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Chapter 9 Sections:9.2, 9.3, 9.4, 9.5

Chapter 9 Sections:9.2, 9.3, 9.4, 9.5. Chapter 9: Phase Diagrams. Why study? One of the reason why a knowledge and understanding of phase diagrams is important to the engineers related to the design and control of heat treating processes.

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Chapter 9 Sections:9.2, 9.3, 9.4, 9.5

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  1. Chapter 9 • Sections:9.2, 9.3, 9.4, 9.5

  2. Chapter 9: Phase Diagrams • Why study? • One of the reason why a knowledge and understanding of phase diagrams is important to the engineers related to the design and control of heat treating processes. • Some properties are functions of their microstructures, and, consequently, of their thermal histories.

  3. Definitions and Basic Concepts • Components : Pure metals and/or compounds of which an alloy is composed • Example: in a copper-zinc brass, the components are Cu and Zn. • System • First meaning: refer to a specific body of material under consideration ( e.g., a ladle of molten steel) • Second meaning: relate to the series of possible alloys consisting of the same components, but without regard to alloy composition (e.g., the iron-carbon system) • Solid solution: Consists of atoms of at least two different types • Solute an element or compound present in a minor concentration • Solvent  an element or compound in greater amount; host atoms. • Solute atoms occupy either substitutional or interstitial positions in the solvent lattice • Crystal structure of the solvent is maintained

  4. 9.2 Solubility Limit • Solubility Limit: The maximum concentration of a solute atoms that may dissolve in the solvent to form a solid solution at some specific temperature. • The addition in excess results in the formation of another solid solution or compound that has a distinctly different composition. • Example: Sugar-Water (C12H22O11-H2O) system • Initially, as sugar added to water, a solution of syrup forms. • As more sugar is added, solution becomes more concentrated • Solution becomes saturated with sugar Solubility limit is reached • Not capable to dissolving more  further addition simply settle to the bottom • System now consists of two separate substances: • A sugar-water syrup liquid solution, and • Solid crystals of undissolved sugar

  5. 9.3 Phases • Phase: defined as a homogeneous portion of a system that has uniform physical and chemical characteristics. • Every pure material is considered to be a phase • Also every solid, liquid, and gaseous solution • e.g., syrup solution is one phase, and solid sugar is another • If more than one phase is present, it is not necessary that there be difference in both physical and chemical properties: • A disparity in one or both is sufficient • e.g., water and ice in a container ( two phase, identical chemically) • When a substance can exist in two or more polymorphic forms (e.g. having both FCC abd BCC)  each structure is a separate phase because of difference in physical properties.

  6. A single-phase system is termed “homogeneous” • Systems composed of two or more phases are termed “mixture” or heterogeneous systems”. • Most metallic alloys, ceramics, polymeric, and composite systems are heterogeneous. • Ordinarily, in multiphase systems • The phases interact such that the property is different and more attractive than individual phases.

  7. 9.4 Microstructure • Physical properties and mechanical behavior depend on the microstructure. • In metal alloys, microstructure is characterized by • Number of phases present • Their proportions • The manner they are distributed or arranged • The microstructure of an alloy depends on such variables as • Alloying elements present • Their concentrations • The heat treatment • Microstructure studies: • surface preparation (Polishing and etching) • For two phase alloys, one phase may appear light and other dark

  8. 9.5 Phase Equilibria • Free energy is a function of the internal energy of a system, and also of the randomness or disorder of the atoms or molecules (or entropy). • A system is at equilibrium if its free energy is at a minimum under some specified combination of temperature, pressure, and composition. • In macroscopic sense, this means that the characteristics of the system do not change with time but persist indefinitely  The system is stable • A change in temperature, pressure, and/or composition in equilibrium  increase in free energy  another equilibrium state whereby the free energy is lowered.

  9. Phase equilibrium refers to equilibrium as it applied to systems in which more than one phase may exist. • Example: • Sugar-water syrup is contained in a closed vessel solution is in contact with solid sugar at 20oC • If system is in equilibrium, • Composition of syrup is 65wt% C12H22O11-35wt% H2O (Fig 9.1) • Amount and composition of syrup and sugar will remain constant • If temperature is raised to 100oC • Equilibrium is temporarily upset • Solubility limit of sugar has increased to 80 wt% • Some of the solid sugar will dissolve until new equilibrium is reached

  10. Metastable state: • Nonequilibrium state • A state of equilibrium is never completely achieved because the rate of approach to equilibrium is extremely slow • Common in many metals or solid solutions • Persist indefinitely with imperceptible changes with time. • Metastable structure: • More practical than equilibrium • Some steel and aluminum rely on this for heat treatment designing

