Atomic Transport Phase Transformations - uni .Atomic Transport & Phase Transformations Lecture 8

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Transcript of Atomic Transport Phase Transformations - uni .Atomic Transport & Phase Transformations Lecture 8

  • Atomic Transport

    &

    Phase Transformations

    Lecture 8

    PD Dr. Nikolay Zotov

    zotov@imw.uni-stuttgart.de

  • Lecture I-8 Outline

    Binary phase diagrams with limited solubility in the liquid state

    Classification of (intermediate) intermetallic compounds

    Formation of intermetallic compounds

    Gibbs energy of intermediate phases

    Examples of phase diagrams with intermediate phases

    Calculation of phase diagrams with intermediate phases

  • Binary Phase DiagramsClassification

    WL = 0

    WS = 0

    Unlimited Solubilityin Liquid and Solid

    Limited Solubilty

    in Solid in Liquid in Liquidand in Solid

    WS > 0 WL > 0

    WL > 0

    WS > 0with intermetallicphases WS < 0

  • Binary Phase Diagrams

    Limited solubility in the Liquid State (WL > 0)

    Regular solution

    ln(gAL) = WL(1 XA

    L)2 > 0 gAL > 1

    ln(gBL) = WL(1 XB

    L)2 > 0 gBL > 1 Tendency for phase separation in the liquid state

    If WL> 0 a miscibility gap will form in the liquid state!

  • Binary Phase Diagrams

    Limited solubility in the Liquid State (WL > 0)

    DeHoff (2006)

    WL = 0 WL = 10000 J/mol WL = 20000 J/mol

  • Binary Phase Diagrams

    Limited solubility in the Liquid State (WL > 0)

    # very different melting points

    # inflection point in the liquidus curve

    # retrograde solubility of Tl in Ag above 300 oC;

    # very low solubility of Ag in Tl;

    # Allotropic phase transition in Tl at 234 oC;

    a(Tl) hexagonal P 63/mmc

    (Tl) cubic Im-3m

  • Binary Phase Diagrams

    Limited solubility in the Liquid State (WL > 0)

    # Maximum of the liquid missibility gap at 1071 K

    # WL = 2R TgmL ~ 17800 J/mol

    # Eutectic point TE ~ 591 K

    # below 591 K two phase mixture Pb + Zn

    Zn hexagonal; Pb cubic

    L1 + L2

    L

    L1 + Zn

    Pb + Zn

    TgmL

    E

  • Binary Phase Diagrams

    Limited solubility in the Liquid State (WL > 0)

    A

    B

    C

    D

    F

    G

    A T > 1071 K homogeneous liquid L with XZn = 0.4

    B L starts to segregate

    XZn(L1) ~ 0.4, XZn(L2) ~ 0.92

    fraction(L1) ~ 100%

    C Two liquids mixture

    XZn(L1) ~ 0.11, XZn(L2) ~ 0.98 (almost pure Zn melt)

    fraction (L1) ~ 56 %

    D The Zn-rich liquid disappears (Zn crystallizes)

    Mixture of Pb-rich liquid (L1) + Zn

    XZn(L1) ~ 0.06, XZn(Zn) ~ 0.999

    fraction(Zn) = 38%

    F Eutectic Tie-line; L1 + Pb + Zn in equilibrium

    XZn(Pb) ~ 0.024, XZn(Zn) ~ 0.99

    G Two phase mixture of solid Pb and solid Zn

  • Binary Phase Diagrams

    Limited solubility in the Liquid State (WL > 0)

    # Temperature of the maximum of theSolubility gap Tgm

    L ~ 879 K at XPb ~0.38

    # WL = 2RTgmL ~ 14600 J/mol

    # B Two liquid mixture

    XPb(L1) ~ 0.13, XPb(L2) ~ 0.76

    # Monotectic point M

    (MM monotectic tie-line)

    XPb(L1) ~ 0.016, XPb(L2) ~ 0.97 XPb(fcc) ~ 0.998

    # Monotectic reaction

    L2 L1 + Pb

    # Below 302 K two phase mixture of Ga and Pb

    Ga orthorhombic oC8 Cmca

    Pb cubic cF4 F m-3m

    TgmL

    L1L1 + L2

    L2

    L

    L1 + Pb

    Ga + Pb

    MM

    B

  • Binary Phase Diagrams

    Limited solubility in the Liquid State (WL > 0)

    M

    # TgmL ~ 3162 K

    WL ~ 52490 J/mol

    # Monotectic point M

    Monotectic T = 2124 K;

    # Solubility of Ag in bcc V

    increases with increasing T

    # Solubility of V in Ag

    negligible:

    V bcc structure I m-3 m

    (5+, 4+, 3+, 2+)

    Ag fcc structure F m -3 m

    TgmL

  • Binary Phase Diagrams

    Limited solubility in the Liquid State (WL > 0)

    # Maximum of the liquid immisibility

    gap unknown

    WL probably very high

    # Very high Monotectic point 3240 oC

    # practically no mutual solubility

    below 2000 oC

  • Binary Phase Diagrams

    Monotetctic Reaction - DG curves

  • Binary Phase Diagrams

    Monotectic Reactions

    # temperature of the maximum of

    the liquid miscibility gap 849 K

    at XTl = 0.32;

    # WL ~ 14100 J/mol;

    # Monotectic Temperature 559 K;

    # Allotropic phase transition

    L1 + L1 + a Tl at 234 oC;

    # 2 phase mixture Ga + aTl below 30 oC.

  • Binary Phase Diagrams

    Invariant reactions - Summary

    Limited Reaction Description

    Solubility

    Solid Eutectic l a +

    Eutectoid g a +

    Peritectic l + a

    Metatectic l + a

    Liquid Monotectic l1 l2 + a

  • Binary Phase Diagrams

    Impossible eutectic phase diagrams

    Gibbs phase rule:

    The invariant tie -line means that the there isno degree of freedom: the composiiton and thetemperature are fixed

    Inclined tie-line in an eutectic phase diagram means thatT can be varied as a function of composition, which is notpossible.

