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Microstructure + Phase Transformations in Multicomponent Systems

Chapter Outline: Phase Diagrams. Microstructure + Phase Transformations in Multicomponent Systems. Definitions and basic concepts Phases and microstructure Binary isomorphous systems (complete solid solubility) Binary eutectic systems (limited solid solubility)

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Microstructure + Phase Transformations in Multicomponent Systems

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  1. Chapter Outline: Phase Diagrams Microstructure + Phase Transformations in Multicomponent Systems • Definitions and basic concepts • Phases and microstructure • Binary isomorphous systems (complete solid solubility) • Binary eutectic systems (limited solid solubility) • Binary systems with intermediate phases/compounds • The iron-carbon system (steel and cast iron) • Not tested: The Gibbs Phase Rule

  2. Components and Phases Component - chemical species (Fe + C in steel; H2O + NaCl in salt water). Binary alloy 2 two components, Ternary alloy – 3, etc. Phase – a portion with distinct, uniform physical or chemical characteristics Single-phase system: Homogeneous. Two or more phases Mixture or Heterogeneous system. e.g. water + ice, separated by a phase boundary

  3. Solubility Limit Solvent - host or major component Solute - minor component (Chapter 4). Solubility Limit = maximum amountthat can be dissolved in a phase (e.g. alcohol has unlimited solubility in water, sugar has a limited solubility, oil is insoluble). Same concepts for solids: Cu and Ni are mutually soluble in any amount (unlimited solid solubility), while C has a limited solubility in Fe.

  4. Microstructure Properties of an alloy depend on proportions of the phases and on how they are arranged at the microscopic level. Microstructure: number of phases, their proportions, and their arrangements Microstructure of cast Iron Alloy of Fe with 4 wt.% C. There are several phases. The long gray regions are flakes of graphite. The matrix is a fine mixture of BCC Fe and Fe3C compound. Phase diagrams help understand and predict microstructures

  5. Equilibrium and Metastable States Equilibrium: at constant temperature, pressure and composition system is stable (Equilibrium is achieved given sufficient time, but that may be very long. ) Metastable:System appears to be stable Equilibrium  minimum in the free energy. • Under conditions of constant temperature, pressure and composition, change is toward lower free energy. equilibrium • Stable equilibrium is state with minimum free energy. • Metastable state is a local minimum of free energy. Free Energy metastable

  6. Phase diagram Phase diagram - combinations of temperature, pressure or composition for which specific phases exist at equilibrium H2O: diagram shows temperature and pressure at which ice (solid),water (liquid) and steam (gas) exist.

  7. Phase diagram Show what phases exist at equilibrium and what transformations we can expect when we change T, P, or composition Consider binary alloys only Pressure constant at one atmosphere.

  8. Binary Isomorphous System (I) Assume Complete Solubility L  + L  Three phases : Liquid (L) , solid + liquid (+L), solid () Liquidusline separates liquid from liquid + solid Solidus line separates solid from liquid + solid

  9. Binary Isomorphous Systems (II) Cu-Ni Complete solubility occurs because Cu and Ni have the same crystal structure (FCC), similar radii, electronegativity and valence

  10. Binary Isomorphous System (III) One-component: melting occurs at a well-defined temperature. Multi-component: melting occurs over range of temperatures between solidus and liquidus lines. Solid and liquid phases are in equilibrium in this temperature range. L Liquid solution  + L Liquid solution + Crystallites of Solid solution  Polycrystal Solid solution

  11. Interpretation of Phase Diagrams Given: temperature + composition  determine 1) Phases present 2) Compositions of phases 3) Relative fractions of phases • Composition in a two phase region: • 1. Locate composition and temperature • 2. Draw tie line or isotherm • Note intersection with phase boundaries • Read compositions at the intersections • Liquid and solid phases have these compositions

  12. The Lever Rule Amounts of each phase in two phase region Locate composition and temperature Draw tie line or isotherm Fraction of a phase =length of tie line to other phase boundary divided by the length of tie line The lever rule is a mechanical analogy to the mass balance calculation. The tie line in the two-phase region is analogous to a lever balanced on a fulcrum.

  13. The Lever Rule Mass fractions: WL = S / (R+S) = (C- Co) / (C- CL) W = R / (R+S) = (Co- CL) / (C- CL)

  14. Derivation of the lever rule Wand WL are fractions of  and L phases 1) All material is in one phase or the other: W+ WL = 1 2) Composition equal composition in one phase + composition second phase at given T: Co = WC + WLCL 3) Solution gives Lever rule. WL = (C- Co) / (C- CL) W = (Co- CL) / (C- CL)

  15. Phase compositions and amounts. An example. Co = 35 wt. %, CL = 31.5 wt. %, C = 42.5 wt. % Mass fractions: WL = (C- Co) / (C- CL) = 0.68 W = (Co- CL) / (C- CL) = 0.32

  16. Microstructure in isomorphous alloys Equilibrium (very slow) cooling

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