  11. Chapter 9 • Sections: 9.6

  12. Equilibrium Phase Diagrams • Equilibrium Phase diagram: • Represents the relationships between temperature and the compositions and the quantities of phases at equilibrium. • Also known as phase, equilibrium or constitutional diagram • A binary alloy is one that contains two components. • Temperature and composition are the variable parameters for binary alloys. • Of more than two components, phase diagrams become extremely complicated and difficult to represents

  13. 9.6 Binary Isomorphous systems • Phase diagram of the copper-Nickel system is shown in Fig 9.2a. • Ordinate  Temperature Abscissa  composition • Composition ranges from 0 wt% Ni (100 wt% Cu) to 100 wt% Ni (0 wt% Cu) • Three different phase regions, or fields, appear • An alpha (a) field • A liquid (L) field • A two-phase (a+L) field

  14. Liquid L: homogeneous liquid solution composed of both copper and nickel • a phase: a substitutional solid solution consisting of both Cu and Ni atoms, and having an FCC crstal structure. • Isomorphous: complete liquid and solid solubility of two components • Copper-Nickel system is Isomorpous • At temperatures below about 1080oC, mutually soluble in solid state for all compositions • Complete solubility is due to same crystal structure (FCC), nearly identical atomic radii and electronegativities, and similar valences

  15. Nomenclature • For metallic alloys, solid solutions are designated by a, b, g, etc. • Liquidus line: liquid phase at all temperature and composition above this line • Solidus line: solid phase below this line at all temperatute and composition • Liquidus and solidus lines intersect at two extreme points • Correspond to melting temperature of pure components • Copper (1085oC) and Nickel (1453oC) • Heating of pure copper • Moving vertically on left-temperature axis • Remains solid until its melting temperature is reached • No further heating possible, until this transformation is complete

  16. For any composition other than pure components • Melting phenomenon occurs over the range of temperature between the solidus and liquidus lines • Both solid a and liquid will be in equilibrium within this range

  17. Interpretation of Phase Diagrams • For binary system of known composition and temperature that is in equilibrium, at least three kinds of information are available: • The phases that are present • The composition of these phases • The % or fraction of the phases • 1.0 Phases present • Relatively simple • Example (refer to Fig 9.2a), 60 wt% Ni-40 wt% Cu at 1100oC Point A a phase 35 wt% Ni-65 wt% Cu at 1250oC Point B a + liquid phases

  18. PHASE DIAGRAMS • Tell us about phases as function of T, Co, P. • For this course: --binary systems: just 2 components. --independent variables: T and Co (P = 1atm is always used). • Phase Diagram for Cu-Ni system Adapted from Fig. 9.2(a), Callister 6e. (Fig. 9.2(a) is adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash (Ed.), ASM International, Materials Park, OH (1991). 5

  19. PHASE DIAGRAMS:# and types of phases • Rule 1: If we know T and Co, then we know: --the # and types of phases present. • Examples: Cu-Ni phase diagram Adapted from Fig. 9.2(a), Callister 6e. (Fig. 9.2(a) is adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash (Ed.), ASM International, Materials Park, OH, 1991). 6

  20. PHASE DIAGRAMS: composition of phases • Rule 2: If we know T and Co, then we know: --the composition of each phase. Cu-Ni system • Examples: Adapted from Fig. 9.2(b), Callister 6e. (Fig. 9.2(b) is adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash (Ed.), ASM International, Materials Park, OH, 1991.) 7

  21. PHASE DIAGRAMS: weight fractions of phases • Rule 3: If we know T and Co, then we know: --the amount of each phase (given in wt%). Cu-Ni system • Examples: = 27wt% Adapted from Fig. 9.2(b), Callister 6e. (Fig. 9.2(b) is adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash (Ed.), ASM International, Materials Park, OH, 1991.) 8

  22. THE LEVER RULE: A PROOF • Sum of weight fractions: • Conservation of mass (Ni): • Combine above equations: • A geometric interpretation: 9

  23. Composition need to be specified in terms of only one of the constituents • For example, composition of Ni is used • Identical results if composition of Cu is used • Co = 35 wt% Ni Ca= 42.5 wt% Ni CL = 31.5 wt% Ni WL = ( 42.5 – 35) / (42.5 – 31.5) = 0.68 Wa = (35 – 31.5) / (42.5 – 31.5) = 0.32 • Volume fraction: See equations 9.5 – 9.7

  24. Volume Fractions

  25. Development of Microstructure in Isomorphous alloys-- Equilibrium Cooling • 35 wt% Ni-65wt% Cu as cooled from 1300oC • Cooling very slowly phase equilibrium is maintained Cooling Moving down At 1300oC, completely liquid At b (1260oC), solidification starts At d (1220oC), solidification completes

