DRJ Phase Transformation Cp

of 37

  • date post

    07-Jul-2018
  • Category

    Documents

  • view

    212
  • download

    0

Embed Size (px)

Transcript of DRJ Phase Transformation Cp

  • 8/18/2019 DRJ Phase Transformation Cp

    1/37

  • 8/18/2019 DRJ Phase Transformation Cp

    2/37

     Thermodynamics of transformations

    ntroduction!

    • De"nition of phase change

    #tom mo$ements in phasetransformation

    •  Types of phase transformations

    Homogeneous $s. heterogeneoustransformations

    •  Thermodynamics of transformations

    %

  • 8/18/2019 DRJ Phase Transformation Cp

    3/37

    De"nition of &hase 'hange

    • # Phase is a

    physically distinct(

    chemically homogeneous and

    mechanically separable part of the system.

    e.g.( ce( )ater( $apor of )ater

    *

  • 8/18/2019 DRJ Phase Transformation Cp

    4/37

     T)o phases are distinguishable from each other( if 

    •  They form di+erent states of aggregation ,solid( liuid and $apor

    • /r in the same state of aggregation( if they ha$e di+erent composition or di+erent crystal structure

    • 0or the same composition and crystal structure( di+erences in the electronic structure

  • 8/18/2019 DRJ Phase Transformation Cp

    5/37

    # phase transformation or transition

    is de"ned as

    •  The change from one or more phases ,called the parent phases to one or more other phases ,called the product &hases.

    • &hase transformation in$ol$es changes in the 1. 2tate of aggregation

    %. 'omposition

    *. 'rystal structure( or

    . 3lectronic structure

    •. t may be also a combination of more than one of the abo$e changes.

    5

  • 8/18/2019 DRJ Phase Transformation Cp

    6/37

    #tom mo$ements in phase

    transformtion

    • 0or solid state phase transformation( )e shall not consider changes in the state of aggregation.

    • No atom mo$ements ta4e place during changes in the electronic structure.

    • 'hanges in composition and crystal structure in the solid state reuire the mo$ement of atoms )ithin the

    solid. 

  • 8/18/2019 DRJ Phase Transformation Cp

    7/37

     Three categories of atom mo$ements during phase transformation

    1. 6o$ements o$er a large number of interatomic distances7

    %. 6o$ements o$er one or t)o interatomic distances7 and

    *. 6o$ements o$er a fraction of an interatomic distance.

    •. 8ong range and 2hort range di+usion ,1 9%

    •. :y process of di+usion in solid state. ;

  • 8/18/2019 DRJ Phase Transformation Cp

    8/37

    • Di+usion  mass

  • 8/18/2019 DRJ Phase Transformation Cp

    9/37

    Di+usionless changes

    • 0or category *( the atoms may mo$e only through a fraction of an interatomic distance.

    • 2uch mo$ements bring about crystal

    structure changes. •  The product crystal structure can be

    generated only )hen the atom mo$ements occur in a coordinated fashion. /ther)ise( an amorphous product )ill result.

    • n the absence of interchange of atom positions by random )al4( the coordinated

    transformations are said to be di+usionless. >

  • 8/18/2019 DRJ Phase Transformation Cp

    10/37

     Types of phase transformation

    1. Transformations )ith a change in composition

    %. Transformations )ith a change in crystal structure

    *. Transformation )ith both composition and crystal structure changes

    . Transformation )ith a change in order

    5. 3lectronic transitions 1?

  • 8/18/2019 DRJ Phase Transformation Cp

    11/37

     Transformations )ith a change in composition

    Al- Zn Phase

    diagram

         T    e     m

        p     e     r    a     t    u     r    e  (

    @eight percent Ainc

    #tomic percent Ainc 11

  • 8/18/2019 DRJ Phase Transformation Cp

    12/37

    1%

  • 8/18/2019 DRJ Phase Transformation Cp

    13/37

     Transformations )ith a change in crystal structure

    1392 911

    structures changes of Fe under cooling

    cool cool  

    C C  BCC BCC  FCC  Fe Fe Feδ γ α   →  → o o

    1*

  • 8/18/2019 DRJ Phase Transformation Cp

    14/37

     Transformation )ith a change in

    order

    1

  • 8/18/2019 DRJ Phase Transformation Cp

    15/37

    3lectronic Transitions!

