Plastic Deformation of Polycrystalline 02 - Phase آ  Equilibrium Phase Diagrams Phase diagram

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Transcript of Plastic Deformation of Polycrystalline 02 - Phase آ  Equilibrium Phase Diagrams Phase diagram


    IE-114 Materials Science and General Chemistry


  •  There is a strong correlation between microstructure and

    mechanical properties.

     Phase diagrams provides information about:

    - The development of microstructure during heating or cooling

    can be understood from the phase diagrams.

    - Melting, casting, crystallization, etc.

    Importance of Phase Diagrams

  •  Solubility Limit

    At some specific temperatures , there

    is a maximum concentration of solute

    atoms that may dissolve in the solvent

    to form a solid solution; this is called

    solubility limit.

    Phase-Diagram of Water-Sugar System

    Question: What is the solubility limit at 20oC?

     Solubility limit increases with T:

    T = 20oC, solubility limit = 65 wt% sugar.

    T = 100oC, solubility limit = 80 wt% sugar.

    Answer: 65wt% sugar.

    If Co < 65wt% syrup

    If Co > 65wt% syrup + sugar.

  •  Phase: Homogenous portion of a system that has uniform physical and

    chemical characteristics

    Aluminum-Copper Alloy

    Component: Components are pure metals/or compounds of which alloy

    is composed. e.g. Brass (Cu-Zn) ; components are Cu and Zn, Fe and C in

    carbon steel, H2O and NaCl in salted water

    Solid Solution: A solid solution consists of solute atoms, which

    occupy either substitutional or interstitial positions in the solvent lattice

    ( , , etc,..)

     Every pure material is considered to be a phase;

    so also is every solid, liquid and gaseous solution

     For example if a substance can exist in two or

    more polymorphic forms (BBC and FCC) each of

    these structures is a separate phase because

    their physical properties are different.

  • Homogeneous system:

     A single phase system

    Mixture or heterogeneous system:

     System of two or more phases.

     Most of the metallic alloys,ceramics, polymeric and composite systems are


    Phase Equilibria:

     A system is said to be at equilibrium when the free energy, which is the

    internal energy and randomness of the atoms, is at minimum under some

    specified combination of temperature, pressure and composition.

  • Equilibrium Phase Diagrams

    Phase diagram is also called equilibrium or constitutional diagram.

    These diagrams defines the relationship between the temperature and

    compositions or quantities of phases at equilibrium. External pressure

    could also be another parameter affecting the phase distribution but it

    remains constant at 1 atm in most of the applications.

    - Isomorphous Binary Phase Diagrams

    - Eutectic Binary Phase Diagrams

  • 1) Isomorphous Binary Systems:

    Binary systems are composed of two components and they are isomorphous since there is a complete solubility of liquids and solids.

    Example: Cu-Ni

    There are 2 phases :

    - L (liquid)

    - α-solid solution

    There are 3 phase fields :

    liquid, L+α, α

    Liquidus line:The line separating L and α+L phases.

    Solidus line: The line separating

    α+L and α phases is called.

    Cu Ni wt.% Ni

  •  If we know T and Co, then we know the number and types of phases



    1) Number and types of phases

    1) Cu-35Ni Alloy at 1250oC

    (Co = 35 wt.%Ni)

    2 phases: α+L

    2)Cu-60Ni Alloy at 1100oC

    (Co = 60 wt.%Ni)

    1 phase: α

    From the phase diagrams we can learn the followings:

    -Number and types of phases that are present at different temperatures for a fixed composition

    -Composition of the phases

    -Fractions of the phases

  •  If we know T and Co, then we know the composition of each phase.

    2) Composition of phases:

    For Cu-35Ni Alloy (Co=35wt%Ni)

    at T

    A :

    -Phases: 1(only Liquid)

    -Composition of the alloy:

    CL = Co (=35 wt%Ni, 65 wt%Cu)

    at T

    B :

    -Phases: 2 (Liquid +α) -Composition of the alloy:

    CL = Cliquidus (32wt%Ni, 68 wt% Cu)

    Cα = Csolidus (43wt%Ni, 57wt%Cu)

    at T

    D :

    -Phases: 1 (only α)

    -Composition of the alloy:

    Cα=Co (35 wt%Ni, 65 wt%Cu)

  • 3) Weight fractions (or percentage) of phases:

     If we know T and Co, then we know the amount of each phase

    (given in wt%).

