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  • Byeong-Joo Leewww.postech.ac.kr/~calphad

    ByeongByeong--Joo LeeJoo Lee

    POSTECH POSTECH -- MSEMSE

    calphad@postech.ac.krcalphad@postech.ac.kr

  • Pure W W + 0.4wt% Ni

    Surface Transition and Alloying Effect Surface Transition and Alloying Effect N.M. Hwang et al., 2000.N.M. Hwang et al., 2000.

    Byeong-Joo Leewww.postech.ac.kr/~calphad

    Pure W W + 0.4wt% Ni

    Vaccum Annealing

  • Abnormal Grain Growth Abnormal Grain Growth from N.M. Hwang from N.M. Hwang

    Byeong-Joo Leewww.postech.ac.kr/~calphad

  • Abnormal Grain Growth Abnormal Grain Growth from N.M. Hwang from N.M. Hwang

    Byeong-Joo Leewww.postech.ac.kr/~calphad

  • ScopeScope

    Fundamentals

    1. Concept of Surface Energy2. A Rough Estimation of Solid Surface Energy3. Anisotropy of Surface Energy4. Curvature Effect

    Capillary Pressure Vapor Pressure Solubility

    Byeong-Joo Leewww.postech.ac.kr/~calphad

    Solubility Melting Point

    5. Measurement of Surface/Interface Energy

    Interface Phenomena

    1. Adsorption2. Segregation3. Crystal Shape 4. Grain Growth

  • Fdxdxl =2

    PTA

    G

    ,

    =dAVdPSdTdG ++=

    Concept of Surface Energy and Surface TensionConcept of Surface Energy and Surface Tension

    Byeong-Joo Leewww.postech.ac.kr/~calphad

    l

    F

    2=

    Surface Energy and Tensionfor Liquids and Solids

  • A

    s

    N

    Hw

    42

    3 ==

    As ZNH 5.0=Pair approximation

    Necessary Work for Creationof (111) surface in fcc (/atom)

    For fcc (111): N/A = 4/(31/2a2)fcc (100): N/A = 2/a2

    Rough Estimation of Solid Surface EnergyRough Estimation of Solid Surface Energy

    =A

    N

    N

    H

    A

    s

    4

    Byeong-Joo Leewww.postech.ac.kr/~calphad

    15.13

    2

    )111(

    )100( ==

    For Cu: a = 3.615 Hs =337.7J/mol(111) = 2460 erg/cm

    2 (1700 by expt.)

    For fcc Origin of Anisotropy

    fcc (100): N/A = 2/a

  • Approximation for Estimation of Grain Boundary EnergyApproximation for Estimation of Grain Boundary Energy

    Byeong-Joo Leewww.postech.ac.kr/~calphad

  • Anisotropy of Grain Boundary Energy Anisotropy of Grain Boundary Energy [100] and [110] tilt Bd. of Al [100] and [110] tilt Bd. of Al

    Byeong-Joo Leewww.postech.ac.kr/~calphad

  • Why Interface/Grain Boundary Properties?Why Interface/Grain Boundary Properties?

    Byeong-Joo Leewww.postech.ac.kr/~calphad

    Wetting angle : 36o Wetting angle : 120o

    Fe - 0.5% Mn 0.1% C, dT/dt = 1 oC/s

    from SG Kim, Kunsan University

  • Grain Boundary Identification SchemeGrain Boundary Identification Scheme

    How to uniquely define misorientation and inclination between two neighboring grains