  • Binary Phase Diagrams

    Impossible eutectic phase diagrams

    Prince (1966)

    Complete misciblity is not possible

    Addition of B into A (or B in A) will increase the Entropy of mixing and reduce the Gibbs eneryg of the solution

  • Binary Phase DiagramsClassification

    WL = 0

    WS = 0

    Unlimited Solubilityin Liquid and Solid

    Limited Solubilty

    in Solid in Liquid in Liquidand in Solid

    WS > 0 WL > 0

    WL > 0

    WS > 0with intermetallicphases WS < 0

  • Intermetallic Compounds

    Classification

    Entropy

    ordered disordered

    Variations in chemical composition

    Stoichiometric Non-stoichiometricDefect compounds

    Electronic configuration

    Normal ValenceCompounds

    Hume-Rotheryphases

  • Binary Phase DiagramsIntermediate phases - Formation

    # Enthalpy stabilisation with respect to the termianl solid solutions

    Strong preference for the formation of bonds between unlike atoms in the solid

    De = eAB (eAA + eBB ) < 0 WS < 0

    # usually (very) different structures from the terminal solid solutions

  • Binary Phase DiagramsFormation of intermediate phases

    WS < 0

    WL = 0

    # WS < 0 and WL = 0 Increase of the melting temperatures

    of the solid solutions with respect to the pure components

    is observed;

    # congruent melting at XBCM

    # Congruent melting (freezing) the melt freezes in a solid phase

    with the same composition

    # Incongruent melting (freezing) the solid and the melt do not have

    the same composition

    XBCM

  • Binary Phase DiagramsFormation of intermediate phases

    Extention of the Regular solution model:

    DH mix = XB(1 XB)

    WS(XB) = - a[b(1-2XB)4 + c/(d XB)

    2]

    The second term describes a strong tendency for

    unlike bond formation

    -ac/(d XB)2 ; XB d deep minimum

    0,0 0,2 0,4 0,6 0,8 1,0

    -4000

    -2000

    0

    DH

    mix

    (J/m

    ol)

    XB

    a

    a+ a+ a

    Appearance of an

    intermediate phase

    Relatively wide

    compositional range

    Prince (1966)

    WS(XB); WS(XB) < 0

  • Binary Phase DiagramsFormation of intermediate phases

    Stoichiometric (line) compounds compounds with

    Infinitely large curvature!!!

  • Binary Phase DiagramsFormation of intermediate phases

    The curvature of the DG curve the phase determines the stability range

    Prince (1966)

  • Binary Phase DiagramsPhase diagrams with Intermediate Phases

    FeCr

    s FeCr phase

    Tetragonal, P 42/mnm; 30 atoms in the unit cell

    Compositional range 45 49 wt% Cr

    Fe DHM = 13.8 kJ/mol

    Cr DHM = 21.0 kJ/mol

  • Binary Phase DiagramsPhase diagrams with Intermediate Phases

    Very large compositional range

    35 65 wt% V!!!

    Fe V

    WS

  • Binary Phase DiagramsPhase diagrams with Intermediate Phases

    # Intermediate phase with relatively wide compositional range

    # congruent melting of the phase for the composition X*.

    # The phase diagram could be regarded as two eutectic phase

    diagrams: A X and X B;

    XBb/T ~ DHsol

    ab/ T(XB XB

    a) 2Gmb/(XB

    b)2;

    T/ XBb ~ T 2Gm

    b/(XBb)2 (X* XB

    a) / DHsolab ;

    # very large curvature of the Gibbs free energy of the

    phase vertical phase boundary

    # very small solubility of the a phase in

    vertical phase boundary

    X*

  • Binary Phase DiagramsPhase diagrams with Intermediate Phases

    # Congruent melting at 1065 oC;

    # extremely narrow stability range of Mg2Sn(Stoichiometric compound);

    # Mg2Sn cubic, antifluoride structure, F m -3 m

    # Extremely low solubility of Mg in Sn and Sn in Mg

    Different structure

    Compared to termianl phases

    Mg hexagonal

    P 63/mmc

    Sn tetragonal

    I 41/

  • Binary Phase DiagramsPhase diagrams with Intermediate Phases

    # Congruent melting at 1065 oC

    # extremely narrow stability range

    (Stoichiometric compound);

    # Mg2Si cubic, antifluoride structure, F m -3 m

    # Extremely low solubility of Mg in Si and

    Si in Mg

    Mg hexagonal

    P 63/mmc

    Si cubic

    F d -3 m

  • Binary Phase DiagramsPhase diagrams with Intermediate Phases

    A

    B

    A Liquid with composition XSi(L) = 0.4

    B L + Mg2Si

    XSi(Mg2Si) = 0.333, XSi(L) = 0.45

    fraction (Mg2Si) ~ 50%

    C Mg