For a 99.6 wt% Fe-0.40 wt % C steel at a temperature just below the eutectoid, determine the following: a) The compositions of Fe3C and ferrite (). b) The amount of cementite (in grams) that forms in 100 g of steel.
- 66. 66 Solution to Example Problem WFe3C R R S C0 C CFe3C C 0.40 0.022 6.70 0.022 0.057 b) Using the lever rule with the tie line shown a) Using the RS tie line just below the eutectoid C = 0.022 wt% C CFe3C = 6.70 wt% C Fe 3 C (cementite) 1600 1400 1200 1000 800 600 400 0 1 2 3 4 5 6 6.7 L (austenite) +L + Fe3C + Fe3C L+Fe3C C, wt% C 1148°C T(°C) 727°C C0 R S CFe C 3 C Amount of Fe3C in 100 g = (100 g)WFe3C = (100 g)(0.057) = 5.7 g
- 67. 67 Alloying steel with other elements changes the Eutectoid Temperature, Position of phase boundaries and relative Amounts of each phase
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- 73. 73 • Phase diagrams are useful tools to determine: -- the number and types of phases present, -- the composition of each phase, -- and the weight fraction of each phase For a given temperature and composition of the system. • The microstructure of an alloy depends on -- its composition, and -- rate of cooling equilibrium Summary
- 74. 74 Review
- 75. 75 • Heating a copper-nickel alloy of composition 70 wt% Ni-30 wt% Cu from 1300°C. At what temperature does the first liquid phase form? • Solidus - Temperature where alloy is completely solid. Above this line, liquefaction begins. • Answer: The first liquid forms at the temperature where a vertical line at this composition intersects the α-(α + L) phase boundary--i.e., about 1350°C; • 2 phases: L (liquid) (FCC solid solution) • 3 phase fields: L L + wt% Ni 20 40 60 80 100 0 1000 1100 1200 1300 1400 1500 1600 T(°C) L (liquid) (FCC solid solution) L + liquidus solidus Wt% Ni
- 76. 76 • (b) What is the composition of this liquid phase? • Answer: The composition of this liquid phase corresponds to the intersection with the (α + L)-L phase boundary, of a tie line constructed across the α + L phase region at 1350°C, 59 wt% Ni; Wt% Ni • 2 phases: L (liquid) (FCC solid solution) • 3 phase fields: L L + wt% Ni 20 40 60 80 100 0 1000 1100 1200 1300 1400 1500 1600 T(°C) L (liquid) (FCC solid solution) L + liquidus solidus
- 77. 77 • (c) At what temperature does complete melting of the alloy occur? • Liquidus - Temperature where alloy is completely liquid. Below this line, solidification begins. • Answer: Complete melting of the alloy occurs at the intersection of this same vertical line at 70 wt% Ni with the (α + L)-L phase boundary--i.e., about 1380°C; • 2 phases: L (liquid) (FCC solid solution) • 3 phase fields: L L + wt% Ni 20 40 60 80 100 0 1000 1100 1200 1300 1400 1500 1600 T(°C) L (liquid) (FCC solid solution) Wt% Ni
- 78. 78 • (d) What is the composition of the last solid remaining prior to complete melting? • Answer: The composition of the last solid remaining prior to complete melting corresponds to the intersection with α-(α + L) phase boundary, of the tie line constructed across the α + L phase region at 1380°C--i.e., about 78 wt% Ni. • 2 phases: L (liquid) (FCC solid solution) • 3 phase fields: L L + wt% Ni 20 40 60 80 100 0 1000 1100 1200 1300 1400 1500 1600 T(°C) L (liquid) (FCC solid solution) Wt% Ni
- 79. • Sum of weight fractions: 9 • Conservation of mass (Ni): • Combine above equations: WL W 1 Co WLCL WC R R S W Co CL C CL S R S WL C Co C CL • A geometric interpretation: Co R S W WL CL C moment equilibrium: 1 W solving gives Lever Rule WLR WS THE LEVER RULE: A PROOF