  26. Development of Microstructure -- Non-Equilibrium Cooling • Extremely slow cooling not valid • Temperature change  readjustment in composition  diffusional processes • Diffusion rates are low for the solid phase and, for both phases, decrease with diminishing temperature • Practical solidification processes, cooling rates are much too rapid to allow these compositional readjustments and maintenance of equilibrium  different microstructure develops

  27. At b’,a phase begin to form [a(46Ni)] • At c’, • liquid composition: 29wt% Ni-71 wt% Cu • Solid phase: 40 wt% Ni-60 wt% Cu [a(40Ni)] • Since diffusion in solid is relatively slow, a phase formed at b’ has not changes composition appreciably  still [a(46Ni)] • Composition of a grains continuously changes radially from 46 wt% Ni at center to 40 wt% Ni at the outer grains  average composition (say 42 wt%Ni) • Solidus line has shifted

  28. Chapter 9 • Sections: 9.7

  29. 9.7 Binary Eutectic Systems • Binary Eutectic Phase Diagram • Another type of common and relatively simple phase diagram • Figure 9.6 shows for the copper-silver system • Features of Binary Eutectic Phase Diagram • Feature 1: Three single-phase regions ( a, b, and liquid ) • The a phase: solid solution rich in copper, silver as solute, FCC • The b phase: solid solution rich in silver, copper as solute, FCC • Solubility in each of these solids phases is limited • Solubility limit for a phase • Line ABC ( Increases with temperature, maximum, decreases to minimum) • Solvus line (BC) • Solidus line (AB)

  30. Solubility limit for b phase • Line FGH ( Increases with temperature, maximum, decreases to minimum) • Solvus line (GH) • Solidus line (FG) • Line BEG is also solidus line • Maximum solubility in both a and b phases occur at 779oC • Feature 2: Three two-phase regions • a + L • b + L • a + b

  31. As silver is added to copper, • The melting temperature of copper is lowered by silver additions. • Line AE: the liquidus line • Same is true as copper is added to silver • Point E is called the invariant point (CE = 71.9 wt% Ag, TE = 779oC) • At E, an important reaction occurs • Upon cooling, a liquid phase is transformed into a and b solid phases • The opposite reaction occurs upon heating • This is called eutectic reaction ( Eutectic means easily melted) • CE and TE represents eutectic composition and temperature • Horizontal solidus line at TE is called the eutectic isotherm

  32. The eutectic reaction, upon cooling, is similar to solidification of pure components: • Reaction proceeds to completion at a constant temperature • Isothermal at TE • Solid products of eutectic solidification is always two solid phases • Another common eutectic system is that for lead and tin • The phase diagram is shown in Figure 9.7 • Example 9.2 • Example 9.3

  33. Development of Microstructure in Eutectic Alloys • Depending on composition, several different types of microstructures • These possibilities considered in terms of the lead-tin phase diagram • Figure 9.7

  34. First case: Composition C1 • Range: Composition ranging between a pure metal and the maximum solid solubility for that component at room temperature (20oC) • Lead-rich alloy (0-2 wt% Sn) • Slowly cooled down

  35. Second Case: Composition C2 • Range: Composition ranging between the room temperature solubility and the maximum solid solubility at the eutectic temperature. • Corresponds: 2 wt% Sn to 18.3 wt% Sn

  36. Third Case: Composition C3 • Solidification of the eutectic composition • Corresponds: 61 wt% Sn • The microstructure at i is known as eutectic structure.

  37. Lamellae : • The microstructure of a solid consisting of alternating layers • Shown in Figure 9.12

  38. Fourth Case: Composition C4 • All composition other than the eutectic composition • At m, a phase will be present in both : • Eutectic a • Primary a

  39. Microconstituents • An element of the microstructure having an identifiable and characteristic structure. • At m, two microconstituents ( primary a and the eutectic structure )

  40. Relative amounts of both eutectic and primary a microconstituents • Eutectic microconstituents forms from liquid having eutectic composition (61 wt% Sn, Fig 9.11, point i) • Apply lever rule using tie line • Eutectic fraction We = WL = P / (P+Q) • Primary a fraction Wprimary a = Q / (P+Q) • Total a fraction (primary plus eutectic) Wa = (Q+R) / (P+Q+R) • Total b fraction (primary plus eutectic) Wb = P / (P+Q+R)

  41. Chapter 9 • Sections: 9.8, 9.9, 9.13

  42. 9.8 Equilibrium Diagrams Having Intermediate Phases or Compounds • Terminal solid solutions • Solid phases exist over the composition ranges near the concentration extremities of the phase diagram • Examples: Copper-Silver system (Figures 9.6) • Lead –Tin system (Figure 9.7) • Intermediate solid solutions • Intermediate phases • Solid phases at other than the two composition extremes • Example: Cupper-Zinc system (Figure 9.17)

  43. Intermetallic compounds • Discrete intermediate compounds rather than solid solutions • These compounds have distinc chemical formulas

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