    15

  • 8/18/2019 DRJ Phase Transformation Cp

    16/37

    Homogeneous $s. heterogeneous transformations

    • # transformation that ta4es place more or less simultaneously in all parts of an assembly is regarded as

    homogeneous transformation.

    • Reactions in the gaseous phases are homogeneous.

    • 'hanges in$ol$ing electronic transitions are homogeneous.

    1

  • 8/18/2019 DRJ Phase Transformation Cp

    17/37

    • # heterogeneous transformation is of the nucleation and gro)th type.

     Tiny $olumes of the product phase called nuclei( often assumed to be the same in structure and composition as the transformation product( form "rst.

    • # sharp boundary delineates the nuclei from the surrounding matriB.

    •  These small regions subseuently gro) by the out)ard mo$ement of the boundary( )ith corresponding changes in composition ,and crystal structure behind the ad$ancing front.

    1;

  • 8/18/2019 DRJ Phase Transformation Cp

    18/37

     Transformation occurring by

    nucleation and gro)th.

    1=

  • 8/18/2019 DRJ Phase Transformation Cp

    19/37

     Thermodynamics of Transformations

    • # phase transformation can occur spontaneously

    only )hen the free energy change during the transformation is negati$e.

    • n order to 4no) )hether this condition is satis"ed for a transformation( )e need to 4no) the free

    energy of the parent and the product phases. •  The free energies of elemental crystals and solid

    solutions are discussed here as a function of composition and the eBternal parameters!

    temperature and pressure. •  The thermodynamic order of transformations is

    de"ned.

    • t is sho)n ho) a dri$ing force arises for "rst-order

    transformations )ith and )ithout compositionalchanges. 1>

  • 8/18/2019 DRJ Phase Transformation Cp

    20/37

    0R33 3N3RC /0 38363NT#8 'R2T#82

    n elements( the composition is not a$ariable.

    • #ssume that the elemental crystals are perfect( so that there is no con"gurational

    entropy associated )ith crystal imperfections. •  The $ariables considered are the eBternal

    $ariables( e.g.( temperature and pressure.

    •  The Cibbs free energy C of the crystal is

    gi$en by

    %?

      (1)G H TS  = − )here H and 2 are the enthalpy and the

    entropy of the crystal and T is the absolutetem erature in 4el$in .

  • 8/18/2019 DRJ Phase Transformation Cp

    21/37

     The enthalpy term can be )ritten as

    )here Ho is the residual enthalpy at ?

    K and

    cp is the heat capacity at constant

    pressure.

     The entropy of the crystal is gi$en by

    %1

    0

    0   (2)

     p H H c dT = + ∫ 

    0

      (3)

     pc dT  S 

    T  = ∫ 

  • 8/18/2019 DRJ Phase Transformation Cp

    22/37

    'ombining 3.,1 through ,*( )e obtain at constant pressure

    ntegrating 3., )ithin appropriate

    limits( )e can )rite

    %%

      (4)  P 

    G  s T 

    ∂   = − ÷∂  

    0 0

    0

    0

    0

    0 0

      (5)

    (6)

    G T 

     H 

    T T   p

    dG SdT  

    G H SdT  

    c dT   H dT 

    = −

    = −

       = −    ÷

      

    ∫ ∫ 

    ∫  ∫ ∫ 

  • 8/18/2019 DRJ Phase Transformation Cp

    23/37

    •0igure 1,a is a schematic plot of the $ariation in the Cibbs free energy as a function of temperature at constant pressure.

    • The cur$e has Aero slope at ? K( the $alue at that temperature being the residual enthalpy or bond energy Ho.

    • The slope becomes more and more negati$e( as the temperature is

    increased. • The rate at )hich the slope decreases )ith temperature is dependent on the $alue of the heat capacity( )hich is usually a function of temperature.

    •0rom the thermodynamic la)s( )e can sho) that

    %*

    2chematic $ariation of the

    Cibbs free energy Cas afunction of ,a temperature at constant pressure( and ,b pressure at constant temperature.

      (7)

    G V 

     P 

    ∂   = ÷

    ∂  

  • 8/18/2019 DRJ Phase Transformation Cp

    24/37

    •  Thus( the Cibbs free energy $ariation )ith pressure at a constant temperature has a positi$e slope( eual to the molar $olume E( as illustrated schematically in 0ig. 1,b.

    •  The abo$e description of the free energy of elemental crysta