    WL S

    R S

    W R

    R S

    %73100 3243

    3543 wtx

    = 27wt%



  • • Binary System (2 components)

    •Isomorphous i.e., complete solubility of one

    component in another;

    phase field extends from

    0 to 100wt% Ni.

    Microstructural development during

    cooling a Cu-Ni alloy

  • Binary Eutectic Systems

    There are three phases : Liquid, and

    Cu Ag

    max. solubility of Cu

    in Ag (8.8 wt%)

    Eutectic line. This line shows the minimum

    temperature for the liquid

    phase existence.



    of Ag in Cu

    8 wt% Ag at




    Melting point of

    pure Cu Melting point of

    pure Ag

    Eutectic composition: 71.9wt%Ag, 28,1wt%Cu

    Eutectic temperature: 779oC

    Eutectic reaction: Liquid (71.9%) (8%Ag) + (91.2% Ag) Cooling


  •  For a 40wt%Sn-60wt%Pb alloy at 150oC, find:

    1) the phases present

    2) the compositions of the phases

  •  For a 40wt%Sn-60wt%Pb alloy at 150oC, find:

    --the phases present: +

    --the compositions of the phases:

    C = 11wt%Sn, 89wt%Cu

    C = 99wt%Sn, 1wt%Cu

    --the relative amounts of each phase:



  • Microstructural Development During

    Cooling of Pb-Sn Alloys

  • • 18.3wt%Sn < Co < 61.9wt%Sn

    • Room temperature microstructure: crystals and a eutectic microstructure

  • Cooling of an Alloy Having Eutectic Composition

    alternating layers of and crystals.

     The alloy having eutectic composition is called eutectic alloy

  • Hypoeutectic and Hypereutectic Alloy

  • For some alloy systems, discrete intermediate compounds rather than solid

    solutions may be observed in phase diagrams. For example; Mg-Pb system.

    These are called intermetallic compounds. The compound Mg2Pb is shown

    as a vertical line on the diagram rather than a phase region since it exists

    precisely at the composition defined.

    Intermetallic Compounds

  • Eutectoid and Peritectic Reactions

    Eutectoid reaction: 5600C and 74 wt% Zn-26 wt% Cu

    Peritectic reaction: 5980C and 78.6 wt% Zn-21.4 wt% Cu

    γ + cooling


    + L cooling


    Consider Cu-Zn system.

  •  Phase transformations can be classified according to whether or not there

    is any change in composition.

    Congruent and Incongruent Phase


    Phase transformations in which there is no

    changes in composition are called as congruent transformations. The

    opposite is incongruent

    transformation. Allotropic transformations

    are congruent as well as melting pure metals.

    Eutectic, eutectoid or melting alloy systems

    are incongruent transformations.

  •  This is the most important system in manufacturing since primary

    structural materials are essentially Fe-C alloys, such as, steel and

    cast iron.

    Iron Carbon System


  • Iron-Iron Carbide Equilibrium Phase Diagram

    Phases and phase mixtures present in iron alloys;

    • Ferrite (α)

    • Cementite (Fe3C)

    • Pearlite (ferrite + cementite)

    • Austenite (γ)

    • -ferrite

    • Ledeburite (austenite + cementite)

  • Definition and Properties of Phases 1) Ferrite : -iron, Solid Solution, max. Carbon solubility 0.022%wt. at 727oC

    BCC structure, SOFT

    2) Cementite : Iron carbide(Fe3C), contains 6.67% wt. C

    Orthorhombic structure, HARD and BRITTLE

    3) Pearlite : Phase mixture (ferrite+cementite), Lamellar structure, contains ~0.8% wt. C

    Produced from austenite decomposition

    4) Austenite : -iron, Solid solution, stable at higher temperatures (>727oC)

    Max. Carbon solubility is 2.14%wt. at 1147oC, FCC structure


    5) Ledeburite: Eutectic phase mixture(austenite+Fe3C),