    (RD) 1x

    TD)(2x

    ND)(3x

    cx2

    cx1

    cx1

    cx1

    cx1

    cx1

    cx1

    cx2cx2

    cx2cx2

    cx2

    cx3

    cx3

    cx3

    cx3

    cx3

    cx3

    Byeong-Joo Leewww.postech.ac.kr/~calphad

  • Grain Boundary Energy of BCC FeGrain Boundary Energy of BCC Fe

    Byeong-Joo Leewww.postech.ac.kr/~calphad

    Sigma () Theta () (hkl) plane Sigma () Theta () (hkl) plane

    5 36.87 100 11 144.9 3103 70.53 110 5 180 31011 50.48 110 7 115.38 3109 38.94 110 3 146.44 3113 60 111 9 67.11 3117 38.21 111 11 180 3113 131.81 210 5 95.74 3119 96.38 210 11 100.48 3207 73.4 210 7 149 3205 180 210 7 180 3213 180 211 9 123.75 3215 101.54 211 9 152.73 32211 62.96 211 11 82.16 3317 135.58 211 7 110.92 3319 90 221 5 154.16 3315 143.13 221 11 180 332

  • Curvature Effect Curvature Effect Capillary PressureCapillary Pressure

    dAdVPP

    dAdVPdVP

    dAPdVSdTdF

    +=

    +=

    +=

    )(

    System condition

    T = constantV = V = V = constant

    @ equilibrium

    Byeong-Joo Leewww.postech.ac.kr/~calphad

    2121 rrrdV =

    2121212

    212122112211 )()()()()( rrrrrrrrrrrrrdA +++=++=

    @ equilibrium

    dV

    dAPPP == )(

    +==

    21

    11)(

    rrPPP

    =

    +===

    21

    11

    rrVPVGGG mmmm

  • Curvature Effect Curvature Effect Capillary Pressure Effect on Vapor Pressure and SolubilityCapillary Pressure Effect on Vapor Pressure and Solubility

    Solubility of pure B phase in a dilute solution

    o

    o

    rvrvmcrc

    P

    PRTV

    r === ln

    2,,,,

    Vapor Pressure

    rRT

    V

    P

    P mo

    o

    r 2ln =

    Byeong-Joo Leewww.postech.ac.kr/~calphad

    1, = Bxk

    Solubility of pure B phase in a dilute solution

    rRT

    V

    x

    xBAm

    B

    rB

    =2

    ln,

    ,

    rBBmBA

    BrB kxRTaRTVr

    ,,, lnln2

    ===

    =

    ,

    ,,, ln

    B

    rB

    BrBx

    xRT

  • Curvature Effect Curvature Effect Capillary Pressure Effect on Melting PointCapillary Pressure Effect on Melting Point

    22

    r

    drVdTS mLSm =

    02)()(2=

    r

    drVdPVVdTSS SSLLSLSL

    rPP LSLS

    +=2

    LLLL dPVdTSd +=

    ++=+=

    rPdVdTSdPVdTSd SLLSSSSS

    2

    Byeong-Joo Leewww.postech.ac.kr/~calphad

    22

    rVdTS mLSm =

    rH

    TV

    rS

    VT

    m

    mmLS

    m

    mLS

    m

    122

    =

    =

    22

    r

    drVdTS

    rr T

    TmLS

    T

    Tm

    =

    r

    VTSTTS mLSmmrm

    ==

    2)(

  • Thermodynamics of Nano Particles or Thermodynamics of Nano Particles or NanowiresNanowires

    Byeong-Joo Leewww.postech.ac.kr/~calphad

    Size dependence of melting points of Au nano particles.

  • Au

    Melting points of Nano ParticlesMelting points of Nano Particles

    PtNi

    Byeong-Joo Leewww.postech.ac.kr/~calphad

    Pt

    WMg

  • PtNi

    Melting points of Nano WiresMelting points of Nano Wires

    Byeong-Joo Leewww.postech.ac.kr/~calphad

    Pt

    WMg

  • Measurement of Surface Energy Measurement of Surface Energy Surface Energy of LiquidSurface Energy of Liquid

    Byeong-Joo Leewww.postech.ac.kr/~calphad

    Rgh

    =

    cos2

    cos/Rr =

    rPPP oi

    2==

  • r

    mg

    =

    Measurement of Surface Energy Measurement of Surface Energy Surface Energy of SolidSurface Energy of Solid

    dAdlmgwrev ==

    dll

    rdr

    2

    1=

    rlA 2=

    .2 constlrV ==

    )(2 ldrrdldA +=

    02 2 =+= dlrldrdV

    Byeong-Joo Leewww.postech.ac.kr/~calphad

    r =

    ( )2rnddAgb =

    gbl

    nrrmg 2=

    gbgbdAdAdlmg +=

  • Measurement of Surface Energy Measurement of Surface Energy Relative Interface Energy of SolidRelative Interface Energy of Solid

    2

    31

    3

    12

    1

    23

    sinsinsin

    ==

    =2

    cos2 1211

    Byeong-Joo Leewww.postech.ac.kr/~calphad

    SVLS

    LV cosLVLSSV +=

    2

  • Interfacial Phenomena Interfacial Phenomena AdsorptionAdsorption

    aaKR

    PKR

    =

    = )1(

    Physisorption : Van der Waals

    Chemisorption : Chemical Bonding

    Langmuir adsorption : monolayer chemisorption : fraction of surface site covered

    Byeong-Joo Leewww.postech.ac.kr/~calphad

    KP

    KP

    +=1

    )()1( 2

    1 TKK

    K

    P==

    da KPK = )1(

    dd KR =

    @ equilibrium

  • )()1(

    TKP

    AA =

    Interfacial Phenomena Interfacial Phenomena Competitive AdsorptionCompetitive Adsorption

    BAAaa

    KR

    PKR

    =

    = )1(

    A : fraction of coverage of AB : fraction of coverage of B

    A(g) + S AS B(g) + S BS

    For A :

    Byeong-Joo Leewww.postech.ac.kr/~calphad

    )()1(

    TKP

    A

    BAA

    =

    BB

    AA

    B

    A

    PTK

    PTK

    )(

    )(=

    Bdd

    BABaa

    KR

    PKR

    =

    = )1(

    Add KR =

    For B : )()1(

    TKP

    B

    BAB

    B =

  • Interfacial Phenomena Interfacial Phenomena Multilayer Adsorption (BET isotherm)Multilayer Adsorption (BET isotherm)

    1. A(g) + S AS 1 = 0 K1P2. A(g) + AS A2S 2 = 1 K2P3. .n. A(g) + An-1S AnS n = n-1 KnP

    K1 : chemisorption

    Byeong-Joo Leewww.postech.ac.kr/~calphad

    11 )(

    = nn KP

    K1 : chemisorptionK2, , Kn : the same physisorption (interface)

    assume K2 = K3 = = Kn = K

  • Interfacial Phenomena Interfacial Phenomena Segregation (Guttmann)Segregation (Guttmann)

    iiiii

    o XRTG +=+ ln

    Assume a one atomic layer surface phase and consider equilibrium

    between bulk and surface

    where i is the molar surface areaAssume i = j = =

    B

    i

    B

    i

    B

    i

    B

    i

    o XRTG =+ ln

    Bfrom = iiBooX

    RTRTGG

    lnln][ ++=

    Byeong-Joo Leewww.postech.ac.kr/~calphad

    RTG

    B

    n

    B

    i

    n

    iseg

    eX

    X

    X

    X /=

    B

    iifrom =

    =

    +=

    1

    1

    /

    /

    )1(1n

    j

    RTGB

    j

    RTGB

    ii

    segj

    segi

    eX

    eXXnentsmulticompofor

    B

    i

    i

    B

    i

    iB

    i

    o

    i

    o

    X

    XRTRTGG

    lnln][ ++=

    B

    in

    B

    niB

    n

    o

    n

    oB

    i

    o

    i

    oseg RTGGGGG

    ln][][ +=

  • Interfacial Phenomena Interfacial Phenomena Segregation (Physical Meaning of Quantities)Segregation (Physical Meaning of Quantities)

    Bfrom =

    ][][

    ln][][

    B

    n

    xsB

    i

    xs

    n

    xs

    i

    xs

    n

    o

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